Aerodynamics for Navy Aviators

NA VAIR 00·801·80

AERODYNAMICS FOR NAVAL

AVIATORS

BY H. H. HURT, JR.

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PREFACE

The purpose of this textbook is to present the elements of applied aerodynamics and aeronautical engineering which relate directly to All Naval Aviators possessa natural the problems of flying operations.

interest in the basic aerodynamic factors which affect the performance of all aircraft. Due .to the increasing complexity of modern aircraft, this natural interest must be applied to develop a sound understanding of basic engineering principles and an appreciation of some of the more The safety and advanced problems of aerodynamics and engineering.

effectiveness of flying operations will depend greatly on the under- standing and appreciation of how and why an airplane flies. The principles of aerodynamics will provide the foundations for developing exacting and precise flying techniques and operational procedures.

The content of this textbook has been arranged to provide as com- plete as possible a reference for all phases of flying in Naval Aviation.

Hence, the text material is applicable to the problems of flight train- ing, transition training, and general flying operations. The manner of presentation throughout the text has been designed to provide the elements of both theory and application and will allow either directed or unassisted study. As a result, the text material’ will be applicable to supplement formal class Iectures and briefings and provide reading material as a background for training and flying operations.

Much of the specialized mathematical detail of aerodynamics has been omitted wherever it was considered unnecessary in the field of flying operations. Also, many of the basic assumptions and limita- tions of certain parts of aerodynamic theory have been omitted for the sake of simplicity and clarity of presentation. In order to contend with these specific shortcomings, the Naval Aviator should rely on the assistance of certain specially qualified individuals within Naval Avia- tion. For example, graduate aeronautical engineers, graduates of the Test Pilot Training School at the Naval Air Test Center, graduates of the Naval Aviation Safety Officers Course, and technical representatives of the manufacturers are qualified to assist in interpreting and applying the more difficult parts of aerodynamics and aeronautical engineering.

To be sure, the specialized qualifications of these individuals should be utilized wherever possible.

iii NAVWEPS 00-801-80 PREFACE The majority of aircraft accidents are due to some type of error of the pilot. This fact has been true in the past and, unfortunately, most probably will be true in the future. Each Naval Aviator should strive to arm himself with knowledge, training, and exacting, professional attitudes and techniques. The fundamentals of aerodynamics as pre- sented in this text will provide the knowledge and background for safe and effective flying operations. The flight handbooks for the air- craft will provide the particular techniques, procedures, and operating data which are necessary for each aircraft.

Diligent study and continu- ous training are necessary to develop the professional skills and tech- niques for successful flying operations.

The author takes this opportunity to express appreciation to those who have assisted in the preparation of the manuscript. In particular, thanks are due to Mr. J. E. Fairchild for his assistance with the por- tions dealing with helicopter aerodynamics and roll coupling phenom- ena. Also, thanks are due to Mr. J. F. Detwiler and Mr. E. Dimitruk for their review of the text material.

HUGH HARRISON HURT, Jr.

August 1959 University of Southern California Los Angelesj Cnlif.

iv

NAVWEPS OO-801-8O TABLE OF CONTENTS

TABLE OF CONTENTS

PREFACE.. ,., . iii

CHAPTERI: BASIC AERODYNAMICS

WING AND AIRFOIL FORCES PROPERTIES OF THE ATMOSPHERE.

Static pressure Temperature Density Viscosity Standard atmosphere Pressure altitude Density altitude BERNOULLI’ S PRINCIPLE AND SUBSONIC AIRFLOW.. 4 Bernoulli’ s equation, Incompressible tlow Variation of static pressure and velocity Kinetic and porcntial energy of flow Static and dynamic prcssurc, 4 Factors affecting dynamic pressure Airspeed measurement.. . .

Stagnation prcssurc Measurement of dynamic pressure Pitot and static sources Indicated airspeed .......

DEVELOPMENT OF AERODYNAMIC FORCES..

Streamline pattern and pressure distribution.

.......

Generatioaoflift..........................................

Circulation Pressure distribution Airfoil terminology. ‘ ,: Aerodynamic force coefficient . .

Basic lift equation 2 3 Lift coefficient Dynamic prcssurc and surface area ” NAVWEPS OO-EOT-80 TABLE OF CONTENTS PW Interpretation of the lift equation.. . . . . . . . .

Lift cocfficicnt versus angle of attack Stall speed and angle of attack Angle of attack versus velocity Primary control of airspeed . . _ . . . _ .

mrfou un cnacactectsucs. . . . 27 Section angle of attack and lift coefficient Ty ical section chvactctistics E&t of thickness and cambet Drag characteristics, . . . . . . . :. 29 Drag equation Drag cocficicnt versus angle of attack Lift-drag ratio Power-off glide pctformancc Airfoil drag chanwteristics.. ) . . .

Section drag cocfficicnt Ty ical section characteristics E 2 ect of thickness and cunbcr Low drag sections FLIGHT AT HIGH LIFT CONDITIONS. . . ... . . 35 StaII speeds. . . . . . . . . .,. . . . . . . 3.5 Maximum lift cc&cicnt Stall angle of attack ..,e * . .

~lrecrorwergnt....................................................

Effect of maneuvering flight,. . :: Load factor ~ets~s bank angle Stall spad versus load factor Effect of high lift devices., . 37 Effect on stall speed Stall angle of attack and stall recovery. . .. . . 39 HIGH LIFT DEVICES. 39 Types of high lift devices., . 41 Plain flap S lit flap S otted flap P Fowler flap Slots and slats Boundary layer control Operation of high lift devices. 43 Flap retraction and extension Chan es in lift, drag, and trim Effect of power DEVELOPMENT OF AERODYNAMIC PITCHING MOMENTS Pressure distribution. .~. : . ! . : a: Center of pressure and aerodynamic center.

Pitching moment coefficient. . , 49 Effect of camber Effect of flaps Relationship between center of pressure, aerodynamic centet, and moment coefficient Application to longitudinal stability. . 51 Stability and trim Effect of supersonic flow vi NAVWEPS OO-BOT-BO TABLE OF CONTENTS FRICTION EFFECTS.

Viscous Bow..

Boundarglayers....................................................

Laminar flow Transition Turbulent flow ReyooldsNumber..................................................

Definition Skin friction versus Reynolds Number Airflowseparatioa..................................................

Pressure distribution Prcswrc gradient and boundary layer energy Factors affecting separation Scaleeffect.........................................................

Effect on aerodynamic characteristics Reynolds Number correlation PLANFORM EFFECTS AND AIRPLANE DRAG EFFECT OF WING PLANFORM..

. .

Descr1puon of planform Area, span,, and chord Aspect ratm and taper Sweepback Mean aerodynamic chord Development of lift by a wing.. .

vortex system Ti and bound vortices I&cd flow and downwash Scction angle of attack Induced angle of attack INDUCED DRAG. : Induced angle of attack and inclined lift.

Induced drag coefficient, Effect of lift coefficient Effect of aspect ratio Effectoflift........................................................

Effea of altitude..

2; EffectofsPeed......................................................

Effect of aspect ratio.

Lift and dra characteristics Influcncc of ow aspxt ratio configurations f EFFECT OF TAPER AND StiEEPtiACK.

Spanwise lift distribution localinducedflow.................................................

Effect on lift and drag characteristics. .‘ , STALL PATI’ ERNS.

Pnvorablestallpattern..............................................

:: EffeaofpIanform..................................................

Taper Sweepback Modifications for stall characteristics.

vii NAVWEPS 00-801-80 TABLE OF CPNTENTS *am PARASITE DRAG.

Sources of parasite drag. .

Parasite drag coefficient.. . . .

Parasite and induced drag.

Mi.li$z’ .?1 p” ‘ “ “ ite dr2g CxEciczt Airplane efficiency factor Equivalent parasite area Effect of configuration.

Effect of altitude., ;: Effectofspeed......................................................

AIRPLANE TOTAL DRAG.. 92 Drag variation with speed Induced and parasite drag Stall speed Minimum drag Specific performance conditions Compressibility drag rise

CHAPTER 2. AIRPLANE PERFORMANCE

REQUIRED THRUST AND POWER DEFINITIONS.

$6 Pan&e 14 ;n&Ced drw _ _.-__.__._- _- Thrustandpowerrequir~~::::::::::::::::::::::::::::::::::::::::: 97 VARIATION OF THRUST AND POWER REQUIRED Effect of gross weight.

Effect of configuratmn.

Effect of altitude.

AVAILABLE THRUST AND POWER PRINCIPLES OF PROPULSION.

Mass flow, velocity change, momentum change..

Newton’ s laws, Wastedpower...............................:.....................

Power available.

Propulsion efficiency.

TURBOJET ENGINES Operatingcycle....................................................

Function of the components.

Inlet or diffuser Compressor Combustion chamber Turbine Exhaust nozzle Turbojet operating characteristics.. :_ Thrust and power available Effect of velocity Effect of engine speed Specific fuel consumption Effect of altitude Governing apparatus Steady state, acceleration, deceleration Instrumentation viii NAVWEPS 00-SOT-80 TABLE OF CONTENTS Pam Turbojet operating limitations 124 Exhaust gas temperature b&pr~$or stall or surge Compressor inlet air temperature Engine speed Time limitations Thrust augmentation.

Afterburner Water injection The gas turbine-propeller combination.

Equivalent shaft horsepower Governing requirements Operating limitations performance characteristics THE RECIPROCATING ENGINE, 135 . .

Operating chatacterlsucs.

Operating cycle Brake horsepower Torque, RPM, and BMEP Normal combustion Preignition and detonation Fuel qualities Specific fuel consum tion Effect of altitude an supercharging 8 Effect of humidity Operating limitations.

Detonation and preignition Water injection Time limitations Reciprocating loads AIRCRAFT PROPELLERS Operating characteristics, Flow patterns Propulsive cficiency Powerplant matching Governing and feathering Operating limitations..

ITEMS OF AIRPLANE PERFORMANCE STRAIGHT AND LEVEL FLIGHT.

Equilibrium conditions Thrust and power required Thrust and powec available Maximum and minimum speed CLIMB PERFORMANCE.

Steady and transient climb.

Forces acting on the airplane Climb angle and obstacle clcarancc Rate of climb, primary control of altitude Propeller and jet aircraft Climb performance.

Effect of weight and altitude Descending flight ix NAWEPS 00-801-8~ TABLE OF CONTENTS :; RANGE PERFORMANCE.

General range performance. 158 Specific range, v&city, fuel flbw Specific endurance Cruise control and total range Range, propeller driven airplanes.

Aerodynamic conditions Effect of weight and altitude Reciprocating and turboprop airplanes Range, turbojet airplanes. :. 164 Aerodynamic conditions Effect of weight and altitude Constant altitude and cruise-climb profiles Effect of wind oh ‘ PY~C........,....................................

ENDURANCE PERFORMANCE. 170 General endurance performance.. :. . 170 Spxific cndurancc, velocity, fuel flow Effect of altitude op endurance, : . . . . . .

Propcllcr driven airplanes Turbojet aitplaocs OFF-OPTIMUM RANGE AND ENDURANCE. 172 Reciprocating powered airplane.. 172 Turboprop powered airplane, , . ..

Turbojet powered airplane... . . I.. .

MANEUVERING PERFORMANCE. 176 Relationships of turning flight. . . . . . .

Steady turn, bank angle and load factor Induced drag Turning performance.. . .

Tom radius and turn rate Effect of bank aaglc and velocity Tactical performance, .

Maximum lift FhZZF%3:~2:; pfOt”l~“CC TAKEOFF AND LANDING PERFORMANCE.. .~, Relationships of accelerated motion. .

Acceleration, vclocit distance Uniform and nonum arm acceleration ,J Takeoff performance.. . . .

Forces acting on the airplane Accelerated motion Factors of technique Factors affecting takeo# performance. .

Effect of gross weight Rffcct of wind Effect of runway slope F’ qxt takeoff vcloclty.

Effect of altitude and tempcraturc Handbook data Y NAVWEPS OO-BOT-BO TABLE OF CONTENTS Landing performance.. . . . . 192 Forces acting on the airplane Accclanted motion Factors of technique Factors affecting landing performance. . . .

E&t of gross weight Effect of wind Fg; ~~~~~~~;mpcntwc ro a Impmtance of handbook performance data. . .

CHAPTER 3. HIGH SPEEDAERODYNAMICS

GENERAL CONCEPTS AND SUPERSONIC FLOW PATTERNS NATURE OF COMPRESSIBILITY.

........................................

Definition of Mach number.

.......

Sttbsonic, traasonic, supersonic, and hypersonic flight regimes.

Compressible flow conditions Comparison of compressible and incompressible flow.

TYPICAL SUPERSONIC FLOW PATTERNS., Obliqueshockwave ................................................

Normalshockwave ................................................

Ex nsionwave ....................................................

E t9” ect on velocity, Mach number, density, pressure, energy.

SECTIONS IN SUPERSONIC FLOW.

nowpatterns ......................................................

Pressure distribution.

21s Wavedrag .........................................................

.................................... 21s Location of aerodynamic center.

CONFIGURATION EFFECTS TRANSONIC AND SUPERSONIC FLIGHT. . 215 Critical Mach ntlm~r 2 15 . . . . . . . . . . . . 218 Shock wave formatton.

$2: Shock induced separation.. i..

Porcedivergence...................................................

Phenomena of transonic flight.. .

Phenomena of supersonic Bight.. .

TRANSONIC AND SUPERSONIC CONFIGURATIONS. 220 Airfoil sections.. . 220 Transonic sections Supctsonic sections Wave drag characteristics Effect of Mach number on airfoil characteristics Plaaform effects.

Effect of swcc ack p” Advantages o swcepback Disadvantages of sweepback Effect of nspct ratio and tip shape . . . . . . . . .

Control surfaces.

Powered controls All movable surfaces NAWEPS 00-801-80 TABLE OF CONTENTS Supersonic engine inlets. .

Internal and external comprcsrion inlets Inlet performance and powerplant matching Supersonic configurations.

AERODYNAMIC HEATING.

Ram temperature rise.. _.

Effect on structural materials and powerplant performance.

CHAPTER 4. STABILITY AND CONTROL

DEFINITIONS STATIC STABIL .ITY.

DYNAMIC STAB1 TRIM AND CONTROLLABI AIRPLANE REFERENCE AXES.

LONGITUDINAL STABILITY AND CONTROL STATIC LONGITUDINAL STABILITY.

. ............... .:..1... ... -25’ 0.

Generalconsiderations:. .. :,_~. ...... . ....

Wing Fuselage and nacelles Horizontal tail Control force stability.

Maneuvering control requirement.

Takeoff control requirement.

Landing control requirement. .......................................

LONGITUDINAL DYNAMIC STABILITY.

Short period motions ...............................................

MODERN CONTROL SYSTEMS.

Conventional Boosted Power operated DIRECTIONAL STABILITY AND CONTROL DIRECTIONAL STABILITY. ......................................

... 284 Defimtuxu .......................................................

Contribution of the airplane components Vertical tail Wing Fuselage and nacelles Power effects ..

DIRECTIONAL CONTROL .......................

Directional control requirements.

Adverseyaw .......................................................

xii NAVWEPS 00-BOT-80 TABLE OF CONTENTS Pace Spinrecovety..; ...................................................

Slipstream rotatmn.

...................................

Cross wind takeoff and landing.

Asymmetrical power.

LATERAL STABILITY AND CONTROL LATERAL STABILITY, Definlttons ...........................................................

CONTRIBUTION OF THE AIRPLANE COMPONENTS.

Wing.........~.........~ Fuselage and wmg powton,...................................................................................

Sweepback .........................................................

........................................................

Vertical tail.

LATERAL DYNAMIC EFFECTS, Directional divergence Spiral divergence Dutch roll CONTROL IN ROLL . .

Rolhsg motmn of an airplane.

Roliing performance, Critical requirements.

MISCELLANEOUS STABILITY PROBLEMS LANDING GEAR CONFIGURATIONS Tail wheel type Tricyde type Bicycle type SPINS AND PROBLEMS OF SPIN RECOVERY Principal prospin moments Fundamental principle of recovery Effect of configuration .........................................................

PITCH-UP., Definition Contribution of the airplane components EFFECTS OF HIGH MACH NUMBER..

Longitudinal stability and control Directional stability Dynamic stability and damping PILOT INDUCED OSCILLATIONS.. _.

Pilot.control system-airplane coupling High q aed low stick force stability ROLL COUPLING.

Inertia and aerodynamic coupling Inertia and wind axes Natural pitch, yaw, and coupled pitch-yaw frequencies Critical roll rates Autorotative rolling Operating limitations HELICOPTER STABILITY AND CONTROL.

Rotor gyroscopic effects Cyclic and collective pitch Lon itudinal, lateral, and directional control f Ang e of attack and velocity stability Dynamic stability xiii NAVWEPS OO-BOT-80 TABLE OF CONTENTS

CHAPTER 5. OPERAilNG STRENGTHLIMITATIONS

GENERAL OEFlNlTlONS AND STRUCTURAL REQUlREMENTS STATIC STRENGTH .._.......... ~.~~~.~ ~..~ Limit load Factor of safety Material properties SERVICE LIFE Pati e consideration Loa r spectrum attd cumulative damage Creep considerations AEROELASTIC EFFECTS.

Stiffness and rigidity AIRCRAFT LOADS AND OPERATING LIMITATIONS FLIGHT LOADS-MANEUVERS AND GUSTS.

Loadfactor..................................................... ,... 331 Maneuvering load factors.. .I ,.., Maximum lift capability Effect of gross weight ^ . ._ Gust load increment Effect of gust intensity and lift curve slope Effect of wing loading and altitude Effect of overstrea.

,’ 334 THE V-n OR V-g DIAGRAM.

Effect of weight, configuration;altihtde, and symmetry of Ior-Ang Limit load factors Ultitnute load facvxs Maximum lift capability Limit airspeed Operating env+pe Maneuver’ speed and penetration of turbulence EFFECT OF HIGH SPEED FLIGHT..

Critical gust Aileron reversal Divergence PIutter Compressibility problems LANDING AND GROUND LOADS.

Landing load factor Effect of touchdown rate of descent Effect of gross weight Ported landing on unprepared .surfaces EFFECT OF OVERSTRESS ON SERVICE LIFE 344 Recognition of overstress’ damage Importance of operating limitations xiv NAVWEPS 00401-80 TABLE OF CONTENTS

CHAPTER6. APPLICATION OF AERODYNAMICS TO

SPECIFIC PROBLEMSOF FLYING

mrx

PRIMARY CONTROL OF AIRSPEED AND ALTITUDE.. 349 Angle of attack versus airspeed Rate of climb and descent Flying technique REGION OF REVERSED COMMAND. .

Regions of normal and reversed command Features of flight in the normal and reversed regions of command THE ANGLE OF ATTACK INDICATOR AND THE MIRROR LANDING SYSTEM. . . 357 The angle of attack indicator The mirror landing system THE APPROACH AND LANDING., The approach The landing flare and touchdown Typical errors THE TAKEOFF.. 365 Takeoff speed and distance Typical errors GUSTS AND WIND SHEAR.. _. t,.

Vertical and horizontal gusts POWER-OFF GLIDE PERFORMANCE. . 369 Glide angle and lift-drag ratio Factors affecting glide performance The flameout pattern EFFECTOF ICE AND FROST ON AIRPLANE PERFORMANCE..

Effect of ice Effect of frost ENGINE FAILURE ON THE MULTI-ENGINE AIRPLANE. 376 Effecf of weight and altihtde Control requirements Effeti on performance Etrect of turning flight and configuration GROUND EFFECT., _, Aerodynamic influence of ground effect Ground effect on specific flight conditions INTERFERENCE BETWEEN AIRPLANES IN FLIGHT.. 383 Effect of lateral, vertical, and IongiNdinal separation Collision possibility NAVWEPS 00-BOT-BO TABLE OF CONTENTS Pam BRAKING PERFORMANCE. .........................................

Friction cbaracte~istics Braking technique Typical errors of braking technique REFCTSAL SPEEDS LINE SPEEDS, AND CRITICAL FIELD , LENGTH. .............................................................

Refusal speed Line speeds Critical field length, multi-engine operation SONIC BOOMS. .......................................................

Shock waves and audible sound Precautions HELICOPTER PROBLEMS. ...........................................

Retreating blade stall ...................................................

Compressjbility effects ..................................................

Autorotatton charactertsttcs .............................................

Powersettling .........................................................

THE FLIGHT HANDBOOK. ........................................

SELECTED REFERENCES. .....................................

Iklr\C”

xvi

NAVWEPS 00-BOT-BO BASIC AERODYNAMICS

Chapter 1

BASIC AERODYNAMKS

In order to understand the characteristics of WING AND AIRFOIL FORCES his aircraft and develop precision flying tech- niques, the Naval Aviator must be familiar PROPERTIES OF THE ATMOSPHERE with the fundamentals of aerodynamics. There The aerodynamic forces and moments acting are certain physical laws which describe the behavior of airflow and define the various on a surface are due in great part to the prop- aerodynamic forces and moments acting on a erties of the air mass in which the surface is surface. These principles of aerodynamics pro- operating.~ The composition, of the earth’ s vide the foundations for good, precise flying atmosphere by volume is approximately 78 techniques. percent. nitrogen, 21 percent oxygen, and 1 NAVWEe3 OO-BOT-80 BASIC AERODYNAMICS the proportion of the ambient air temperature argon, carbon dioxide, percent water vapor, and the standard sea level air temperature.

etc. For the majority of all aerodynamic con- This temperature ratio is assigned the short- siderations air is considered as a uniform hand notation of 0 (theta).

mixture of these gases. The usual quantities Temperature ratio used to define the properties of an air mass are as follows: Ambient air temperature STATIC PRESSURE. The absolute static =Standard sea level air temperature pressure of the air is a property of primary @=TITtl The static pressure of the air importance.

,+273 at any altitude results from the mass of air supported above that level. At standard sea Many items of compressibility effects and jet level conditions the static pressure of the air engine performance involve consideration of is 2,116 psf (or 14.7 psi, 29.92 in. Hg, etc.)

the temperature ratio.

and at 40,000 feet altitude this static pressure DENSITY.

The density of the air is a prop- decreases to approximately 19 percent of the erty of greatest importance in the study of sea level value. The shorthand notation for aerodynamics. The density of air is simply “p” and the the ambient static pressure is the mass of air per~cubic foot of volume and standard sea level static pressure is given the is a direct measure of the quantity of matter subscript “a” for zero altitude, pa. A more in each cubic foot of air.

Air at standard sea usual reference in aerodynamics and perform- lcvcl conditions weighs 0.0765 pounds per cubic ance is the proportion of the ambient sta~tic foot and has a density of 0.002378 slugs per pressure and the standard sea level static cubic foot. At an altitude of 40,000 feet the pressure. This static pressure ratio is assigned air density is approximately 25 percent of the the shorthand notation of 8 (delta).

sea level value.

The shorthand notation used for air density Altitude pressure ratio is p (rho) and the standard sea level air density Ambient static pressure is then pO. In many parts of aerodynamics it =Standard sea level static pressure is very convenient to consider the proportion 6 = PIP0 of the ambient air density and standard sea level air density. This density ratio is assigned Many items of gas turbine engine perform- the shorthand notation of c (sigma).

ance are directly related to some parameter ambient air density involving the altitude pressure ratio.

density ratio= standard sea level air density TEMPERATURE. The absolute tempera- a = PIP0 cure of the air is another important property.

The ordinary temperature measurement by the A general gas law defines the relationship of Centigrade scale has a/datum at the freezing pressure temperature, and density when there point of water but absolute zero temperature is no change of state or heat transfer.

Simply is obtained at a temperature of -273“ Centi- stated this would be “density varies directly grade. Thus, the standard sea level tcmpera- with pressure, inversely with temperature.” ture of 15” C. is an absolute temperature of Using the properties previously defined, 288”. This scale of absolute temperature using density ratio= Pressure rat’ o.

the Centigrade increments is the Kelvin scale, temperature rat10 e.g., o K. The shorthand notation for the ambient air temperature is “T” and the stand- ard sea level air temperature of 288’ K. is signified by Ta.

The more usual reference is, ,. n ,:,j ,-g # I PlAVWEPS 00-8OT-80 BASIC AERODYNAMICS Thus, certain corrections must apply to the This relationship has great application in instrumentation as well as the aircraft per- aerodynamics and is quite fundamental and formance if the operating conditions do not necessary in certain parts of airplane perform- fit the standard atmosphere. In order to prop- ance.

erly account for the nonstandard atmosphere VISCOSITY. The viscosity of the air is certain terms must be defined. Pressure.&itudc important in scale and friction effects. The is the altitude in the standard atmosphere coefficient of absolute viscosity is the propor- corresponditrg to a particular pressure. The tion between the shearing stress and velocity aircraft altimeter is essentially a sensitive gradient for a fluid flow. The viscosity of barometer calibrated to indicate altitude in gases is unusual in that the viscosity is gen- the staotlard atmosphere. If the altimeter is erally a function of temperature alone and an set for 29.92 in. Hg the altitude indicated is increase in temperature increases the viscosity.

the pressure altitude-the altitude in the stand- The coefficient of absolute viscosity is assigned ard atmosphere corresponding to the sensed the shorthand notation I, (mu). Since many Of course, this indicated pressure pressure.

parts of aerodynamics involve consideration of altitude may not be the actual height above viscosity and density, a more usual form of sea level due to variations in remperature, viscosity measure is the proportion of the co- lapse rate; atniospheric pressure, and possible efficient of absolute viscosity and density.

errors in the sensed pressure.

This combination is termed the “kinematic The more appropriate term for correlating viscosity” and is noted by Y (nu).

aerodynamic performance in the nonstandard atmosphere is density &it&-the altitude in kinematic viscosity the standard atmosphere corresponding to a coefficient of absolute viscosity particular value of air density. The computa- cc density tion of density altitude must certainly involve consideration of pressure (pressure altitude) v=PlP and temperature. Figure 1.6 illustrates the manner in which pressure altitude and tem- The kinematic viscosity of air at standard sea perature combine to produce a certain density level conditions is 0.0001576 square feet per altitude. This chart is quite standard in use second. At an altitude of 40,000 feet the and is usually included in the performance kinematic viscosity is increased to 0.0005059 section of the flight handbook. Many subject square foot per second.

areas of aerodynamics and aircraft performance In order to provide a common denominator will emphasize density altitude and temperature for comparison of various aircraft, a standard as the most important factors requiring con- atmosphere has been adopted. The standard sideration.

atmosphere actually represents the mean or average properties of the atmosphere. Figure 1.1 illustrates the variation of the most im- BERNOULLI’ S PRINCIPLE AND SUBSONIC portant properties of the air throughout the AIRFLOW standard atmosphere. Notice that the lapse rate is constant in the troposphere and the All of the external aerodynamic forces on a stratosphere begins with the isothermal region. surface are the result of air pressureor air fric- Since all aircraft performance is compared tion. Friction effects are generally confined to and,evaluated in the environment of the stand- a thin layer of air in the immediate vicinity of the surface and friction forces are not the pre- ard atmosphere, all of the aircraft instrumenta- tion is calibrated for the standard atmosphere. dominating aerodynamic forces. Therefore, NAVWEPS OO-ROT-80 BASIC AERODYNAMICS ICAO STANDARD ATMOSPHERE *GEOPOTENTIAL OF THE TROPOPAUSE Figure 1.7. Standard Altitude Table NAVWEPS 00401-80 BASIC AERODYNAMICS the pressure forces created on an aerodynamic be an unbalance of force to provide the ac- surface can be studied in a simple form which celeration. Since there is only air within the at first neglects the effect of friction and vis- tube, the unbalance of force is provided by cosity of the airflow. The most appropriate the static pressure at station 1 being greater means of visualizing the effect of airflow and than the static pressure at the constriction, the resulting aerodynamic pressures is to study station 2.

the fluid flow within a closed tube.

(2) The total energy of the air stream in the tube is unchanged. However, the air- Suppose a stream of air is flowing through .’ stream energy may be in two forms. The the tube shown in figure 1.2. The airflow at airstream may have a potential energy which station 1 in the tube has a certain velocity, is related by the static pressure and a kimtic static pressure, and density.

As the airstream energy by virtue of mass and motion. As approaches the constriction at station 2 certain the total energy is unchanged, an increase in changes must take place. Since the airflow velocity (kinetic energy) will be accompa- is enclosed within the tube, the mass flow at nied by a decrease in static pressure (poten- any point along the tube must be the same and tial energy). This situation is analagous to the velocity, pressure, or density must change a ball rolling along-a smooth surface. As to accommodate this continuity of flow.

the ball rolls downhill, the potential energy BERNOULLI’ S EQUATION. A distin- due to position is exchanged for kinetic guishing feature of submnic airflow is that energy of motion. If .friction- were negli- changes in pressure and velocity take place gibie, the change of potential energy would with sniall and negligible changes in density.

equal the change in ki,netic energy. This- is For this reason the study of subsonic airflow also the case for the airflow within the tube.

can be simplified by neglecting the variation The relationship of static pressure and veloc- of density in the flow and assuming the flow ity is maintained throughout the length of the to be incomprmiblc. Of course, at high flow tube. As the flow moves past the constriction speeds whjch approach the speed of sound, the toward station 3, the velocity decreases and flow must be considered as compressible and the static pressure increases.

“compressibility effects” taken into account.

However, if the flow through the tube of The Bernoulli equation for incompressible figure 1.2 is considered subsonic, the density of flow is most readily explained ,by accounting the airstream is essentially constant at all sta- for the energy of the~airflow within the tube.

tions along the length. As the airstream has no energy added or sub- tracted at any point, the sum of the potential If the density of the flow remains constant, +id kinetic energy must be constant. The static pressure and velocity are the variable kinetic energy of an object is found by: quantities.

As the flow approaches the con- striction of station 2 the velocity must increase “KE. =%MV= to maintain the same mass flow. As the where K;E. = kinetic energy, ft.-lbs.

velocity increases the static pressure will de- M = mass, slugs crease and the decrease in static pressure which V’ =velocity, ft./set.

accompanies the increase in velocity can be The kinetic energy of a cubic foot of air is: verified in two ways: K&x,, (I) Newton’ s laws of motion state the requirement of an unbalanced force to pro- where g= kinetic energy per cu. ft., psf duce an acceleration (velocity change). If the airstream experiences an increase in veloc- p=air density, slugs per cu. ft.

ity approaching the constriction, there must V=ait velocity, ft./set.

NAWEPS DD-BDT-BD BASIC AERODYNAMICS INCREASEOVELOC DECREASE0 HEIG PE + KE = CONSTANT Ftaure 1.2. Airflow Within a Tube NAVWEPS 00-ROT-80 BASIC AERODYNAMICS H=P+q 2500 I I 1500 I P ci d q 500 I 70K P=21 16 PSF P = 2014 PSF P = 2133 PSF q= 34 PSF 9 = 136 PSF q= I7 PSF H- 2150 PSF H = 2150 PSF H = 2150 PSF Figure 1.3. Variation o\ Pressure in Tube NAVWEPS 00-801-80 BASIC AERODYNAMICS TABLE l-l. Effect of Speed and Altitvde on Dwzmnic Prerrure If the potential energy is represented by the static pressure, p, the sum of the potential and kinetic energy is the total pressure of the air- stream. True air - speed (fr./scc.)

H=p+% P V’ ,I I where H=total pressure, psf (sometimes re- ferred to as “head ’ pressure) m= c p=static pressure, psf.

_- p=density, siugs per cu. ft.

V= velocity, ft./set.

This equation is the Bernoulli equation for ‘ incompressible flow. It is important to ap- I, 013 preciate that the term >$pV2has the units of pressure, psf. This term is one of the most important in all aerodynamics and appears so frequently t&it is given the name “dynamic pressure” and the shorthand notation “4”.

q= dynamic pressure, psf = jgpv2 With this definition it could be said that the sum of static and dynamic pressure in the flow tube remains constant.

Figure 1.3 illustrates the variation of static, dynamic, and total pressure of air flowing AIRSPEED MEASUREMENT. If a sym- through a closed tube. Note that the total metrically shaped object were placed in a pressure is con,stant throughout the length moving airstream, the flow pattern typical of and any change in dynamic pressure produces figure 1.4 would result.

The airstream at the the same magnitude change in static pressure.

very nose of the object would stagnate and the The dynamic pressure of a free airstream is relative flow velocity at this point would be the one ‘ common denominator of all aero- zero. The airflow ahead of the object pos- dynamic forces and moments. Dynamic pres- sesses some certain dynamic pressure and sure represents the kinetic energy of the free ambient static pressure. At the very nose of airstream and is a factor relating the capability the object the local velocity will drop to zero for producing changes in static pressure on a and the airstream dynamic pressure will be surface. As defined, the dynamic, pressure converted into an increase in static pressure at varies directly as the density and the square of the stagnation point. In other words, there the velocity.

Typical values of dynamic pres- will exist a static pressure at the stagnation sure, 4, are shown in table l-1 for various true point which is equal to the airstream total airspeeds in the standard atmosphere.

Notice pressure-ambient static pressure plus dynamic that the dynamic pressure at some fixed veloc- pressure.

ity varies directly with the density ratio at any altitude. Also, appreciate the fact that at an Around the surface of the object the airflow altitude of 40,oM) feet (where the density ratio, will divide and the local velocity will increase b, is 0.2462) it is necessary to have a true air from zero at the stagnation point to some velocity twice that at sea level in order to maximum on the sides of the object.

If fric- product the same dynamic pressure.

tion and viscosity effects are neglected, the NAVWEPS OO-EOT-80 BASIC AERODYNAMICS AFT STAGNATION FORWARD STAGNATION POINT POINT AIRSTREAM AHEAD STAGNATION PRESSURE HAS AMBIENT STATIC IS AIRSTREAM TOTAL PRESSURE AND DYNAMIC PRESSURE PRESSURE P+q Ftgure 1.4. Flow Pattern on a Symmetrical Object The pressure gauge is then cali- surface anflow continues to the aft stagnation pressure, q.

brated to indicate flight speed in the standard point where the local velocity is again zero.

sea level air mass. For example, a dynamic The important point of this example of aero- pressure of 305 psf would be realized at a sea dynamic flow is existence of the stagnation level flight ,speed of 300 knots.

point. The change in airflow static pressure Actually there can be many conditions of which takes place at the stagnation point IS equal to the free stream dynamic pressure, q. flight where the airspeed indicator does not The measurement of free stream dynamic truly reflect the actual velocity through the pressure is fundamental to the indication of air mass. The corrections that must be applied airspeed. In fact, airspeed indicators are sim- are many and lisred in sequence below: ply pressure gauges which measure dynamic (1) The indicated airspeed (IAS) is the pressure related to various airspeeds. Typical actual instrument indication for some given airspeed measuring systems are illustrated in flight condition. Factors such as an altitude figure 1.5. The pitot head has no internal other than standard sea level, errors of the flow velocity and the pressure in the pitot tube instrument and errors due to the installation, is equal to the total pressure of the airstream.

compressibility, etc. may create great vari- The purpose of the static-ports is to sense the ance between this instrument indication and true static pressure of the free airstream. The the actual flight speed.

total pressure and static pressure lines are (2) The calibrated airspeed (CM) is the attached to a differential pressure gauge and the net pressure indicated is the dynamic result of correcting IAS for errors of the NAVWEPS 00-807-80 BASIC AERODYNAMICS PITOT-STATIC SYSTEM PITOT WITH SEPARATE STATIC SOURCE

:%

.I.

q

w/

PRESSURE INDICATED BY GAUGE IS DIFFERENCE BETWEEN TOTAL AND STATIC PRESSURE, H-p= q Figure. 1.5. Airspeed Measurement 0.05 psi position error is an airspeed error instrument and errors due to position or lo- of 10 knots. A typical variation of air- cation of the installation. The instrument speed system position error is illustrated in error must be small by design of the equip- ment and is usually negligible in equjpment figure 1.6.

(3) The equivalent airspeed (PAS) is the which is properly maintained and cared for.

The position error of the installation must result of correcting the (CAS) for compressi- be small in the range of airspeeds involving bility effects. At high flight speeds the critical performance conditions. Position stagnation pressure recovered in the pitot tube is not representative of the airstream errors are most usually confine,d to the static dynamic pressure due to a magnification source in that the actual static pressure by compressibility. Compressibility of the sensed at the static port may be different airflow produces a stagnation pressure in from the free airstream static pressure.

When the .,aircraft is operated through a the pitot which is greater than if the flow were incompressible. As a result, the air- large range’ of angles of attack, the static pressure distribution varies ‘ quite greatly speed indication is given an erroneous mag- and it becomes quite difficult to’ minimize nihcation. The standard airspeed indicator is calibrated to read correct when at standard the static source error. In most instances a sea level conditions and thus has a com- compensating group of static sources may pressibility correction appropriate for these be combined to reduce the position error.

conditions. However, when the aircraft is In order to appreciate the magnitude of this problem, at flight speed near 100 knots a operating above standard sea level altitude, Revised January 1965 NAVWEPS 00-801-80 BASIC AERODYNAMICS TYPICAL POSITION ERROR CORRECTION INDICATED AIRSPEED, KNOTS COMPRESSIBILITY CORREt CALIBRATED AIRSPEED, KNOTS Figure 1.6. Airspeed Corrections (sheet 1 of 2) NAVWEPS 00-801-80 BASIC AERODYNAMICS DENSITY ALTITUDE CHART +g& ‘ Id -30fl1111v AlISNxl Figure 1.6. Airspeed Corrections (sheet 2 of 2) NAVWEPS 00-SOT-80 BASIC AERODYNAMICS Thus, the airspeed indicator system measures the inherent compensation is inadequate and dynamic pressure and will relate true flight additional correction must be applied. The velocity when instrument, position, compress- subtractive corrections that must be applied ibility, and density corrections are applied.

to CA$ depend on pressure altitude and CAS and are shown on figure 1.6 for the subsonic These corrections are quite necessary for ac- curate determination of true airspeed and flight range. The equivalent airspeed (EAS) is the flight speed in the standard sea level accurate navigation.

Bernoulli’ s principle and the concepts of air mass which would produce the same free static, dynamic, and total pressure are the basis stream dynamic pressure as the actual flight of aerodynamic fundamentals. The pressure condition.

distribution caused by the variation of local (4) The true airspeed (TAS) results when stack and dynamic pressures on a surface is the &4X is corrected for density altitude.

the source of the major aerodynamic forces Since the airspeed indicator is calibrated and moment.

for the dynamic pressures corresponding to airspeeds at standard sea level conditions, variations in air density must be accounted DEVELOPMENT OF AERODYNAMIC for. To relate EAS and TAX requires con- FORCES sideration that the EAS coupled with stand- The typical airflow patterns exemplify the .ard sea level density produces the same dy- relationship of static pressure and velocity namic pressure as the TAX Soupled with the defined by Bernoulli.

^^_._^1 .:.. 2---:... ,.f *L., bl:A.* Any object placed in an rnrJ;r;m..

dCLUd, ‘ all UcIIJIcy “I L11L“ ‘ 6°C C”IIUACI”L‘ .

airstream will have the a& to impact or stag- From this reasoning, it can be shown that: nate at some point near the leading edge. The (TAS)2p=(EAS)2 po pressure at this point of stagnation will be an absolute static pressure equal to the total pres- - or, TAS=EAS sure of the airstream. In other words, the d P static pressure at the stagnation point will be greater than the atmospheric pressure by the TAS= EAS 2 amount of the dynamic pressure of the air- stream. As the flow divides and proceeds where TAX= true airspeed around. the object, the increases in local ve- EAS=equivalent airspeed locity produce decreases in static pressure.

p=actual air density This procedure of flow is best illustrated by the PO=standard sea level air density flow patterns and pressure distributions of n=altitude density ratio, p/pa figure 1.7.

The result shows that the TAX is a function STREAMLINE PATTERN AND PRES- of EAS and density altitude. Figure 1.6 shows SURE DISTRIBUTION. The flow pattern of a chart of density altitude as a function of the cylinder of figure 1.7 is characterized by pressure altitude and temperature. Each par- the streamlines which denote the local flow ticular density altitude fixes the proportion direction. Velocity distribution is noted by between TAX and EAS. The use of a naviga- the streamline pattern since the streamlines tion computer requires setting appropriate effect a boundary of flow, and the airflow values of pressure altitude and temperature on between the streamlines is similar to flow in a the scales which then fixes rhe proportion be- closed tube. When the streamlines contract tween the scales of TAS and EAS (or TAS and and are close together, high local velocities CAS when compressibiliry corrections are exist; when the streamlines expand and are applicable).

far apart, low local velocities exist. At the Revlted Jmuoy 1965 NAVWEPS 00-8OT-80 BASIC AERODYNAMICS )ER PRESSURE DISTRIBUTION ON A 5v’ PEAK SUCTION PRESSURE STAGNATION CONSIDERING FRICTION EFFECTS NEGLECTING FRICTION (VISCOUS FLOW) (PERFECT FLUID) PRESSURE DISTRIBUTION ON A SYMMETRICAL AIRFOIL AT ZERO LIFT -PEAK SUCTION S AFT STAGNATION POINT NEGLECTING FRICTION VISCOUS FLOW Figure 1.7. Streamline Pattern and Pressure Distribution NAVWEPS OO-BOT-80 BASIC AERODYNAMICS forward stagnation point the local velocity airfoil do not ,necessarily occtir at the point of maximum thickness.

is zero and the maximum positive pressure re- However, a similarity sults. As the flow proceeds from the forward does exist in that the minimum pressure points stagnation point the velocity increases as correspond to the points where the streamlines shown by the change in streamlines. The are closest together and this condition exists local velocities reach a maximum at the upper when the streamlines are forced to the great- and lower extremities and a peak suction pres- est curvature.

sure is produced at these points on the cylinder. GENERATION OF LIFT. An important phenomenon associated with the production (NOTE: Positive pressures are pressures above of lift by an airfoil is the “circulation” im- atmospheric and negative or .ruction pressures parted to the airstream. The best practical are less than atmospheric.) As the flow illustration of this phenomenon is shown in continues aft from the peak suction pressure, the diverging streamlines indicate decreasing figure 1.8 by the streamlines and pressure dis- tributions existing on cylinders in an airstream.

local velocities and increasing local pressures.

If friction and compressibility effects are not The cylinder without circulation has a sym- metrical streamline pattern and a pressure dis- considered, the velocity would decrease to zero at the aft stagnation point and the full stagna- tribution which creates n-0 n_et lift. If the cylinder is given a clockwise rotation and tion pressure would be recovered. The pressure induces a rotational or circulatory flow, a dis- distribution for the cylinder in perfect fluid tinct change takes place in the streamline pat- flow would be symmetrical and no net force tern and p’ ess.~re &str~‘ “ u~~oii, The vriocitirs (lift or dragj wvuid rcsuit. Of course, thr relationship between static pressure and ~eloc- due to the vortex of circulatory flow cause ity along the surface is defined by Bernoulli’ s increased 104 velocity on the upper surface of the cylinder and decreased local velocity on equation.

the lower surface of the cylinder. Also, the The flow pattern for the cylinder in an actual fluid demonstrates the effect of friction or circulatory flow produces an upwash immedi- The viscosity of air produces a thin ately ahead and downwash immediately be- viscosity.

layer of retarded flow immediately adjacent hind the cylinder and both fore and aft stagna- to the surface. The energy expended in this tion points are lowered.

“boundary layer” can alter the pressure dis- The effect of the addition of circulatory flow tribution and destroy the symmetry of the is appreciated by the change in the pressure pattern. The force unbalance caused by the distribution on the cylinder. The increased change in pressure distribution creates a drag local velocity on the upper surface causes an force which is in addition to the drag due to increase in upper surface suction while the skin friction. decreased local velocity on the lower surface The streamline pattern for the symmetrical causes a decrease in lower surface suction. As airfoil of figure 1.7 again provides the basis a result, the cylinder with circulation will for the velocity and pressure distribution. produce a net lift. This mechanically induced At the leading edge the streamlines are widely circulation-called Magnus effect-illustrates diverged in the vicinity of the positive pres- the relationship between circulation and lift sures. The maximum local velocities and and is important to golfers, baseball and tennis suction (or negative) pressures exist where the players as well as pilots and aerodynamicists.

streamlines are the closest together, The curvature of the flight path of a golf ball One notable difference between the flow on the or baseball rcluites an unbalance df force cylinder and the airfoil is that the maximum which is created by rotation of the ball.

The velocity and minimum pressure points on the pitcher that can accurately control a .powerful NAVWEPS 00-8OT-80 BASIC AERODYNAMICS INCREASED LOCAL VELOCITY UPWASH mSWNWASH ---- \ LDECREASED LOCAL VELOCITY CYLINDER WITH CIRCULATION CYLINDER WITHOUT CIRCULATION MAGNUS EFFECT BY ROTATING CYLINDER AIRFOIL LIFT -ZERO LIFT

I

UPWASH INCREASED LOCAL ,-VELOCITY

I

POSITIVE LIFT DECREASED LOCAL VELOCITY Figure 1.8. Generation of Lift (sheet 1 of 2) NAVWEPS 00-SOT-80 BASIC AERODYNAMICS Figure 7.8. Generation of Lift (sheet 2 of 2) NAVWEPS GO-BOT-BO BASIC AERODYNAMlCS BASIC AIRFOIL SHAPE AND ANGLE OF ATTACK ORIGINAL ANGLE OF ATTACK AND DYNAMIC/PRESSURE, ORIGINAL ANGLE OF ATTACK BUT INCREASED DYNAMIC PRESSURE ORIGINAL ANGLE OF ATTACK AND DYNAMIC PRESSURE BUT ONE-HALF ORIGINAL SIZE AIRFOIL SHAPE AND ANGLE OF ATTACK DEFINE RELATIVE PRESSURE DISTRIBUTION Figure 1.9. Airfoil Pressure Distribution NAVWEPS 00-801-80 BASIC AERODYNAMICS rotation will be quite a “curve ball artist” The effect of free stream density and velocity the golfer that cannot control the lateral mo- is a necessary consideration when studying the tion of the club face striking the golf ball will development of the various aerodynamic forces.

Suppose that a particular shape of airfoil is impart an uncontrollable spin and have trouble with a “hook” or “slice.” fixed at a particular angle to the airstream.

The relative velocity and pressure distribution While a rotating cylinder can produce a net lift from the circulatory flow, the method is will be determined by the shape of the airfoil relatively inefficient and only serves to point and the angle to the airstream. The effect of out the relationship between lift and circula-, varying the airfoil size, air density and air- tion. An airfoil is capable of producing lift speed is shown in figure 1.9. If the same air- with relatively high efficiency and the process foil shape is placed at the same angle to an airstream with twice as great a dynamic pres- is illustrated in figure 1.8. If a symmetrical sure the magnitude of the pressure distribution airfoil is placed at zero angle of attack to the airstream, the streamline pattern and pressure will be twice as great but the r&rive shape of the pressure distribution will be the same.

distribution give evidence of zero lift.

HOW- With twice as great a pressure existing over ever, if the airfoil is given a positive angle of the surface, all aerodynamic forces and mo- attack, changes occur in the streamline pattern ments will ~double. If a half-size airfoil ib and pressure distribution similar to changes placed at the same angle to the original air- caused by the addition of circulation to the stream, the magnitude of the pressure distri- cylinder. The positive angle of attack causes increased velocity on the upper surface with bution is the same as the origina! airfoi! and an increase in upper surface suction while the again the relative shape of the pressure dis- tribution is identical.

decreased velocity on the lower surface causes The same pressure act- a decrease in lower surface suction. Also, ing on the half-size surface would reduce all upwash is generated ahead of the airfoil, the aerodynamic forces to one-half that of the forward stagnation point moves under the original. This similarity of flow patterns leading edge, and a downwash is evident aft means that the stagnation point occurs at the of the airfoil. The pressure distribution 0” same place, the peak suction pressure occurs the airfoil now provides a net force perpendicu- at the same place, and the actual magnitude of lar to the airstream-lift. the aerodynamic forces and moments depends The generation of lift by an airfoil is depend- upon the airstream dynamic pressure and the ent upon the airfoil being able to create circu- surface area. This concept is extremely im- lation in the airstream and develop the lifting, portant when attempting to separate and ana- pressure distribution on the surface. In all lyze the most important factors affecting the cases, the generated lift will be the net force development of aerodynamic forces.

caused by the distribution of pressure over the AIRFOIL TERMINOLOGY. Since the upper and lower surfaces of the airfoil. At shape of an airfoil and the inclination to the low angles of attack, suction pressures usually airstream are so important in determining the will exist on both upper and lower surfaces. pressure distribution, it is necessary to properly but the upper surface suction must be greater define the airfoil terminology. Figure 1.10 for positive lift. At high angles of attack shows a typical airfoil and illustrates the near that for maximum lift, a positive pressure various items of airfoil terminology will exist on the lower surface but this will (1) The chord line is a straight line connect- account for approximately one-third the net ing the leading and trailing edges of the lift. airfoil.

NAVWEPS 00-8DT-80 BASIC AERODYN,AMlCS LOCAT,ON DF THICKNESS UPPER SURFACE MAX. THICKNESS MEAN CAMBER CH6RD t -I CA v LOCATION OF MAXIMUM CAMBER t- LIFT G RE;L:r; & DRAG \ a Figure 1.10. Airfoil ~erminoh NAVWEPS oOgOT-8O BASIC AERODYNAMICS angle of attack. Regardless of the condi- (2) The chord is the characteristic dimen- tion of flight, the instantaneous flight path sion of the airfoil.

of the surface determines the direction of the (3) The mean-camberline is a line drawn oncoming relative wind and the angle of halfway between the upper and lower sur- attack is the angle between the instantaneous faces. Actually, the chord line connects the relative wind and the chord line. To respect ends of the mean-camber line.

the definition of angle of attack, visualize (4) The shape of the mean-camber line is the flight path of the aircraft during a loop very important in determining the aerody- and appreciate that the relative wind is namic characteristics of an airfoil section.

defined by the flight path at any point dur- The maximum camber (displacement of the mean line from the chord line) and the Ioca- ing the maneuver.

Notice that the description of an airfoil tion of the maximum camber help to define profile is by dimensions which are fractions or the shape of the mean-camber line. These percent of the basic chord dimension. Thus, quantities are expressed as fractions or per- when an airfoil. profile is specified a relative cent of the basic chord dimension. A typi- shape is described. (NOTB: A numerical sys- cal iow speed airfoil may have a maximum tem of designating airfoil profiles originated camber of 4 percent located 40 percent aft of by the National ~Advisory Committee for Aero- the leading edge.

nautics [NACA] is used to describe the main (5) The thickness and thickness distribu- geometric features and certain aerodynamic tion of the profile are important properties of a section. The maximum tbicknus and properties. NACA Report Nol 824 wi!! pro- location of maximum thickness define thick- vide the detail of this system.)

AERODYNAMIC FORCE COEFFICIENT.

ness and distribution of thickness and are The aerodynamic forces of lift and drag depend expressed as fractions or percent of the chord.

on the combined effect of many different vari- A typical low speed airfoil may have a.

ables. The important single variables could maximum thickness of 12 percent located IX: 30 percent aft of the leading edge.

(1) Airstream velocity (6) The leading edgeradius of the airfoil is (2) Air density the radius of curvature given the leading edge (3) Shape or profile of the surface shape. It is the radius of the circle centered (4) Angle of attack on a line tangent to the leading edge camber (5) Surface area and connecting tangency pcints of upper and (6) Compressibility effects lower surfaces with the leading edge. Typi- (7) Viscosity effects cal leading edge radii are zero (knife edge) If the effects of viscosity and compressibility to 1 or 2 percent.

are not of immediate importance, the remain-

(7) The Iift produced by an airfoil is the

ing items can be combined for consideration.

net force produced perpendicular to the n&a- Since the major aerodynamic forces are the tive wind.

result of various pressures distributed on a (8) The drag incurred by an airfoil is the surface, the surface area will be a major factor.

net force produced parallel to the relative wind.

Dynamic prcssurc of the airstream is another (9) The angle of attack is the angle between common denominator of aerodynamic forces the chord line and the relative wind. Angle and is a major factor since the magnitude of a of attack is given the shorthand notation pressure distribution depends on the source a (alpha). Of course, it is important to dif- energy of the free stream. The remaining i ferentiate between pitch attitude angle and major factor is the relative peJJ#re dittribution NAVWEPS m-60T-30 BASIC AERODYNAMICS existing on the surface. Of course, the ve- It is derived from the relative pressure and locity distribution, and resulting pressure dis- velocity distribution.

(2) Influenced only by the shape of the tribution, is determmed by the.shape or pro- surface and angle of attack since these factors file of the surface and the angle of a’ track.

determine the pressure distribution.

Thus, any aerodynamic force can be repre- (3) An index which allows evaluation of sented as the product df three major factors: the effects of compressibility and viscosity.

the surface area of the objects Since the effects of area, density, and velocity the dynamic pressure of the airstream are obviated by the coefficient form, com- the coefficient or index of force determined pressibility and viscosity effects can be by the relative pressure distribution separated for study.

This relationship is expressed by the following THE BASIC LIFT EQUATION. Lift has equation : been dehned as the net force developed per- F= C,qS pendicular to the relative wind. The aero- where dynamic force of lift on an airplane results F = aerodynamic force, lbs.

from the generation of a pressure distribution C,=coeflicient of aerodynamic force on the wing. This lift force is described by ,iay;mic pressure, psf the following equation: L=C& S=surface area, sq. ft.

where In order to fully appreciate the importance L=lift, lbs.

of the aerodynamic force coe&cient, C,, the , C, = lift coefficient.

above equation is rearranged to alternate q= dy;:mic pressure, psf forms : +p S= wing surface area, sq. ft.

The lift coefhcient used in this equation is the ratio of the lift pressure and dynamic pressure and is a function of the shape of the wing and In this form, the aerodynamic force coefficient angle of attack. If the lift coefficient of a Js appreciared as the aerodynamic force per conventional airplane wing planfoi-m were surface area and dynamic pressure. In other plotted versus angle of attack, the result would words, the force coefficient is a dimensionless be typical of the graph of figure 1.11. Since ratio between the average aerodynamic pres- the effects of speed, density, area, weight, alti- sure (aerodynamic force.per ‘ area) and the air- tude, etc., are eliminated by the coefficient form, stream dynamic pressure. All the aerodynamic an indication of the true lift capability is ob- forces of lift and drag are studied on this basis- tained. Each angle of attack produces a par- the common denominator in each case being ticular lift coefficient since the angle of attack By such a surface area and dynamic pressure.

is the controlling factor in the pressure dis- definition, a “lift coefficient” would .be the tribution. Lift coeflicient increases with angle ratio between lift pressure and dynamic pres- of attack up to the maximum lift coefficient, “drag coefficient” would be the ratio c L,,,~., and, sure; a as angle of attack is increased be- between drag pressure and.:d.ynamic pressure. yond the maximum lift angle, the airflow is The use of the coefficient form of an aero- unable to adhere to the upper surface. The dynamic force is necessary since the force airflow then separates from the upper surface coellicient is: and stall occurs.

JNTERPRETATION OF THE LIFT EQUA- (1) An index 04 the aerodynamic force TION. Several important relationships are independent of area, density, and velocity.

LIFT COEFFICIENT CL LIFT PRESSURE DYNAMIC PRESSURE H L P qs ANGLE OF ATTACK, DEGREES a Figure 7.7 1. Typical lib Characteristics NAVWEPS 00.401-80 BASIC AERODYNAMICS Thus, a sea level airspeed (or EAS) of 100 derived from study of the basic lift equation knots would provide the dynamic pressure and the typical wing lift curve. One impor- necessary at maximum lift to produce 14,250 tant fact to be appreciated is that the airplane Ibs. of lift. If the airplane were operated at a shown in figure 1.11 stalls at the same angle higher weight, a higher dynamic pressure of attack regardless of weight, dynamic pres- would be required to furnish the greater lift sure, bank angle, etc. Of course, the stall and a higher stall speed would result.

If the speedof the aircraft will be affected by weight, airplane were placed in a steep turn, the greater bank angle, and other factors since the product lift required in the turn would increase the of dynamic pressure, wing area, and lift co- stall speed. If the airplane were flown at a efficient must produce the required lift. A higher density altitude the TAX at stall would rearrangement of the basic lift equation de- increase. However, one factor common to fines this relationship.

each of these conditions is that the angle of L = c&Y attack at C,,,, is the same. It is important to realize that stall warning devices must sense using q =$ (I’ in knots, TAX) angle of attack (a) or pressure distribution (related to CL).

Another important fact related by the basic solving for V, lift equation and lift curve is variation of angle - of attack and lift coefficient with airspeed.

V=17.2 & Suppose that the example airplane is flown in J L,J steady, wing 1eveJ flight at various airspeeds Since the stall speed is the minimum flying with lift equal to the weight. It is obvious speed necessary to sustain flight, the lift co- that an increase in airspeed above the stall efficient must be the maximum (CL,,,,).

speed will require a corresponding decrease in Suppose that the airplane shown in’ figure lift coeflicient and angle of attack to maintain 1.11 has the following properties: steady, lift-equal-weight flight. The exact Weight = 14,250 lbs relationship of lift coefficient and airspeed is evolved from the basic lift equation assuming Wing area=280 sq. ft.

constant lift (equal to weight) and equivaIent C&=1.5 airspeeds.

If the airplane is flown in steady, level flight at

v, p

C‘

sea level with lift equal to weight the stall

-= -

V C speed would be: %n.* ,- V.= 17.24&$ The example airplane was specified to have: where Weight = 14,250 lbs.

V.= stall speed, knots TAS CL,,,=lS W= weight, lbs. (lift = weight) V,= 100 knots EAS The following table depicts the lift coefficients va= 17.2J (I.&4E;280) and angles of attack at various airspeeds in = 100 knots steady flight.

NAWWEPS 00-8OT-80 BASIC AERODYNAMICS NAVWEPS WOT-BO BASIC AERODYNAMICS angle of attack indicator allows precision con- trol of the airspeed. The accomplished insttu- ment pilot is the devotee of “attitude” flying technique-his creed being “attitude plus loo. ................. 1.30 20.00 l.lm power equals performance.” During a GCA 1.24 15.P 110.................. ,826 1.04 12.7’ 17.0 .................. ,694 approach, the professional instrument pilot .61 8.20 lY) .................. .444 controls airspeed with stick (angle of attack) 200.................. .38 4.6’ and rate of descent with power adjustment.

MO. ................. .I7 2.10 ,111 4&l. ................. .o!J 1.10 .c453 Maneuvering flight and certain transient .06 .T= 30.7.................. ,040 conditions of flight tend to complicate the .04 .5O 600.................. .028 relationship of angle of attack and airspeed.

However, the majority of flight and, certainly, Note that for the conditions of steady flight, the most critical regime of flight (takeoff, ap- each airspeed requites a specific angle of attack proach, and landing), is conducted in essen- and lift coefficient. This fact provides a fun- tially steady flight condition.

damental concept of flying technique: Angle AIRFOIL LIFT CHARACTERISTICS. Air- of attack is tbs primary Controlof airspeedin steady foil section properties differ from wing or flight. Of course, the control stick or wheel airplane properties because of the effect of the allows the pilot to control the angle of attack planform. Actually, the wing may have vati- and, thus, control the airspeed in steady flight.

ous airfoil sections from root to tip with taper, In the same sense, the throttle controls the twist, sweepback and local flow components output of the powerplant and allows the pilot in a spanwise direction. The resulting aeto- to control rate of climb and descent at various dynamic properties of the wing are determined airspeeds.

by the action of each section along the span The teal believers of these concepts ate pro- and the three-dimensional flow. Airfoil sec- fessional instrument pilots, LSO’ s, and glider tion properties are derived from the basic shape pilots.. The glider pilot (or flameout enthusi- or profile in two-dimensional flow and the force ast) has no recourse but to control airspeed by coefficients are given a notation of lower case angle of attack and accept whatever rate of letters. For example, a wing or airplane lift descent is incurred at the various airspeeds.

coefficient is C, while an airfoil section lift The LSO must become quite proficient at judg- coefficient is termed cr. Also, wing angle of ing the flight path and angle of attack of the attack is Q while section angle of attack is airplane in the pattern. The more complete differentiated by the use of 01~. The study of visual reference field available to the LSO section properties allows an objective consider- allows him to judge the angle of attack of ation of the effects of camber, thickness, etc.

the airplane mote accurately than the pilot.

The lift characteristics of five illustrative When the airplane approaches the LSO, the airfoil sections are shown in figure 1.12. The precise judgment of airspeed is by the angle section lift coe&icient, c,, is plotted versus of attack rather than the rate of closure. If section angle of attack, olO,for five standard the LSO sees the airplane on the desired flight N A C A airfoil profiles. One characteristic fea- path but with too low an angle of attack, the ture of all airfoil sections is that the slope of airspeed is too high; if the angle of attack is the various lift curves is essentially the same.

too high, the airspeed is too low and the ait- At low lift coefhcients, the section lift coeffi- plane is approaching the stall. The mirror cient increases approximately 0.1 for each landing system coupled with an angle of attack degree increase in angle of attack. For each indicator is an obvious refinement.

The mit- of the airfoils shown, a S ’ change in angle of tot indicates the desired flight path and the NAVWEPS OD-8OT-80 BASIC AERODYNAMICS (DATA FROM NACA REPORT NO. 824) SECTION ANGLE OF ATTACK mo, DEGREES Figure 1.12. Lift Characteristics of lypicol Airfoil Sections NAVWEPS OO-BOT-BO BASIC AE,RODYMAMlCS sections have zero lift at zero angle of attack, attack would produce an approximate 0.5 the sections with positive camber have nega- change in lift coefficient. Evidently, lift,~curve tive angles for zero lift.

slope is not a factor important in the selection The importance of maximum lift coefficient of an airfoil.

is obvious. If the maximum lift coefficient is An important lift property affected by the high, the stall speed will be low. However, airfoil shape is the section maximum lift co- the high thickness and camber necessary for efficient, ci-. The effect of airfoil shape on high section maximum lift coefficients may ci- can be appreciated by comparison of the produce low critical Mach numbers and large lift curves for the five airfoils of figure 1.12.

twisting moments at high speed. In other The NACA airfoils 63X06,63-009, and 63i-012 words, a high maximum lift coefficient is just ate symmetrical sections of a basic thickness one of the many features desired of an airfoil distribution but maximum thicknesses of 6, 9, and 12 percent respectively. The effect of section.

DRAG CHARACTERISTICS. Drag is the obvious from an inspec- thickness on ~1% is net aerodynamic force parallel to the relative tion of these curves : wind and its source is the pressure distribution and skin friction on the surface.

Large, thick bluff bodies in an airstream show a predomi- nance of form drag due to the unbalanced pres- Cl.82 9.0° NACA 63-005 .~. :.

sure distribution. However, streamlined 1.10 10.5~ NACA 6Mo9.

1.40 13.80 NACA 63‘ -01?,.

bodies with smooth contours show a ptedomi- nance of drag due to skin friction. In a fashion similar to other aerodynamic forces, The 12-percent section has a cr- approxi- drag forces may be considered in the form of a mately 70 percent greater than the 6-percent coefficient which is independent of dynamic thick section. In addition, the thicker airfoils pressure and surface area. The basic drag have greater benefit from the use of various equation is as follows: high lift devices.

D=GqS The effect of camber is illustrated by the lift where curves of the NACA 4412 and 631-412 sections.

D=drag, lbs.

The NACA 4412 section is a 12 percent thick C,= drag coefficient airfoil which has 4 percent maximum camber q= dynamic pressure, psf located at 40 percent of the chord. The UP =z (V in knots, TAS) NACA 63i-412 airfoil has the same thickness and thickness distribution as the 631-012 but S= wing surface area, sq. ft.

camber added to give a “design” ’ lift coefficient The force of drag is shown as the product of (c, for minimum section drag) of 0.4. The dynamic pressure, surface area, and drag co- lift curves for these two airfoils show that efficient, C,. The drag coefficient in this camber has a beneficial e&t on cl-.

equation is similar to any other aerodynamic force coefficient-it is the ratio of drag pres- ScCdO” a0 for “&* %.I sure to dynamic pressure. If the drag co- efficient of a conventional airplane were plotted NACA 6h-312 (symmctricd) :.

1.40 13.e versus angle of attack, the result would be NACA 631-412 Whmd).

1.73 IS. z” typical of the graph shown in figure 1.13. At low angles of attack the drag coefficient is An additional effect of camber is the change low and small changes in angle of attack create in zero lift angle. While the symmetrical only slight changes in drag coefficient. At NAVWEPS 00-BOT-80 BASIC AERODYNAMICS ANGLEOFATTACK,DEGREES I a Figure 7.73. Drag Characteristics (sheet 1 of 21 CD ANGLE OF ATTACK, DEGREES a Figure 7.13. Brag Characferistics (sheet 2 of 2) NAVWEPS Oe8OT-80 BASIC AERODYNAMICS The configuration of an airplane has a great higher angles of attack the drag coefficient is effect on the lift-drag ratio. Typical values much greater and small changes in angle of attack cause significant changes in drag. As are listed for various types of of (L/D),..

airplanes. While the high performance sail- stall occurs, a large increase in drag takes plane may have. extremely high lift-drag place.

ratios, such an aircraft has no real economic A factor more important in airplane per- or tactical purpose. The supersonic fighter formance considerations is the lift-drag ratio, L/D. With the lift and drag data available for may have seemingly low lift-drag ratios in subsonic flight but the airplane configurations the airplane, the proportions of CL and CD can required for supersonic flight (and high [L/D]‘ * be calculated for each specific angle of attack.

at high Mach numbers) precipitate this situa- The resulting plot of lift-drag ratio with angle tion.

of attack shows that L/D increases to some Many important items of airplane perform- maximum then decreases at the higher lift coefficients and angles of attack. Note that ance are obtained in flight at (L/D),... Typi- cal performance conditions which occur at the maximum lift-drag ratio, (L/D),,,, occurs at one specific angle of attack and lift coefIi- (L/D),., are: cient. If the airplane is operated in steady maximum endurance of jet powered air- the total drag is at a mini: flight at (L/D),,,, planes mum. Any angle of attack lower or higher maximum range of propeller driven air- than that for (L/D),,, reduces the lift-drag planes ratio and consequently increases -the total maximum climb angle for jet powered air- drag for a given airpiane iift.

planes The airplane depicted by the curves of Figure maximum power-off glide range, jet or 1.13 has a maximum lift-drag ratio of 12.5 at Prop an angle of attack of 6”. Suppose this airplane The most immediately interesting of these is operated in steady flight at a gross weight items is the power-off glide range of an air- of 12,500 lbs. If flown at the airspeed and plane. By examining the forces acting on an angle of attack corresponding to (L/D),.., airplane during a glide, it can be shown that the drag would be 1,000 lbs. Any higher or the glide ratio is numerically equal to the lower airspeed would produce a drag greater lift-drag ratio. For example, if the airplane than 1,000 lbs. Of course, this same airplane in a glide has an (L/D) of 15, each mile of alti- could be operated at higher or lower gross tude is traded for 15 miles of horizontal dis- weights and the same maximum lift-drag ratio tance. Such a fact implies that the airplane of 12.5 could be obtained at the same angle of should be flown at (L/D)- to obtain the attack of 6”. However, a change’ in gross weight would require a change in airspeed to greatest glide distance.

support the new weight at the same lift co- An unbelievable feature of gliding perform- efficient and angle of attack.

ance is the effect of airplane gross weight.

Since the maximum lift-drag ratio of a given Type airplane: (L/D) emz airplane is an intrinsic property of the aero- High performance sailplane. 25-40 dynamic configuration, gross weight will not Typical patrol or transport.. 12-20 affect the gliding performance. If a typical High Performance bomber. 2~25 jet trainer has an (L/@- of 15, the aircraft 1 Propellerpoweredtrainer.. 1~15 can obtain a maximum of 15 miles horizontal et trainer.. 14-16 J distance for each mile of altitude.

Transonic fighter or attack.. lo-13 This would Supersonic fighter or attack. 4-9 (subsonic) be true of this particular airplane at any gross Revised Januay 1965 NAVWEPS OO-EOT-RO BASIC AERODYNAMICS weight if the airplane is flown at the angle 40 percent chord. When this section is com- of attack for (L/D),. Of course, the gross pared with the NACA 0006 section the effect weight would affect the glide airspeed neces- of camber can be appreciated. At low lift sary for this particular angle of attack but the coefficients the thtn, symmetrical section has However, at lift coeffi- glide ratio would be unaffected. much lower drag.

AIRFOIL DRAG CHARACTERISTICS. cients above 03 the thicker, cambered section The total drag of an airplane is composed of has the lower drag. Thus, proper camber and the drags of the individual components and thickness can improve the lift-drag ratio of the forces caused by interference between these the section.

components. The drag of an airplane con- The NACA 63,412 is a cambered 12 percent figuration must include the various drags due thick airfoil of the ‘ “ laminar flow” type.

to lift, form, friction, interference, leakage, This airfoil is shaped to produce a design lift etc. To appreciate the factors which affect coe5cient of 0.4. Notice that the drag curve the drag of an airplane configuration, it is of this airfoil has distinct aberrations with most logical to consider the factors which very low drag coefficients near the lift coeffi- affect the drag of airfoil sections. cient of 0.4. This airfoil profile has its camber In order to allow an objective consideration of the effects and thickness distributed to produce very low of thickness, camber, etc., the properties of uniform velocity on the forward surface (mini- two-dimensional sections must be studied. mum pressure point well aft) at this lift coeffi- Airfoil section properties are derived from the cient. The resulting pressure and velocity basic profile in two-dimensional. flow and are distribution enhance extensive laminar flow provided the lower case shorthand notation in the boundary layer and greatly reduce the to distinguish them from wing or airplane skin friction drag. The benefit of the laminar properties, e.g., wing or airplane drag coe5- flow is appreciated by comparing the minimum cient is C, while airfoil section drag coefficient drag of this airfoil with an airfoil which has one-half the maximum thickness-the NACA is c,.

The drag characteristics of three illustrative ooo6.

airfoil sections are shown in figure 1.14. The choice of an airfoil section will depend The on the consideration oftmany different factors.

section drag coe&cient, c,, is plotted versus the section lift coefficient, cr. The drag on While the cI, of the section is an important the airfoil section is composed of pressure drag quality, a more appropriate factor for con- sideration is the maximum lift coefficient of and skin friction. When the airfoil is at low the section when various high lift devices are lift coe&cients, the drag due to skin friction predominates. The drag curve for a conven- applied. Trailing edge flaps and leading edge tional airfoil tends to be quite shallow in this high lift devices are applied to increase the region since there is very little variation of for low speed performance. Thus, an cr,, skin friction with angle of attack. appropriate factor for comparison is the ratio When the airfoil is at high lift coefficients, form or of section drag coe5cient to section maximum pressure drag predominates and the drag co- lift coefficient with flaps-cd/crm,. When this efficient varies rapidly with lift coefficient. quantity is corrected for compressibility, a preliminary selection of an airfoil section is The NACA 0006 is a thin symmetrical profile possible. The airfoil having the lowest value which has a maximum thickness of 6 percent of c&~, at the design flight condition (en- located at 30 percent of the chord. This section shows a typical variation of cd and cr. durance, range, high speed, etc.) will create The NACA 4412 section is a 12 percent thick the least section drag for a given .design stall airfoil with 4 percent maximum camber at speed.

NAVWEPS DD-BOT-BD BASK AERODYNAMICS (DATA FROM NACA REPORT ~0.824) SMOOTH SURFAC e-L-- -.2 Cl .2 .4 .6 .8 LO’ ---I.2 1.4 1.6 1.8 SECTION LIFT COEFFICIENT Cl Figure 1.14. Drag Characteristics of Typical Airfoil Sections NAVWEPS 00-BOT-RO BASIC AERODYNAMICS PLIGHT AT HIGH LIFT CONDITIONS fuel. Hence, the gross weight and stall speed of the airplane can vary considerably through- It is frequently stated that the career Naval out the flight. The effect of only weight on Aviator spends more than half his life “below stall speed can be expressed by a modified form a thousand feet and a hundred knots.” Re- of the stall speed equation where density ratio, gardless of the implications of such a state- c r,,,.,, and wing area are held constant.

ment, the thought does cunnute the relation- V K _i_z- ship of minimum flying speeds and carrier J v.,- K aviation. Only in Naval Aviation is there where such importance assigned to precision control V*,=stall speed corresponding to some Safe of the aircraft at high lift conditions.

gross weight, WI operation in carrier aviation demands precision V@a=stall speed corresponding to a dif- control of the airplane at high lift conditions.

ferent gross weight, WP The aerodynamic lift characteristics of an airplane are portrayed by the curve of lift As an illustration of this equation, assume coefficient versus angle of attack. Such a that a particular airplane has a stall speed of curve is illustrated in figure 1.15 for a specific 100 knots at a gross weight of 10,000 lbs.

airplane in the clean and flap down configura- The stall speeds of this Sam: airplane at other tions. A given aerodynamic configuration ex- gross weights would be: periences increases in lift coefficient with in- creases in angle of attack until the maximum lift coefficient is obtained.

A further increase in angIe of attack produces stall and the lift ‘ &~=lO,

ll,W

100x

coefficient then decreases. Since the maximum 4, 12,ooO 110 lift coefficient corresponds to the minimum 14,4al 120 speed available in flight, it is an important 9mJ point of reference. The stall speed of the air- 8,100 90 craft in level flight is related by the equation: Figure 1.15 illustrates the effect of weight on stall speed on a percentage basis and will be V7.=17.2 c w J-- valid for any airplane. Many specific condi- .ln2s tions of flight are accomplished at certain fixed where angles of attack and lift coefficients. The V.-stall speed, knots TAS effect of weight on a percentage basis on the W=gross weight, lbs.

speeds for any specific lift coefficient and angle c Lnoz=airplane maximum lift coefficient of attack is identical. Note that at small csaltitude density ratio variations of weight, a rule of thumb may S= wing area, sq. ft.

express the effect of weight on stall speed- This equation illustrates the effect on stall “a 2 percent change in weight causes a I per- speed of weight and wing area (or wing load- cent change in stall speed.” ing, W/S), maximum lift coefficient, and alti- EFFECT OF MANEUVERING FLIGHT.

tude. If the stall speed is desired in EAS, the Turning flight and maneuvers produce an density ratio will be that for sea level (u= effect on stall speed which is similar to the 1.000). effect of weight. Inspection of the chart on EFFECT OF WEIGHT. Modern configu- figure 1.16 shows the forces acting on an airplane rations of airplanes are characterized by a large in a steady turn. Any steady turn requires percent. of the maximum gross weight being that the vertical component of Iift be equal to NAVWEPS OD-SOT-80 BASIC AERODYNAMICS EFFECT OF FLAPS CL LIFT COEFFICIENT IO I5 20 25 ANGLE OtATTACK I EFFECT OF WEIGHT ON STALL SPEED Figure 1.15. Flight at High Lift Conditions NAVWEPS 00-8OT-80 BASIC AERODYNAMICS EFFECT OF HIGH LIET DEVICES. The weight of the airplane and the horizontal com- primary purpose of high lift devices (flaps, ponent of lift be equal to the centrifugal force.

slots, slats, etc.) is to increase the CLn, of the Thus, the aircraft in a steady turn develops a airplane and reduce the stall speed. The take- lift greater than weight and experiences in- off and landing speeds are consequently re- creased stall speeds.

duced. The effect of a typical high lift device Trigonometric ‘ relationships allow deter- is shown by the airplane lift curves of figure mination of the effect of bank angle on stall 1.15 and is summarized here: speed and load factor. The load factor, B, is the proportion between lift and weight and is determined by: (II far C‘ , c.mip~tion L.

L fizz-- W clun(tla~Up) . . . . . . . . . . . . . 1.5 200 Php down. 2.0 IS.9 n=- cos I$ where The principal effect of the extension of flaps is n=load factor (or “G”) to increase the C,, and reduce the angle of cos 6 = cosine of the bank angle, + (phi) attack for any given lift coefficient. The in- crease in CL,, afforded by flap deflection re- Typical values of load factor determined by duces the stall speed in a certain proportion, this relationship are: the effect described by the equation: - 600 759 .+.- 00 130 300 450 v,=v, z% J Ch, n-l.00 1.035 1.154 1.414 z.ooo 4.ooo where The stall speed in a turn can be determined by: V,,= stall speed with flaps down v,=stall speed without flaps where v,+= stall speed at some bank angle + C,= maximum lift coefficient of V,= stall speed for wing level, lift-equal- the clean configuration weight flight n=load factor corresponding to the C&,= maximum lift coefficient bank angle with flaps down The percent increase in stall speed in a turn is shown on figure l.i6. Since this chart is predi- For example, assume the airplane described by cated on a steady turn and constant CL,, the the lift curves of figure 1.15 has a stall speed of figures a!e valid for any airplane. The chart 100 knots at the landing weight in the clean shows that no appreciable change in load fac- configuration. If the flaps are lowered the tor or stall speed occurs at bank angles less than reduced stall speed is reduced to: 30“. Above 4S” of bank the increase in load factor and stall speed is quite rapid. This fact emphasizes the need for avoiding steep turns at low airspeeds-a flight condition common to =86.5 knots stall-spin accidents.

NAVWWS 00-8OT-80 BASIC AERODYNAMICS .#a, GANK~ANGLE, DEGREES EFFECT OF c ONSTALL SPEED LMAX ANT % IO 20 30 40 50 PERCENTDECREASE IN STALL SPEED Figure 7.76. Flight at High Liff Conditions Revised Jarwary 1965 NAVWEPS OO-EOT-RO BASIC AERODYNAMICS Thus, wirh rhe higher lift coefficienr available, angle of attack is unaffected. At any parricu- less dynamic pressure is required to provide lar altitude, the indicated stall speed is a func- the necessary lift.

tion of weight and load factor. An increase Because of the stated variation of stall speed in altitude will produce a decrease in density with C-, large changes in CL- are necessary and increase the true airspeed at stall. Also, to produce significant changes in stall speed. an increase in altitude will alter compressibility This effect is illustrated by the graph in figure and viscosity effects and, generally speaking, 1.16 and certain typical values are shown cause the in,&ztcd stall speed to increase.

below: This parti&lar consideration is usually sig- nificant only above altitudes of 20,000 ft.

Percentincrease in CL. .~.

2 10 so loo 300 Recovery from stall involves a very simple concept. Since stall is precipitated by an Percent reductionin stall speed 1 5 18 29 50 excessive angle of attack, the angle of attack The contribution of the high lift devices must must be dccmmd. This is a fundamental princi- be considerable to cause large reduction in ple which is common to any airplane.

stall speed. The most elaborate combination An airplane may be designed to be “stall- of flaps, slots, slats, and boundary layer con- proof” simply by reducing the effectiveness of trol throughout the span of the wing would the elevators. If the elevators are not power- be required to increase C,- by 300 percent. ful enough to hold the airplane to high angles of attack, the airplane cannot be stalled in any A common case is that of a typical propeller condition of flight. Such a requirement for a driven transport which experiences a 70 per- tactical military airplane would seriously re- cent increase in CzIM1by full flap deflection.

duce performance. High lift coefficients near A typical single engine jet fighter with a thin the maximum are required for high maneuver- swept wing obtains a 20 percent increase in ability and low landing and takeoff speeds.

CL- by full flap deflection. Thin airfoil sec- Hence, the Naval Aviator must appreciate the tions with sweepback impose distinct limita- effect of the many variables affecting the stall tions on the effectiveness of flaps and the 20 speed and regard “attitude flying,” angle of percent increase in CL- by flaps is a typical- attack indicators, and stall warning devices if not high-value for such a configuration.

as techniques which allow more precise control One factor common to maximum lift condi- of the airplane at high lift conditions.

tion is the angle of attack and pressure distri- bution. The maximum lift coefficient of a HIGH LIFT DEVICES particular wing configuration is obtained at one angle of attack and one pressure distribu- There are many different types of high lift tion. Weight, bank angle, load factor, density devices used to increase the maximum lift co- altitude, and airspeed have no direct effect on efficient for low speed flight. The high lift the stall angle of attack. This fact is sufficient devices applied to the trailing edge of a section justification for the use of angle of attack indi- consist of a flap which is usually 15 to 25 per- cators and stall warning devices which sense cent of the chord. The deflection of a flap pressure distribution on the wing. During produces the effect of a large amount of camber flight maneuvers, landing approach, takeoff, added well aft on the chord. The principal turns, etc. the airplani will stall if the critical types of flaps are shown applied to a basic sec- angle of attack is cxcccdcd. The airspeed ar tion of airfoil. The effect of a 30’ deflection of which stall occurs will be determined by a 25 percent chord flap is shown on the lift weight, load factor, and altitude but the stall and drag curves of figure 1.17.

NAVWEPS 00-BOT-80 BASIC AERODYNAMICS BASIC SECTION SPLIT FLAP PLAIN FLAP FOWLER FLAP SLOTTED FLAP EFFECT ON SECTION-LIFT AND DRAG CHARACTERISTICS OF A 25% CHORD FLAP DEFLECTED 30° I FOW&ER SLOTTED 3.0 - 2.5 - 2.0 - 1.5 - I.O- .5 - 0 -I- O SECTION DRAG COEFFICIENT SECTION ANGLE OF ATTACK o,,, DEGREES cd Figure 1.17. Flap Configurations Revised January 1965 NAVWEPS OO-BOT-BO BASIC AERODYNAMICS The plainjap shown in figure 1.17 is a simple loads on the structure and pitching moments hinged portion of the trailing edge. The effect that must be controlled with the horizontal of the camber added well aft on the chord tail. Unfortunately, the flap types producing causes a significant increase in cbr. In addi- the greatest increases in c,,- usually cause the tion, the zero lift angle changes to a more greatest twisting moments. The Fowler flap negative value and the drag increases greatly. causes the greatest change in twisting moment The split flap shown in figure 1.17 consist of while the split flap causes the least. This plate deflected from the lower surface of the factor-along with mechanical complexity of section and produces a slightly greater change the installation-may complicate the choice in cImoT than the plain flap. However, a much of a flap configuration.

The effectiveness of flaps on a wing con- larger change in drag results from the great figuration depend on many different factors.

turbulent wake produced by this type flap.

One important factor is the amount of the The greater drag’ may not be such a disadvan- wing area affected by the flaps. Since a rage when ir is realized that it may be advan- certain amount of the span is reserved for tageous to accomplish steeper landing ap- ailerons, the actual wing maximum lift prop- proaches over obstacles or require higher power erties will be less than that of the flapped from the engine during approach (to minimize two-dimensional section. If the basic wing engine acceleration time for waveoR).

has a low thickness, any type of flap will be The slottedPap is similar to the plain flap but less effective than on a wing of greater thick- the gap between the main section and flap ness. Sweepback of the wing can cause an leading edge is given specific contours. High additional significant reduction in the effec- energy air from the lower surface is ducted to tiveness of flaps.

the flap upper surface. The high energy air High lift devices applied to the leading edge from the slot accelerates the upper surface boundary layer and delays airflow separation of a section consist of slots, slats, and small to some higher lift coefficient. The slotted amounts of local camber. The fixed slot in a flap can cause much greater increases in c,,, wing conducts flow of high energy air into the than the plain or split flap and section drags boundary layer on the upper surface and delays are much lower.

airflow separation to some higher angle of The Fowkr&zp arrangement is similar to the attack and lift coefficient. Since the slot slotted flap. The difference is that the de- alone effects no change in camber, the higher flected flap segment is moved aft along a set of maximum lift coefficient will be obtained at a tracks which increases the chord and effects higher angle of attack, i.e., the slot simply an increase in wing area. The Fowler flap is delays stall to a higher angle of attack. An characterized by large increases in c,,, with automatic slot arrangement consists of a minimum changes in drag. ,.

leading edge segment (slat) which is free to One additional factor requiring consider- move on tracks. At low angles of attack the ation in a comparison of flap types is the aero- slat is held flush against the leading edge by dynamic twisting moments caused by the flap. Positive camber produces a nose down the high positive local pressures.

When the section is at high angles of attack, the high twisting moment-especially great when large local suction pressures at the leading edge camber is used well aft on the chord (an create a chordwise force forward to actuate obvious implication is that flaps are not prac- tical on a flying wing or tailless airplane). the slat. The slot formed then allows the The deflection of a flap causes large nose down section to continue to a higher angle of attack and produce a clno. greater than that of the moments which create important twisting NAVWEPS CO-BOT-BO BASIC AERODYNAMICS AUTOMATIC SLOT BOUNDARYLAYERCONTROL BY UPPER SURFACE SUCTION BOUNDARY LAYER CONTROL BY FLAP AUGMENTATION 0 2.4 FIXED SLOT\ I LOW SUCTION ,BASIC SECTION NO SUCTION 0-l 0~ : -5 0 5 IO I5 20 0 5 IO I5 20 25 SECTION ANGLE OF ATTACK SECTION ANGLE OF ATTACK 00, DEGREES 00, DEGREES Figure 7.18. Ekt of Slots and Boundary Layer Control NAVWEPS OO-BOT-RO BASIC AERODYNAMICS basic section. The effect of a fixed slot on stagnate and come to a stop. If this happens the lift characteristics is shown in figure 1.18.

the airflow will separate from the surface and stall occurs. Boundary layer control for high .UO~Jana’ &Z~J can produce significant in- lift applications features various devices to creases in cl, but the increased angle of maintain high velocity in the boundary layer attack for maximum lift can be a disadvantage.

to allay separation of the airflow.

This con- If slots were the only high lift device on the trol of the boundary layer kinetic energy can wing, the high take off and landing angles of be accomplished in two ways. One method is attack may complicate the design of the the application of a suction through ports to landing gear. For this reason slots or slats draw off low energy boundary layer and replace are usually used in conjunction with flaps it with high velocity air from outside the since the flaps provide reduction in the maxi- boundary layer. The effect of surface suction mum lift angle of attack. The use of a slot boundary layer control on lift characteristics has two important advantages: there is only a is typified by figure 1.18. Increasing surface negligible change in the pitching moment suction produces greater maximum lift coe5- due to the slot and no significant change in cients which occur at higher angles of attack.

section drag at low angles of attack. In fact, The effect is similar to that of a slot because the slotted section will have less drag than the slot is essentially a boundary layer control the basic section near the maximum lift angle device ducting high energy air to the upper for the basic section.

surface.

The slot-slat device finds great application Another method of boundary layer control in modern airplane configurations. The tail- is accomplished by injecting a high speed jet less airplane configuration can utilize only the of air into the boundary layer.

This method high lift devices which have negligible effect produces essentially the same results as the on the pitching moments. The slot and slat suction method and is the more practical in- are often used to increase the cl- in high speed stallation. The suction type BLC requires the flight when compressibility effects are con- installation of a separate pump while the siderable. The small change in twisting mo- “blown” BLC system can utilize the high pres- ment is a favorable feature for any high lift sure source of a jet engine compressor.

The device to be used at high speed. Leading edge typical installation of a high pressure BU high lift devices are more effective on the system would be the augmentation of a de- highiy swept wing than trailing edge flaps flected flap. Since any boundary layer control since slats are quite powerful in controlling the tends to increase the angle of attack for maxi- flow pattern. Small amounts of local camber mum lift, it is important to combine the bound- added to the leading edge as a high lift device ary layer control with flaps since the flap de- is most effective on wings of very low thick- flection tends to reduce the angIe of attack for ness and sharp leading edges. Most usually maximum lift the slope of the leading edge high lift device OPERATION OF HIGH LIFT DEVICES.

is used to control the spanwise lift distribution The management of the high lift devices on an on the wing.

airplane is an important factor in flying opera- ‘ Boundary larcr control devices are additional tions. The devices which are actuated auto- means of increasing the maximum lift coe&- matically-such as automatic slats and slots- cient of a section. The thin layer of airflow are usually of little concern and cause little adjacent to the surface of an airfoil shows re- complication since relatively small changes in duced local velocities from the effect of skin drag and pitching moments take place. How- friction. When at high angles of attack this ever, the flaps must be properly managed by boundary layer on the upper surface tends to the pilot to take advantage of the capability S3lWvNAaOtl3v~ mva 08-108-00 Sd3MAQN NAVWEPS OO-EOT-SO BASIC AERODYNAMICS of such a device. To illustrate a few principles When the flaps are lowered for landing essen- tially the same items must be considered. Ex- of flap management, figure 1.19 presents the lift and drag curves of a typical airplane in the tending the flaps will cause these. changes to clean and flap down configurations.

take place: In order to appreciate some of the factors (1) Lowering the flaps requires retrim- involved in flap management, assume that the ming to balance the nose down moment airpIane has just taken off and the flaps are change.

extended. The pilot should not completely (2) The increase in drag requires a higher retract the flaps until the airplane has sufficient power setting to maintain airspeed and speed. If the flaps are retracted prematurely altitude.

at insufhcient airspeed, maximum lift coefi- (3) The angle of attack required to pro- cient of the clean configuration may not be duce the same lift coefficient is less, e.g., able to support the airplane and the airplane flap extension tends to cause the airplane to will sink or stall. Of course, this same factor “balloon.” must be considered for intermediate flap posi- An additional factor which must be consid- tions between fully retracted and fully ex- ered when rapidly accelerating after takeoff, tended. Assume that the airplane is allowed or when lowering the flaps for landing, is the to gain speed and reduce the flight lift coefii- limit airspeed for flap extension. Excessive cient to the point of flap retraction indicated airspeeds in the flap down configuration may on figure 1.19. As the configuration is altered cause structural damage.

from the “cluttered” to the clean configura- In many aircraft the effect of intermediate tion, three important changes take place: flap deflection is of primary importance in (1) The reduction in camber by flap re- certain critical operating conditions. Small traction changes the wing pitching moment initial deflections of the flap cause noticeable and-for the majority of airplanes-requires changes in C’ s,, without large changes in drag retrimming to balance the nose up moment coefficient. This feature is especially true of change. Some airplanes feature an automat- the airplane equipped with slotted or Fowler ic retrimming which is programmed with flaps (refer to fig. 1.17). Large flap deflections flap deflection. past 30’ to 33’ do not create the same rate of (2) The retraction of flaps shown on change of Cs- but do cause greater changes in figure 1.19 causes a reduction of drag coeffi- CD. A fact true of most airplanes is that the cient at that lift coefficient. This drag first 50 percent of flap deflection causes mwc reduction improves the acceleration of the than half of the total change in Cr.- and the airplane.

last 50 percent of flap deflection causes mo~c (3) The retraction of flaps requires an than half of the total change in Cs.

increase in angle of attack to maintain the The effect of power on the stall speed of an same lift coefficient. Thus, if airplane accel- airplane is determined by many factors. The eration is low through the flap retraction most important factors affecting this relation- speed range, angle of attack must be in- ship are powerplant type (prop or jet), thrust- creased to prevent the airplane from sinking.

to-weight ratio, and inclination of the thrust This situation is typical after takeoff when vector at maximum lift. The effect of the gross weight, density altitude, and tempera- propeller is illustrated in figure 1.20. The ture are high. However, some aircraft have slisstream velocity behind the propeller is such high acceleration through the flap re- different from the free stream velocity depend- traction speed that the rapid gain in air- ing on the thrust developed. Thus, when the speed requtres much less noticeable attitude propeller driven airplane is at low air+ceds change.

NAVWEPS OO-BOT-80 BASIC AERODYNAMICS INDUCED FLOW FROM PROPELLER

n

r SLIPSTREAM n c; figure 1.20. Power Effects NAVWEPS 00-801~0 BASIC AERODYNAMICS and high power, the dynamic pressure in the net lift produced by the airfoil is difference shaded area can be much greater than the free between the lifts on the upper and lower sur- stream and this causes considerably greater faces. The point along the chord where the lift than at zero thrust. At high power con- distributed lift is effectively concentrated is ditions the induced flow also causes an effect termed the “center of pressure, c.p.“ The similar to boundary layer control and increases center of pressure is essentially the “center of The typical the maximum lift angle of attack. gravity” of the distributed lift pressure and four-engine propeller driven airplane may have the location of the c.p. is a function of camber 60 to 80 percent of the wing area affected by and section lift coe&cient the induced flow and power effects on stall Another aerodynamic reference point is the speeds may be considerable. Also, the lift of “aerodynamic center, d.e.” The aerodynamic the airplane at a given angle of attack and air- center is defmed as the point along the chord speed will be greatly affected. Suppose the where all changesin lift effectively take place.

airplane shown is in the process of landing To visualize the existence of such a point, flare from a power-on approach. If there is notice the change in pressure distribution with a sharp, sudden reduction of power, the air- angle of attack for the symmetrical airfoil plane may drop suddenly because of the reduced of figure 1.21. When at zero lift, the upper lift. and lower surface lifts are equal and located The typical jet aircraft does not experience at the same point. With an increase in angle the induced flow velocities encountered in of attack, the upper surface lift increases while propeller driven airplanes, thus the only sig- the lower surface lift decreases. The change nificant factor is the vertical component of ,of lift has taken place with no change in the thrust. Since this vertical component con- center of pressure-a characteristic of sym- tributes to supporting the airplane, less aero- metrical airfoils.

dynamic lift is required to hold the airplane Next, consider the cambered airfoil of in flight. If the thrust is small and the thrust figure 1.21 at zero lift. To produce zero lift, inclination is slight at maximum lift angle, the upper and lower surface lifts must be equal.

only negligible changes in stall speed will re- One difference noted from the symmetrical air- sult. On the other hand, if the thrust is very foil is that the upper and lower surface lifts are great and is given a large inclination at maxi- not opposite one another. While no net lift mum lift angle, the effect on stall speed can exists on the airfoil, the couple produced by be very large. One important relationship the upper and lower surface lifts creates a nose remains-since there is very little induced flow down moment. As the angle of attack is in- from the jet, the angle of attack at stall is creased, the upper surface lift increases while essentially the same power-on or power-off. the lower surface lift decreases. While a change in lift has taken place, no change in DEVELOPMENT OF AERODYNAMIC moment takes place about the point where PITCHING MOMENTS the lift change occurs. Since the moment The distribution of pressure over a surface about the aerodynamic center is the product is the ,source of the aerodynamic moments as of a force (lift at the c.P.) and a lever arm well as the aerodynamic forces. A typical (distance from c.9. to a.~.), an increase in lift example of this fact is the pressure distribution moves the center of pressure toward the aero- acting on the cambered airfoil of figure 1.21.

dynamic center.

The upper surface has pressures distributed It should be noted that the symmetrical air- which produce the upper surface lift; the lower surface has pressures distributed which pro- foil at zero lift has no pitching moment about duce the lower surface lift. Of course, the the aerodynamic center because the upper and NAVWEPS DD-BOT-80 BASIC AERODYNAMICS CAMBERED AIRFOIL UPPER DEVELOPING POSITIVE LIFT NET LIFT LOWER SURFACE LIFT SYMMETRICAL AIRFOIL CAMBERED AIRFOIL AT ZERO LIFT AT ZERO LIFT UPPER SURFACE UPPER SURFACE

A-

LOWER SURFACE FLOWER SURFACE LIFT LIFT SYMMETRICAL AIRFOIL CAMBERED AIRFOIL AT POSITIVE LIFT AT POSITIVE LIFT UPPER SURFACE LIFT UPPER SURFACE LIFT

A-

LOWER SURFACE LIFT LOWER SURFACE LIFT CHANGE IN LIFT CHANGE IN LIFT k- t + + c PITCHING MOMENT O.C. 0.e.

Figure 1.27. Development of Pitching Moments NAVWEPS O&601-80 BASIC AERODYNAMICS versus lift coefficient for several repre-.

lower surface lifts act along the same vertical C%C.

line. An increase in.lift on the symmetrical sentative sections. The sign convention ap- plied to moment coefficients is that the nose-up airfoil produces no change in this situation and the center of pressure remains fixed at the aero- moment is positive.

The NACA Ooog airfoil is a symmettical sec- dynamic center.

tion of 9 percent maximum thickness. Since The location of the aerodynamic center of an airfoil is not affected by camber, thickness, and the mean line of this airfoil has no camber, angle of attack. In fact, two-dimensional in- the coefhcient of moment about the aerody- compressible airfoil theory will predict the namic center is zero, i.e., the c.p. is at the ac.

aerodynamic center at the 25 percent chordpoint The departure from zero cno.+ occurs only as the airfoil approaches maximum lift and the stall for any airfoil regardless of camber, thickness, and angle of attack. Actual airfoils, which produces a moment change in the negative are subject to real fluid flow, may not have the (nose-down) direction. The NACA 4412 and lift due to angle of .attack concentrated at the 63,-412 sections have noticeable positive cam- exact 25 percent chord point. However, the ber which cause relatively large moments about actual location of the aerodynamic center for the aerodynamic center. Notice that for each various sections is rarely forward of 23 percent sectionshowninfrgure 1.22, the c,,,....isconstant or aft of 27 percent chord point. for all lift coefficients less than cl,-.

The moment about the aerodynamic center The NACA 23012 airfoil is a very efficient has its source in the relative pressure distribu- conventional section which has been used on tion and requires application of the coefficient many airplanes. One of the features of the form of expression for proper evaluation. The ~section is a relatively high c& with only a moment about the aerodynamic center is ex- small c,,,,,,; The pitching moment coefficients 1 pressed by the following equation : for this section are shown on figure 1.22 along with the effect of various type flaps added to the basic section. Large amounts of camber where applied well aft on the chord cause large nega- tive moment coefficients. This fact is illus- A&, = moment about the aerodynamic center, trated by the large negative moment coefli- a.c., ft.-lbs.

cients produced by the 30” deflection of a 25 percent chord flap.

CMa.c,=coefbcient of moment about the a.c.

is a quantity determined by the me kc.

shape of the mean-camber line. Symmetrical q= dynamic pressure, psf airfoils have zero c,,,,. and the c.p. remains at the a.~. in unstalled flight. The airfoil with S=wing area, sq ft.

positive camber will have a negative c,,,~,~, c=chord, ft. which means the c.p. is behind the a.~. Since is constant in unstalled flight a certain the c5.c.

The moment coefficient used in this equation is relationship between lift coefficient and center the dimensionless ratio of the moment pressure of pressure can be evolved. An example of to dynamic pressure moment and is a function this relationship is shown in figure 1.22 for the NACA 63i-412 airfoil by a plot of c.p. versus ML3.C.

c c,. Note that at low lift coefficients the center %.c. = p- of pressure is well aft-even past the trailing edge-and an increase in C~ moves the c.p, for- of. the shape of the airfoil mean camber line.

Figure 1.22 shows the moment coefficient, ward toward the a.~. The c.9. approaches the Revised Jmuoy 1965 NAVWEPS 00-801-80 BASIC AERODYNAMICS

1 I 25k I I

NACA 23012 WITH SPLIT FLAP AT 3D” g -0.2 \ I z I I ” I 1 1 I F 25% I NACA 23012 WITH PLAIN FLAP AT 30’ -0.3 - .

1 I

\

--T--rT~, I I I

NACA 23012 WITH SLOTTED FLAP &T 30” -0.4 CP POSITION PERCENT CHORD AFT OF LEADING EDGE Figure 1.22. Section Moment Characteristics Revised January 1965 NAVWEPS D&801-80 BASIC AERODYNAMICS CHANGE IN LIFT CHANGE IN LIFT DUE TO UPGUST DUE TO UPGUST t (UNSTABLE) C:G. 1 O.C.

C:G.

LIFT t WEIGHT Figure 1.23. Application to Stability AC. as a limit but as stall occurs, the drop in aerodynamic center. This very necessary fea- suction near the leading’ edge cause the c.p. to ture can be visualized from the illustrations of move aft. figure 1.23.

Of course, if the airfoil has negative camber, If the two symmetrical airfoils are subject or a strongly reflexed trailing edge, the moment to an upgust, an increase in lift will take place about the aerodynamic center will be positive. at the 4.c. If the c.g. is ahead of the ax., the In this case, the location of the aerodynamic change in lift creates a nose down moment about the c.g. which tends to return the air- center will be unchanged and will remain at the quarter-chord position. foil to the. equilibrium angle of attack.

This The aerodynamic center is the point on the “weathercocking” tendency to return stable, chord where the coefficients of moment are to equilibrium is a very necessary feature in constant-the point where all changes in lift any airplane. If the c.g. is aft of the a.~., the take place. change in lift due to the upgust takes place at The aerodynamic center is an cx- tremely important aerodynamic reference point the AC. and creates a nose up moment about the c.g.

and the most direct application is to the longi- This nose up moment tends to displace tudinal stability of an airplane. To simplify the airplane farther from the equilibrium and is unstable-the airplane is similar to a ball the problem assume that the airplane is a balanced on a peak.

tailless or flying wing type. In order for this Hence, to have a stable airplane, the c.g. must be located ahead of the type airplane to have longitudinal stability, the center of gravity must be ahead of the airplane rl.c.

NAVWEPS OO-SOT-SO BASIC AERODYNAMICS boundary layer. This smooth laminar flow An additional requirement of stability is exists without the air particles moving from that the airplane must stabilize and be trimmed a given elevation.

for flight at positive lift. When the c.g. is As the flow continues back from the leading located ahead of d.c., the weight acting at the edge, friction forces in the boundary layer c.g. is supported by the lift developed by the continue to dissipate energy of the airstream section. Negative camber is required to pro- and the laminar boundary layer increases in duce the positive moment about the aerody- thickness with distance from the leading edge.

namic center which brings about equilibrium After some distance back from the leading ot balance at positive lift.

edge, the laminar boundary layer begins an Supersonic flow produces important changes oscillatory disturbance which is unstable. A in the aerodynamic characteristics of sections.

waviness occurs in the laminar boundary layer The aerodynamic center of airfoils in subsonic which ultimately grows larger and more flow is located at the 25 percent chord point.

severe and destroys the smooth laminar flow.

As the airfoil is subject to supersonic flow, the Thus, a transition takes place in which the aerodynamic center changes to the 50 percent laminar boundary layer decays into a “turbu- chord point. Thus, the airplane in transonic lent” boundary layer. The same sort of flight can experience large changes in longitu- transition can be noticed inthe smoke from a dinal stability because of the large changes in cigarette in still air. At, first, the smoke the position of the aerodynamic center.

ribbon is smooth and laminar, then develops FRICTION EFFXTS a definite waviness, and decays into a random &--v~se the +ir hAas.~~.v-~c~~vair -7ill --- , .“I”., L, , I. 11 -11 turbulent smoke pattern.

counter resistance to flow over a surface. The As soon as the transition to. the turbulent viscous nature of airflow reduces the local boundary layer takes place, the boundary velocities on a surface and accounts for the layer thickens and grows at a more rapid rate.

drag of skin friction. The retardation of air (The small scale, turbulent flow within the particles due to viscosity is greatest immedi- boundary layer should not be confused with ately adjacent to the surface.

At the very sur- the large scale turbulence associated with face of an object, the air particles are slowed to airflow separation.) The flow in the turbu- a relative velocity of near zero. Above this lent boundary layer allows the air particles to area other particles experience successively travel from one layer to another producing an smaller retardation until finally, at some dis- energy exchange.

However, some small lami- tance above surface, the local velocity reaches nar flow continues to exist in the very lower the full value of the airstream above the sur- levels of the turbulent boundary layer and is face. This layer of air over the surface which referred to as the “laminar sub-layer.” The shows local retardation of airflow from vis- turbulence which exists in the turbulent bound- cosity is termed the “boundary layer.” The ary layer allows determination of the point of characteristics of this boundary layer are illus- transition by several means. Since the turbu- trated in figure 1.24 with the flow of air over lent boundary layer transfers heat more easily a smooth flat plate.

than the laminar layer, frost, water, and oil The beginning flow on a smooth surface gives films will be removed more rapidly from the evidence of a very thin boundary layer with area aft of the transition point.

Also, a-small the flow occurring in smooth laminations, probe may be attached to a stethoscope and The boundary layer flow near the leading edge positioned at various points along a surface.

is similar to layers or laminations of air slid- ing smoothly over one another and the obvi- When the probe is in the laminar area, a low ous term for this type of flow is the “laminar” “hiss” will be heard; when the probe is in DEVELOPMENT OF BOUNDARY L~AYER ON A SMOOTH FLAT PLATE TURBULENT BOUNDARY LLAMINAR SUB-LAYER COMPARISON OF VELOCITY PROFILES FOR LAMINAR AND TURBULENT BOUNDARY LAYERS TURBULENT PROFILE I I LAMINAR PROFILE - LOW THICKNESS - GREATER THICKNESS - HIGHER VELOCITIES NEXT TO SURFACE - LOW VELOCITIES NEXT TO SURFACE - SHARP VELOCITY CHANGE - GRADUAL VELOCITY CHANGE - LOW SKIN FRICTION - HIGHER SKIN FRICTION figure 7.24. Boundary Layer Charactorisfics NAVWEPS CO-SOT-80 BASIC AE,RODYNAMlCS the turbulent area, a sharp “crackling” will trays the relative magnitude of dynamic and viscous forces in the flow.

be audible.

In order to compare the characteristics of the laminar and turbulent boundary layers, the velocity profiles (the variation of boundary where layer velocity with height above the surface) should be compared under conditions which RiV=Reynolds Number, dimensionless could produce either laminar or turbulent V= velocity, ft. per sec.

flow. The typical laminar and turbulent pro- files are shown in figure 1.24. The velocity x= distance from leading edge, ft.

profile of the turbulent boundary layer shows a much sharper initial change of velocity but Y= kinematic viscosity, sq. ft. per sec.

a greater height (or boundary layer thickness) While the actual magnitude of the Reynolds required to reach the free stream velocity.

As a result of these differences, a comparison Number has no physical significance, the quantity is used as an index to predict and will show: correlate various phenomena of viscous fluid, (1) The turbulent boundary layer has a flow. When the RN is low, viscous or fric- fuller velocity profile and has higher local tion forces predominate; when the RN is high, velocities immediately adjacent to the sur- dynamic or inertia forces predominate. The face. The turbulent boundary layer has effect of the variables in the equation for higher kinetic energy in the airflow next to Reynolds Number should be understood. The the surface.

RN varies directly with velocity and distance (2) At the surface, the laminar boundary back from the leading edge and inversely with layer has the less rapid change of velocity kinematic viscosity. High RN’ s are obtained with distance above the plate. Since the with large chord surfaces, high velocities, and shearing stress is proportional to the velocity low altitude; low RN’ sresult from small chord gradient, the lower velocity gradient of the surfaces, low velocities, and high altitudes- laminar boundary layer is evidence of a lower friction drag on the surface. If the high altitudes producing high values for kine- conditions of flow were such that either a matic viscosity.

turbulent or a laminar boundary layer could The most direct use of Reynolds Number is exist, the laminar skin friction would be the indexing or correlating the skin friction about one-third that for turbulent flow. drag of a surface. Figure 1.25 illustrates the The low friction drag of the laminar bound- variation of the friction drag of a smooth, ary layer makes it quite desirable. However, flat plate with a Reynolds Number which is the transition tends to take place in a natural based on the length or chord of the plate.

fashion and limit the extensive development The graph shows separate lines of drag coeffi- of the laminar boundary layer. cient if the flow should be entirely laminar or REYNOLDS NUMBER. Whether a lam- entirely turbulent. The two curves for lam- inar or turbulent boundary layer exists depends inar and turbulent friction drag illustrate the on the combined effects of velocity, viscosity, relative magnitude of friction drag coefficient distance from the leading edge, density, etc. if either type of boundary layer could exist.

The effect of the most important factors is The drag coefficients for either laminar or tur- combined in a dimensionless parameter called bulent flow decrease with increasing RN since “Reynolds Number, RN.” The Reynolds the velocity gradient decreasesas the boundary Number is a dimensionless ratio which por- layer thickens.

NAWWEPS OD-EOT-SO BASIC AERODYfflAMICS FRICTION DRAG OF A SMOOTH FLAT PLATE ,020 - c E D ,010 - iii .008 - yu’ .%2 - O” 0 :% - :: ,002 - ‘ \ 2i ‘ 1 .OOl * 1 I 1 1 1 0.1 0.5 1.0 5.0 10.0 50 100 REYNOLDS NUMBER RN(MILLIONS) CONVENTIONAL AfdD LAMINAR FLOW SECTIONS TRANSITION / NACA L NACA 0009 DRAG BUCKET”

P

I I I.§ .5 I.0 -1.0 -3 0 SECTION LIFT COEFFICIENT, cl Figure 7.25. Skin Friction Drag Weaised January 1965 NAVWEPS 00-SOT-80 BASIC AERODYNAMICS If the surface of the plate is smooth and the delay the transition to some point farther aft original airstream has no turbulence, the plate on the chord. The subsequent reduction in at low Reynolds Numbers will exist with pure friction drag at the low angles of attack ac- laminar flow. When the RN is increased to counts for the “drag bucket” shown on the approximately 530,000, transition occurs on graphs of cd and cI for these sections. Of course, the advantages of the laminar flow the plate and the flow is partly turbulent.

Once transition takes place, the drag coefficient airfoil are apparent only for the smooth airfoil of the plate increases from the laminar curve since surface roughness or waviness may pre- to the turbulent curve. As the RN approaches clude extensive development of a laminar very high values (20 to 50 million) the drag boundary layer.

curve of the plate approaches and nearly equals AIRFLOW SEPARATION. The character the values for the turbulent curve. At such of the boundary layer on an aerodynamic surface is greatly influenced by the pressure high RN the boundary layer is predominantly turbulent with very little laminar flow-the gradient. In order to study this effect, the transition point is very close to the leading pressure distribution of a cylinder in a perfect edge. While the smooth, flat plate is not ex- fluid is repeated in figure 1.26. The airflows actly representative of the typical airfoil, basic depict a local velocity of !zero at the forward stagnation point and a maximum local velocity fluid friction phenomena are illustrated. At RN less than a half million the boundary layer at the extreme surface. The airflow moves will be entirely laminar unless there is extreme from the high positive pressure to the minimum surface roughness or turbulence induced in the pressure point-a favorable pressure gradient airstream. Reynolds Numbers between one (high to low). As the air moves from the and five million produce boundary layer flow extreme surface aft, the local velocity decreases which is partly laminar and partly turbulent. to zero at the aft stagnation point. The static At RN above ten million the boundary layer pressure increases from the minimum (or max- characteristics are predominantly turbulent.

imum suction) to the high positive pressure In order to obtain low drag sections, the at the aft stagnation point-an adverse pres- transition from laminar to turbulent must be sure gradient (low to high).

delayed so that a greater portion of the sur- The action of the pressure gradient is such face will be influenced by the laminar bound- that the favorable pressure gradient assists ary layer. The conventional, low speed air- the boundary layer while the adverse pressure foil shapes are characterized, by minimum gradient impedes the flow of the boundary pressure points very close to the leading edge. layer. The effect of an adverse pressure gradi- Since high local velocities enhance early ent is illustrated by the segment X-Y of figure transition, very little surface is covered by 1.26. A corollary of the skin friction drag is the laminar boundary layer, A comparison the continual reduction of boundary layer of two 9 percent thick symmetrical airfoils is energy as flow continues aft on a surface. * The presented in figure 1.25. One section is the velocity profiles of the boundary layer are “conventional” NACA C!UO~section which shown on segment X-Y of figure 1.26. In the has a minimum pressure point at approxi- area of adverse pressure gradient the bound- mately 10 percent chord at zero lift. The other ary layer flow is impeded and tends to show a section is the NACA 66039 which has a reduction in velocity next to the surface. If minimum pressure point at approximately 60 the boundary layer does not have sufhcient percent chord at zero lift. The lower local kinetic energy in the presence of the adverse velocities at the leading edge and the favor- pressure gradient, the lower levels of the able pressure gradient of the NACA 66-009 boundary layer may stagnate prematurely.

NAWWEPS 00-8OT-80 BASIC AERODYNAMICS NO SEPARATION SEPARATION 1 BOUNDARY LAYER SEPAF --‘ -.’ iAT ION /------- REVERSE FLOW SEPARATION AT STALL SHOCK WAVE

b

SHOCK WAVE INDUCED FLOW SEPARATION Figure 1.26. Airflow Separation (sheet 7 of 2) Figure 7.26. Airflow Separation (sheet 2 of 2) NAVWEPS OO-SOT-80 BASIC AERODYNAMICS Premature stagnation of the boundary layer to increase the kinetic energy of the upper sur- means that all subsequent airflow will overrun face boundary layer to withstand the more this point and the boundary layer will separate severe pressure gradients common to the higher from the surface. Surface flow which is aft of lift coefficients. Extreme surface roughness the separation point will indicate a local flow on full scale aircraft (due to surface damage, direction forward toward theseparation point- heavy frost, etc.) causes higher skin friction a flow reversal. If separation occurs the posi- and greater energy loss in the boundary layer.

tive pressures are not recovered and form drag The lower energy boundary layer may cause a results. The points of separation on any aero- In noticeable change in C,-” and stall speed.

dynamic surface may be noted by the reverse the same sense, vortex generators applied to flow area. Tufts of cloth or string tacked to the surfaces of a high speed airplane may allay the surface will lie streamlined in an area of compressibility buffet to some degree. The unseparated flow but will lie forward in an function of the vortex generators is to create a area behind the separation point.

strong vortex which introduces high velocity, The basic feature of airflow separation is high energy air next to the surface to reduce stagnation of the lower levels of the boundary These or delay the shock induced separation.

layer. Airjh ~cparation muh when the lower examples serve as a reminder that separation is lcvcls of the boundary layer do not have sujicicnt the result of premature stagnation of the kinetic cncrgy in the prwncc of an advcm ps.wrc boundary layer-insufficient kinetic energy in gradient. The most outstanding cases of air- the presence of an adverse pressure gradient.

flow separation are shown in figure 1.26. An SCALE EFFECT. Since the boundary layer airfoil at some high angle of attack creates a friction and kinetic energy are dependent on the characteristics of the boundary layer, pressure gradient on the upper surface too Reynolds Number is important in correlating severe to allow the boundary layer to adhere The variation of aerodynamic characteristics.

to the surface. When the airflow does not the aerodynamic characteristics with Reynolds adhere to the surface near the leading edge Number is termed “scale effect” and is ex- the high suction pressures are lost and stall tremely important in correlating wind tunnel occurs. When the shock wave forms on the test data of scale models with the actual flight upper surface of a wing at high subsonic speeds, characteristics of the full size aircraft. The the increase of static pressure through the two most important section characteristics shock’ wave creates a very strong obstacle for affected by scale effects are drag and maximum the boundary layer. If the shock wave is lift-the effect on pitching moments usually sufhciently strong, separation will follow and being negligible. From the known variation “compressibility buffet” will result from the of boundary layer characteristics with Rey- turbulent wake or separated flow.

nolds Number, certain general effects may be In order to prevent separation of a boundary anticipated. With increasing Reynolds Num- layer in the presence of an adverse pressure ber, it may be expected that the section maxi- gradient, the boundary layer must have the mum lift coefficient will increase (from the highest possible kinetic energy.

If a choice is higher energy turbulent boundary layer) and available, the turbulent boundary layer would that the section drag coefficient will decrease be preferable to the laminar boundary layer (similar to that of the smooth plate). These because the turbulent velocity profile shows effects are illustrated by the graphs of figure higher local velocities next to the surface.

1.27.

The most effective high lift devices (slots, The characteristics depicted in figure 1.27 slotted flaps, BLC) utilize various techniques are for the NACA 4412 airfoil (4 percent RN - 1.5 MILLION RN MILLION -6.0 11 I s

-I- I I 1-

I.0 1.5 -.5 0 .5 4 8 12 16 20 SECTION LIFT COEFFICIENT SECTION ANGLE OF ATTACK =o 1 DEGREES c.l figure 1.27. Effect of Reymafds Number on Section Ckacteristics of NACA 4412 NAVWEPS DD-RDT-80 BASIC AERODYNAMICS camber at 40 percent chord, 12 percent thick- boundary layer obtained may reduce the form ness at 30 percent chord)--a fairly typical drag due to separation. In each instance, the “conventionaal” airfoil section. forced transition will be beneficial if the reduc- The lift curve show a steady increase in cl with increasing tion in form drag is greater than the increase in skin friction. Of course, this possibility RN. However, note that a>maller change in cr occurs between Reynolds Numbers of 6.0 exists only at low Reynolds Numbers.

1,n a similar sense, “trip” wires or small ad 9.0 million than occurs between 0.1 and 3.0 million. In other words, greater changes surface protuberances on a wind tunnel model occur in the range of Reynolds Num- may be used to force transition of the boundary in CI bers zhere the laminar (low energy) boundary layer and simulate the effect of higher Reynolds layer predominates. The drag curves for the Numbers.

section show essentially the same feature-the greatest variations occur at very low Reynolds PLANFORM EFFECTS AND Numbers. Typical full scale Reynolds Num- AIRPLANE DRAG bers for aircraft in flight may be 3 to 5@O million EFFECT OF WING PLANFORM where the boundary layer is predominately turbulent. Scale model tests may involve The previous discussion of aerodynamic forces concerned the properties of airfoil sec- Reynolds Numbers of 0.1 to 5 million where the boundary layer be predominately laminar. tions in two-dimensional flow with no consid- Hence, the “scale” corrections are very neces- eration given to the influence of the planform.

sary to correlate the principal aerodynamic When the effects of wing planform are intro- characteristics. duced, attention must be directed to the ex- The very large changes in aerodynamic istence of flow components in the spanwise characteristics at low Reynolds Numbers are direction. In other words, airfoil section due in great part to the low energy laminar properties deal with flow in two dimensions I boundary layer typical of low Reynolds Num- while plonform properties consider flow in bers. Low Reynolds Numbers are the result three dimensions.

of some combination of low velocity, small In order to fully describe the planform of a wing, several terms are required. The terms size, and high kinematic viscosity RN= ( 3 having the greatest influence on the aerody- Thus, small surfaces, low flight speeds, or very namic characteristics are illustrated in figure high altitudes can provide the regime of low 1.28.

Reynolds Numbers. One interesting phenom- (1) The wing r?rc11, S, is simply the plan enon associated with low BN is the high form surface area of the wing. Although a por- drag due to separation of the low energy tion of the area may be covered by fuselage boundary layer. The ordinary golf ball oper- or nacelles, the pressure carryover on these ates at low RN and would have very high surfaces allows legitimate consideration of the entire plan area.

form drag without dimpling. The surface (2) The wing ~ptia, 6, is measured tip to roughness from dimpling disturbs the laminar tip.

boundary layer forcing a premature transition (3) The avcragc chord, c, is the geometric to turbulent. The forced turbulence in the average.

The product of the span and the boundary layer reduces the form drag by pro- average chord is the wing area (6X6=$).

viding a higher energy boundary layer to (4) The aspect ratio, AR, is the proportion allay separation. Essentially the same effect of the span and the average chord.

can be produced on a model airplane wing by roughening the leading edge-the turbulent AR=b/c NAVWEPS 00-SOT-80 BASIC AERODYNAMICS p-----y S= WING AREA, SO. FT.

b= SPAN, FT c = AVERAGE CHORD, FT AR = ASPECT RATIO AR = b/c AR= b:s b ----_I

I

CR = ROOT CHORO, FT Ct = TIP CHORD, FT x = TAPER RATIO A= SWEEP ANGLE, DEGREES MAC : MEAN AERODYNAMIC CHORD, FT.

Figure 1.28. Description of Wing Planform NAVWEPS OO-BOT-BO BASIC AERODYNAMICS If the planform has curvature and the aver- root chord but an MAC equal to two-thirds age chord is not easily determined, an ~‘ of the root chord.

alternate expression is: The aspect ratio, taper ratio, and sweepback of a planform are the principal factors which AR = b2/.S determine the aerodynamic characteristics of a .wing. These same quantities also have a defi- The aspect ratio is a fineness ratio of the nite influence on the structural weight and stiff- wing and this quantity is very powerful in ness of a wing.

determing the aerodynamic characteristics DEVELOPMENT OF LIFT BY A WING.

and structural weight. Typical aspect ratios In order to appreciate the effect of the planform vary from 33 for a high performance sail- on the aerodynamic characteristics, it is neces- plane to 3.5 for a jet fighter to 1.28 for a sary to study the manner in which a wing flying saucer.

produces lift.’ Figure 1.29 illustrates the three- (5) The raat chord, c,, is the chord at the dimensional flow pattern which results when wing centerline and the rip chord, c,, is the rectangular wing creates lift.

measured at the tip.

J.f a wing is producing lift, a pressure differ- (6) Considering the wing planform to ential will exist between the upper and lower have straight lines for the leading and trail- surfaces, i.e., for positive lift, the static pres- ing edges, the taper ratio, A (lambda), is the sure on the upper surface will be less than on ratio of the tip chord to the root chord.

the lower surface. At the tips of the wing, the existence of this pressure differential creates A=& the spanwise flow components shown in figure 1.29: For the rectangular wing, the lateral The taper ratio affects the lift distribution flow developed at the tip is quite strong and a and the structural weight of the wing. A strong vortex is created at the tip. The lateral rectangular wing has a taper ratio of 1.0 ‘ flow-and consequent vortex strength-reduces while the pointed tip delta wing has a taper inboard from the tip until it is zero at the ratio of 0.0.

centerline.

(7) The sweep angle, A (cap lambda), is The existence of the tip vortex is described usually measured as the angle between the by the drawings of figure 1.29. The rotational line of 25 percent chords and a perpendicular to the root chord. The sweep of a wing pressure flow combines with the local airstream causes definite changes in compressibility, flow to produce the resultant flow of the maximum lift, and stall characteristics.

trailing vortex. Also, the downwash flow (8) The mean aerodynamic chord, MAC, field behind a delta wing is illustrated by the is the chord drawn through the centroid photographs of figure 1.29. A tuft-grid is (geographical center) of plan area. A rec- mounted aft of the wing to visualize the local tangular wing of this chord and the same flow direction by deflection of th,e tuft ele- span would have identical pitching moment ments. This tuft-grid illustrates the existence characteristics. The MAC is located on the of the tip vortices and the deflected airstream reference axis of the airplane and is a primary aft of the wing. Note that an increase in reference for longitudinal stability considera- angle of attack increases lift and increases the tions. Note that the MAC is not the average flow deflection and strength of the tip vortices.

chord but is the chord through the centroid Figure 1.30 illustrates the principal effect of area. As an example, the pointed-tip of the wing vortex system. The wing pro- delta wing with a taper ratio of zero would ducing lift can be represented by a series of have an average chord equal to one-half the NAWWEPS 00-8OT-80 BASIC AERODYNAMICS WING UPPER SURFACE TIP VORTEX WING LOWER SURFACE VORTICES ALONG TRAILING EDGE TRAILING EDGE I/ I I I UPPER SURFACE FLOW LEADING EDGE FLOW LOW PRESSURE- ,- HIGH PRESSURE) Figure 1.29. Wing Three Dimensional Flow (sheet 1 of 2) Revised January 1965 NAVWEPS OO-BOT-RD BASIC AERODYNAMICS DOWNWASH FLOW FIELD BEHIND A DELTA WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS AT VARIOUS ANGLES OF ATTACK 30” OF FLOW ANGULARITY --A-- II “T (DEG) I) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE.

TRAILING EDGE.

FROM NACA TN 2674 Figure 1.19. Wing Three Dimensional Flow (sheet 2 of 2) NAVWEPS 00-8OT-80 BASIC AERODYNAMICS vortex filaments which consist of the tip or age relative wind which is different from the trailing vortices coupled with the bound or remote free stream wind. Since the aerody- line vortex. The tip vortices are coupled with namic forces created by the airfoil sections of a the bound vortex when circulation is induced wing depend upon the immediate airstream in with lift. The effect of this vortex system is which they operate, consideration must be to create certain vertical velocity components given to the effect of the inclined average rela- tive wind.

in the vicinity of the wing. The illustration of these vertical velocities shows that ahead To create a certain lift coefficient with the of the wing the bound vortex induces an up- airfoil section, a certain angle must exist be- wash. Behind the wing, the coupled action tween the airfoil chord line and the avcragc of the bound vortex and the tip vortices in- relative wind. This angle of attack is a,,, the duces a downwash. With the action of tip section angle of attack. However, as this lift and bound vortices coupled, a final vertical is developed on the wing, downwash is in- curred and the average relative wind is in- velocity (220) is imparted to the airstream by the wing producing lift. This result is an clined. Thus, the wing must be given some inevitable consequence of a finite wing pro- angle attack greater than the required section ducing lift. The wing Producing lift applies angle of attack to account for the inclination of the equal and opposite force to the airstream the average relative wind. Since the wing and deflects it downward. One of the impor- must be given this additional angle of attack tant factors in this system is that a downward because of the induced flow, the angle between velocity is created at the aerodynamic center the average reiative wind arid tlie remote fiCC (w) which is one half the final downward stream is termed the induced angle of attack, velocity imparted to the airstream (2~). ai. From this influence, the wing angle of The effect of the vertical velocities in the attack is the sum of the section and induced vicinity of the wing is best appreciated when angles of attack.

they are added vectorially to the airstream a=ul)+a; velocity. The remote free stream well ahead where a= wing angle of attack of the wing is unaffected and its direction is OLD= section angle of attack opposite the flight path of the airplane. ‘ Aft OI;= induced angle of attack of the wing, the vertical velocity (2~) adds to the airstream velocity to produce the down- INDUCED DRAG wash angle e (epsilon). At the aerodynamic Another important influence of the induced center of the wing, the vertical,velocity (w) flow is the orientation of the actual lift on a adds to the airstream velocity to produce a wing. Figure 1.30 illustrates the fact that the downward deflection of the airstream one-half lift produced by the wing sections is perpen- that of the downwash angle. In other words, dicular to the average relative wind. Since the wing producing lift by the deflection of an the average relative wind is inclined down- airstream incurs a downward slant co the wind ward, the section lift is inclined aft, by the in the immediate vicinity of the wing. Hence, same amount-the induced angle of attack, the JeCtionJof the wing operatein an average rela- ai. The lift and drag of a wing must continue tive wind which is inclined downward one-half the to be referred perpendicular and parallel to the final dowraw& angle. This is one important remote free stream ahead of the wing. In this feature which distinguishes the aerodynamic respect, the lift on the wing has a component properties of a wing from the aerodynamic of force parallel to the remote free stream.

properties of an airfoil section.

The induced velocities existing at the aero- This component of lift in the drag direction dynamic center of a finite wing create an aver- is the undesirable-but unavoidable-conse- NAVWEPS DD-ROT-80 BASIC AERODYNAMICS BOUND OR :INE VORTEX , OR TIP VORTEX DEFLECTED AIRSTREAM (UPW BOUND VORTEX ONLY VERTICAL VELOCITIES IN THE VICINITY OF THE WING COUPLED BOUND AND TIP VORTICES AVERAGE RELATIVE WIND AT WING A.C.

V t DOWNWASH REMOTE FREE STREAM ANGLE D it INDUCED DRAG EFFECTIVE LIFT- REMOTE FREE STREAM Figure 1.30. Wing Vortex System and Induced Flow NAVWEPS OO-SOT-~O BASIC AERODYNAMICS quence of developing lift with a finite wing (3) The induced angle of attack can be and is termed INDUCED DRAG, D+ In- derived as: duced drag is separate from the drag due to form and friction and is due simply to the de- a~= 18.24 & (degrees) ( ) velopment of lift.

By inspection of the force diagram of figure (NOTE: the derivation of these relationships 1.30, a relationship between induced drag, lift, may be found in any of the standard engi- and induced angle of attack is apparent. The neering aerodynamics textbooks.)

induced drag coeficient, CDi, will vary directly These relationships facilitate an understanding with the wing lift coefficient, C,, and the in- and appreciation of induced drag.

duced angle of attack, as. The effective lift is the vertical component of the actual lift and, The induced angle of attack Eli= 18.~4$~ ( > if the induced angle of attack is small, will be depends on the lift coefficient and aspect ratio.

essentially the same as the actual lift. The Flight at high lift conditions such as low speed J horizontal and vertical component of drag is or maneuvering flight will create high induced insignificant under the same conditions. By a angles of attack while high speed, low lift detailed study of the factors involved, the fol- flight will create very small induced angles .of lowing relationships can be derived for a wing attack. The inference is that high lift coefli- with an elliptical lift distribution: cients require large downwash and result in (1) The induced drag equation follows the large ,induced angles of attack. The effect of same form as applied to any other aerody- aspect ratio is significant since a very high namic force.

aspect ratio would produce a negligible induced Di=CDigS angle of attack. If the aspect ratio were in- finite, the induced angle of attack would be where zero and the aerodynamic characteristics of the Di=induced drag, lbs.

wing would be identical with the airfoil sec- 4= :Vymic pressures; psf tion properties. On the other hand, if the wing aspect ratio is low, the induced angle of =295 attack will be large and the low aspect ratio Cni= induced drag coefficient airplane must operate at high angles of attack S=wing area, sq. ft.

at maximum lift. Essentially, the low aspect ratio wing affects a relatively small mass of (2) The induced drag coefficient can be air and consequently must provide a large de- derived as : flection (downwash) to produce lift.

CD,-C, sin ai EFFECT OF LIFT. The induced drag co- or C&l e&cient CDi=0.31E - shows somewhat sim- AR ( ,I CD& ilar effects of lift coefficient and aspect ratio.

Becauseof the power of variation of induced drag c,P =0.318 -Jjj coefficient with lift coefficient, high lift coefli- ( ) where cients provide very high induced drag and low C,= lift coefficient lift coefficients very low induced drag. The di- sin ai=natural sine of the induced angle rect effect of C, can be best appreciated by assum- of attack, Eli, degrees ing an airplane is flying at a givenweight, alti- r=3.1416, constant tude, and airspeed. If the airplane is maneuvered AR= wing aspect ratio from steady level flight to a load factor of two, hWd Jonua~ 1965 NAVWEPS 0040240 BASIC AERODYNAMICS the lift coefficient is doubled and the induced air density requires a greater deflection of the drag is four times 0.1 grsat. If the flight load airstream to produce the same lift. However, factor is changed from one to five, the induced if the airplane is flown at the same EAS, the dynamic pressure will be the same and induced drag is twenty-five times as great. If all other factors are held constant to single out this drag will not vary. In this case, the TAS effect, it could be stated that “induced drag would be higher at altitude to provide the varies as the square of the lift” same EAS.

EFFECT OF SPEED. The general effect of Di, ’ speed on induced drag is unusual since low air- L!

Di,= L1 speeds are’ associated with high lift coefficients and high lift coefficients create high induced where drag coefficients. The immediate implication Di,= induced drag corresponding to is that induced drag inmaw with decreasingair some original lift, L1 J@. If all other factors are held constant to Di,= induced drag corresponding to single out the effect of airspeed, a rearrange- some new lift, Lp ment of the previous equations would predict (and q (or EAS), S, AR are constant) that “induced drag varies inversely as ,the square of the airspeed.” This expression defines the effect of gross weight, maneuvers, and steep turns on the induced drag, e.g., 10 percent higher gross weight increases induced drag 21 percent, 4G maneuvers cause 16 times as much induced where drag, a turn with 4s0 bank requires a load factor of 1.41 and this doubles the induced Dil= induced drag corresponding to some orig- drag.

inal speed, Vi EFFECT OF ALTITUDE. The effect of Di,= induced drag corresponding to some new altitude on induced drag can be appreciated by speed, Vs holding all other factors constant. The gen- eral effect of altitude is expressed by: (and L, S, AR, ,J are constant) Such an effect would imply that a given air- plane in steady flight would incur one-fourth as great an induced drag at twice as great a where speed or four times as great an induced drag at Dil= induced drag corresponding to some orig- half the original speed. This variation may inal altitude density ratio, 0, be illustrated by assuming that an airplane in steady level flight is slowed from 300 to 150 D&= induced drag corresponding to some new knots. The dynamic pressure at 1% knots is altitude density ratio, q one-fourth the dynamic pressure at 300 knots (and L, S, AR, V are constant) and the wing must deflect the airstream four times as greatly to create the same lift.

The This relationship implies that induced drag same lift force is then slanted aft four times would increase with altitude, e.g., a given as greatly and the induced drag is four times airplane flying in level flight at a given TAS as great.

at 40,000 ft. (u=O.25) would have four times The expressed variation of induced drag with as much induced drag than when at sea level speed points out that induced drag will be of (u= 1.00). This effect results when the lower NAVWEPS OD-SOT-BO BASIC AERODYNAMICS typical only of a wing planform of extremely greatest importance at low speeds and prac- tically insignificant in flight at high dynamic high (infinite) aspect ratio. When a wing of some finite aspect ratio is constructed of this pressures. For example, a typical single en- gine jet airplane at low altitude and maximum basic section, the principal differences will be level flight airspeed has an induced drag which in the lift and drag characteristics-the mo- is less than 1 pcrccont of the total drag. How- ment characteristics remain essentially the ever, this same airplane in steady flight just same.

The effect of decreasing aspect ratio on above the stall speed could have an induced the lift curve is to increase the wing angle of drag which is approximately 75 pnrcnt of the attack necessary to produce a given lift co- total drag. efficient. The difference between the wing EFFECT OF ASPECT RATIO. The effect angle of attack and the section angle of attack of aspect ratio on the induced drag is the induced angle of attack, orit18.24 L AR’ which increases with decreasing aspect ratio.

The wing with the lower aspect ratio is less sensitive to changes in angle of attack and re- is the principal effect of the wing planform.

quires higher angles of attack for maximum The relationship for induced drag coefIicient lift. When the aspect ratio is very low (below emphasizes the need of a high aspect ratio 3 or 6) the induced angles of attack are not for the airplane which is continually accurately predicted by the elementary equa- operated at high lift coefficients. In other tion for 01~ and the graph of C, versus 01 develops words, airplane configurations designed to distinct curvature. This effect is especially operate at high lift coefficients during the true at high lift coefhcients where the lift major portion of their flight (sailplanes, cargo, curve for the very low aspect ratio wing is transport; patrol, and antisubmarine types) very shallow and CL- and stall angle of attack demand a high aspect ratio wing to minimize are less sharply defined.

the induced drag. While the high aspect The effect of aspect ratio on wing drag char-.

ratio wing will minimize induced drag, long, acteristics may be appreciated from inspection of thin wings increase structural weight and have figure 1.31. The basic section properties are relatively poor stiffness characteristics. This shown as the drag characteristics of an infinite fact will temper the preference for a very high aspect ratio wing. When a planform of some aspect ratio. Airplane configurations which finite aspect ratio is constructed, the wing drag are developed for very high speed flight (es- coefficient is the rtlm of the induced drag coe&- specially supersonic flight) operate at relatively c,” and the section drag co- cient, C,,=O.318 AR, low lift coefficients and demand great aero- dynamic cleanness. These configurations of efhcient.

Decreasing aspect ratio increases the airplanes do not have the same preference for wing drag coefficient at any lift coefficient since high aspect ratio as the airplanes which op- the induced drag coefficient varies inversely erate continually at high lift coefficients.

with aspect ratio. When the aspect ratio is This usually results in the development of low very low, the induced drag varies greatly with aspect ratio planforms for these airplane con- lift and at high lift coefficients, the induced figurations.

drag is very high and increases very rapidly The effect of aspect ratio on the lift and drag with lift coefficient.

characteristics is shown in figure 1.31 for While the effect of aspect ratio on lift curve wings of a basic 9 percent symmetrical section.

slope and drag due to lift is an important re- The basic airfoil section properties are shown lationship, it must be realized that design for on these curves and these properties would be NAVWEPS 00-8OT-80 BASIC AERODYNAMICS 0’ I-- E E :: i (NO SWEEPBACK) t i (3 WING ANGLE OF ATTACK BASIC SECTION I .4 a DEGREES 1 \A”=‘ NFl~;~lB AR,=5 AR = 2.5 (LOW MACH NUMBER)

I I I I

.I5 .20 .25 .I0 WING DRAG COEFFICIENT, CD I Figure 1.31. Effect of Aspect Ratio on Wing Characteristics NAWEPS OO-BOT-BO BASIC AERODYNAMICS takeoff distance may occur. very high speed flight does not favor the use of Also, the initial climb performance may be marginal at an high aspect ratio planforms.

Low aspect ratio excessively low airspeed. planforms have structural advantages and There are modern configurations of airplanes of very low aspect allow the use of thin, low drag sections for high ratio (plus sweepback) which-if over- speed flight. The aerodynamics of transonic rotated during a high altitude, high gross and supersonic flight also favor short span, low weight takeoff-cannot fly out of ground aspect ratio surfaces. Thus, the modern con- effect. With the more conventional airplane figuration of airplane designed for high speed configuration, an excess angle of attack pro- flight will have a low aspect ratio planform duces a well defined stall. However, the with characteristic aspect ratios of two to four.

modern airplane configuration at an excessive The most important impression that should angle of attack has no sharply defined stall result is that the typical modern configuration but developes an excessive amount of induced will have high angles of attack for maximum drag.

To be sure that it will not go unsaid, lift and very prodigious drag due to lift at low an excessively low angle of attack on takeoff flight speeds. This fact is of importance to creates its own problems-excess takeoff theNaval Aviator becausethe majority of pilot- speed and distance and critical tire loads.

caused accidents occur during this regime of (2) During appra& where the pilot must flight-during takeoff, approach, and landing.

exercise proper technique to control the Induced drag predominates in these regimes of flight path. “Attitude plus power equals flight.

performance.” The modern high speed con- The modern configuration of high speed air- figuration at low speeds will have low lift- plane usually has a low aspect ratio planform drag ratios due to the high induced drag 1 with high wing loading. When wing sweep- and can require relatively high power set- back is coupled with low aspect ratio, the wing tings during the power approach. If the lift curve has distinct curvature and is very flat pilot interprets that his airplane is below at high angles of attack, i.e., at high CL, C, in- the desired glide path, his first reaction rnu~t creases very slowly with an increase in 01.

In trot be to just ease the nose up.

An increase addition, the drag curve shows extremely rapid in angle of attack without an increase in rise at high lift coefficients since the drag due power will lower the airspeed and greatly to lift is so very large. These effects produce increase the induced drag. Such a reaction flying qualities which are distinctly different could create a high rate of descent and lead from a more “conventional” high aspect ratio to very undesirable consequences. The an- airplane configuration.

gle of attack indicator coupled with the Some of the most important ramifications of mirror landing system provides reference to the modern high speed configuration are: the pilot and emphasizes that during the (1) During takeoff where the airplane must steady approach “angle of attack is the not be over-rotated to an excessive angle of primary control of airspeed and power is the attack. Any given airplane will have some primary control of rate of climb or descent.” fixed angle of attack (and CJ which produces Steep turns during approach at low airspeed the best takeoff performance and this angle are always undesirable in any type of air- of attack will not vary with weight, density plane because of the increased stall speed and altitude, or temperature.

An excessive angle induced drag. of attack produces additional induced drag Steep turns at low airspeeds in a low aspect ratio airplane can create and may have an undesirable effect on takeoff extremely high induced drag and can incur performance. Takeoff acceleration may be dangerous sink rates. seriously reduced and a large increase in Revised January 1965 NAVWEPS 004OT-80 BASIC AERODYNAMICS speed for (L/D)-. The additional speed pro- (3) During the landing phase where an excessive angle of attack (or excessively low vides a more favorable margin of flare capabil- airspeed) would create high induced drag ity for flameout landing from a steep glide path and a high power setting to control rate of (low aspect ratio, low (L/D)-, low glide descent. A common error in the technique ratio).

of landing modern conbgurations is a steep, The landing technique must emphasize low power approach to landing. The steep proper control of angle of attack and rate of flight path requires considerable maneuver descent to prevent high sink rates and hard to flare the airplane for touchdown and landings. As before, to be sure that it will necessitates a definite increase in angle of not go unsaid, excessive airspeed at landing attack. Since the maneuver of the flare is a creates its own problems-excessive wear and transient condition, the variation of both tear on tires and brakes, excessive landing lift and drag with angle of attack must be distance, etc.

considered. The lift and drag curves for a The effect of the low aspect ratio planform high aspect ratio wing (fig. 1.31) show con- of modern airplanes emphasizes the need for tinued strong increase in C, with 01 up to stall proper flying techniques at low airspeeds.

and large changes in Co only at the point of Excessive angles of attack create enormous stall. These characteristics imply that the induced drag which can hinder takeoff per- high aspect ratio airplane is usually capable formance and incur high sink rates at landing.

of flare without unusual results. The in- Since such aircraft have intrinsic high mini- __^_“^ :- ---I.. -c _&-__ 1. .-* n.-. -..- : 1 C,LaLDC 111 a,l5~~ VI ~LL~CLdo *we p~ovmes the mum flying speeds, an excessively low angle of increase in lift to change the flight path attack at takeoff or landing creates its own direction without large changes in drag to problems. These facts underscore the im- decelerate the airplane.

portance of a “thread-the-needle,” professional The lift and drag curves for a low aspect flying technique.

ratio wing (fig. 1.31) show that at high angles of attack the lift curve is shallow, i.e., small EFFECT OF TAPER AND SWEEPBACK changes in C, with increased a. This implies a large rotation needed to provide the lift to The aspect ratio of a wing is the primary flare the airplane from a steep approach. The factor in determining the three-dimensional drag curve for the low aspect ratio wing shows characteristics of the ordinary wing and its large, powerful increases in C, with Cr. well drag due to lift. However, certain local effects below the stall. These lift and drag charac- take place throughout the span of the wing and teristics of the low aspect ratio wing create these effects are due to the distribution of area a distinct change in the flare characteristics.

throughout the span. The distribution of lift If a flare is attempted from a steep approach at along the span of a wing cannot have sharp low airspeed, the increased angle of attack discontinuities. (Nature just doesn’ t arrange may provide such increased induced drag and natural forces with sharp discontinuities.)

rapid loss of airspeed that the airplane does not The typical lift distribution is arranged in actually flare. A possible result is that an A representative dis- some elliptical fashion.

even higher sink rate may be incurred. This tribution of the lift per foot of span along the is one factor favoring the use of the “no-flare” scan of a wing is shown in figure 1.32.

or “minimum flare” type landing technique The natural distribution of lift along the for certain modern configurations. These same span of a wing provides a basis for appreciating aerodynamic properties set the best glide the effect of area distribution and taper along the span. If the elliptical lift distribution is speeds of low aspect ratio airplanes above the NAVWEPS OfJ-RDT-8D BASIC AERODYNAMICS A I I TYPlChL L&i. PER kT. OF ‘ SPAN ’ LIFT DISTRIBUTION Figure 4.32. Sponwise Lift Distribution NAVWEPS OD-8OT-80 BASIC AERODYNAMICS exists. This situation creates an induced angle matched with a planformwhose chord is dis- of attack at the root which is less than the tributed in an elliptical fashion (the elliptical average for the wing and a local section angle wing), each square foot of area along the span of attack higher than the average for the wing.

produces exactly the same lift pressure. The The result is shown by the graph of figure 1.32 elliptical wing planform then has each section which depicts a local lift coefficient at the root of the wing working at exactly the same local almost 20 percent greater than the wing lift lift coefhcient and the induced downflow at coefficient.

the wing is uniform throughout the span. In the aerodynamic sense, the elliptical. wing is The effect of the rectangular planform may the most efficient planform because the uni- be appreciated by matching a near elliptical lift distribution with a planform with a formity of lift coefficient and downwash incurs rbt iea$t induced drag for a given aspect ratio. constant chord. The chords near ‘ the tip develop less lift pressure than the root and The merit of any wing @anform is then meas- ured by the closeness with which the distribu- consequently have lower section lift coe&- cients. The great nonuniformity of local lift tion of lift coefficient and downwash approach coefficient along the span implies that some that of the elliptical planform.

sections carry .more than their share of the The effect of the elliptical planform is illus- load while others carry less than their share trated in figure 1.32 by the plot of local lift of the load. Hence, for a given aspect ratio, versus coefficient to wing lift coefficient, f!

the rectangular planform will be less efficient G’ -11:. -!-~I -t-- -L.

wing p* ,4;..t,or, Tbac e!liptical scm:spnn L.“CY.ICG. LlLill UK C‘ lqJLlCal wing. For exampie, a rectangular wing of AR=6 would have 16 duces a constant value of$=J.O throughout percent higher induced angle of attack for the the span from root to tip.‘ Thus, the local wing and 5 percent higher induced drag than section angle of attack, LYE, and local induced an elliptical wing of the same aspect ratio.

angle of attack, CY,,are constant throughout At the other extreme of taper is the pointed the span. If the planform area distribution is wing which has a taper ratio of zero. The anything other than elliptical, it may be ex- extremely small parcel of area at the pointed pected that the local section and induced angles tip is not capable of holding the main tip of attack will not be constant along the span.

vortex at the tip and a drastic change in down- A planform previously considered is the wash distribution results. The pointed wing simple rectangular wing which has a taper has greatest downwash at the root and this ratio of 1.0. A characteristic of the rectangular downwash decreases toward the tip. In the wing is a strong vortex at the tip with local immediate vicinity of the pointed tip, an downwash behind the wing which is high at upwash is encountered which indicates that This large non- the tip and low at the root.

negative induced angles of attack exist in this uniformity in downwash causes similar varia- area. The resulting variation of local lift tion in the local induced angles of attack along coefficient shows low cr at the root and very the span. At the tip, where high downwash high c, at the tip. This effect may be appre- exists, the local induced angle of attack is ciated by realizing that the wide chords at greater than the average for the wing. Since the root produce low lift pressures while the the wing angle of attack is composed of the very narrow chords toward the tip are sub- sum of at and aor a large local (x, reduces the ject to very high lift pressures.. The varia- local a0 creating low local lift coefficients at tion of 2 throughout the span of the wing of the tip. ‘ Ihe reverse is true at the root of the L rectangular wing where low local downwash taper ratio==0 is shown on the graph of figure NAVWEPS OD-ROT-RO RASIC AERODYNAM!CS advantages of root stall first are that ailerons 1.32. As with the rectangular wing, the non- remain effective at high angles of attack, uniformity of downwash and lift distribution favorable stall warning results from the buffet result in inefficiency of rhis planform. For on the empennage and aft portion of the fuse- example, a pointed wing of AR=6 would have 17 percent higher induced angle of attack for lage, and the loss of downwash behind the root usually ptovides a stable nose down moment the wing and 13 percent higher induced drag to the airplane. Such a stall pattern is favored than an elliptical wing of thesame aspect ratio.

but may be difficult to obtain with certain wing Between the two extremes of taper will configurations. The types of stall patterns in- exist planforms of more tolerable efficiency.

herent with various planforms are illustrated The variations of 2 for a wing of taper ratio in figure 1.33. The various planform effects =0.5 closely approxtmates the lift distribution are separated as follows : of the elliptical wing and the drag due to lift (A) The elliptical planform has constant characteristics are nearly identical. A wing local lift coefficients throughout the span from of AR=6 and taper ratio=0.5 has only 3 root to tip. Such a lift distribution means that percent higher ai and 1 percent greater CD: than all sections will reach stall at essentially the an elliptical wing of the same aspect ratio.

same wing angle of attack and stall will begin ,A separate effect on the spanwise lift dis- and progress uniformly throughout the span.

tribution is contributed by wing sweepback.

While the elliptical wing would reach high Sweepback of the planform tends to alter the lift coefficients before incipient stall, there lift distribution similar to decreasing the taper would be little advance warning of complete ratio. Also, large sweepback tends to increase stall. Also, the ailerons may lack effectiveness induced drag.

when the wing operates near the stall and lat- The elliptical wing is the ideal of the sub- eral control may be difficult.

sonic aerodynamic planform since it provides (B) The lift distribution of the rectangular a minimum of induced drag for a given aspect wing exhibits low local lift coefficients at the ratio. However, the major objection to the tip and high local lift coe5cients at the root.

elliptical planform is the extreme difficulty of Since the wing will initiate stall in the area of mechanical layout and construction.

A highly highest local lift coefficients, the rectangular tapered planform is desirable from the stand- wing is characterized by a strong root stall point of structural weight and stiffness and tendency. Of course, this stall pattern is fav- the usual wing planform may have a taper orable since there is adequate stall warning ratio from 0.45 to 0.20. Since structural con- buffet, adequate aileron effectiveness, and usu- siderations are quite important in the develop- ally strong stable moment changes on the ait- ment of an airplane configuration, the tapered plane.

Because of the great aerodynamic and planform is a necessity for an efficient configu- structural ine&ciency of this planform, the ration. In order to preserve the aerodynamic rectangular wing finds limited application only efficiency, the resulting planform is tailored The sim- to low cost, low speed light planes.

by wing twist and section variation to obtain plicity of construction and favorable stall as near as possible the elliptic lift distribution.

characteristics are predominating requirements of such an airplane. The stall sequence fot a STALL PATTERNS rectangular wing is shown by the tuft-grid pictures. The progressive flow separation il- An additional effect of the planfotm area lustrates the strong root stall tendency.

distribution is on stall pattern of wing. The (C) The wing of moderate taper (taper desirable stall pattern of any wing is a stall ratio=0.5) has a lift distribution which closely which begins on the root sections first. The NAVWEPS 00-SOT-80 BASIC AERODYNAMICS .5- SPANWISE LIFT DISTRIBUTION I ROOT TIP ELLIPTICAL RECTANGULAR, X=1.0 n ~PROGRE,,,s= HIGH TAPER, A=O.25 MODERATE TAPER, A= 0.5 Figure 1.33. Stall Patterns (sheet I of 8) Revised January 1965 NAVWEPS OeBOT-80 BASIC AERODYNAMICS DOWNWASH FLOW FIELD BEHIND A RECTANGULAR WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS AR=2.31, k=l.O 30° OF FLOW ANGULARITY -II- OT (DEG) ‘ 8 - STALL (b) TUFT GRID 24 INCHES FROM (a) TUFT GRID 6 INCHES FROM TRAILING EDGE TRAILING EDGE FROM NACA TN 2674 F;gure 1.33. Stall Patterns (sheet 2 of 8) NAWEPS oD-80~~0 BASIC AERODYNAMICS SURFACE TUFT PHOTOGRAPHS FOR RECTANGULAR WING AR=2.31, k-l.0 STALL FROM NACA TN 2674 Figuse 1.33. Stall Patterns (sheet 3 of 8) NAVWEPS Oo-8OT-80 BASIC AERODYNAMICS DOWNWASH FLOW FIELD 8EHlNO A SWEPT TAPERED WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS 45’ DELTA, AR=4.0,X=O 30° OF FLOW ANGULARITY -It- (DEG) STALL STALL (a) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE TRALLING EDGE FROM NACA TN 2674 Figure 1.33. Staff Patterns (sheet 4 of 81 NAVWEPS 00-BOT-BO BASIC AERODYMAAlllCS SURFACE TUFT PHOTOGRAPHS FOR A SWEPT, TAPERED WING 45O DELTA, AR=4.0. x=0 i =0 DEGREES a = 8 DEGREES a = 12 DEGREES B = 16 DEGREES a = 20 DEGREES FROM NACA TN 2674 Figure 1.33. Stall Patterns (sheet 5 of 8’ ) NAVWEPS OO-SOT-80 S )YE STREAMERS OhI F!ilJ MOnFl Ftgure 7.33. Staff Patterns (sheet 6 of 8) NAVWEPS 00-8OT-80 BASIC AERODYNAMICS DOWNWASH FLOW FIELD BEHIND A SWEPT,TAPERED WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS 60° DELTA, AR=2.31, X = 0 30” OF FLOW ANGULARITY --+-- QT (DEG) I6 STALL STALL (a) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM TRAILING EDGE TRAILING EDGE FROM NACA TN 2674 Figure 1.33. Stall Patterns (sheet 7 of 8) NAVWEPS OD-801-80 BASIC AERODYNAMICS SURFACE TUFT PHOTOGRAHS FOR A SWEPT, TAPERED WlNG 60° DELTA, AR=2.31, A=0 a = 0 DEGEES /STALL .

d a =32 DEGREES FROM NACA TN 2674 Figure 1.33. Std Patterns (sheet 8 018) NAVWEPS 00-801-80 BASIC AERODYNAMICS practical application to an airplane which is approximates that of the elliptical wing.

definitely subsonic in performance.

Hence, the stall pattern is much the same as the elliptical wing. (F) Sweepback applied to a wing planform (D) The highly tapered wing of taper alters the lift distribution similar to decreasing ratio=0.25 shows the stall tendency inherent taper ratio. Also, a predominating influence with high taper. The lift distribution of such of the swept planform is the tendency for a a wing has distinct peaks just inboard from the strong crossflow of the boundary layer at high tip. Since the wing stall is started in the lift coefficients. Since the outboard sections vicinity of the highest local lift coefficient, of the wing trail the inboard sections, the out- this planform has a strong “tip stall” tendency. board suction pressures tend to draw the The initial stall is not started at the exact tip boundary layer toward the tip. The result is but at the station inboard from the tip where a thickened low energy boundary layer at the highest local lift c,oefficients prevail. If an tips which is easily separated. The develop actual wing were allowed to stall in this ment of the spanwise flow in the boundary fashion the occurrence of stall would be typi- layer is illustrated by the photographs of fied by aileron buffet and wing drop. There figure 1.33. Note that the dye streamers on would be no buffet of the empennage or aft the upper surface of the~swept wing develop a fuselage, no strong nose down moment, and strong spanwise crossflow at high angles of very little-if any-aileron effectiveness. In attack. Slots, slats, and flow fences help to order to prevent such undesirable happenings, allay the strong tendency for spanwise flow.

the wing must be tailored to favor the stall When sweepback and taper are combined in pattern. The wing may be given a geometric.

a planform, the inherent tip stall tendency is twist or “washout” to decrease the local considerable. If tip stall of any significance is angles of attack at the tip. allowed to occur on the swept wing, an addi- In addition, the tional complication results: the forward shift airfoil section may be varied throughout the in the wing center of pressure creates an un- span such that sections with greater thickness The stall stable nose up pitching moment.

and camber are located in the areas of highest sequence of a swept, tapered wing is indicated local lift coefhcients. The higher ct- of by the tuft-grid photographs of figure 1.33.

such sections can then develop the higher local An additional effect on sweepback is the re- C~S and be less likely to stall. The addition duction in the slope of the lift curve and maxi- of leading edge slots or slats toward the tip mum lift coeflicient. When the sweepback is increase the local c t- and stall angle of attack large and combined with low aspect ratio the and are useful in allaying tip stall and loss of lift curve is very shallow and maximum lift aileron effectiveness. Another device for im- coefficient can occur at tremendous angles.of proving the stall pattern would be the forcing attack. The lift curve of one typical low of stall in the desired location by decrctisingthe aspect ratio, highly tapered, swept wing air- section ctmarin this vicinity.

The use of sharp plane depicts a maximum lift coefficient at Such dras- leading edges or “stall strips” is a powerful approximately 43’ angle of attack.

device to control the stall pattern. tic angles of attack are impractical in many .(E) The pointed tip wing of taper ratio If the airplane is operated at such respects.

equal to zero develops extremely high local high angles of attack an extreme landing gear lift coefficients at the tip. For all practical configuration is required, induced drag is ex- purposes, the pointed tip will be stalled at any tremely high, and the stability of the airplane Thus, the modern condition of lift unless extensive tailoring is may seriously deteriorate.

applied to the wing.

Such a planform has no conhguration of airplane may have “minimum NAVWEPS OO-ROl-80 BASIC AERODYNAMICS the wing root boundary layer to be more easily control speeds” set by these factors rather than simple stall speeds based on C&,. separated in the presence of an adverse pressure gradient. Since the upper wing surface has the When a wing of a given planform has various more critical pressure gradients, a low wing high lift devices added, the lift distribution and position on a circular fuselage would create stall pattern can be greatly affected. Deflec- greater interference drag than a high wing tion of trailing edge flaps increases the local position. Adequate filleting and control of lift coe5cients in the flapped areas and since local pressure gradients is necessary to mini- the stall angle of the flapped section is de- mize such additional drag due to interference.

creased, initial stall usually begins in the The sum of all the drags due to form, fric- flapped area. The extension of slats simply tion, leakage and momentum losses, and inter- allows the slatted areas to go to higher lift coe5cients and angles of attack and generally ference drag is termed “parasite” drag since it is not directly associated with the develop- delays stall in that vicinity. Also, power ment of lift. While this parasite drag is not effects may adversely affect the stall pattern of directly associated with the production of lift the propeller powered airplane. When the it is a variable with lift. The variation of propeller powered airplane is at high power and low speed, the flow induced at the wing parasite drag coefficient, C+, with lift coef- root by the slipstream may cause considerable ficient, C,, is shown for a typical airplane in delay in the stall of the root sections. Hence, figure 1.34. The minimum parasite drag co- occurs at or near zero the propeller powered airplane may have its efficient, CDpmi,, usually most undesirable stall characteristics during the lift and parasite drag coefficient increases power-on stall rather than the power-off stall.

above this point,in a smooth curve. The in- duced drag coefficient is shown on the same graph for purposes of comparison since the PARASITE DRAG total drag of the airplane is a sum of the In addition to the drag caused by the de- parasite and induced drag.

velopment of lift (induced drag) there is the In many parts of airplane performance it is obvious drag which is nor due to the develop necessary to completely distinguish between ment of lift. A wing surface even at zero lift drag due to lift and drag not due to lift. The will have “profile” drag due to skin friction total drag of an airplane is the sum of the para- and form. The other components of the air- site and induced drags.

plane such as the fuselage, tail, nacelles, etc., G=c++cD; contribute to drag because of their own form and skin friction. Any loss of momentum of where the airstream due to powerplant cooling, air C, = airplane drag coefficient conditioning, or leakage through construction C+=parasite drag coefficient or access gaps is, in effect, an additional drag.

C,,= induced drag coeaicient When the various components of the airplane are put together the total drag will be greater than the sum of the individual components because of “interference” of one surface on the other.

From inspection of figure 1.34 it is seen that The most usual interference of importance both CD, and CD, vary with lift coefticient.

occurs at the wing-body intersection where the However, the usual variation of parasite drag growth of boundary layer on the fuselage re- allows a simple correlation with the induced duces the boundary layer velocities on the wing drag term. In effect, the part of parasite drag root surface. This reduction in energy allows above the minimum at zero lift can be “lumped” a7 NAVWEPS 00-801-80 BASIC AERODYNAMICS 1.4 1.2 iL i 0.4 0.2 .05 ;!O .!5 DRAG COEFFICIENT, CD I.4 I.2 j 1.0 ^ t 0.6 ii kl $ 0.6 t i 0.4 0.2 DRAG COEFFICIENT, CD Figure 1.34. Airplane Parasite and Induced Drag NAVWEPS 00-8OT-80 BASIC AERODYNAMICS ure is not too accurate because of the sharper in with the induced drag coefficient by a con- variation of parasite drag at high angles of stant factor which is defined as the “airplane attack. In a sense, the airplane efficiency fac- By this method of ac- e5ciency factor”, c.

tor would change from the constant value and counting the airplane drag coe5cient is ex- decrease.

The deviation of the actual airplane pressed as : drag from the approximating curve is quite noticeable for airplanes with low aspect ratio and sweepback.

Another factor to consider is the effect of compressibility.

Since compressi- bility effects would destroy this relationship, where the greatest application is for subsonic perform- minimum parasite drag ance analysis.

C DPmB= coefficient The total airplane drag is the sum of the parasite and induced drags. CD;= induced drag coe5cient e= airplane e5ciency factor D= D,+D< where In this form, the airplane drag coefficient is Di= induced drag expressed as the sum of drag not due to lift =(0.318 $+S ) and drag due to lift (G). The air- F%d” and plane efficiency factor is some co&ant (usually D,= parasite drag less than unity) which includes parasite drag due to lift with the drag induced by lift.

is invariant with lift and represents the CDpmr” When expressed in this form the induced drag, parasite drag at zero lift. A typical value of Di, includes all drags due to lift and is solely would be 0.020, of which the wing may Cr,Pmin a function of lift. The parasite drag, D,, is account for 50 percent, the fuselage and nacelles the parasite drag and is completely independent 40 percent, and the tail 10 percent. The term of lift-it could be called the “barn door” accounts for all drag due’ to of 0.318 g drag of the airplane.

> ( An alternate expression for the parasite drag lift-the drag induced by lift and the extra is: parasite drag due to lift. Typical values of the airplane efficiency factor range from 0.6 to

R=fq

0.9 depending on the airplane configuration where and its characteristics. While the term of f = equivalent parasite area, sq. ft.

drag due to lift does include some parasite drag, it is still generally referred to as induced

f = CDPmi,S

drag.

The second graph of figure 1.34 shows that q= dynamic pressure, psf and G can approximate the the sum of CD, UP -mm e =- actual airplane CD through a large range of lift or coefficients. For airplanes of moderate aspect DpEfg ratio, this representation of the airplane total drag is quite accurate in the ordinary range of In this form, the equivalent parasite area, f, lift coefficients up to near 70 percent of CL,,.

is the product of CDPml” and S and relates an At high lift coefficients near CL-, the proced- B I Y NAVWEK OD-BOT-BO BASIC AERODYNAMICS be appreciated. The general effect of altitude impression of the “barn door” size. Hence, is expressed by: parasite drag can be appreciated as the result of the dynamic pressure, 4, acting on the equivalent parasite area, j. The “equivalent” parasite area is defmed by this relationship as a hypothetical surface with a C,=l.O which where produces the same parasite drag as the air- plane. An analogy would be a barn door in D,, = parasite drag corresponding to some orig- the airstream which is equivalent to the air- inal altitude density ratio, 0, Typical values for the equivalent para- plane.

site area range from 4 sq. ft. for a clean fighter D,,=parasite drag corresponding to some new type airplane to 40 sq. ft. for a large transport altitude density ratio, (ra Of course, when any airplane type airplane.

(and f, V are constant) is changed from the clean configuration to the landing configuration, the equivalent parasite This relationship implies that parasite drag area increases.

would decrease at altitude, e.g., a given air- EFFECT OF CONFIGURATION. The par- plane in flight at a given T.4.Y at 40,COOft.

is unaffected by lift, but is asite drag, D,, (e=O.29 would have one-fourth the parasite variable with dynamic pressure and equivalent drag when at sea level (u=l.OO). This effect parasite area. This principle furnishes the results when the lower air density produces basis for illustrating the variation of parasite less dynamic pressure. However, if the air- drag with the various conditions of flight.

plane is flown at a constant EAS, the dynamic If all other factors are held constant, the para- pressure and, thus, parasite drag do not vary.

site drag varies directly with the equivalent In this case, the TASwould be higher at altitude parasite area.

to provide the same EAS.

EFFECT OF SPEED. The effect of speed D,,= b alone on parasite drag is the most important.

D,, I

C) If all other factors are held constant, the effect

of velocity on parasite drag is expressed as: where

&, V, *

-=-

D,,= parasite drag corresponding to some orig-

(3

D,, V

inal parasite area, fi where D,,==parasite drag corresponding to some new D,,=parasite drag corresponding to some orig- parasite area, fi inal speed, Vi (V and (r are constant) D,,=parasite drag corresponding to some new speed, VS As an example, the lowering of the landing gear and flaps may increase the parasite area (j and o are constant) 80 percent. At any given speed and altitude This relationship expresses a powerful effect this airplane would experience an 80 percent of speed on parasite drag. As an example, a increase in parasite drag.

given airplane in flight at some altitude would EFFECT OF ALTITUDE. In a similar man- have four times as much parasite drag at twice ner the effect of altitude on parasite drag may NAVWEPS 00-801-80 BASIC AERODYNAMICS fuselage and nacelles of high fineness ratio, as great a speed or one-fourth as much parasite well faired canopies, and thin wing sections drag at half the original speed. This fact may which have very smooth uniform pressure dis- be appreciated by the relationship of dynamic tributions. -Low aspect ratios and sweepback pressure with speed-twice as much V, four are favorable in delaying and reducing the times as much 4, and four times as much D,.

compressibility drag rise. In addition, inter- This expressed variation of parasite drag with ference effects are quite important in transonic speed points out that parasite drag will be of and supersonic flight and the airplane cross greatest importance at high speeds and prac- section area distribution must be controlled tically insignificant in flight at low dynamic to minimize local velocity peaks which could pressures. To illustrate this fact, an airplane create premature strong shock wave formation.

in flight just above the stall speed could have a The modern configuration of airplane will parasite drag which is only 25 percent of the illustrate the features required to effect very total drag. However, this same airpfane at high speed performance-low aspect ratio, maximum level flight speed at low altitude sweepback, thin low drag sections, etc.

These would have a parasite drag which’ is very same features produce flight characteristics at nearly 100 percent of the total drag. The low airspeeds which necessitate .proper flying predominance of parasite drag at high flight technique.

speeds emphasizes the necessity for great aero- dynamic cleanness (low j) to obtain high speed AIRPLANE TOTAL DRAG performance.

I%,- rn+ql Jr,, nf ~ln eimlooe in fl.jght is the AI&CCYCYl Y Ye v YIL L”y’ “ “ c In the subsonic regime of flight, the ordinary sum of the induced and parasite drag. Figure configuration of airplane has a very large por- I.35 illustrates the variation of toral drag tion of the equivalent parasite area determined with speed for a given airplane in level flight by skin friction drag. As the wing contrib- at a particular weight, configuration, and alti- utes nearly half of the total parasite drag, the tude. The parasite drag increases with speed profile drag of the wing can be minimized by varying as the square of the velocity while the the use of the airfoil sections which produce induced drag decreases with speed varying in- extensive laminar flow. A subtle effect on versely as the square of the velocity. The parasite drag occurs from the influence of the total drag of the airplane shows the predomi- wing area. Since the wing area (S) appears nance of induced drag at low speed and parasite directly in the parasite drag equation, a reduc- drag at high speed. Specific points of interest tion in wing area would reduce the parasite on the drag curve are as follows: drag if all other factors were unchanged.

(A) Stall of this particular airplane occurs While the exact relationship involves con- at 100 knots and is indicated by a sharp rise sideration of many factors, most optimum in the actual drag.

Since the generalized iqua- airplane configurations have a strong preference tions for induced and parasite do not account for the highest practical wing loading and for conditions at stall, the actual drag of the minimum wing surface area.

airplane is depicted by the “hook” of the As the flight speeds of aircraft approach the dotted line.

speed of sound, great care must be taken to (B) At a speed of 124 knots, the airplane delay and alleviate compressibility effects.

would incur a minimum rate of descent in In order to delay and teduce the drag rise power-off flight. Note that at this speed the associated with compressibility effects, the induced drag comprises 75 percent of the total components of the airplanes must be arranged drag. If this airplane were powered with a to reduce the early formation of shock waves reciprocating-propeller type powerplant, maxi- on the airplane. This will generally require mum endurance would occur at this airspeed.

NAVWEPS OO-ROT-80 BASIC AERODYNAMICS VELOCITY KNOTS Figure 9.35. Typical Airplane Drag Curves NAVWEPS OO-BOT-80 BASIC AE,RODYNAMlCS 215 knots. This point on the drag curve pro- (C) The point of minimum total drag occurs at a speed of 163 knots. Since this speed in- duces the highest proportion between velocity curs the least total drag for lift-equal-weight and drag and would be the point for maximum range if the airplane were jet powered. Be- flight, the airplane is operating at (L/D)ma,.

cause of the high proportion of parasite drag Because of the particular manner in which at this point the long range jet airplane has parasite and induced drags vary with speed great preference for great aerodynamic clean- (parasite drag directly as the speed squared; ness and less demand for a high aspect ratio induced drag inversely as the speed squared) the minimum total drag occurs when the in- than the long range propeller powered airplane.

(E) At a speed of 400 knots, the induced duced and parasite drags are equal.

The speed drag is an extremely small part of the total for minimum drag is an important reference for One drag and parasite drag predominates.

many items of airplane performance.

(P) As the airplane reaches very high flight item previously ,presented related glide per- speeds, the drag rises in a very rapid fashion formance and lift-drag ratio. At the speed of due to compressibility. Since the generalized 163 knots this airplane incurs a total drag of equation for parasite drag does not account for 778 lbs. while producing 12,000 lbs. of lift.

These figures indicate a maximum lift-drag compressibility effects, the actual drag rise is ratio of 15.4.and relate a glide ratio of 15.4.~ typified by the dashed line.

The airplane drag curve shown in figure 1.34 In addition, if this airplane were jet powered, the airplane would achieve maximum en- is particular to one weight, configuration, and altitude in level flight. Any change in one of durance at this airspeed for ‘ the specified alti- these variables will affect the specific drags at tude. If this airplane were propeller powered, specific velocities.

the airplane would achieve maximum range at The airplane drag curve is a major factor in this airspeed for the specified altitude.

many items of airplane performance. Range, (D) Point (D) is at an airspeed approxi- mately 32 percent greater than the speed for endurance, climb, maneuver, landing, takeoff, etc., performance are based on some relation- (L/D),.,. Note that the parasite drag com- prises 75 percent of the total drag at a speed of ship involving the airplane drag curve.

NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE The performance of an aircraft is. the most operating limitations and insight to obtain the design performance of his aircraft. The important feature which defines its suitability performance section of the flight handbook for specific missions. The principal items of provides the specific information regarding the airplane performance deserve detailed consid- capabilities and limitations of each airplane.

eration in order to better understand and Every Naval Aviator must rely upon these appreciate the capabilities of each airplane.

handbook data as the guide to safe and effec- Knowledge of the various items of airplane rive operation of his aircraft.

performance will provide the Naval Aviator with a more complete appreciation of the NAVWEPS 00-ROT-80 AIRPLANE PER,FORMANCE knots requires one horsepower of propulsive REQUIRED THRUST AND POWER However, each pound of drag at 650 power.

DEFINITIONS knots requires two horsepower while each All of the principal items of flight perform- pound of drag at 162.5 knots requires one-half ance involve steady state flight conditions and horsepower. The term “power” implies work For the airplane equilibrium of the airplane. rate and, as such, will be a function of the speed to remain in steady level flight, equilibrium at which a particular force is developed.

must be obtained by a lift equal to the air- Distinction between thrust required and plane weight and a powerplant thrust equal to pawcr required is necessary for several reasons.

the airplane drag. Thus, the airplane drag For the items of performance such as range and defines the thrust required to maintain steady endurance, it is necessary to relate powerplant level flight.

fuel flow with the propulsive requirement for The total drag of the airplane is the sum of steady IeveI flight. Some powerplants incur the parasite and induced drags: Parasite drag fuel flow rate according to output thrust while is the sum of pressure and friction drag which other powerplants incur fuel flow rate depend- is due to the basic configuration and, as de- ing on output power. For example, the turbo- fined, is independent of lift. Induced drag is jet engine is principally. a thrust producing the undesirable but unavoidable consequence machine and fuel flow is most directly related In the process of of the development of lift.

to thrust output. The reciprocating engine is creating lift by the deflection of an airstream, principally a power producing machine and the actuai iift is inclined and a coimponcn: of fuei flow is most directiy reiated to power lift is incurred parallel to the flight path direc- output. For these reasons the variation of tion. This component of lift combines with thrust required wil1 be of greatest interest in any change in pressure and friction drag due the performance of the turbojet powered air- to change in lift to form the induced drag.

plane while the variation of power required While the parasite drag predominates at high will be of greatest interest in the performance speed, induced drag predominates at low speed.

of the propeller powered airplane. Also, dis- Figure 2.1 illustrates the variation with speed tinction between power and thrust required is of the induced, parasite, and total drag for a necessary in the study of climb performance.

specific airplane configuration in steady level During a steady climb, the rate of climb will flight.

depend on excess power while the angle of The power required for flight depends on the climb is a function of excess thrust.

thrust required and the flight velocity. By The total power required for flight can be definition, the propulsive horsepower required considered as the sum of induced and parasite is related to thrust required and flight velocity effects similar to the total drag of the airplane.

by the following equation: The induced power required is a function of the induced drag and velocity.

pr= Trv 3%

p,,,!g

where Pr=power required, h.p.

Tr= thrust required (total drag), Ibs.

where V= true airspeed, knots Pri= induced power required, h.p.

D<=induced drag, lbs.

By inspection of this relationship, it is appar- V= true airspeed, knots ent that each’ pound of drag incurred at 325 NAVWEPS 00-8OT-80 AIRPLANE PERFORMAN:CE PrPs=parasite power required corresponding to Thus, induced power required will vary with some different speed, I’ , lift, aspect ratio, altitude, etc., in the same manner as the induced drag. The only differ- For example, if an airplane in steady flight is ence will be the variation with speed. If all operated at twice as great a speed, the parasite other factors remain constant, the induced drag is four times as great but the parasite power required varies inversely with velocity ~;;zr required is eight times the original while induced’ drag varies inversely with the square of the velocity.

Figure 2.1 presents the thrust required and power required for a specific airplane configu- ration and altitude. The curves of figure 2.1 are applicable for the following airplane data: gross weight, W= 15,000 Ibs.

where span, b=40 ft.

Pri,=induced power required corresponding to equivalent parasite area, f=7.2 sq. ft.

some original speed, Vi airplane efficiency factor, c= ,827 I+;,= induced power required corresponding to sea level altitude, C= 1.000 some different speed, V, compressibility corrections neglected For example, if an airplane in steady level flight The curve of drag or thrust required versus is operated at.twice as great a speed, the in- velocity shows the variation of induced, para- duced drag is one-fourth the original value but site, and total drag. Induced drag predomi- the induced power required is one-half the nates at low speeds. When the airplane is original value.

operated at maximum lift-drag ratio, (L/D)-, The parasite power required is a function the total drag is at a minimum and the induced of the parasite drag and velocity.

and parasite drags are equal. For the specific airplane of figure 2.1, (,L/D),, and minimum total drag are obtained at a speed of 160 knots.

The curve of power required versus velocity shows the variation of induced, parasite, and where total power required. As before, induced Pr,=parasite power required, h.p.

power required predominates at low speeds and D,=paraSite drag, lbs.

parasite power required predominates at high V= true airspeed, knots speeds and the induced and parasite power are Thus, parasite power required will vary with equal at (L/D),,. However, the condition of altitude and equivalent parasite area ( f) in the (L/D&- defines only the point of minimum same manner as ‘ the parasite drag. However, drag and does not define the point of minimum the variation with speed will be different. If pozver required. Ordinarily, the point of mini- all other factors are constant, the parasite drag mum power required will occur at a speed varies as the square of velocity but parasite which is 76 percent of the speed for minimum power varies as the cube of velocity.

drag and, in the case of the airplane configura- tion of figure 2.1, the speed for minimum power

Pb% v* 3

required would be 122 knots. The total drag

Ph VI

-=(-I

at the speed for minimum power required is 15 percent higher than the drag at (L/D)- but the where minimum power required is 12 percent lower Prpl= parasite power required corresponding to some original speed, Vi than the power required at (L/D)-.

NAVWEPS OO-ROT-80 AIRPLANE PERFORMANCE Figure 2.1. Airplane Thrust and Power Required NAVWEPS OO-.ROT-80 AtRPlANE PERFORMANCE Induced drag predominates at speeds below

v, Tg

the point of minimum total drag. When the

-=J

VI E

airplane is operated at the condition of mini- mum power required, the total drag is 75 where percent induced drag and 25 percent parasite drag. Thus, the induced drag is three times as Vi = speed corresponding to a specific C, great as the parasite drag when at minimum and weight, W, power required.

Va=speed corresponding to the same C, VARIATIONS OF THRUST REQUIRED AND but a different weight, Ws POWER REQUIRED For the example airplane of figure 2.2, a change The curves of thrust required and power of gross weight from 15,000 to 22,500 lbs. re- required versus velocity provide the basis for quires that the airplane operate at speedswhich comprehensive analysis of all the major items are 22.5 percent greater to maintain a specific of airplane performance. The changes in the lift coefficient. For example, if the 15,000-lb.

drag and power curves with variations of air-- airplane operates at 160 knots for (L/D)-, the plane gross weight, configuration, and altitude speed for (L/D)mz at 22,500 lbs. is: furnish insight for the ‘ variation of range, endurance, climb performance, etc., with these

v, = VI@

same items.

The effect of a change in weight on the thrust and power required is illustrated by figure 2.2.

=I&) 22,500

-\i- 15,000

1 The primary effect of a weight change is a change in the induced drag and induced power = (160) (1.225) required at any given speed. Thus, the great- est changes in the curves of thrust and power = 196 knots required will take place in the range of low The same situation exists with respect to the speed flight where the induced effects pre- curves of power required where a change in dominate. The changes in thrust and power weight requires a change of speed to maintain required in the range of high speed flight are flight at a particular CL. For example, if the relatively slight because parasite effects pre- 15,000-lb. airplane achieves minimum power dominate at high speed. The induced effects required at 122 knots, an increase in weight to at high speed are relatively small and changes 22,500 Ibs. increases the speed for minimum in these items produce a small effect on the total thrust or power required. power required to 149 knots.

In addition to the general effect on .the in- 0f course, the thrust and power required at specific lift coefficients are altered by changes in duced drag and power required at particular speeds, a change in weight will require that the weight. At a specific C,, any change in weight causes a like change in thrust required, e.g., a airplane operate at different airspeeds to main- tain conditions of a specific lift coefficient and 50-percent increase in weight causes a 50-per- cent increase in thrust required at the same C,.

angle of attack. If the airplane is in steady flight at a particular C,,, the airpseed required The effect of a weight change on the power re- for this CL will vary with weight in the fol- quired at a specific CL is a bit more complex be- cause a change in speed accompanies the change lowing manner : Revised January 1965 NAVWEPS OO-ROT-80 AIRPLANE PERFORMANCE Figure 2.2. Effect of Weight on Thrust and Power Required NAVWEPS 00-501-50 AMPLANE PERFORMANCE in drag and there is a two-fold effect. A 50- an increase in f to account for the additional percent increase in weight produces an increase changes in parasite drag which may vary with of 83.8 percent in the power required to main- C‘ .

tain a specific CL. This is the result of a 50- A change in altitude can produce signifi- percent increase in thrust required coupled with cant changes in the curves of thrust and power a 22.5-percent increase in speed. The effect of a required. The effects of altitude on these weight change on thrust required, power re- curves providea great part of the explanation of quired, and airspeed at specific angles of attack the effect of altitude on range and endurance.

and lift coefficients provides an important basis Figure 2.4 illustrates the effect of a change in for various techniques of cruise and endurance altitude on the curves of thrust and power re- conditions of flight. quired for a specific airplane configuration and 1 Figure 2.3 illustrates the effect on the curves gross weight. As long as compressibility effects are negligible, the principal effect of of thrust and power required of a change in the equivalent parasite area,!, of the configuration. increased altitude on the curve of thrust re- quired is that specific aerodynamic conditions Since parasite drag predominates in the region of high flight speed, a change in f will produce occur at higher true airspeeds.

For example, the subject airplane at sea level has a minimum the greatest change in thrust and power re- quired at high speed. Since parasite drag is drag of 1,250 lbs. at 160 knots. The same relatively small in the region of low speed airplane would incur the same drag at altitude flight, a change in f will produce relatively if operated at the same cqthdcnt airsprcd of 160 small changes in thrust and power required at knots. However, the equivalent airspeed of low speeds. 160 knots at 22,000 ft. altitude would produce The principal effect of a change in equivalent parasite area of the configuration is a true airspeed of 227 knots. Thus, an in- to change the parasite drag at any given air- crease in altitude will cause the curve of thrust speed. required to flatten out and move to the direc- The curves of figure 2.3 depict the changes in tion of higher velocity. Note that altitude the curves of thrust and power required due alone will not alter the value of minimum drag.

to a 50 percent increase in equivalent parasite The effect of altitude on the curve of power area of the configuration. required can best be considered from the effect The minimum total drag is increased by an increase in f and the on true airspeed to achieve a specific aero- is reduced. ‘ Also, the increase in f dynamic condition. The sea level power re- GWL quired curve of figure 2.4 indicates that will increase the CL for (L/D)- and require a occurs at 160 knots and requires 615 reduction in speed at the new, but decreased, CW>mz h.p. If this same airplane is operated at (L/D)-. The point of minimum power re- quired occurs at a lower airspeed and the value at an altitude of 22,000 ft., the same WD)ma drag is incurred at a higher velocity and re- of the minimum power required is increased quires a higher power. The increase in ve- slightly. Generally, the effect on the mini- mum power required is slight because the para- locity to 227 knots accounts for the increase in power required to 872 hp. Actually, the site drag is only 25 percent of the total at this various points on the curve of power required specific condition of flight.

can be considered affected in this same fashion.

An increase in the equivalent parasite area At specific lift coefficients and angles of attack, of an airplane may he brought about by the a change in altitude will alter the true airspeed deflection of flaps, extension of landing gear, extension of speed brakes, addition of external particular to these points and cause a change stores, etc. In such instances a decrease in the in power required because of the change in airplane efficiency factor, c, may accompany true airspeed. An increase in altitude will Revised Januaty 1965 NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE VELOCITY-KNOTS VELOCITY-KNOTS Figure 2.3. Effect of Equivalent Parasite Area, f, on Thrust and Power Required NAVWEPS Oo-8oT-80 AIRPLANE PERFORMANCE THRUST REQUIRED (LB9 VELOCITY-KNOTS (TAS) POWER :D REK?

VELOCITY-KNOTS (TAS) Figure 2.4. Ekf of Altitude on Thrust and Power Required NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE cause the power required curve to flatten out The development of thrust by a turbojet or and move to higher velocities and powers ramjet powerplant is illustrated by figure 2.5.

Air approaches at a velocity, Vi, depending on required.

The curves of thrust and power required and the flight speed and the powerplant operates on a certain mass flow of air, Q, which passes their variation with weight, altitude, and con- figuration are the basis of all phases of airplane through the engine. Within the powerplant performance. These curves define the require- the air is compressed, energy is added by the lnent~ of the airplane and must be considered burning of fuel, and the mass flow is expelled with the power and thrust available from the from the nozzle finally reaching a velocity, powerplants to provide detailed study of the V;. The momentum change accomplished bv various items of airplane performance.

this action produces the thrust, Ttz=Q (V,V,) AVAILABLE THRUST AND POWER where PRINCIPLES OF PROPULSION Ta= thrust, lbs.

All powerplants have in common certain general principles. Regardless of the type of Q= mass flow, slugs per sec.

propulsion device, the development of thrust is related by Newton’ s laws of motion.

Vi= inlet (or flight) velocity, ft. per sec.

F=ma V,= jet velocity, ft. per sec.

or F-d(mV) df The typical ramjct or turbojet powerplane de- where rives its thrust by working with a mass flow relatively smaller than that of a propeller but $=force or thrust, lbs.

a relatively greater change of velocity. From the previous equation it should be appreciated m=mass, slugs that the jet thrust varies directly with the mass a=acceleration, ft. per sec.% flow Q, and velocity change, Va-Vi. This fact is useful in accounting for many of the d=derivative with respect to time, e.g., performance characteristics of the jet power- dr rate of change with time plant.

mV=momentum, lb.-sec., product of mass In the process of creating thrust by mo- and velocity mentum change of the airstream, a relative velocity, Vz-V1, is imparted to the airstream.

The force of thrust results from the accelera- Thus, some of the available energy is essen- The tion provided the mass of working fluid.

tially wasted by this addition of kinetic energy magnitude of thrust is accounted for by the The change of kinetic energy to the airstream.

rate of change of momentum produced by the per time can account for the power wasted in powerplant. A rocket powerplant creates the airstream.

thrust by creating a very large change in veloc- ity of a relatively small mass of propellants.

Pw=KE/t A propeller produces thrust by creating a com- paratively small change in velocity of a rela- tively large mass of air.

NAVWEPS Oo-ROT-80 AIRPLANE PERFORMANCE F=mo F=$(mV) T, = Q (V,-V,) Pa= T,, V, Pw=Q/,(v2-v,)2 2VI 7)p=- v2 +v, 1.0 .9 .6 .7 .6 7p .5 .4 .3 .2 .I 1.0 0 .I .2 .3 .4 .5 .6 .? .6 .9 %f2 Figure 2.5. Principles of Propulsion NAWEPS 0040140 AlRPLANE PERFORMANCE to produce the required thrust with the highest Of course, the development of thrus,t with possible mass flow and lowest possible velocity some finite mass flow will require some finite change.

velocity change and there will be the inevita- The graph of figure 2.5 shows the variation ble waste of power in the airstream. In order of propulsion efficiency, qP, with the ratio of to achieve high efficiency of propulsion, the flight speed to jet velocity, VJV,. To achieve thrust should be developed with a minimum a propulsion efficiency of 0.85 requires that the of wasted power.

flight velocity be approximately 75 percent of The propulsion efficiency of the jet power- the slipstream speed relative to the airplane.

plant can be evaluated by comparing the Such a propulsive efficiency could be typical propulsive output power with the input power.

of a propeller powered airplane which derives Since the input power is the sum of the output its thrust by the propeller handling a large power and wasted power, an expression for mass flow of air.

propulsion efficiency can be derived. The typical turbojet power- plant cannot achieve such high propulsive Pa ethciency because the thrust is derived with a vp=Pa+Pw relatively smaller mass flow and larger vcloc- ity change. For example, if the jet velocity is zv, 1,200 ft. per sec. at a flight velocity of 600 ft.

')p= v*+v1 per sec., the propulsion efficiency is 0.67.

The where ducted fan, bypass jet, and turboprop are vari- aCon -which impiove tliC propulsive efIiciency trp= propulsion efficiency of a type of powerplant which has very high power capability.

9=“eta” When the conditions of range, endurance, or Pa = propulsive power available economy of operation are predominant, high propulsion efhciency is necessary. Thus, the = TCZV~ propeller powered airplane with its inherent high propulsive efliciency will always find ap Pw= power wasted plication. The requirements of very high speed and high altitude demand very high The resulting expression for propulsion effi- propulsive power from relatively small powcr- ciency, v,,, shows a dependency on the flight plants. When there are practical limits to the velocity, V,, and the jet velocity, VZ. When increase of mass flow, high output is obtained the flight velocity is zero, the propulsion by large velocity changes and low propulsive efficiency is zero since all power generated is efficiency is an inevitable consequence.

wasted in the slipstream and the propulsive power is zero. The propulsion efliciency would TURBOJET ENGINES be I.00 (or 100 percent) only when the flight velocity, Vi, equals the jet velocity, Vz. The turbojet engine has foundwidespread USC Actually, it would not be possible to produce in aircraft propulsion because of the relatively thrust under such conditions with a finite mass high power output per powerplant weight and flow. While 100 percent efficiency of propul- size. Very few aircraft powerplants can com- sion can not be attained practically, some pare with the high output, flexibility, simplic- insight is furnished to the means of creating ity, and small size of the aircraft gas turbine.

high values of propulsion efficiency. To ob The coupling of the propeller and recipro- tain high propulsion efficiency it is necessary cating engine is one of the most efficient means NAVWEPS 00-801-80 ARPLANE PERFORMANCE compressor pressure ratio should be high to known for converting fuel energy into propul- produce a high thermal efliciency in the engine sive energy. However, the intermittent action The area XCDZ represents the work done by of the reciprocating engine places practical the compressor during the compression of the limits to the airflow that can be processed and unit weight of air. Of course, certain losses restricts the development of power. The con- and inefliciencies are incurred during the com- tinuous, steady flow feature of the gas turbine allows such a powerplant to process consider- pression and the power required to operate the compressor will be greater than that indicated ably greater airflow and, thus, utilize a greater by the work done on the engine airflow.

expenditure of fuel energy. While the pro- Compressed air is discharged from the com- pulsive efficiency of the turbojet engine is con- siderably below that of the reciprocating en- pressor to the combustion chamber at condition D. Fuel is added in the combustion chamber, gine-propeller combination, the specific power and the combustion of fuel liberates consider- output of the turbojet at high speeds is quite able heat energy.

superior. The combustion process in the gas turbine differs from that of the recipro- The operation of the turbojet engine involves cating engine in that the process is essentially a relatively large change in velocity being im- a constant pressure addition of heat energy.

parted to the mass flow through the engine.

As a result, the combustion of fuel causes a Figure 2.6 illustrates the operation of a typical turbojet engine by considering the processing large change in temperature and large change given a unit weight of inlet airflow. of volume of the unit weight of airflow.

Consider The a unit weight of ambient air approaching the process in the combustion chamber is repre- inlet to the engine then experiencing the sented by the change from point D to point E of changes in pressure and volume as it is proc- the pressure-volume diagram of figure 2.6.

essed by’ the turbojet. The chart of pressure The combustion products are delivered to the versus volume of figure 2.6 shows that the unit turbine section where sufficient work must be weight of airflow at atmospheric condition A extracted to power the compressor section.

is delivered to the inlet entrance at condition The combustion chamber discharges high tem- B. The purpose of the inlet or diffuser as to perature, high pressure gas to the turbine where reduce the velocity and increase the pressure a partial expansion is accomplished with a drop of the flow entering the compressor section.

in pressure and increase in volume to point F Thus, the aerodynamic compression produces on the pressure-volume diagram. The work an increase in pressure and decrease in volume extracted from the unit weight of air by the of the unit weight of air and delivers air to turbine section is represented by the area the compressor at condition C.

The work done ZEFY. As with the compressor, the actual by the aerodynamic compression of the inlet shaft work extracted by the turbine will differ ot diffuser is represented by the area ABCX.

from that indicated by the pressure-volume Generally, most conventional turbojet engines diagram because of certain losses incurred require that the compressor inlet flow be sub- through the turbine section.

sonic and supersonic flight will involve con- For steady, sta- bilized operation of the turbojet engine the siderable aerodynamic compression in the inlet.

power extracted by the turbine will equal the Air delivered to the compressor inlet at con- power required to operate the compressor.

dition C is then subject to further compression If the turbine power exceeds the compressor through the compressor section. As a result power required, the engine will accelerate; if of the function of the compressor, the unit the turbine power is less than the compressor weight of air is subject to a decrease in volume power required, the engine will decelerate.

and increase in pressure to condition D. The NAVWEPS 00-807-80 AIRPLANE PERFORMANCE TAILPIPE COMBUSTION INLET OR NOZZLE DIFFUSER COMPRESSOR CHAMBER TURBINE TURBOJET ENGINE CYCLE iiT!

TURBINE WORK .

E Y E it COMPRESSOR I c VOLUME. CU. FT.

Figure 2.6. Turbojet Engines NAVWEPS OO-ROT-RO AtRPlANE PERFORMANCE The partial expansion of the gases through boundary layer along the fuselage surface. At the turbine will provide the power to operate supersonic flight speeds, the diffuser must slow the air to subsonic with the least waste of the engine. As. the gases are discharged from the turbine at point F, expansion will continue energy in the inlet air and accomplish the through the tailpipe nozzle. until atmospheric process with a minimum of aerodynamic drag.

pressure is achieved in the exhaust. Thus, In addition, the inlet must be efIicient and continued expansion in the jet nozzle will re- stable in operation throughout the range of duce the pressure and increase the volume of angles of attack and Mach numbers of which the unit weight of air to point G on the pressure the airplane is capable.

volume diagram. As a result, the final jet The operation of the compressor can be af- fected greatly by the uniformity of flow at the velocity is greater than the inlet velocity and the momentum change necessary for the .de- compressor face. When large variations in velopment of thrust ha~s’ been created. The flow velocity and direction exist at the face of area YFGA represents the work remaining to the axial compressor, the efficiency and stall- provide the expansion to jet velocity after the surge limits are lowered. Thus, the flight turbine has extracted the work requited to conditions which involve high angle of attack operate the compressor. and high sideslip can cause deterioration of Of course, the combustion chamber discharge inlet performance.

The compreJ.ror s&on is one of the most im- could be more completely expanded through a portant components of the turbojet engine.

larger turbine section and the net power could be used to operate a propeller rather than pro- The compressor must furnish the combustion vide high exhaust gas velocity. For certain chamber with large quantities of high pressure air in a most efficient manner. Since the com- applications, the gas turbine-propeller combi- nation could utilize the high power capability pressor of a jet engine has no direct cooling, the compression process takes place with a of the gas turbine with greater propulsive minimum of heat Ioss of the compressed air.

efficiency.

Any friction loss or inefficiency of the com- FUNCTION OF THE COMPONENTS.

Each of the engine components previously de- pression process is manifested as an undesirable scribed will contribute some function affecting additional increase in the temperature of the compressor discharge air. Hence, compressor the efficiency and output of the turbojet engine.

For this reason, each of these components efficiency will determine the compressor power should be analyzed to determine the requite- necessary to create the pressure rise of a given ments for satisfactory operating characteristics. airflow and will affect the temperature change which can take place in the combustion The i&t or &@er must be matched to the powerplant to provide the compressor entry chamber.

with the required airflow. Generally, the The compressor section of a jet engine may be an axial flow or centrifugal flow compressor.

compressor inlet must receive the required air- The centrifugal flow compressor has great util- flow at subsonic velocity with uniform dis- tribution of velocity and direction at the ity, simplicity, and flexibility of operation.

compressor face. The diffuser must capture The operation of the centrifugal compressor high energy air and deliver it at low Mach requires relatively low inlet velocities and a number uniformly to the compressor. When plenum chamber or expansion space must be the inlet is along the sides of the fuselage, the provided for the inlet. The impeller rotating edges of the inlet must be located such that at high speed receives the inlet air and pto- the inlet receives only high energy air and vides high acceleration by virtue of centrifugal force. As a result, the air leaves the impeller provision must be made to dispose of the NAVWEPS GOdOT- AIRPLANE PERFORMANCE CENTRIFUGAL COMPRESSOR DWGLE ENTRY CENfRlFuGAL COMPRESSCR

9A

f-~&ARGE AXIAL FLOW COMPRESSOR STA’ VM BLADES7 USCHARGE INLET SHAFT7 COMPRESSOR BLADING ROTATING Rows Figure 2.7. Compressor Types NAWEPS 00-8OT-80 AIRPLANE PERFORMANCE at very high velocity and high kinetic energy. from five to ten (or greater) with efficiencies A pressure rise is produced by subsequent ex- which cannot be approached with a multi- pansion in the diffuser manifold by converting stage centrifugal compressor.

the kinetic energy into static pressure energy. The axial flow compressor can provide The manifold then distributes the high pres- efficiently the high. pressure ratios necessary sure discharge to the combustion chambers. for low fuel consumption. Also, the axial A double entry impeller allows a given diam- compressor is capable of providing high air- eter compressor to process a greater airflow.

flow with a minimum of compressor diameter.

The major components of the centrifugal com- When compared with the centrifugal com- pressor are illustrated in figure 2.7.

pressor, the design and construction of the The centrifugal compressor can provide a axial compressor is relatively complex and relatively high pressure ratio per stage but the costly and the high efficiency is sustained over provision of more than one or two stages is a much narrower range of operating conditions.

rarely feasible for aircraft turbine engines. For these reasons, the axial compressor finds The single stage centrifugal compressor is greatest application where rhe demands of capable of producing pressure ratios of about efficiency and output predominate over con- three or four with reasonable efficiency. &es- siderations. of cost, simplicity, flexibility of sure ratios greater than four require such high operation, etc. Multispool compressors and impeller tip speed that compressor efficiency variable statot blades serve to improve the decreases very rapidly. Since high pressure operating characteristics of the axial com- ratios are necessary to achieve low fuel con- pressor and increase the flexibility of operation.

sumption, the centrifugal compressor finds The combustionchambermust convert the fuel greatest application to the smaller engines chemical energy into heat energy and cause a where simplicity and flexibility of operation are large increase in the total energy of the engine the principal requirements rather than high airflow. The combustion chamber will opet- efficiency. ate with one principal limitation: the dis- The axial flow compressor consists of altet- charge from the combustion chamber must be nate rows of rotating and stationary airfoils. at temperatures which can be tolerated by the The major components of the axial flow com- turbine section. The combustion of liquid pressor ate illustrated in figure 2.7. A pressure hydrocarbon fuels can produce gas temperatures rise occurs through the row of rotating blades which are in excess of 1,700 to 1,800° C.

since the airfoils cause a decrease in velocity However, the maximum continuous turbine relative to the blades. Additional pressure blade operating temperatures rarely exceed rise takes place through the row of stationary NO0 to J,OOO” C and considerable excess air blades since these airfoils cause a decrease in must be used in the combustion chamber to the absolute velocity of flow. The decrease prevent exceeding these temperature limits.

I in velocity, relative or absolute, eEeLts a com- While the combustion chamber design may 1 ptession of the flow and causes the increase in .take various forms and configurations, the static pressure. While the pressure rise pet main features of a typical combustion chamber stage of the axial compressor is relatively Jo%-, ate illustrated by figure 2.8. The combustion the efficiency is very high and high pressure chamber receives the high pressure discharge ratios can be obtained efficiently by successive from the compressor and introduces apptoxi- axial stages. Of course, the eficient pressure mately one half of this air into the immediate rise in each stage is limited by excessive gas area of the fuel spray. This primary combus- velocities. The multistage axial flow com- tion air must be introduced with relatively pressor is capable of providing pressure ratios high turbulence and quite low velocities to Revised Januwy 1965 NAVWEPS 00-80T-80 AIRPLANE PERFORMANCE TYPICAL COMBUSTION CHAMBER PRIMARY SECONDARY Al R COMBUSTION OR COOLING FLOW AIR7 FUEL DISCHARGE SPRAY TO TURBINE NOZZLE NOZZLES COMBUsTlON NUCLEUS TURBINE SECTION TUR’ BINE NOZZLE VANES r

/

TmaiNt BLADES TURBINE WHEEL SHAFT TURBIhE BLADING (STATIONARY) (ROTATING) TURBINE BLADES Figure 2.8. Combustion Chamber and Turbine Components NAVWEPS O(L8OT-80 AIRPLANE PERFORMANCE energy to drive the propeller in addition to the maintain a nucleus of combustion in the com- bustion chamber. In rhe normal combustion compressor and accessories.

process, the speed of flame propagation is quite The combustion chamber delivers high en- low and, if the local velocities are too high at ergy combustion gases to the turbine section at the forward end of the combustion chamber, high pressure and tolerable temperature. The turbine nozzle vanes are a row of stationary poor combustion will result and it is likely rhar the flame will blow out. The secondary blades immediately ahead of the rotating tur- bine. These blades form the nozzles which air-or cooling flow-is introduced downstream from the combustion nucleus to dilute the com- discharge the combustion gases as high ve- bustion products and lower the discharge gas locity jets onto the rotating turbine. In this manner, the high pressure energy of the com- temperature.

bustion gases is converted into kinetic energy The fuel nozzle must provide a finely atomized, evenly distributed spray of fuel and a pressure and temperature drop takes through a wide range of flow rates. Very place. The function of the turbine blades specialized design is necessary to provide a operating in these jets is to develop a tangen- nozzle with suitable characteristics. The tial force along the turbine wheel thus extract- spray parrern and circulation in the combustion ing mechanical energy from the combustion chamber must make efficient use of the fuel by gases. This is illustrated in figure 2.8.

complete combustion. The temperatures in The form of the turbine blades may be a com- the combustion nucleus can exceed 1,700” to bination of two distinct types. The imp&c 1,SW’ C but the secondary air will dilute the type turbine relies upon the nozzle vanes to gas and reduce the temperature to some value accomplish the conversion of combustion gas which can be tolerated in the turbine section.

static pressure to high velocity jets. The A pressure drop will occur through the com- impulse turbine blades are shaped to produce bustion chamber to accelerate the combustion a large deflection of the gas and develop the gas rearward. In addition, turbulence and tangential force by the flow direction change.

fluid friction will cause a pressure drop but this In such a design, negligible velocity and pres- loss must be held to the minimum incurred by sure drop occurs with the flow across the tur- providing complete combustion. Heat trans- bine rotor blades. The reaction type turbine ferred through the walls of the combustion differs in that large velocity and pressure chamber constitutes a loss of thermal energy changes occur across the turbine rotor blades.

and should be held to a minimum.

Thus, the In the reaction turbine, rhe stationary nozzle combustion chamber should enclose the com- vanes serve only to guide the combustion gas bustion space with a minimum of surface area onto the turbine rotor with negligible changes to minimize heat and friction losses. Hence, in velocity and pressure. The reaction tur- the “annular” typ: combustion chamber offers bine rotor blades are shaped to provide a pres- certain advantages over the multiple “can” sure drop and velocity increase across the type combustion chamber. blades and the reaction from this velocity in- The tur6inc sectionis the most critical element crease provides the tangential force on the of the turbojet engine. The function of the wheel. Generally, the turbine design is a turbine is to extract energy from the combus- form utilizing some feature of each of the two tion gases and furnish power to drive the com- types.

pressor and accessories. In the case of the The turbine blade is subjected to high turboprop engine, the turbine section must ex- centrifugal stresses which vary as the square tract a very large portion of the exhaust gas of the rorative speed. In addition, the blade Revised January 1965 NAVWEPS 00-801-80 AIRPLANE PERFORMANCE is subjected to the bending and torsion of area is too large, incomplete expansion will the tangential impulse-reaction forces. The take place; if the exit area is too small, an over blade must wirhstand these stresses which are expansion tendency results. The exit area can generally of a vibratory and cyclic nature affect the upstream conditions and must be while at high temperatures. The elevated properly proportioned for overall performance.

temperatures at which the turbine must func- When the ratio of exhaust gas pressure to tion produce extreme conditions for struc- ambient pressure is greater than some critical due, sonic flow can exist and the nozzle will tural creep and fatigue considerations.

Conse- quently, the engine speed and temperature op- be choked or limited to some maximum flow.

When supersonic exhaust gas velocities are re- erating limits demand very careful considera- tion. Excessive engine temperatures or speeds quired to produce the necessary momentum may produce damage which is immediately change, the expansion process will require the apparent. However, creep and fatigue damage convergent-divergent nozzle illustrated in fig- is cumulative and even though damage may ure 2.9. With sui?icient pressure available the not be immediately apparent by visual inspec- initial expansion in the converging portion is tion, proper inspection methods (other than subsonic increasing to sonic velocity at the visual) must be utilized and proper records throat. Subsequent expansion in the divergent kept regarding the occurrence. portion of the nozzle is supersonic and the re- Actually, the development of high tempera- sult is the highest exit velocity for a given ture alloys for turbines is a critical factor in the pressure ratio and mass flow. When the pres- develop,mcnt of high ei%ciciicy, high output sure ratio is very high the final exit diameter aircraft gas turbines. The higher the tem- required to expand to ambient pressure may be peratute of gases entering the turbine, the very large but is practically. limited to the higher can be the temperature and pressure of fuselage or nacelle afterbody diameter. If the the gases at discharge from the turbine with exhaust gases exceed sonic velocity, as is porsi- greater exhaust jet velocity and thrust. ble in a ramjet combustion chamber or after- The function of the t&pipe or exhaust no?& burner section, only the divergent portion of is to discharge the exhaust gases to the atmos- the nozzle may be necessary.

phere at the highest possible velocity to pro- Figure 2.9 provides illustration of the func- duce the greatest momentum change and thrust. tion of the various engine components and the If a majority of the expansion occurs through changes in static pressure, temperature, and the turbine section, there remains only to con- velocity through the engine. The conditions duct the exhaust gases rearward with a mini- at the inlet provide the initial properties of the mum energy loss. However, if the turbine engine airflow. The compressor section fur- operates against a noticeable back pressure, the nishes the compression pressure rise with a nozzle must convert the remaining pressure certain unavoidable but undesirable increase in Under ideal energy into exhaust gas velocity.

temperature. High pressure air delivered to conditions, the nozzle would expand the flow combustion chamber receives heat from the to the ambient static pressure at the exhaust combustion of fuel and experiences a rise in and the area distribution in the nozzle must temperature. The fuel flow is limited so that provide these conditions. When the ratio af the turbine inlet temperature is within limits exhaust gas pressure to ambient pressure is which can be tolerated by the turbine structure.

relatively low and incapable of producing sonic The combustion takes place at relatively con- flow, a converging nozzle provides the expan- stant pressure and initially low velocity. Heat sion. The exit area must be of proper size to addition then causes large increases in gas vol- bring about proper exit conditions. If the exit ume and flow velocity.

NAVWEPS 00-801-80 AIRPLANE PERFORMANCE NOZZLE TYPES CONVERGENT NOZZLE CONMRGPIT-DDMRGENT NOZZLE --3- ~-- ENGINE OPERATING CONOITIONS EXHAUST COMPRESSOR TURBlElE NOZZLE STATIC PRESSURE INLET TEMPERATURE CHANGE INLET VELOCITY CHANGE INLEl Figure 2.9. Exhaust Nozzle Types and Engine Operating Conditions NAVWEPS 00-801-80 AIRPLANE PERFORMANCE Generally, the overall fuel-air ratio of the obtained only if there is an increase in mass turbojet is quite low because of the limiting flow, Q, or jet velocity, Vs, When at low velocity, an increase in velocity will reduce turbine inlet temperature. The overall air- fuel ratio is usually some value between 80 to the velocity change through the engine with- 40 during ordinary operating conditions be- out a corresponding increase in mass flow and cause of the large amount of secondary air or the available thrust will decrease. At higher cooling flow. velocity, the beneficial ram helps to overcome High temperature, high energy combustion this effect and the available thrust no longer gas is delivered to the turbine section where decreases, but increases with speed.

power is extracted to operate the compressor The propulsive power available from the section. Partial or near-complete expansion turbojet engine is the roduct of available thrust and velocity. t T e propulsive horsc- can take place through the turbine section with power available from the turbojet engine’ is the accompanying pressure and tempcratute related by the following expression: drop. The exhaust nozzle completes the ex- pansion by producing the final jet velocity and -- momentum change necessary in the develop- pyav ment of thrust.

where TURBOJET OPERATING CHARACTER- ISTICS. The turbojet engine has many oper- Pa=propulsive power available, h.p.

ating characteristics which are of great im- T.-*Le..;- ;--;11.1*~ portance to the various items of jet airp!ane LC‘ --LL,IlLSL ‘ t”.uiaOK, ibs.

performance. Certain of these operating char- V= flight velocity, knots acteristics will provide a strong influence on the range, endurance, etc., of the jet-powered The factor of 321 evolves from the use of the airplane. Other operating characteristics will nautical unit of velocity and implies that require operating techniques which differ each pound of thrust developed at 325 knots greatly from more conventional powerplants.

is the equivalent of one horsepower of propul- The turbojet engine is essentially a thrust- sive power. Since the thrust of the turbojet producing powerplant and the propulsive engine is essentially constant with speed, tht power produced is a result of the flight speed.

power available increases almost linearly with The variation of available thrust with speed is speed. In this sense, a turbojet with 5000 Ibs.

relatively small and the engine output is very of thrust available could produce a propulsive nearly constant with flight speed. The mo- power of 3,ooO h.p. at 325 knots or 10,000 mentum change given the engine airflow de- h.p. at 650 knots.

The tremendous propulsive velops thrust by the following relationship: power at high velocities is one of the principal features of the turbojet engine. When the engine RPM and operating altitude arc fixed, where the variation with speed of turbolet thrust and power available is typified by the first graph Ta= thrust available, lbs.

of figure 2.10.

Q=mass flow, slugs per sec.

The variation of thrust output with engine vi=inlet or flight velocity, ft. per sec.

speed is a factor of great importance in the operation of the turbojet engine. By reason- Va= jet velocity, ft. per see.

ing that static pressure changes depend on the Since an increase in flight speed will increase square of the flow velocity, the changer of the magnitude of Vi, a constant thrust will be pressure throughout the turbojet engine would NAVWEPS 00-801-80 AlR,PlANE PERFORMANCE be appreciated. If the turbojet powerplant be expected to vary as the square of the rota- operates at less than the “trimmed” or adjusted tive speed, N. However, since a variation in speed for maximum thrust, the deficiency of rotative speed will alter airflow, fuel flow, thrust for takeoff may cause a considerable compressor and turbine efficiency, etc., the thrust variation will be much greater than increase in takeoff distance.

During approach, just the second power of rotative speed. In- an excessively low RPM may cause very low stead of thrust being proportional to iV2, the thrust and produce a very steep glide path.

typical fixed geometry engine develops thrust In addition, the low RPM range involves the approximately proportional to N3.6. Of course, much greater engine acceleration time to pro- such a variation is particular to constant alti- duce thrust for a waveoff. Another compli- tude and speed. cation exists when the thrust is proportional Figure 2.10 illustrates the variation of per- to some large power of rotative speed, e.g., cent maximum thrust with percent maximum Nb.O. The small changes in RPM produce RPM for a ‘ typical fixed geometry engine. such large variations in thrust that instruments Typical values from this graph are as follows: other than the tachometer must be furnished for accurate indication of thrust output.

Pmwit IMX. tlJrw,r P<m#r ma%. RPM 100 loo (of course) The “specific fuel consumption, ci’ is an 99 96.5 important factor for evaluating the perform- 83.6 ance and efficiency of operation of a turbojet 69.2 engine. The specific fuel consumption is the 45.8 proportion between the fuel flow (in lbs. per 28.7 hr.) and the thrust (in lbs.). For example, Note that in the top end of power output, each an engine which has a fuel flow of 14,000 lbs.

1 percent RPM change causes a 3.5-percent per hr. and a thrust of 12,500 lbs. has a specific change in thrust output. This illustrates the fuel consumption of: power of variation of thrust with rotative Fuel flow speed which, iii this example, is N3.“. Also “= Thrust note that the top 20 percent of RPM controls more than half of the output thrust.

14,000 lbs./hr.

While the fixed geometry engine develops ‘ I= 12,500 lbs.

thrust approximately proportional to Na.“, the engine with variable geometrywill demonstrate c,=1.12 lbs./hr./lb.

a much more powerful effect of rotative speed.

When the jet engine is equipped with a vari- Thus, each unit pound of thrust requires 1.12 able nozzle, multispool compressor, variable lbs. per hr. fuel flow.

Obviously, high engine stator blades, etc., the engine is more likely efficiency would be indicated by a low value of to develop thrust proportional to rotative c,. Typical values for turbojet engines with speed from values of N4.6 to N6.0. For ex- relatively high pressure ratios range from 0.8 ample, if a variable geometry engine develops to 1.2 at design operating conditions in sub- sonic flight. High energy fuels and greater thrust proportional to Ns.‘ , each one per cent RPM change causes a 5.0-percent thrust change pressure ratios tend to produce the lower values of ct.

at the top end of power output. Also, the Supersonic flight with the attendant in- top 13 percent of RPM would control the top let losses and high compressor inlet air tem- peratures tend to increase the specific fuel con- 50 percent of thrust output.

sumption to values of 1.2 to 2.0.

The powerful variation of thrust with engine Of course, the use of an afterburner is quite inefficient speed has certain ramifications which should NAVWEPS 00-801-80 AIRPLANE PERFORMANCE VARIATION OF THRUST AN0 POWER WITH VELOCITY / /STATIC THRUST .

THRUST THRUST AVAILABLE AvA’ &?eLE POWER / AVAILABLE / AV!$%EHp’ E (CONSTANT ALTITUDE 8 RPM) VELOCITY, KNOTS VARIATION OF THRUST WITH RPM (CONSTANT ALTITUDE

a VELOCITY)

i-cl PERCENT 6o ThrN3.5 mmlgTM 50 IO I 1 04 I 0 1 0 IO 20 30 40 50 SO 70 80 90 100 PERCENT MAXIMUM RPM VARIATION OF SPECIFIC FUEL CONSUMPTION WITH RPM

I

3.0 (CONSTANT ALTITUDE 8 VELOCITY) 2.0 sEzc CONSUMPTION ct 1.0 .T, * I I I I I I I I.

0 IO 20 30 40 50 60 70 80 90 100 PERCENT MAXIMUM RPM Figure 2.10. Turbojet Performance NAVWEPS 00-8OT-80 AtRPlANE PERFORMANCE due to thc~ low combustion pressure and values If the fixed geometry engine is operated at a constant V (TAS) in subsonic flight and con- of c, from 2.0 to 4.0 are typical with aftet- stant N (RPM) the inlet velocity, inlet ram, burner operation.

The turbojet engine usually has a strong and compressor pressure ratio are essentially preference fot high RPM to produce low specif- constant with altitude. An increase in alti- ic fuel consumption. Since the normal rated tude then causes the engine air mass flow to decrease in a manner very nearly identical to thrust condition is a particular design point the altitude density ratio. Of coutsc, this de- for the engine, the minimum value of c, will crease in mass flow will produce a significant occur at or near this range of RPM. The e&ct on the output thrust of the engine.

illustration of figure 2.10 shows a typical vati- Actually, the variation of thrust with altitude ation of c, with percent maximum RPM where is not quite as severe as the density variation values of RPM less than 80 to 85 percent pro- because favorable decreases in temperature duce a specific fuel consumption much greater occut. The decrease in inlet air temperature than the minimum obtainable. This pref- will provide a relatively greater combustion erence for high.RPM to obtain low values of gas &ergy and allow a greater jet velocity.

C, is very pronounced in the fixed geometry engine. Turbojet engines with multispool The increase in jet velocity somewhat offsets compressors tend to be less sensitive in this the decrease in mass flow. Of course, an in- crease in altitude provides lower temperatures respect and are more flexible in their operating below the tropopause. Above the tropopause, characteristics.

Whenever low values of cI ate no further favorable decrease in temperature necessary to obtain range or endurance, the takes place so a more rapid variation of thrust preference of the turboiet engine for the design will take place. The approximate variation operating RPM can be a factor of great of thrust with altitude is represented by figure influence.

2.11 and some typical values at specific alti- Altitude is one factor which strongly affects tudes ate as follows : the performance of the turbojet engine. An RIrioof Tbrvrt at dri14 increase in altitude produces a decrease in Altitude, ft. : Thi ti I,‘ bwl ( ) density and pressure and, if below the tropo- Scalevel............................. 1.m 5,ooo................................ ,888 pause, a decrease in temperature.

If a typical lO,ooo............................... .785 nonaftcrbutning turbojet engine is operated at 2o,ooo............................... ,604 a constant RPM and true airspeed, the vatia- 35,Mx)............................... .392 tion of thtust and specific fuel consumption 40,Ko. .315 =Jo,ocQ ._._..,...._....._,.,.__.,..... .180 with altitude can be approximated from figure 221. The variation of density in the standard Since the change in density with altitude is atmosphere is shown by the values of density quite rapid at low altitude turbojet takeoff pet- ratio at vatious altitudes. Typical values of formance wil1 Abegreatly affected at high alti- the density ratio at specific altitudes are as tude.

Also note that the thrust at 35,000 ft.

follows: is approximately 39 percent of the sea level value.

Altitude, ft.: Dews@ ra#ie The thrust added by the afterburner of a scaleeel . . . . . . . .. . . . . . . . . . . . . . . . . . . . .

Loo0 5,ooo.. :. . turbojet engine is not affected so greatly by .a617 lO,coo.............................. .7385 altitude as the basic engine thrust. The use of .?2#XQ.

.4976 afterburner may provide a thrust increase of 50 35,cao . . . . . . . . . . . . . . . . . . . . .

.3099 percent at low altitude or as much as 100 per- 40,oal.. . . .

.2462 ~,OUO. . . . cent at high altitude.

.lS32 kAVWEPS OO-EOT-80 AIRPLANE PERFORMANCE

\ I

50,ooc

\\

!

45,ooc

\

\\

40,ooc 35,ooc CONSUMPTION 30.000 t I 0” 2 25,000 a 20,000 ,FIXED GEOMETRY SEA LEVEL’ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1.0 RATIO OF WANTITY) AT ALTITUDE (QUANTIT’ I) AT SEA LEVEL Figure 2.7 1. Approximate Eftect of Altitude on Engine Performance NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE When the inlet ram and compressor pressure flow, nozzle area, etc. to provide engine per- formance scheduled by the throttle or power ratio is fixed, the principal factor affecting the lever. These regulatory functions provided specific fuel consumption is the inlet air temp- must account for variations in altitude, tem- erature. When the inlet air temperature is lowered, a given heat addition can provide perature, and flight velocity.

One principal governing factor which must relatively greater changes in pressure or vol- be available is that a selected power setting ume. As a result, a given thrust output (RPM) must be maintained throughout a wide requires less fuel flow and the specific fuel con- range of flight conditions. Figure 2.12 illus- sumption, c,, is reduced. While the effect of trates the sariation of fuel flow with RPM for altitude on specific fuel consumption does not a turbojet operating at a particular set of compare with the effect on thrust output, the flight conditions. Curve 1 depicts the varia- variation is large enough to strongly influence tion with RPM of the fuel flow required for range and endurance conditions. Figure 2.11 stabilized, ste,ady state operation of the engine.

illustrates a typical variation of specific fuel consumption with altitude. Generally, the Each point along this curve 1 defines the fuel flow which is necessary to achieve equilib- specific fuel consumption decreases steadily rium at a given RPM. The steady state fuel with altitude until the tropopause is reached flow produces a turbine, power to equal the and the specific fuel consumption at this point compressor power requirement at a particular is approximately 80 percent of the sea level RPM. The throttle position primarily com- value.

mands .a given, engine speed and, as changes Above the tropopause the temperature is con- occur in the ambient pressure, temperature, stant and altitudes slightly above the tropo- pause cause no further decrease in specific fuel and flight speed, the .steady state fuel flow will .

vary. The governing’ apparatus must account consumption. Actually, altitudes much above the tropopause bring about a general deteriora- for these variations in flight conditions and tion of overall engine efficiency and the~spkific maintain the power setting scheduled by fuel consumption begins an increase with throtrle position.

In addition to the maintenance of steady altitude. The extreme altitudes above the tropopause produce low combustion chamber state operation, the fuel control and associ- pressures, low compressor Reynolds Numbers, ated engine control itemsmust provide for the low fuel flow, etc. which are notconduci,ve to transient conditions of engine acceleration and high engine efficiency. deceleration. In order to accelerate the en- Because of the variation of c, with altitude, gine, the fuel control must supply a fuel flow the majority of turbojet engines achieve maxi- greater than that required for steady state mum efficiency at or above 35,000 ft. For this operation to ,produce a’turbine power greater than the compressor power requirement. How- reason, the turbojet airplane will find optimum ever, the additional fuel flow to accelerate the range and endurance conditions at. or above engine must be controlled and regulated to 35,000 ft. provided the aircraft is not thrust prevent any one or combination of the follow- or compressibility limited at these altitudes.

ing items: The governingapparatus of the turbojet engine (1) compressor stall or surge consists primarily of the, items which control (2) excessive turbine inlet temperature the flow of fuel to the engine. In addition, (3) excessively rich fuel-air ratio which there may be included certain functions which may not sustain combustion operate variable nozzles, variable stator vanes, Generally, the stall-surge and turbine tem- variable inlets, etc. Generally, the fuel con- perature limits predominate to form an ac- trol and associated items should regulate fuel celeration fuel flow boundary typified by curve NAVWEPS 00-807-80 AIRPLANE PERFORMANCE ALL CURVES APPROPRIATE FOR A PARTICULAR: ALTITUDE r M&N NUMBER BOUNDARY A& BOUNDARY DECELEFlATlON MAFfGIN w

I

E

(IDLE) (MA%) N-RPM EXHAUST GAS TEMPERATURE RPM c rAILPIPE TOTAL - - . _ . _ _- PRESSURE PRESSURE TEMPERATURE Figure 2.12. Engine Governing and Instrumentation NAVWEPS 00-8OT-30 AIRPLANE PERFORMANCE During deceleration conditions, the mini- 2 of figure 2.12. Curve 2 of this illustration defines an upper limit of fuel flow which can mum allowable fuel flow is defined by the lean limit to support combustion.

be tolerated within stall-surge and tempera- If the fuel flow ture limits. The governing apparatus of the is reduced below some critical value at each RPM, lean blowout or flameout will occur.

engine must limit the acceleration fuel flow within this boundary. This condition is illustrated by curve 3 of To appreciate the governing requirements figure 2.12 which forms the deceleration fuel during the acceleration process, assume the flow boundary.

The governing apparatus must engine described in figure 2.12 is in steady state regulate the deceleration fuel flow within this stabilized operation at point A and it is desired boundary.

to acceler&the engine to maximum RPM and To appreciate the governing requirements stabilize:at point C. As the throttle is placed during the deceleration process, assume the at the position for maximum RPM, the fuel engine described in figure 2.12 is in stabilized, control will increase the fuel flow to point B steady state operation at point C and it is to provide acceleration fuel flow. As the desired to decelerate to idle conditions and engine accelerates and increases RPM, the fuel stabilize at point E. As the throttle is placed control will continue to increase the fuel flow at the position for idle RPM, the fuel control within the acceleration boundary until the will decrease the fuel flow to point D to provide engine speed approaches the controlled maxi- the deceleration fuel flow. As the engine mum RPM at point C. As the engine speed decelerates and decreases RPM, the fuel gov- nears the maximum at point C, the fuel contrcl’ erning will continue to decrease the fuel flow will reduce fuel flow to produce stabilized oper- within the deceleration boundary until the idle ation at this point and prevent the engine fuel flow is reached and RPM is established at overspeeding the commanded RPM. point E. Of course, if the throttle is closed Of course, if the throttle is opened very gradually, the very slowly, the deceleration fuel flow is barely below the steady state condition and the engine acceleration fuel flow is barely above the steady state condition and the engine does not ap- does not approach the deceleration fuel flow proach the acceleration fuel flow boundary. boundary. The fuel control must provide a deceleration flow close to the boundary to While this technique is recommended for ordinary conditions to achieve trouble free provide rapid decrease in thrust and satisfactory operation and good service life, the engine must flight control.

be capable of good acceleration to produce In most cases, the deceleration fuel flow rapid thrust changes for satisfactory flight boundary is considerably below the steady control. state fuel flow and no great problem exists in In order for the powerplant to achieve mini- obtaining satisfactory deceleration character- mum acceleration times, the fuel control must istics. In fact, the greater problem is con- cerned with obtaining proper acceleration provide acceleration fuel flow as close as characteristics. For the majority of centrifu- practical to the acceleration boundary. Thus, gal flow engines, the acceleration boundary is a maximum controlled acceleration may pro- set usually by temperature limiting conditions duce limiting turbine inlet temperatures or rather than compressor surge conditions.

slight incipient stall-surge of the compressor. Peak operating efficiency of the centrifugal com- Proper maintenance and adjustment of the pressor is obtained at flow conditions which engine governing apparatus is essential to are below the surge limit, hence acceleration produce minimum acceleration times without fuel flow boundary is determined by turbine incurring excessive temperatures or heavy stall- temperature limits. The usual result is that surge conditions.

NAVWEPS 00-801-80 AIRPLANE PERFORMANCE RPM. Since the variation of thrust with the centrifugal flow engine has relatively large RPM is quite powerful, the tachometer in- acceleration margins and good acceleration dication is a powerful reference.

characteristics result with the low rotational (2) The exhaust gas temperature gauge inertia. The axial flow compressor must oper- provides an important reference for engine ate relatively close to the stall-surge limit to operating limitations. While the tempera- obtain peak efficiency. Thus, the acceleration ture probe may be located downstream from fuel flow boundary for the axial flow engine is set by these stall-surge limits which are more the turbine (tailpipe or turbine discharge immediate to steady state conditions than tur- temperature) the instrument should provide an accurate reflection of temperatures up- bine temperature limits. The fixed geometry stream in the turbine section. The exhaust axial flow engine encounters relatively small gas temperature relates the energy change acceleration margins and, when compared to accomplished by fuel addition.

the centrifugal flow engine with larger accel- (3) The fuel flowmeter can provide a fair eration margins and lower rotational inertia, has inferior acceleration characteristics. Cer- reflection of thrust output. and operating efficiency. Operation at high density alti- tain variation of the axial flow engine such as variable nozzles, variable stator blades, multi- tude or high inlet air temperatures-reduces ple-spool compressors, etc., greatly improve the output thrust and this effect is related by the acceleration characteristics. a reduction of fuel flow.

A note of caution is appropriate at this (4) The’ tailpipe total pressure (p+q in point. If the main fuel control and govern- the tailpipe) can be correlated with the jet ing apparatus should malfunction or become thrust for a given engine geometry and set of inoperative and an unmodulated secondary or operating conditions. The output thrust emergency system be substitued, extreme care can be related accurately with various com- must be taken to avoid abrupt changes in binations of compressor inlet total pressure, throttle position. In such a case, very gradual tailpipe total pressure, ambient pressure and movement of the throttle is necessary to ac- temperature. Hence; pressure differential complish changes in power setting without (Ap), pressure ratio, and ,tailpipe total pres- excessive turbine temperatures, compressor sure instruments can provide more accurate stall or surge, or flameout.

immediate indications of output thrust than There are various instruments to relate irnr combined indications of RPM and EGT.

portant items of turbojet engine performance.

This is especially true with variable geom- Certain combinations of these instruments are etry or multiple spool engines.

capable of immediately relating the thrust Many other specialized instruments furnish output of the powerplant in a qualitative man- additional information for more detailed items ner. It is difficult to provide an instrument or of engine performance. Various additional combination of instruments which immedi- engine information is realized from fuel pres- ately relate the thrust output in a ~arrantitativ~ sure, nozzle positions, compressor inlet air manner. As a result, the pilot must rely on temperature, etc.

a combination of instrument readings and judge TURBOJET OPERATING LIMITATIONS.

the output performance according to standard The operating characteristics of the turbojet values particular to the powerplant.

Some of engine provide various operating limitations the usual engine indicating instruments are as which must be given due respect. Operation follows : of the powerplant within the specified limita- (1) The tachometer provides indication of tions is absolutely necessary in order to obtain engine speed, N, by percent of the maximum NAVWEPS OO-SOT-RO AIR.PLANE PERFORMANCE excess of the operational limits for these con- the design service life with trouble-free opera- tion. The following items describe the critical ditions will increase the possibility of early failure of the turbine components.

areas encountered during the operational use While the turbine components are the most of the turbojet engine: critically stressed high temperature elements (1) The limiting exhaust gag tcmpcra;wcs pro- vide the most important restrictions to the op- they are not the only items. The combustion eration of the turbojet engine. The turbine chamber components may be critical at low components are subject to centrifugal loads of altitude where high combustion chamber pres- rotation, impulse and reaction loads on the sures exist. Also, the airframe structure and equipment adjacent to the engine may be sub- blades, and various vibratory loads which may be inherent with the design. When the turbine ject to quite high temperatures and require provision to prevent damage by excess time at components are subject to this variety of stress high temperature.

in the presence of high temperature, two types of structural phenomena must be considered. (2) The c~mprcs~or Jtall or surge has the pos- when a part is subject to a certain stress at some sibility of producing damaging temperatures high temperature, weep failure will take place in the turbine and combustion chamber or un- after a period of time. Of course, an increase usual transient loads in the compressor.

While in .tcmperature or stress will increase the rate the stall-surge phenomenon is possible with at which creep damage is accumulated and the centrifugal compressor, the more common reduce the time required to cause failure. An- .occurrence is with the axial flow compressor.

other problem results when a part is subjected Figure 2.13 depicts the pressure distribution to a repeated or cyclic stress. F&&e failure that may exist for steady state operation of will occur after a number of cycles of a varying the engine. In order to accelerate the engine stress. An increase in temperature or magni- to a greater speed, more fuel must be added to tude of cyclic stress will increase the rate of increase the turbine power above that required fatigue damage and reduce the number of cycles to operate the compressor.

necessary to produce failure. It is important Suppose that the fuel flow is increased be- to note that both fatigue and creep damage are yond the steady state requirement without a cumulative.

change in rotative speed. The increased com- A gross overstress or overtemperature of the bustion chamber pressure due to the greater turbine section will produce damage that is fuel flow requires that the compressor dis- immediately apparent. However, the creep charge pressure be higher. For the instant and fatigue damage accumulated through pe- before an engine speed change occurs, an in- riods of less extreme’ overstress or overtem- crease in compressor discharge pressure will be perature is more subtle. If the turbine is accompanied by a decrease in compressor flow sibject to repeated excessive temperatures, the velocity. The equivalent effect is illustrated greatly increased rate of creep and fatigue by the flow components onto the rotating com- damage wiIl produce failure early within the pressor blade of figure 2.13. One component anticipated service life. of velocity is due to rotation and this compo- nent remains unchanged for a given rotative Generally, the operations which produce velocity of the single blade. The axial flow the highest exhaust gas temperatures are velocity for steady state operation combines starting, acceleration, and maximum thrust with rotational component to define a result- at high altitude. The time spent at these ant velocity and direction. If the axial flow temperatures must be limited arbitrarily to component is reduced, the resultant velocity prevent excessive accumulation of creep and fatigue. Any time spent at temperatures in and direction provide an increase in angle of NAVWEPS 00-BOT-80 AIRPLANE PERFORMANCE COMPRESSOR STALL COMBUSTION EXHAUST COMPRESSOR CHAMBER T”RB,NE NOZZLE PRESSURE RISE LIMITED BY STATIC PRESSURE CHANGE INLET INCREASED BLADE ANGLE ,STEADY STATE AXIAL FLOW VEL .OCITY ROTATING COMPRESSOR -REDUCED AXIAL FLOW VELOCITY / VELOCITY COMPONENT DUE TO ROTATION EFFECT OF INLET TEMPERATURE EXHAUST TEMPERATURE CHANGE TEMPERATURE RISE THROUGH COMBUSTION CHAMBER -- INLET COMPRESSOR COMBUSTION TURBINE EXHAUST CHAMBER NOZZLE Figure 2.13. Effect of Compressor Stall ond Inlet Temperature on Engine Operation NAVWEPS 00-801-80 AIRMANE Pl?RFORMANCE (c) Very high altitude flight produces low attack for the rotating blade with a subsequent compressor Reynolds numbers and an effect increase in pressure rise. Of course, if the similar to that of airfoil sections. As a change in angle of attack or pressure rise is decrease to low Reynolds numbers reduces beyond some critical value, stall will occur.

the section c&, very high altitudes reduce While the stall phenomenon of a series of rotating compressor blades differs from that the maximum pressure ratio of the com- of a single airfoil section in a free airstream, pressor. The reduced stall margins increase the cause and effect are essentially the same.

the likelihood of compressor stall.

If an excessive pressure rise is required Thus, the recovery from a compressor stall through the compressor, stall may occur with must entail reduction of throttle setting to the attendant breakdown of stable, steady flow reduce fuel flow, lowering angle of attack and through the compressor.

As stall occurs, the sideslip and increasing airspeed to improve pressure rise drops and the compressor does not inlet condition, and reducing altitude if high furnish discharge at a pressure equal to the altitude is a contributing factor.

combustion chamber pressure. As a result, a (3) While the j7ameout is a rare occurrence flow reversal or backfire takes place. If the with modern engines, various malfunctions stall is transient and intermittent, the indica- and operating conditions allow the flameout to tion will be the intermittent “bang” as back- remain a possibility. A uniform mixture of fire and flow reversal take place. If the stall fuel and air will sustain combustion within a develops and becomes steady, strong vibration relatively wide range of fuel-air ratios. Com- and a loud (and possibly expensive) roar bustion can be sustained with a fuel-air ratio develops from the continuous flow reversal.

as rich as one to five or as lean as one to twenty- The increase in compressor power required five. Fuel air ratios outside these limits will tends to reduce RPM and the reduced airflow not support combustion due to the deficiency and increased fuel flow cause rapid, immediate of air or deficiency of fuel. The characteristics rise in exhaust gas temperature. The pos- of the fuel nozzle and spray pattern as well as sibility of damage is immediate with the steady the governing apoaratus must insure that the stall and recovery must be accomplished nucleus of combt .,on is maintained through- quickly by reducing throttle setting, lowering out the range of engine operation.

the airplane angle of attack, and increasing If the rich limit of fuel-air ratio is exceeded airspeed. Generally, the compressor stall is in the combustion chamber, the flame will caused by one or a combination of the fol- blow out. While this condition is a pos- lowing items: sibility the more usual cause of a flameout is (ti) A malfunctioning fuel control or gov- exceeding the lean blowout limit. Any con- dition which produces some fuel-air ratio erning apparatus is a common cause. Proper maintenance and adjustment is a necessity for leaner than the lean limit of combustion will produce a flameout. Any interruption of the stall-free operation. The malfunctioning is fuel supply could bring on this condition.

most usually apparent during engine Fuel system failure, fuel system icing, or pro- acceleration.

longed unusual attitudes could starve the flows (6) Poor inlet conditions are typical at high angles of attack and sideslip. These of fuel to the engine. It should be noted the conditions reduce inlet airflow and create majority of aviation fuels are capable of holding in solution a certain small amount of nonuniform flow conditions at the com- water. If the aircraft is refueled with rela- pressor face. Of course, these conditions are tively w&m fuel then flown to high altitude, at the immediate control of the pilot.

NAVWEPS OO-BOT-80 AIRPLANE PERFORMANCE provide a convenient limit to sustained high the lower temperatures can precipitate this water out of solution in liquid or ice crystal speed flight.

(5) The effect of engine overspeed or critical vi- form.

High altitude flight produces relatively small bration speedranger is important in the service air mass flow through the engine and the rela- life of an engine. One of the principal sources tively low fuel flow rate. At these conditions of turbine loads is the centrifugal loads due to a malfunction of the fuel control and governing rotation. Since the centrifugal loads vary as apparatus could cause flameout. If the fuel the square of the rotative speed, a 5 percent overspeed would produce 10.25 percent over- control allows excessively low fuel flow during stress (1.05*= 1.1025). The large increase in controlled deceleration, the lean blow out limit may be exceeded. Also, if the governed idle stress with rorative speed could produce very rapid accumulation of creep and fatigue dam- condition allows any deceleration below the idle condition the engine will usually continue age at high temperature. Repeated overspeed and, hence, overstress can cause failure early to lose speed and flameout.

in the anticipated service life.

Restarting the engine in flight requires sufli- Since the turbojet engine is composed of cient RPM and airflow to allow stabilized op- many different distributed masses and elastic eration. Generally, the extremes of altitude structure, there are certain vibra~tory modes are most critical for attempted airstart.

(4) An increased compressor inlet air tcmpcra- and frequencies for the shaft, blades, etc.

While it is necessary to prevent any resonant tare can have a profound effect on the output tbLrust of 2 rnrhniet m&n,= As shown in conditions from existing within the normal ---“-,-- --o---.

figure 2.13, an increase in compressor inlet operating range, there may be certain vibra- temperature produces an even greater increase tory modes encountered in the low power range in the compressor discharge temperature. Since common to ground operation, low altitude the turbine inlet temperature is limited to endurance, acceleration or deceleration. If some maximum value, any increase in com- certain operating RPM range restrictions are pressor discharge temperature will reduce the specified due to vibratory conditions, opera- temperature change which can take place in tions must be conducted with a minimum of the combustion chamber. Hence, the fuel flow time in this area. The greatly increased will be limited and a reduction in thrust is stresses common to vibratory conditions are incurred. quite likely to cause fatigue failures of the The effect of inlet air temperature on thrust offending components.

output has two special ramifications. At rakc- The operating limitations of the engine are off, a high ambient air temperature at a given usually specified by various combinations of pressure altitude relates a high density altitude. RPM, exhaust gas temperature, and allowable Thus, the takeoff thrust is reduced because of time. The conditions of high power output low density and low mass flow. In addition and acceleration have relatively short times to the loss of thrust due to reduced mass flow, allowable to prevent abuse of the powerplant thrust and fuel flow are reduced further be- and obtain good service life. While the al- cause of the high compressor inlet temperature. lowable times at various high power and In flight at Sigh Mach number, the aerodynamic acceleration condition appear arbitrary, the heating will provide an increase in compressor purpose is to reduce the spectrum of loading inlet temperature. Since the compressor inlet which contributes the most rapid accumulation temperature will reflect the compressor dis- of creep and fatigue damage. In fact, in some charge temperature and the allowable fuel instances, the arbitrary time standards can be flow, the compressor inlet air temperature may set to suit the particular requirements of a NAVWEPS OO-EOT-80 AIRPLANE PERFORMANCE afterburner and very high temperatures can be certain type of operation. Of course, the tolerated.

effect on service life of any particular load The combustion of fuel in the after- burner brings additional increase in tempera- spectrum must be anticipated.

ture and volume and\ adds considerable energy One exception to the arbitrary time standard to the exhaust. gases producing increased jet for operation at high temperatures or sus- velocity. The major components of the after- tained high powers is the case of the after- burner operation. When the cooling flow is burner are illustrated in figure 2.14.

One necessary feature of the turbojet engine only that necessary to prevent excessive tem- equipped with afterburner is a variable nozzle peratures for adjacent structure and equipment, area. As the afterburner begins functioning, sustained operation past a time limit may cause the exit nozzle area must increase to accom- damage to these items.

modate the increased combustion products.

THRUST AUGMENTATION. Many op- If the afterburner were to begin functioning erating performance conditions may require without an increase in exit area, the mass flow that additional thrust be provided for short through the engine would drop and the tem- periods of time. Any means of augmenting peratures would increase rapidly. The nozzle the thrust of the turbojet engine must be ac- complished without an increase in engine speed area must be controlled to increase as after- burner combustion, begins. As a result, the or maximum turbine section temperature. The engine mass flow is given a large increase in various forms of afterburning or water injection allow the use of additional fuel to provide jet velocity with the corresponding increase in ., thrust augmentation without increase in engine thrust.

speed or turbine temperature. The combustion of fuel in the afterburner takes place at low pressures and is relatively The aftsrbumer is a relatively simple means inefficient.

of thrust augmentation and the principal fea- This basic inefficiency of the low pressure combustion is given evidence by the tures are light weight and large thrust increase.

A typical afterburner installation may add only large increase in specific fuel combustion.

Generally, the use of afterburner at least will 10 to 20 percent of the basic engine wei,ght but double the specihtfuel consumption. As an can provide a 40- to 60-percent increase in the example, consider a turbojet engine capable static sea level thrust. The afterburner con- of producing 10,000 lbs. of thrust which can sists of an additional combustion area aft of develop 15,ooO lbs.. of thrust with the use of the turbine section with an arrangement of fuel nozzles and flameholders. afterburner. Typical values for specific fuel Because the local flow velocities in the afterburner are consumption would. be c,= 1.05 for the basic quite high, the flameholders are necessary to engine or t,= 2.1 when the afterburner is in use. The fuel flow during operation would be provide the turbulence to maintain combustion within the afterburner section. The turbojet as follows: fuel flow = (thrust) (specific fuel consump- engine operates with airflows greatly in excess tion) of that chemically required to support combus- without afterburner, tion of engine fuel. This is necessary because fuel flow=(10,000) (1.05) of cooling requirements and turbine tempera- = 10,500 lbs./hr.

ture limitations. Since only 15 to 30 percent with afterburner, of the engine airflow is used in the combustion fuel flow=(15,COO) (2.1) chamber, the large excess air in the turbine =31,500 lbs./hr.

discharge can support combustion of large The low efficiency of the afterburner is illus- amounts of additional fuel. Also, there are trated by the additional 21,CCOlbs./hr. of fuel no highly stressed, rotating members in the flow to create the additional 5,ooO lbs. of NAVWEPS 0040T-80 AIRPLANE PERFORMANCE AFTERBURNER COMPONENTS AFTt$lRNRNER HOLDERS WATER INJECTION WATER INJECTION NOZZLES CHAMBER NOZZLE PRE -COMPRESSOR INJECTION TURBINE-PROPELLER COMBINATION REDUCTION TURBINES CHAMBER NOZZLE Figure 2.14. Thrust Augmentation and the Gas Turbine-Propeller Combination NAVWEPS 00-30T-30 AIRPLANE PERFORMAPJCE thrust. Because of the high fuel consumption immediate advantage in that it prevents fouling during afterburner operation and the adverse of the plumbing from the freezing of residual effect on endurance, the use of the afterburner fluid at low temperatures. In addition, a large should be limited to short periods of time. concentration of alcohol in the mixture can In addition, there may be limited time for the provide part of the additional chemical energy use of the afterburner due to critical heating required to maintain engine speed. In fact, of supporting or adjacent structure in the vicin- the large concentration of alcohol in the in- ity of the afterburner. jection mixture is a preferred means of adding The specific fuel consumption of the basic additional fuel energy. If the added chemical engine will increase with the addition of the energy is included with the water flow, no afterburner apparatus. The losses incurred by abrupt changes in governed fuel flow are the greater fluid friction, nozzle and flame- necessary and there is less chance of underspeed holder pressure drop, etc. increase the specific with fluid injection and overspeed or over- fuel consumption of the basic engine approxi- temperature when fluid flow is exhausted. Of mately 5 to 10 percent.

course, strict proportions of the mixture are The principal advantage of afterburner is the necessary. Since most water injection devices ability to add large amounts of thrust with are essentially an unmodulated flow, the use relatively small weight penalty. The applica- of this device is limited to high engine speed tion of the afterburner is most common to the and low altitude to prevent the water flow interceptor, fighter, and high speed type from quenching combustion.

aircraft.

The use of wafer injection in the turbojet en- THE GAS TURBINE-PROPELLER COM- gine is another means of thrust augmentation BINATION.

The turbojet engine utilizes the which allows the combustion of additional fuel turbine to extract suflicient power to operate within engine speed and temperature limits.

the compressor. The remaining exhaust gas The most usual addition of water injection de- energy is utilized to provide the high exhaust vices is to supplement takeoff and climbout gas velocity and jet thrust. The propulsive performance, especially at high ambient tem- efficiency of the turbojet engine is relatively peratures and high altitudes. The typical low because thrust is produced by creating a water injection device can produce a 25 to 35 large velocity change with a relatively small percent increase in thrust.

mass flow. The gas turbine-propeller combin- The most usual means of water injection is ation is capable of producing higher propulsive direct flow of the fluid into the combustion efficiency in subsonic flight by having the pro- chamber. This is illustrated in figure 2.14.

peller operate on a much greater mass flow.

The addition of the fluid directly into the com- The turboprop or propjet powerplant re- bustion chamber increases the mass flow and quires additional turbine stages to continue reduces the turbine inlet temperature. The drop in temperature reduces the turbine power expansion in the turbine section and extract a very large percent of the exhaust gas energy and a greater fuel flow is required to maintain as shaft power. In this sense, the turboprop engine speed. Thus, the mass flow is increased, is primarily a power producing machine and more fuel flow is allowed within turbine limits, and greater, energy is imparted to the exhaust the jet thrust is a small amount of the output gases. propulsive power. Ordinarily, the jet thrust The fluid injected into the combustion cham- of the turboprop accounts for 15 to 25 percent bers is generally a mixture of water and alco- of the total thrust output. Since the turbo- prop is primarily a power producing machine, hol. The water-alcohol solution has one 3~PWbWtlOdWd 3NVldUlV 08-108-00 SdSMAVN NAVWEPS Oo-ROT-30 AIRPLANE PERFORMANCE engine-propeller combination is operated at a the turboprop powerplant is rated by an “equivalent shaft horsepower.” constant RPM throughout the major range of output power and the principal variables ofcon- T,y trol are fuel flow and propeller blade angle.

ESHP= BHP+325vp In the major range of power output, the where throttle commands a certain fuel flow and the ESHP=equivalent shaft horsepower propeller blade angle adjusts to increase the EHP= brake horsepower, or shaft horse- propeller load and remain at the governed power applied to the propeller speed.

T,= jet thrust, lbs.

The operating limitations of the turboprop V=flight velocity, knots, TAS powerplant are quite similar in nature to the operating limitations of the turbojet engine.

‘ 1s = propeller efficiency Generally, the turbine temperature limnations The gas turbine engine is capable of processing are the most critical items. In addition, over- large quantities of air and can produce high speed conditions can produce overstress of the output power for a given engine size. Thus, gearing and propeller as well as overstress of the principal advantage of the turboprop the turbine section.

powerplant is the high specific power output, The performance of the turboprop illustrates high power per engine weight and high power the typical advantages of the propeller-engine per engine size.

combination. Higher propulsive efficiency The gas turbine engine must operate at quite and high thrust and low speeds provide the high rotative speed to process large airflows characteristic of range, endurance, and takeoff and produce high power. However, high performance superior to the turbojet. As is rotative speeds are not conducive to high typical of all propeller equipped powerplants, propeller efficiency because of compressibility the power available is nearly constant with A large reduction of shaft speed must effects. speed. Because the power from the jet thrust be provided in order to match the powerplant depends on velocity, the power available in- and the propeller. The reduction gearing must creases slightly with speed. However, the provide a propeller shaft speed which can be thrust available decreases with speed. The utilized effectively by the propeller and, be- equivalent shaft horsepower, ESHP, of the cause of the high rotative speeds of the turbine, turboprop is affected by mass ,flow and inlet gearing ratios of 6 to 15 may be typical.

The temperature in fashion similar to that of the transmission of large shaft horsepower with turbojet. Thus, the ESHP will vary with such high gearing involves considerable desi,gn altitude much like the thrust output of the problems to provide good service life. The turbojet because the higher altitude produces problems of such gearing were one of the much lower density and engine mass flow.

greatest difficulties in the development of The gas turbine-propeller combination utilizes turboprop powerplants. a number of turbine stages to extract shaft The governing apparatus for the turboprop power from the exhaust gases and, as high powerplant must account for one additional compressor inlet temperatures reduce the fuel variable, the propeller blade angle. If the flow allowable within turbine temperature propeller is governed separately from the tur- limits, hot days will cause a noticeable loss of Generally, the turboprop is bine, an interaction can exist between the output power.

engine and propeller governers and various just as sensitive, if not more sensitive, to com- “hunting,” pressor inlet air temperature as the turbojet overspeed, and overtemperature conditions are possible. For this reason, the engine.

NAVWEPS 00-8OT-80 AlR,Pl.ANE PERFORMANCE heat and causes the rise of pressure along line The specific fuel consumption of the turbo- CD. The power stroke utilizes the increased prop powerplant is defined as follows : pressure through the expansion along line DE.

specific fuel consumption= Then the exhaust begins by the initial rejection engine fuel flow along line EB and is completed by the upstroke equivalent shaft horsepower along line BA.

The net work produced by the cycle of opera- c=lbs. per hr.

tion is idealized by the area BCDE on the ESHP pressure-volume diagram of figure 2.15. Dur- Typical values for specific fuel consumption, c, ing the actual rather than ideal cycle of op- range from 0.5 to 0.8 lbs. per hr. per ESHP.

eration, the intake pressure is lower than the The variation of specific fuel consumption with exhaust pressure and the negative work repre- operating conditions is similar to that of the sents a pumping loss. The incomplete expan- turbojet engine. The minimum specific fuel sion during the power stroke represents a basic consumption is obtained at relatively high loss in the operating cycle because of the re- power setting and high altitudes. The low jection of combustion products along line EB.

inlet air temperature reduces the specific fuel The area EFB represents a basic loss in the consumption and the lowest values of c are ob- operating cycle because of the rejection of tained near altitudes of 25,ooO to 3900 ft.

combustion products along line EB. The area Thus; the turboprop as well as the turbojet has EFB represents a certain amount of energy of a preference for high altitude operation.

the exhaust gases, a part of which can be ex- tracted by exhaust turbines as additional shaft THE RECRIPROCATING ENGINE power to be coupled to the crankshaft (turbo- The reciprocating engine is one of the most compound engine) or to be used in operating a efficient powerplants used for aircraft power.

supercharger (turbosupercharger). In addi- The combination of the reciprocating engine tion, the exhaust gas energy may be utilized to and propeller is one of the most efficient means augment engine cooling flow (ejector exhaust) of converting the chemical energy of fuel into and reduce cowl drag.

flying time or distance. Because of the in- Since the net work produced during the op- herent high efficiency, the reciprocating engine erating cycle is represented by the enclosed area is an important type of aircraft powerplant.

of pressure-volume diagram, the output of the OPERATING CHARACTERISTICS. The engine is affected by any factor which influences function of the typical reciprocating engine in- this area.

The weight of fuel-air mixture will volves four strokes of the piston to complete determine the energy released by combustion one operating cycle. This principal operating and the weight of charge can be altered by cycle is illustrated in figure 2.15 by the varia- altitude,supercharging,etc. Mixturestrength, tion of pressure and volume within the cylin- preignition, spark timing, etc., can affect the der. The first stroke of the operating cycle is energy release of a given airflow and alter the the downstroke of the piston with the intake work produced during the operating cycle.

valve open. This stroke draws in a charge of The mechanical work accomplished during fuel-air mixture along AB of the pressure- the power stroke is the result of the gas pres- volume diagram. The second stroke accom- sure sustained on the piston.

The linkage of plishes compression of the fuel-air mixture the piston to a crankshaft by the connecting along line EC. Combustion is initiated by a rod applies torque to the output shaft.

During spark ignition apparatus and combustion takes this conversion of pressure energy to mechani- place in essentially a constant volume. The cal energy, certain losses are inevitable because combustion of the fuel-air mixture liberates NAVWEPS 00-801-80 AIRPLANE PERFORMANCE POWER EXHAUST COMPRESSION COMBUSTION INTAKE RECIPROCATING ENGINE OPERATING CYCLE E \ \ ‘ .

-.

-\ ------==.f= B EXHAUST VOLUME Figure 2.15. Reciprocating Engines NAVWEPS 00401-30 AlRPlANE PERFORMANCE of friction and the mechanical output is less the power stroke. As such, BMEP is a con- venient index for a majority of items of recip- than the available pressure energy. The power rocating engine output, efficiency, and operat- output from the engine will be determined by ing limitations.

the magnitude and rate of the power impulses.

The actual power output of any reciptocat- In order to determine the power output of the ing engine is a direct function of the combina- reciprocating engine, a brake or load device is tion of engine torque and rotative speed.

attached to the output shaft and the operating Thus, output brake horsepower can be related characteristics are determined. Hence, the by the combination of BMEP and RPM or term “brake” horsepower, BHP, is used to denote the output power of the powerplant. torque prc~surc and RPM. No other engine From the physical definition of “power” and instruments can provide this immediate indi- the particular unit of “horsepower” (1 h.p. = cation of output power.

33,ooO ft.-lbs. per min.), the brake horsepower If all other factors are constant, the engine can be expressed in the following form. power output is directly related to the engine airflow. Evidence of this fact could be appre- ciated from the equation for BHP in terms of BHP=G BMEP.

or BHP = @M.W(DXN) TN 792,000 BHP= 5255 where This equation relates that, for a given BMEP, BHP= brake horsepower the BHP is determined by the product of en- T=output torque, ft.-lbs.

gine RPM, N, and displacement, D. In a N=output shaft speed, RPM sense, the reciprocating engine could be con- sidered primarily as an air pump with the In this relationship, the output power is ap- pump capacity directly affecting the power preciated as some direct variable of torque, T, output. Thus, any engine instrumems which and RPM. Of course, the output torque is relate factors affecting airflow can provide some some function of the combustion gas pressure indirect reflection of engine power. The pres- during the power stroke. Thus, it is helpful sure and temperature of the fuel-air mixture to consider the mean effective gas pressure decide the density of the mixture entering the during the power stroke, the “brake mean cylinder. The carburetor air temperature will effective pressure” or BMEP. With use of provide the temperature of the inlet air at the this term, the BHP can be expressed in the carburetor. While this carburetor inlet air following form.

is not the same temperature as the air in the cylinder inlet manifold, the carburetor inlet

BHP=@MEP)(D)(N)

792,m temperature provides a stable indication inde- pendent of fuel flow and can be used as a stand- where ard of performance. Cylinder inlet manifold BHP= brake horsepower temperature is difficult to determine with the BMEP= brake mean effective pressure, psi same degree of accuracy because of the normal D=engine displacement, cu. in.

variation of fuel-air mixture strength. The N= engine speed, RPM inlet manifold pressure provides an additional indication of the density of airflow entering the The BMEP is not actual pressure within the combustion chamber. The manifold absolute cylinder, but an effective pressure representing the mean gas load acting on the piston during pressure, MAP, is affected by the carburetor NAVWEPS 00-801-80 AIRPLANE PRRFORMANCE inlet pressure, throttle position, and super- flame propagation speed, fuel distribution, charger or impeller pressure ratio. Of course, temperature variation, etc., the maximum the throttle is the principal control of mani- power obtained with a fixed airflow occurs at fold pressure and the throttling action controls fuel-air ratios of approximately 0.07 to 0.08.

the pressure of the fuel-air mixture delivered The first graph of figure 2.16 shows the varia- to the supercharger inlet. The pressure re- tion of output power with fuel-air ratio for a ceived by the supercharger is magnified by a constant engine airflow, i.e., constant RPM, the supercharger in some proportion depend- MAP, and CAT (carburetor air temperature); ing on impeller speed. Then the high pressure Combustion can be supported by fuel-air ratios mixture is delivered to the manifold.

just greater than .0.04 but the energy released Of course, the engine airflow is a function of is insufficient to overcome pumping losses and RPM for two reasons. A higher engine speed engine mechanical friction. Essentially, the increases the pumping rate and the volume flow same result is obtained for the rich fuel-air through the engine. Also, with the engine ratios just below 0.20. Fuel-air ratios be- driven supercharger or impeller, an increase in tween these limits produce varying amounts of engine speed increases the supercharger pres- output power and the maximum power output sure ratio. With the exception of near closed generally occurs at fuel-air ratios of approxi- throttle position, an increase in engine speed mately 0.07 to 0.08. Thus, this range of fuel- will produce an increase in manifold pressure. air ratios which produces maximum power for The many variables affecting the character a given airflow is termed ,the “best power” ,.F the romL.,*r;nn :...^---” At jo,me lower range of f-ue;-air rariop, “1 L..,, c YYU”Cl”Y process a:e an I.n~“Lrant range.

subject of reciprocating engine operation.

a maximum of power per fuel-air ratio is ob- Uniform mixtures of fuel and air will support tained and this the “best economy” range.

combustion between fuel-air ratios of approxi- The best economy range generally occurs be- mately 0.04 and 0.20. The chemically correct When tween fuel-air ratios of 0.05 and 0.07.

proportions of air and hydrocarbon fuel would maximum engine power is required for take- be 15 lbs. of air for each lb. of fuel, or a fuel- off, fuel-air ratios greater than 0.08 are neces- This chemically correct, or air ratio of 0.067.

sary to suppress detonation. Hence, fuel-air “stoichiometric,” fuel-air ratio would provide ratios of 0.09 to 0.11 are typical during this the proportions of fuel and air to produce operation.

maximum release of heat during combustion of The pattern of combustion in the cylinder is a grven weight of mixture. If the fuel-air best illustrated by the second graph of figure ratio were leaner than stoichiometric, the ex- 2.16. The normal combustion process begins cess of air and deficiency of fuel would produce lower combustion temperatures and reduced by spark ignition toward the end of the com- If heat release for a given weight of charge.

pression stroke. The electric spark provides the fuel-air ratio were richer than stoichio- the beginning of combustion and a flame front metric, the excess of fuel and deficiency of air is propagated smoothly through the com- would produce lower combustion temperatures pressed mixture. Such normal combustion is and reduced heat release for a given weight of shown by the plot of cylinder pressure versus charge. Spark ignition begins a smooth piston travel.

The stoichiometric conditions would pro- rise of cylinder pressure to some peak value duce maximum heat release for ideal conditions with subsequent expansion through the power of combustion and may apply quite closely for stroke. The variation of pressure with piston the individual cylinders of the low speed re- travel must be controlled to achieve the great- ciprocating engine. Because of the effects of est net work during the cycle of operation.

NAVWEPS 00-307-80 AIRPLANE PERFORMANCE BEST CONSTANT AIRFLOW PERCENT POWEFI OVERLEAN WER-RICH

I

FUEL-AIR RATIO NORMAL COMBUSTION DETONATION SPARK PLUG FLAME PROPAGATION BURNJNG IGNITION FROM HOT SFfYT NORMAL CCMBUSTION COMPRESSION STROKE POWER STROKE TOP CENTER :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~:::::::::::::::::::::::::::~:::::::::::::::::::::::::::::::::::::::::::::::::::::::::~.:::::::~::::::::::::::~~~~~~~~~~~~~~~~ ::::::::::::::::::::::::::::::::::::::::::~::::~:::::::::::::::::::::::::::::::::::::::::::::::::::~::::::::::::::::::::::::::::~:::::::::::::::::::::::::::::::::::::::::::::::::::...~.............., .. .... .... ... ..

.... ... ... ..... .... .. ..... ... .... .... .... ... .... ... .... ... .. .... ... ... ..... .. ....... . .. ...... ... ... .. .~ .._..______._.,,.,.,,...................,......................,,...............,.....

TAKEOFF RATED MAXIMUM POWER CRUISE POWER

1 1 1

DETONATION ENGINE AIRFLOW, LBS. PER HR.

Figure 2.16. Reciprocating Engine Operation NAVWEPS 00-8OT-RO AIRPLANE PERFORMANCE Denotation offers the possibility of immedi- Obviously, spark ignition timing is an impor- ate destruction of the powerplant. The nor- tant factor controlling the initial rise of pres- sure in the combustion chamber. mal combustion process is initiated by the The ignition spark and beginning of flame front propaga- of the fuel mixture must begin at the proper tion As the flame front is propagated, the time to allow flame front propagation and the release of heat to build up peak pressure for the combustion chamber pressure and temperature begin to rise. Under certain conditions of power stroke .

The speed of flame front propagation is a high combustion pressure and temperature, major factor affecting the power output of the the mixture ahead of the advancing flame front reciprocating engine since this factor controls may suddenly explode with considerable vi- the rate of heat release and rate of pressure rise olence and send strong detonation waves in the combustion chamber. through the combustion chamber. The result For this reason, dual ignition is necessary for powerplants of is depicted by the graph of figure 2.16, whete:a high specific power output. Obviously, nor- sharp, explosive increase in pressure takes place mal combustion can be accomplished more with a subsequent reduction of the mean pres; rapidly with the propagation of two flame sure during the power stroke. Detonation fronts rather than one. The two sources of produces sharp explosive pressure peaks many ignition are able to accomplish the combus- times greater than normal combustion1 Also, tion heat release and pressure rise in a shorter the exploding gases radiate considerable heat period of time. Fuel-air ratio is another factor and cause excessive temperatures for many local parts of the engine.

affecting the flame propagation speed in the The effects of heavy combustion chamber. The maximum flame detonation are so severe that structural damage propagation speed occurs near a fuel-air ratio is the immediate result.

Rapid rise of cylinder of 0.08 and, thus, maximum power output for head temperature, rapid drop in BMEP, and a given airflow will tend to occur at this value loud, expensive noises are evidence of detona- rather than the stoichiometric value. tion.

Two aberrations of the combustion process Detonation is not necessarily confined to. a are preignition and detonation.

Preignition period after the beginning of normal flame front is simply a premature ignition and flame f&t propagation. With extremely low grades of propagation due to hot spots in the combustion fuel, detonation can occur before normal igni- chamber. Various lead and carbon deposits tion. In addition, the high temperatures and and feathered edges on metal surfaces can sup- pressure caused by preignition will mean that ply a glow ignition spot and begin a flame detonation is usually a corollary of preigniticn.

propagation prior to normal spark ignition. Detonation results from a sudden, unstable de- As shown on the graph of figure 2.16, pre- composition of fuel at some critical combina- ignition causes a premature rise of tion of high temperature and pressure. Thus, pressure during the piston travel. detonation is most likely to occur at any op As a result, preignition combustion pressures and tempera- erating condition which produces high com- tures will exceed normal combustion values and bustion pressures and temperatures. Gener- are very likely to cause engine damage. Be- ally, high engine airflow and fuel-air ratios for cause of the premature rise of pressure toward maximum heat release will produce the critical conditions. High engine airflow is common the end of the compression stroke, the net work of the operating cycle is reduced. to high MAP and RPM and the engine is most Preignition is evidenced by a rise in cylinder head tempera- sensitive to CAT and fuel-air ratio in this ture and drop in BMEP or torque pressure.

region.

NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE The detonation properties of a fuel are de- cruise power is the upper limit of power that termined by the basic molecular structure of can be utilized for this operation. Higher air- flows and higher power wirhout a change in the fuel and the various additives. The fuel fuel-air ratio will intersect the knee of the detonation properties are generally specified detonation envelope. by the antidetonation or antiknock qualities of The primary factor relating the efficiency of an octane rating. Since the antiknock proper- ties of a high quality fuel may depend on the operation of the reciprocating engine is the brake specific fuel consumption, iWE%, or mixture strength, provision must be made in. the rating of fuels. Thus, a fuel grade of simply c.

IIS/ would relate a lean mixture antiknock Brake suecific fuel consumution I rating of 115 and a rich mixture antiknock engine fuel flow rating of 145. One of the most common opera- = brake horsepower tional causes of detonation is fuel contamina- lbs. per hr.

C= tion. An extremely small contamination of BHP high octane fuel with jet fuel can cause a serious Typical minimum values for c range from 0.4 ,decrease in the antiknock rating. Also, the to 0.6 lbs. per hr. per BHP and most aircraft contamination of a high grade fuel with the powerplaots average 0.5. The turbocompound next lower grade will cause a noticeable loss of engine is generally the most efficient because antiknock quality.

of the power recovery turbines and can ap- The fuel metering requirements for an engine proach values of c=O.38 to 0.42. It should be are illustrated by the third graph of figure 2.16 noted that the minimum values of specific fuel which is a plot of fuel-air ratio versus engine consumption will be obtained only within the airflow. The carburetor must provide specific range of cruise power operation, 30 to 60 per- fuel-air ratios throughout the range of engine cent of the maximum power output. Gen- airflow to accommodate certain output power.

erally, the conditions of minimum specific fuel Most modern engines equipped with auto- consumption are achieved with auto-lean or matic mixture control provide a scheduling of manual lean scheduling of fuel-air ratios and fuel-air ratio for automatic rich or automatic high BMEP and low RPM. The low RPM is lean operation. The auto-rich scheduling usu- the usual requirement to minimize friction ally provides a fuel-air ratio at or near the horsepower and improve output efficiency.

maximum heat release value for the middle The effect of &it&c is to reduce the engine range of airflows. However, at high airflows airflow and power output and supercharging a power enrichment must be provided to sup- is necessary to maintain high power output press detonation. The auto-rich schedule gen- at high altitude. Since the basic engine is erally will provide an approximate fuel-air able to process air only by the basic volume ratio of 0.08 which increases to 0.10 or 0.11 at displacement, the function of the supercharger the airflow for takeoff power. In addition, is to compress the inlet air and provide a the low airflow and mixture dilution that oc- greater weight of air for the engine to process.

curs in the idle power range requires enrich- Of course, shaft power is necessary to operate ment for satisfactory operation.

the engine driven supercharger and a tempera- The schedule of fuel-air ratios with an auto- ture rise occurs through the supercharger com- matic lean fuel-air ratio will automatically pression. The effect of various forms of super- provide maximum usable economy. If manual charging on altitude performance is illustrated leaning procedures are applicable a lower fuel- in figure 2.17.

air ratio may be necessary for maximum possi- The unsupercharged-or naturally aspi- ble efficiency. The maximum continuous rated-engine has no means of providing a NAVWEPS OO-ROT-RO AIRPLANE PERFORMANCE EFFECT OF SUPERCHARGING ON ALTITUDE PERFORMANCE UNAVAILABLE LOW SLOWER \ LIMIT MAP HIGH SLOWER \ LIMIT MAf f- J _c U&Q CONSTANT

\

N,D

b

Figure 2.17. Fffect of Supercharging on Altitude Performonce NAVWEPS OO-ROT-RO AWIANE PERFORMANCE higher altitude or a lower engine speed would manifold pressure any greater than the induc- produce less supercharging and a given MAP tion system inlet pressure. As altitude is would require a greater throttle opening.

increased with full throttle and a governed Generally, the most important critical alti- RPM, the airflow through the engine is tudes will be specified for maximum, rated, reduced and BHP decreases. The first forms of supercharging were of relatively low pressure and maximum cruise power conditions.

ratio and the added airflow and power could A change of the blower to a high speed will be handled at full throttle within detonation provide greater supercharging but will require more shaft power and incur a greater tempera- limits. Such a “ground boosted” engine ture rise. Thus, the high blower speed can would achieve higher output power at all produce an increase in altitude performance altitudes but an increase in altitude would within the detonation limitations.

produce a decrease in manifold pressure, air- The vari- ation of BHP with altitude for the blower at flow, and power output.

high speed shows an increase in critical alti- More advanced forms of supercharging with higher pressure ratios can produce very large tude and greater BHP than is obtainable in low engine airflow. In fact, the typical case of blower. Operation below the high blower altitude supercharging will produce such high critical altitude requires some limiting mani- airflow at low altitude operation that full fold pressure to remain within detonation throttle operation cannot be utilized within limits. It is apparent that the shift to high detonation limits. Figure 2.17 illustrates this blower is not required just past low blower case for a typical two-speed engine driven critical altitude but at the point where the altitude supercharging installation. At sea transition from low blower, full throttle to level, the limiting manifold pressure produces high blower, limit hiAP will produce greater a certain amount of BHP. Full throttle oper- BHP. Of course, if the blower speed is ation could produce a higher MAP and BHP increased without reducing the throttle if detonation were not the problem. In this can occur.

opening, an “overboost” case full throttle operation is unavailable Since the exhaust gases have considerable because of detonation limits. As altitude is energy, exhaust turbines provide a source of increased with the supercharger or “blower” supercharger power. The turbosupercharger at low speed, the constant MAP is maintained (TB.S) allows control of the supercharger by opening the throttle and the BHP increases speed and output to very high altitudes with above the sea level value because of the re- a variable discharge exhaust turbine (PDT).

duced exhaust back pressure. Opening the The turbosupercharger is capable of providing throttle allows the supercharger inlet to re- the engine airflow with increasing altitude by ceive the same inlet pressure and produce the increasing turbine and supercharger speed.

same MAP. Finally, the increase of altitude Critical altitude for the turbosupercharger is will require full throttle to produce the con- usually defined by the altitude which produces stant MAP with low blower and this point is the limiting exhaust turbine speed.

termed the “critical altitude” or “full throttle The minimum specific fuel consumption of height.” If altitude is increased beyond the the supercharged engine is not greatly affected critical altitude, the engine MAP, airflow, and by altitudes less than the critical altitude. At BHP decrease.

the maximum cruise power condition, specific The critical altitude with a particular super- fuel consumption will decrease slightly with charger installation is specific to a given com- an increase in altitude up to the critical bination of MAP and RPM. Obviously, a altitude. Above critical altitude, maximum lower MAP could be maintained to some ,cruise power cannot be maintained but the NAVWEPS O&ROT-SO AIRPLANE PERFORMANCE specific fuel consumption is not adversely heavy detonation or preignition is common to affected as long as auto-lean or manual lean the high airflow at maximum power, the most power can be used at the cruise power setting. likely chance of detonation or preignition is at One operating characteristic of the recipro- takeoff. In order to suppress detonation or cating engine is distinctly different from that allow greater power for takeoff, water injec- of the turbojet. Water vapor in the air will tion is often used in the reciprocating engine.

cause a significant reduction in output power of At high power’ settings, the injection of the the reciprocating engine but a negligible loss water-alcohol mixture can replace the excess of thrust for the turbojet engine. This basic fuel required to suppress detonation, and de- difference exists because the reciprocating richment provisions can reduce the fuel-air engine operates with a fixed displacement and ratio toward the value for maximum heat re- all air processed is directly associated with the lease. Thus, an increase in power will be ob- combustion process. If water vapor enters the tained by the better fuel-air ratio. In some induction system of the reciprocating engine, instances, a higher manifold pressure can be 1 the amount of air available for combustion is utilized to produce additional power. The in- reduced and, since most carburetors do not jection fluid will require proportions of alcohol distinguish water vapor from air, an enrich- and water quite different from the injection ment of the fuel-air ratio takes place. The fluid for jet engine thrust augmentation.

maximum power output at takeoff requires Since derichment of the fuel-air ratio is de- fuel-air ratios richer than that for maximum sired, the anti-detonant injection (AOZ) will rr\n+l;n ,Ir,.Le, :.. -.....^*;*:- r-^--..-.*--.:J..-l -haezt re1m.e rn ,, C,I+P- nnr:rLmm.c . . ..I1 *-IF- b”IICLIALI PlC”ll”l111 yu‘ a”c’ l’ L~ L” pC”LuL Ic>luual --A-“-\- “W . A....A c. b.IIA.cIIIIICIIL “1111 La&C fluid from fouling the plumbing.

place with subsequent loss of power. The When the fuel grades are altered during oper- turbojet operates with such great excess of air ation and the engine must be’ operated on a that the combustion process essentially is next lower fuel grade, proper account must be unaffected and the reduction of air mass flow made for the change in the operating limita- is the principal consideration. As an example, tions. This accounting must be made for the extreme conditions which would produce high maximum power for takeoff and the maximum specific humidity may cause a 3 percent thrust cruise power since both of these operating con- loss for a turbojet but a 12 percent loss of BHP ditions are near the detonation envelope. In Proper accounting for a reciprocating engine.

addition, when the higher grade of fuel again of the loss due to humidity is essential in the becomes available, the higher operating,limits operation of the reciprocating engine.

cannot be used until it is sure chat no contamina- OPERATING LIMITATIONS. Recipro- tion exists from the lower grade fuel remaining cating engines have achieved a great degree of in the tanks.

refinement and development and are one of the Spark plug fouling can provide certain high most reliable of all types of aircraft power- as well as low limits of operating temperatures.

plants. However, reliable operation of the re- When excessively low operating temperatures ciprocating engine is obtained only by strict are encountered, rapid carbon fouling of the adherence to the specific operating limitations.

plugs will take place. On the other hand, The most important operating limitations of excessively high operating temperatures will the reciprocating engine are those provided to produce plug fouling from lead bromide de- ensure that detonation and preignition do not posits from the fuel additives.

take place. The pilot must ensure that proper Generally, the limited periods of time at fuel grades are used that limit MAP, BMEP, various high power settings are set to mini- RPM, CAT, etc., are not exceeded. Since mize the accumulation of high rates of wear Revised January 1965 NAVWEPS OO-EOT-80 AIRPLANE PERFORMANCE and fatigue damage. By minimizing the disc. In this idealized propeller disc, the pres- amount of total time spent at high power sure difference is uniformly distributed over the setting, greater overhaul life of the powerplant disc area but the actual case is rather different can be achieved. This should not imply that from this.

The final velocity of the propeller slipstream, the-takeoff rating of the engine should not be V,, is achieved some distance behind the pro- used. Actually, the use of the full maximum peller.

power at takeoff will accumulate less total Because of the nature of the flow pat- engine wear than a reduced power setting at tern produced by the propeller, one half of the total velocity change is produced as the flow the same RPM because of less time required to climb to a given altitude or to accelerate to a reaches the propeller disc. If the complete velocity increase amounts to Za, the flow veloc- given speed.

ity has increased by the amount II at the pro- The most severe rate of wear and fatigue peller disc.

damage occurs at high RPM and low MAP. The propulsive e$icien~, vp, of the ideal propeller could be expressed by the fol- High RPM produces high centrifugal loads lowing relationship: and reciprocating iuertia loads. When the large reciprocating inertia loads are not cush- output power ioned by high compression pressures, critical ?%I= .

mput power resultant loads can be produced. Thus, op- erating time at maximum RPM and MAP must TV be held to a minimum and operation at mari- ‘ I’ = T(V+a) mum RPM and low MAP must be avoided.

where v,=propulsive efficiency AIRCRAFT PROPELLERS T=thrust, lbs.

.The aircraft propeller functions to convert V=fligkt velocity, knots the powerplant shaft horsepower into propul- IJ= velocity increment at the sive horsepower. The basic principles of pro- propeller disc, knots pulsion apply to the propeller in that thrust is Since the final velocity, Vs, is the sum of total produced by providing the airstream a mo- velocity change 2a and the initial velocity, mentum change. The propeller achieves high V,, the propulsive efliciency rearranges to a propulsive ef?iciency by processing a relatively form identical to that for the turbojet.

large mass flow of air and imparting a rela- tively small velocity change. The momentum change created by propeller is shown by the VP’ 1+ k illustration of figure 2.18.

The action of the propeller can be idealized by the assumption that the rotating propeller So, the same relationship exists as with the is simply an actuating disc. As shown in fig- turbojet engine in that high efficiency is de- ure 2.18, the inflow approaching the propeller veloped by producing thrust with the highest disc indicates converging streamlines with an possible mass flow and smallest necessary increase in velocity and drop in pressure. The velocity change.

The actual propeller must be evaluated in a converging streamlines leaving the propeller disc indicate a drop in pressure and increase in more exact sense to appreciate the effect of velocity behind the propeller. The pressure nonuniform disc loading, propeller blade drag change through the disc results from the distri- forces, interference flow between blades, etc.

bution of thrust over the area of the propeller With these differences from the ideal Propeller, NAVWEPS 00-801-80 AIRPLANE PERFORMANCE PROPELLER DISC

--

r

-- --- _ =“,.?*a “1 *- - --- ~3 -- -- PRESSURE CHANGE P;;;lW;;E THROUGH DISC , DISTRIBUTION OF VORTEX ROTATIONAL FLOW COMPONENT mDAT TIP ii- 2.18. Rhuiples of Ropellerr NAVWEPS 00-8OL80 AiRPlANE PERFORMANCE it is more appropriate to define propeller effi- angle, and is a function of some proportion of ciency in the following manner: the flight velocity, V, and the velocity due to rotation which is mD at the tip. The pro- ‘ )~= output propulsive power portions of these terms describe the propeller mput shaft horsepower “advance ratio”, J.

where where vP= propeller efficiency J=propeller advance ratio T= propeller thrust V=flight velocity, ft. per sec.

V= flight velocity, knots n=propeller rotative speed, revolutions BHP= brake horsepower applied to the per sec.

propeller D = propeller diameter, ft.

Many di,fferent factors govern the efficiency of The propeller blade angle, fi (beta), varies a propeller. Generally, a large diameter pro- throughout the length of the blade but a peller favors a high propeller efficiency from representative value is measured at 75 percent the standpoint of large mass flow. However, of the blade length from the hub.

a powerful adverse effect on propeller efficiency Note that the difference between the effec- is produced by high tip speeds and conipressi- tive pitch angle, 4, and the blade angle, 8, bility effects. Of course, small diameter pro- determines an effective angle of attack for the pellers favor low tip speeds. In addition, the propeller blade section. Since the angle of propeller and powerplant must be matched for attack is the principal factor affecting the compatibility of output and efficiency.

efficiency of an airfoil section, it is reasonable In order to appreciate some of the principal to make the analogy that the advance ratio, J, factors controlling the efficiency of a given and blade angle, 8, are the principal factors propeller, figure 2.18 Uustrates the distribu- affecting .propeller efficiency. The perform- tion of rotative velocity along the rotating propeller blade. These rotative velocities add ance of a propelleris typified by the chart of figure 2.19 which- illustrates the variation of to the local inflow velocities to produce a propeller efficiency, ~a, with advance ratio, J, variation of resultant velocity and direction for various values of blade angle, 8. The along the blade. The typical distribution of value of vP for each fl increases with J thrust along the propeller blade is shown with until a peak is reached, then decreases.

the predominating thrust being located on the It is apparent that a fixed pitch propeller may be outer portions of the blade. Note that the selected to provide suitable performance in a propeller producing thrust develops a tip vortex similar to the wing producing lift. narrow range of advance ratio but efficiency would suffer considerably outside this range.

Evidence of this vortex can be seen by the con- densation phenomenon occurring at this Ioca- In order to provide high propeller efficiency through a wide range of operation, the pro- tion under certain atmospheric conditions.

peller blade angle must be controllable.

The component velocities at a given propeller The most convenient means of controlling the blade section are shown by the diagram of propeller is the provision of a constant speed figure 2.18. The inflow velocity adds vec- governing apparatus.

torially to the velocity due to rotation to pro- The constant speed gov- duce an inclination of the resultant wind with erning feature is favorable from the standpoint respect to the planes of rotation. This incli- of engine operation in that engine output and nation is termed + (phi), the effective pitch efficiency is positively controlled and governed.

NAVWEPS OO-ROT-RO AIRPLANE PERFORMANCE The governing of the engine-propeller combi- a single feathered propeller is a relatively small nation will allow operation throughout a wide contribution to the airpfane total drag.

range of power and speed while maintaining At smaller blade angles near the Rat pitch efficient operation.

position, the drag added by the propeller is If the envelope of maximum propeller dfi- very large. AC these small blade angles, the ciency is available, the propulsive horsepower propeller windmilling at high RPM can create available will appear as shown in the second such a tremendous amount of drag that the chart of figure 2.19. The propulsive power airplane may be uncontrollable. The propel- available, Pa, is the product of the propeller ler windmilling at high speed in the low range efficiency and applied shaft horsepower.

of blade angles can produce an increasein para- site drag which may be as great as the parasite drag of the basic airplane. An indication of this powerful drag is seen by the hclieopter in autorotation. The windmilling rotor is ca- pable of producing autorotation rates ofdcscent which approach that of a parachute canopy The propellers used on most large reciprocating with the identical disc area laading. THUS, engines derive peak propeller efficiencies on the the propeller windmilling at high speed and order of s,=O.85 to 0.88.

Of course, the peak small blade angle can produce an cffccti+e values are designed to occur at some specific drag coefficient of the disc area which compares design condition. For example, the selection with tha~t of a parachute canopy. The drag of a propel!er for a !ong rasge transport wsuld and yawing moment caused by loss of power require matching of the engine-propeller com- at high engine-propeller speed is considerable bination for peak efhciency at cruise condjtion.

and the transient yawing displaccmcnt of the On the other hand, selection of a propeller for aircraft’ may produce critical loads for the a utility or liaison type airplane would require vertical tail.

For this reason, automatic matching of the engine-propeller combination feathering may be a necessity rather than a to achieve high propulsive power at low speed luxury.

and high power for good takeoff and climb The large drag which can be produced by performance.

the rotating propeller can be utilized to im- Several special considerations must be made prove the stopping performance of the air- for the application of aircraft propellers. In plane. Rotation of the propekr blade to the event of a powerplant malfunction or small positive values or negative values with failure, provision must be made to streamline applied power can produce large drag or re- the propeller blades and reduce drag so that verse thrust. Since the thrust capability of the flight may be continued on the remaining op- propeller is quite high at low speeds, very erating engines. This is accomplished by high deceleration can be provided by reverse feathering the propeller blades which .stops thrust alone, rotation and incurs a minimum of drag for the The qs&zg limitatiar of the pmpcllcr are inoperative engine. The necessity for feather- closely associated with those of the Rower- ing is illustrated in figure 2.19 by the change plant. Overspeed conditions are critical be-

in equivalent parasite area, Af, with propeller

cause of the large centrifugal loads and blade blade angle, 8, of a typical instaliation.

When twisting moments produced by an excessive the propeller blade angle is in the feathered rotative speed.

In addition, the propeller position, the change in parasite drag is at a blades will have various vibratory modes and minimum and, in the case of a typical multi- certain operating limitations may hc necessary engine aircraft, the added parasite drag from to prevent exciting resonant conditions.

NAVWEPS 00-801-80 AIRPLANE PERFORMANCE PRO~‘ ELLER EFFICIENCY ENVELOPE OF MAXIMUM EFFICIENCY PROPELLER EFFICIENCY -lP -I PROPELLER ADVANCE RATIO, J ... ..... .... ... ..

. . . ...._.........._................ ::::::::::::::::::::::::::::::::::::::::::::~~:~~~~~~~~~~~~~~~~~~~~::::::::~::::::: ... ........ . -.-................::::::::: . . .... ... .. ... ... .. ... .. ... .. ... .1: ... ... .. ...... .. ... ..... .... .. ... ... .. .... .. ....~.~~....................................

liiiiiii!lililliiiiiiiliiiii8iiliili::::::::::::::::::::::::::::~~~~~~~~~~~ :::::::::::::::::::::::::~~:::::::::::::.... ... .. ...... .. ... ..... ... ... ... ... .. .... . .... . .

.,............._............................................. I..

POWER AVAILABLE --.

\ BHP \ --- POWER AVAILABLE HP VELOCITY, KNOTS :::::::::::::::::::::::::::::::::::::::~:::::::::::::::::::::::::::::~::::::::::::::::::::::::::::::::.::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~~~~~~~~~~.~: ::::::::::::::::::::::::::::::::::::::::::::::::::::::~::::::::::::::::::::::::::::::::::::::::::::::l::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::............~...,..~..~ PROPELLER DRAG CONTRIBUTION CHANGE IN EQUIVALENT PARASITE AREA Af FEATHEREO POSITION - 30 45 60 0 I5 90 PROPELLER BLADE ANGLE,P Figure 2.79. Propeller Operation MAWEPS 00-801-80 AIRPLANE PERFORMANCE the airspeed corresponding to point A, the power or thrust required curves define a par- ticular value of thrust or power that must be made available from the powerplant ~to achieve The various items of airplane performance equilibrium. Some different airspeed such as result from the combination of airplane and that corresponding to point B changes the powerplant characteristics. The aerodynamic value of thrust or power required to achieve characteristics of the airplane generally define equilibrium. Of course, the change of air- the power and thrust requirements at various speed to point B also would require a change conditions of flight while the powerplant in angle of attack to maintain a constant lift characteristics generally define the power and equal to the airplane weight. Similarly, to thrust available at various conditions of flight.

establish airspeed and achieve equilibrium at The matching of the aerodynamic configura- point C will require a particular angle of attack tion with the powerplant will be accomplished and powerplant thrust or power.

In this case, to provide maximum performance at the speci- flight at point C would be in the vicinity of fic design condition, e.g., range, endurance, the minimum flying speed and a major portion climb, etc.

of the ,thrust or power required would be due STRAIGHT AND LEVEL FLlGHT to induced drag.

The maximum level flight speed for the air- When the airyJane is in steady, level flight, plane will be obtained when the power :or the condition of equilibrium must prevail.

thrust required equals the maximum power or The unaccelerated condition of flight is thrust available from the powerplant. The achieved with the airplane trimmed for lift minimum level flight airspeed is not usually equal to weight and the powerplant set for a defined by thrust or power requirement since thrust to equal the airplane drag. In certain conditions of, stall or stability and control conditions of airplane performance it is con- problems generally predominate.

venient to consider the airplane requirements by the thnr$t required (or drag) while in other CLIMB PERFOLWANCE cases it is more applicable to consider the During climbing flight, the airplane gains power re@red. Generally, the jet airplane will potential energy by virtue of elevation. This require consideration of the thrust required increase in potential energy during a climb is and the propeller airplane will require consid- or a combination, of two provided by one, eration of the power required. Hence, the means: (1) expenditure of propulsive energy airplane in steady level flight will require lift above that required to maintain level flight or equal to weight and thrust available equal to (2) expenditure of airplane kinetic energy, i.e., thrust required (drag) or power available equal loss of velocity by a zoom.

Zooming for alti- to power required.

tude is a transient process of trading kinetic The variation of power required and thrust energy for potential energy and is of considera- required with velocity is illustrated in figure ble importance for airplane configurations 2.20. Each specific curve of power or thrust which can operate at very high levels of kinetic required is valid for a particular aerodynamic energy. However, the major portions of climb configuration at a given weight and altitude.

performance for most airplanes is a near steady These curves define the power or thrust re- process in which additional propulsive energy quired to achieve equilibrium, Jift-equal- is converted into potential energy. The funda- weight, constant altitude flight at various mental parts of airplane climb performance in- airspeeds. As shown by the curves of figure volve a flight condition where the airplane is 2.20, ifit is desired to operate the airplane at in equilibrium but not at constant altitude.

NAVWEPS OO-ROT-80 AIRPLANE PERFORMANCE THRUST c WEIGHT THRUST REQUIRED -MAXIMUM LEVEL FLIGHT SPEED I VELOCITY POWER REQUIRED - MAXIMUM LEVEL FLIGHT SPEED VELOCITY Figure 2.20. Level Right Pedormancc NAVWEPS OO-SOT-80 AIRPLANE PERFORMANCE The forces acting on the airplane during a depends on the difference between thrust and drag (T-D), or excess thrust. Of course, climb are shown by the illustration of figure 2.21. When the airplane is in steady flight when the excess thrust is zero (T-D=0 or with moderate angle of climb, the vertical T=D), the inclination of, the flight path is component of lift is very nearly the same as the zero-and the airplane is in steady, level flight.

actual lift. When the thrust is greater than the drag, the Such climbing flight would exist excess thrust will allow a climb angle depend- with the lift very nearly equal to the weight.

ing on the value of excess thrust.

The net thrust of the powerplant may be in- Also, when the thrust is less than the drag. the deficiency clined relative to the flight path but this effect of thrust will allow an angle ~of descent.

will be neglectec! for the sake of simplicity.

The most immediate interest in the climb Note that the weight of the aircraft is vertical angle performance involves obstacle clearance.

but a component of weight will act aft along The maximum angle of climb would occur the flight path.

where there exists the greatest difference be- If it is assumed that the aircraft is in a steady tweenthrust available and thrust required, i.e., climb with essentially small inclination of the maximum (T-D). Figure 2.21 illustrates the flight path, the summation of forces along the climb angle performance with the curves of flight path resolves to the following: thrust available and thrust required versus Forces forward= Forces aft velocity. The thrust required, or drag, curve is nss,~pued to be ppw=n*~r;.rP nc CnmP+-+a!

y.“- ..I‘ ..&. c “I ““IILL ‘ , y airplane configuration which could be powered where by either a turbojet or propeller type power- T= thrust available, lbs.

plant. The thrust available curves included D= drag, lbs.

are for a characteristic propeller powerplant W= weight, lbs.

and jet powerplant operating at maximum v=flight path inclination or angle ,of output.

climb, degrees (“gamma”) The thrust curves for the representative pro- peller aircraft show the typical propeller thrust This basic relationship neglects some of the which is high at low velocities and decreases factors which may be of importance for air- planes of very high climb performance. For with an. increase in velocity. For the pro- example, a more detailed consideration would peiler powered airplane, the maximum excess account for the inclination of thrust from the thrust and angle of climb will occur at some flight path, lift not equal to weight, subse- speed just above the stall speed. Thus, if it quent change of induced drag, etc.

However, is necessary to clear an obstacle after takeoff, this basic relationship will define the principal the propeller powered airplane will attain factors affecting climb performance. With maximum angle of climb at an airspeed con- this relationship established by the condition veniently close to-if not at-the takeoff of equilibrium, the following relationship speed.

exists to express the trigonometric sine of the The thrust curves for the representative jet climb angle, y: aircraft show the typ~ical turbojet thrust which T-D sin y=- is very nearly constant ~with speed. If the W thrust available is essentially constant with This relationship simply states that, for a speed, the maximum excess thrust and angle

given weight airplane, the angle of climb (7)

of climb will occur where the thrust required NAVWEPS OD-80T-80 AIRPLANE PERFORMANCE COMPONENT OF WEIGHT w SIN ,-- ALONG FLIGHT PATH __---- THRUST - - -- AVAILABLE AVAILABLE JET ACFT AND THRUST REOUIRED LBS.

VELOCITY, KNOTS l=‘ a JET POWER Pr, POWER REOUIRED AVAILABLE AND POWER POWER AVAILABLE PROP ACFT REolYLRED SPEED FOR MAX R.C., JET SPEED FOR MAX R.C., PROP I VELOCITY, KNOTS Figure 2.21. Climb Performance NAVWEPS 00-801-80 AIRPLANE PERFORMANCE is at a minimum, (LID),. Thus, for maxi- where RC=rate of climb, f.p.-.

mum steady-state angle of climb, the turbojet P11=power available, h.p.

aircraft would be operated at the speed ,for Pr=power re uired, h.p.

(L/D),. This poses somewhat of a problem W=weight, 1 % s in determining the proper procedure for ob- V=true airspeed, knots stacle clearance after takeoff. If the obstacle and is a considerable distance from the takeoff 33,000 is the factor converting horsepower to ft-lbs/min point, the problem is essentially that of a long 101.3isthefactorconvertingknocstof.p.m.

term gain and steady state conditions will pre- The above relationship states that, for a given dominate. That is, acceleration from the take- weight airplane, the rate af climb (RC) depends off speed to (L/D), speed will be favorable on the difference between the power available because the maximum steady climb angle can and the power required (Pd- Pr), or excess be attained. However, if the obstacle is a rela- power. Of course, when the excess power is tively short distance from the takeoff point, zero (Pa-Pr=O or Pa==PI), the rate of climb the additional distance required to accelerate is zero and the airplane is in steady level flight.

to (L/D),, speed may be detrimental and the When the power available is greater than the resulting situation may prove to be a short power required, the excess power will, allow a term gain problem. In this case, it may prove rate of climb specific to the magnitude of excess necessary to begin climb out at or near the take- power. Also, when the power available is off speed or hold the aircraft on the runway less than the power required, the deficiency of for extra speed and a subsequent zoom. The power produces a rate of descent.

problem is su&ciently varied that no general This rela- tionship provides the basis for an important conclusion can be applied to all jer aircraft and axiom of flight technique: “For the conditions particular procedures are specified for each air- of steady flight, the power setting is the pri- craft in the Flight Handbook.

mary control of rate of climb or descent”.

Of greater general interest in climb per- One of the most important items of climb

formance are the factors which affect the rate of

performance is the maximum rate of climb.

climb. The vertical velocity of an airplane By the previous equation for rate of climb, depends on the flight speed and the inclination maximum rate of climb would occur where of the flight path. In fact, the rate of climb there exists the greatest difference between is the vertical component of the flight path power available and power required, i.e., velocity. By the diagram of figure 2.21, the maximum (Pa- Pr). Figure 2.21 illustrates following relationship is developed: the climb rate performance with the curves of RC- 101.3 V sin y power available and power required versus since velocity. The power required curve is again a representative airplane which could be powered by either a turbojet or propeller type power- then plant. The power available curves included RC=101.3 V are for a characteristic propeller powerplant and jet powerplant operating at maximum a& 2-v output.

with Pa=% The power curves for the representative pro- peller aircraft show a variation of propulsive and Pr=& power typical of a reciprocating engine-pro- peller combination. The maximum rate of climb for this aircraft will occur at some speed RevId J4mwy 1ws NAVWEPS 06801-80 AIRPLANE PERFORMANCE of climb but the airplane must be operated at near the speed for (L/D&-. There is no direct some increase of speed to achieve the ,smaller relationship which establishes this situation peak climb rate (unless the airplane is compres- since the variation of propeller efficiency is the principal factor accounting for the variation sibility limited).

of power available with velocity. In an ideal The effect of altitude on climb performance is illustrated by the composite graphs of figure sense, if the propeller efficiency were constant, 2.22. Generally, an increase in altitude will maximum rate of climb would occur at the increase the power required and decrease the speed for minimum power required. How- power available. Hence, the climb perform- ever, in the actual case, the propeller efficiency ance of an airplane is expected to be greatly of the ordinary airplane will produce lower power available at low velocity and cause the affected by altitude. The composite chart of climb performance depicts the variation with maximum rate of climb to occur at a speed altitude of the speeds for maximum rate of greater than that for minimum power required.

climb, maximum angle of climb, and maximum The power curves for the representative. jet and minimum level flight airspeeds. As alti- aircraft show the near linear variation of power tude is increased, these various speeds finally available with velocity. The maximum rate converge at the absolute ceiling of the airplane.

of climb for the typical jet airplane will occur at some speed much higher than that for max- At the absolute ceiling, there is no excess of imum rate of climb of the equivalent propeller power or thrust and only one speed will allow powered airplane. In part, this is accounted steady level flight. The variation of rate of for by the continued increase in power avail- climb and maximum level flight’ speed’with able with speed. Note that a 50 percent in- altitude for the typical propeller powered air- increase in thrust by use of an afterburner may plane give evidence of the effect of supercharg- cause an increase in rate of climb of approxi- ing. Distinct aberrations in these curves take mately 100 percent. place at the supercharger critical altitudes and The climb performance of an airplane is ~blower shift points. The curve of time to affected by many various factors. The con- climb is the result of summing.up the incre- ditions of maximum climb angle or climb rate ments of time spent climbing through incre- occur at specific speeds and variations in speed ments of altitude. Note that approach to the will produce variations in climb performance.

absolute ceiling produces tremendous increase Generally, there is sufficient latitude that small in the time curve.

variations in speed from the optimum do not Specific reference points are established by produce large changes in climb performance these composite curves of climb performance.

and certain operational items may require Of course, the absolute ceiling of the airplane speeds slightly different from the optimum. produces zero rate of climb. The serviceceiling Of course, climb performance would be most is specified as the altitude which produces a critical at high weight, high altitude, or dur- rate of climb of 100 fpm. The altitude which Then, opti- ing malfunction of a powerplant. produces a rate of climb of 500 fpm is termed mum climb speeds are necessary. A change the combatceiling. Usually, these specific refer- in airplane weight produces a twofold effect ence points are provided for the airplane at on climb performance. First, the weight, W, the combat configuration or a specific design appears directly in denominator of the equa- configuration.

tions for ,both climb angle and climb rate. The composite curves of climb performance for the typical turbojet airplane are shown in In addition, a change in weight will alter the figure 2.22. One particular point to note is drag and power required. Generally, an in- crease in weight will reduce the maximum rate the more rapid decay of climb performance NAVWEPS C&801-80 AIRPLANE PERFORMANCE TYPICAL PROPELLER AIRCRAFT ALTlTUOE PERFORMANCE RATE OF,CL!MB_, _- .

.

tiAXlMUM LEVEL FLIGHT SPEED HIGH BLOWER CRITICAL ALTITUDE FEE0 FOR MA% R c LOW BLOWER CRITICAL ALTITUDE

= y$y VELOCITY, KNOTS

-e-*-- TROPOPAUSE t- MAXIMUM LEVEL \ \ FLIGHT SPEED \ -RATE OF CLIMB \ \ \ \

I

I I I

b

VELOCITY, KNOTS -8 POWER OFF DESCENT PERFORMANCE POWER REQUIRED HP MINIMUM POWER REP’ D

I VELOCITY, KNOTS

Figure UP, Climb ad Desceni Pedormome lS7 NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE with altitude above the tropopause. This is conditions of steady level flight will define due in great part to the more rapid decay of various rates of fuel flow throughout the range engine thrust in the stratosphere. of flight speed. The first graph of figure 2.23 During a power off descent the deficiency of illustrates a typical variation of fuel flow versus thrust and power define the angle of descent velocity. The specific range can be defined by and rate of descent. TWO particular points the following relationship: are of interest during a power off descent: nautical miles minimum angle of descent and minimum rate specific raw= lbs, of fuel of descent. The minimum angle of descent would provide maximum glide distance through nautical miles/hr.

the air. Since no thrust is available from the ‘ pecific range= lbs. of fuel/hr.

power plant, minimum angle of descent would be obtained at (L/D)-. At (L/D),, the thus, deficiency of thrust is a minimum and, as velocity, knots specific range = shown by figure 2.22, the greatest proportion fuel flow, lbs. per hr.

between velocity and power required is ob- If maximum specific range is desired, the flight tained. The minimum rate of descent in condition must provide a maxinium of velocity power off flight is obtained at the angle of fuel flow. This particular point would be attack and airspeed which produce minimum located by drawing .a straight line from the power required. For airplanes of moderate origin tangent to the curve of fuel flow versus aspect ratio, the speed for minimum rate of velocity.

descent is approximately 75 percent of the The general item of range must be clearly speed for minimum angle of descent distinguished from the item of endurance. The item of range involves consideration of flying RANGE PERFORMANCE distance while enduranceinvolves consideration The ability of an airplane to convert fuel of flying time. Thus, it is appropriate to define energy into flying distance is one of the most a separate term, “specific endurance.” important items of airplane performance. The flight hours problem of eficient range operation of an air- specific endurance= lb. of fuel plane appears of two general forms in flying operations: (1) to extract the maximum flying distance from a given fuel load or (2) to fly a flight hours/hr.

specific endurance = specified distance with minimum expenditure lbs. of fuel/hr.

of fuel. An obvious common denominator for then, each of these operating problems is the “spe- specific endurance= cific range, ” nautical miles of flying distance fuel flow, lbs. per hr.

per lb. of fuel. Cruise flight for maximum range cond.itions should be conducted so that By this definition, the specific endurance is the airplane obtains maximum specific range s&ply the reciprocal of the fuel ~flow. Thus, throughout the flight.

.ifl.maximum endurance is desired, the flight GENERAL RANGE PERFORMANCE.

condition ‘ must provide a minimum of fuel The principal items of range performance can flow. This point is readily appreciated as the be visualized by use of the illustrations of figure lowest point of the curve of fuel flow versus 2.23. From the characteristics of the aero- velocity. Generally, in subsonic performance, dynamic configuration and the powerplant, the the speed at which maximum endurance is NAVWEPS 00-501-50 AIRPLANE PERFORMANCE I APPLICABLE FOR A PARTICULAR: WEIGHT ALTITUDE MAXIMUM CONFIGURATION FUEL ENDURANCE FLOW LINE FROM ORIGIN TANGENT TO CURVE VELOCITY, KNOTS 100% MAXIMUM -- 99% MAXIMUM RANGE SPECIFIC APPLICABLE FOR A PARTICLAR RANGE -CONFIGURATION -ALTITUDE -WEIGHT VELOCITY, KNOTS AREA REPRESENTS Figure 2.23. Geneml Range Performance NAVWEPS oo-80~~80 AIRPLANE PERFORMANCE initial weight of the airplane will require spe- obtained is approximately 75 percent of the speed for maximum range. cific values of airspeed, altitude,’ and power A more exact analysis of range may be ob- setting to produce the recommended cruise tained by a plot of specific range versus velocity condition. As fuel is consumed and the air- similar to the second graph of figure 2.23. Of plane gross weight decreases, the optimum ai,r- course, the source of these values of specific speed and power setting may decrease or the range is derived by the proportion of velocity optimum altitude may increase. Also, the optimum specific range will increase. The and fuel flow from the previous curve of fuel flow versus velocity. The maximum specific pilot must provide the proper cruise control technique to ensure that the optimum condi- range of the airplane is at the very peak of the curve. Maximum endurance point is located tions are maintained.

by a straight line from the origin tangent to The final graph of figure 2.23 shows a typical the curve of specific range versus velocity. variation of specific range with gross weight This tangency point defines a maximum of for some particular cruise operation. At the (nmi/lb.) per (nmi/hr.) or simply a maximum beginning of cruise the gross weight is high of (hrs./lb.). and the specific range is low. As fuel is con- While the very peak value of specific range sumed, and the gross weight reduces, the would provide maximum range operation, long specific range increases. .This’ type of curve range cruise operation is generally recom- relates the range obtained by the expenditure mended at some slightly higher airspeed. of fuel .by the crosshatched area between the Most long range cruise operation is conducted gross weights at beginning and end of cruise.

at the flight condition which provides 99 per- For example, if the airplane begins cruise at cent of the absolute maximum specific range. 18,500 Jbs. and ends cruise at 13,000 lbs., 5,500 The advantage of such operation is that 1 lbs. of fuel is expended. If the average spe- percent of range is traded for 3 to 5 percent cific range were 0.2 nmi/Jb., the total range higher cruise. velocity. Since the higher cruise would be: speed has a great number of advantages, the range=(0.2)$ (5,500) lb.

small sacrifice of range is a fair bargain. The curves of specific range versus velocity are = 1,100 nmi.

affected by three principal variables: airplane Thus, the total range is dependent on both gross weight, altitude, and the external aero- dynamic configuration of the airplane. These the fuel available and the specific range. When curves are the source of range and endurance range and economy of operation predominate, operating data and are included in the per- the pilot must ensure that the airplane will be formance section of the flight handbook. operated at the recommended long range cruise “Cruise control” of an airplane implies that condition. By this procedure, the airplane the airplane is operated to maintain the recom- will be capable of its,maximum design operat- ing radius or flight distances less than the mended long range cruise condition through- maximum can be achieved with a maximtim of out the flight. Since fuel is consumed during cruise, the gross weight of the airplane will fuel reserve at the destination.

RANGE, PROPELLER DRIVEN AIR- vary and optimum airspeed, altitude, and power setting can vary, Generally, “cruise PLANES. The propeller driven airplane com- control” means the control of optimum air- bines the propeller with the reciprocating speed, altitude, and power setting to maintain engine or the gas turbine for propulsive power.

In the case of either the reciprocating engine or the 99 percent maximum specific range condi- tion. At the beginning of cruise, the high the gas turbine combination, powerplant fuel NAVWEPS OS80140 AIRPLANE PERFORMANCE flow is determined mainly by the shaft poluet

v*- E

put into the propeller rather than thrust. Thus,

-4 VI K

the powerplant fuel flow could be related di-

w* s’ *

pr*

rectly to power required to maintain the air-

PC W I

-=H

plane in steady, level flight. This fact allows study of the range of the propeller powered SRs WI -=- airplane by analysis of the curves of power SRI W, required versus velocity.

where Figure 2.24 illustrates a typical curve of condition (1) applies to some known condi- power required versus velocity which, for the tion of velocity, power required, and propeller powered airplane, would be analo- specific range for (L/D),., at some basic gous to the variation of fuel flow versus veloc- weight, WI ity. Maximum endurance condition would be condition (2) applies to some new values of obtained at the point of minimum power re- velocity, power required, and specific quired since this would require the lowest fuel range for (L/D),., at some different flow to keep the airplane in steady, level flight.

weight, WI Maximum range condition would occur where and, the proportion between velocity and power re- V= velocity, knots quired is greatest and this point is located by W= gross weight, Jbs.

a straight line from the origin tangent to the Pr=power required, h.p.

curve.

SK= specific range, nmi/lb.

The maximum range condition is obtained Thus a 10 percent increase in gross weight at maximum lift-drag ratio and it is important would create: to note that (L/D),, for a given airplane a 5 percent increase in velocity configuration occurs at a particular angle of a 15 percent increase in power required attack and li5t coefficient and is unaffected by a 9 percent decrease in specific range weight or altitude (within compressibility when flight is maintained at the optimum con- limits). Since approximately 50 percent of ditions of (L/D),.,. The variations of veloc- the total dra.g a’ t (L/D)* is induced drag, the ity and power required must be monitored by the pilot as part of the cruise control to main- propeller powered airplane which is designed tain .(L/D),.+ When the airplane fuel weight specifically i3r IJong range will have a strong is a small part of the gross-weight and the range preference for rbe thigh aspect rario planform.

is small, then cruise control procedure can be The effect ,df tihe variation of airplane gross simplified to essentially a constant speed and weight is illustrated by the second graph of power setting throughout cruise. However, figure 2.24. ‘ The flight condition of (L/D),., the long range airplane has a fuel weight which is achieved a’ t,one-particular value of lift coefIi- is a conside’ rable part of the gross weight and cient for a given airplane configuration.

cruise control procedure must employ sched- Hence, a variation of gross weight will alter uled airspeed and power changes to maintain the values of airspeed, power required, and spe- optimum range conditions.

cific range obtained at (L/D)m.r. If a given The effect of altitude on the range of the configuration ‘ of airplane is operated at con- propeller powered airplane may be appreciated stant altitude and the lift coefficient for by inspection of the final graph of figure 2.24.

the following relationships will If a given configuration of airplane is operated WDL at constant gross weight and the lift coefficient awb : NAVWEPS OO-ROT-RO AIRPLANE PERFORMANCE GENER,AL. RANGE CONDITIONS PROPELLER AIRPLANE POWER APPLICABLE FOR REO’ D A PARTICULAR -WEIGHT MAXIMUM HP -ALTITUDE ENDURANCE -CONFIGURATION VELOCITY, KNOTS EFFECT OF GROSS WEIGHT HlGHER WT.

POWER REO’ D CONSTANT ALTITUDE VELOCITY, KNOTS EFFECT OF ALTITUDE EFFECT OF ALTITUDE AT ALTITUDE AT ALTITUDE

A

SEA LEVEL SEA LEVEL t CONSTANT CONSTANT WEIGHT WEIGHT HP HP I VELOCITY, KNOTS Figure 2.24. Range Performance, Propeller Aircraft NAWEPS oo-EOT-80 AWPLANE PERFORMAhlCE If compressibility effects are negligible, any a change in altitude will produce for WD)m.z, variation of ~peci)c range with altitude is strictly a the following relationships: function of engine-propeller pcrformanCC.

The airplane equipped with the reciprocating engine will experience very little, if any, variation of specific range with altitude at low altitudes, There is negligible variation of brake specific fuel consumption for values of where BHP below the maximum cruise power rating condition (I) applies to some known condi- of the powerplant which is the auto-lean or tion of velocity and power required for Thus, manual lean range of engine operation.

at some original, basic altitude W ’ ),,,,,z an increase in altitude will produce a decrease condirion (2) applies to some new values of in specific range only when the increased power velocity and power required for (L/D),, requirement exceeds the maximum cruise power at some different altitude rating of the powerplants. One advantage of and supercharging is that the cruise power may be V= velocity, knots (TAX, of course) maintained at high altitude and the airplane Pr=power required, h.p.

may achieve the range at high altitude with o=altitude density ratio (sigma) the corresponding increase in TAS. The prin- cipal differences in the high altitude cruise and Thus, if flight is conducted at 22,000 ft.

low altitude cruise are the true airspeeds and (o=O.498), the airplane will have: climb fuel requirements.

a 42 percent higher velocity The airplane equipped with the turboprop a 42 percent higher power required powerplant will exhibit a variation of specific than when operating at sea level. Of course, range with altitude for two reasons. First, the greater velocity is a higher TAS since the the specific fuel consumption (c) of the turbine airplane at a given weight and lift coefficient engine improves with the lower inlet tem- will require the same PAS independent of peratures common to high altitudes. Also, altitude. Also, the drag of the airplane at the low power requirements to achieve opti- altitude is the same as the drag at sea level but mum aerodynamic conditions at low altitude the higher TAS causes a proportionately necessitate engine operation at low, inefficient greater power required. Note chat the same The increased power require- output power.

straight line from the origin tangent to the sea ments at high .altitudes allow the turbine level power curve also is tangent to the powerplant to operate in an efficient output altitude power curve.

range. Thus, while the airplane has no The effect of altitude on specific range can be particular preference for altitude, the power- appreciated from the previous relationships.

plants prefer the higher altitudes and cause If a change in altitude causes identical changes an increase in specific range with altitude.

in velocity and power required, the proportion Generally, the upper limit of altitude for of velocity to power required would be un- efficient cruise operation is defined by airplane changed. This fact implies that the specific gross weight (and power required) or com- range of the propeller powered airplane would presslbility effects.

be unaffected by altitude. In the actual case, The optimum climb and descent for the this is true to the extent that powerplant specif- propeller powered airplane is affected by ic fuel consumption (c) and propeller efficiency many different factors and no general, all- (qp) are the principal factors which could inclusive relationship is applicable. Hand- book data for the specific airplane and various cause a variation of specific range with altitude.

NAVWEPS OO-SOT-80 AIRPLANE PERFORMANCE On the other hand, since approximately 75 operational factors will define operating pro- percent of the total drag is parasite drag, the cedures.

turbojet airplane designed specifically for long RANGE, TURBOJET AIRPLANES. Many different factors influence the range of the range has the special requirement for great aerodynamic cleanness.

turbojet airplane. In order to simplify the analysis of the overall range problem, it is The effect of the variation of airplane gross weight is illustrated by the second graph convenient to separate airplane factors from powerplant factors and analyze each item of figure 2.25. The flight condition of D IMI is achieved at one value of lift independently. An analogy would be the (mc 1 coefbcient for a given airplane in subsonic study of “horsecart” performance by separat- “cart” performance from “horse” per- flight. Hence, a variation of gross weight will ing formance to distinguish the principal factors alter the values of airspeed, thrust required, which affect the overall performance. and specific range obtained at ,(&/CD)-. If a given configuration is operated at constant In the case of the turbojet airplane, the fuel flow is determined mainly by the thrust altitude and lift coefficient the following re-~ rather than power. Thus, the fuel flow could lationships will apply: be most directly related to the thrust required to maintain the airplane in steady, level flight.

.This fact allows study of the turbojet powered airplane by analysis of the curves of thrust required versus velocity. Figure 2.25 illu- strates a typical curve of thrust required versus velocity which would be (somewhat) analo- SR2 -= (constant .altitude) gous to the variation of fuel flow versus veloc- SRI ity. Maximum endurance condition would where be obtained at (L/D)- since this would incur condition (1) applies to some! known condi- the lowest fuel flow to keep the airplane in tion of velocity, thrust required, and steady, level flight. Maximum range condition specific range for (&/CD)- at some would occur where the proportion between basic weight, Wi velocity and thrust required is greatest and condition (2) applies to some new values of this point is located by a straight line from velocity, thrust required, and specific the origin tangent to the curve.

range for (&/CD)- at some different The maximum range is obtained at the aero- weight, W, dynamic condition which produces a maximum proportion between the square root of the and lift coefficient (CJ and the drag coe&cient V= velocity, knots (CD), or (&/CD)-. In subsonic perform- W=gross weight, lbs.

Tr= thrust required, lbs.

D - occurs at a particular value ance, (G/C > .SR= specific range, nmi/lb.

angle of attack and lift coefficient and is un- affected by weight or altitude (within com- Thus, a 10 percent increase in gross weight pressibility limits). At this specific aerody- would create: namic condition, induced drag is approxi- a 5 percent increase in velocity mately 25 percent of the total drag so the a 10 percent increase in thrust required turbojet airplane designed for long range does a 5 percent decrease in specific range not have the strong preference for high aspect when flight is maintained at the optimum con- ratio planform like the propeller airplane. ditions of (&/CD)-. Since most jet airplanes NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE GENERAL RANGE CONDITIONS TURBOJET MAXIMUM MAXIMUM ENDURANCE THRUST APPLICABLE FOR REO’ D A PARTICULAR LBS -WEIGHT -ALTITUDE -CONFIGURATION VELOCITY, KNOTS EFFECT OF GROSS WEIGHT THRUST REO’ D LBS CONSTANT ALTITUDE EFFECT OF ALTITUDE t AT ALTITUDE .%A LEVEL SEA LEVEL THRUST / REP’ 0 LBS CONSTANT WEIGHT c VELOCITY. KNOTS VELOCITY. KNOTS Ftgure P.25. Rangt Performoncr, Jet Aircraft NAVWEPS 00-801-80 AIRPLANE PERFORMANCE same thrust required must be obtained with a have a fuel weight which is a large part of the gross weight, cruise control procedures will be greater engine RPM.

necessary to account for the changes in opti- At this point it is necessary to consider the mum airspeeds and power settings as fuel is effect of the operating condition on powerplant performance.

consumed. An increase in altitude will im- The effect of altitude on the range of the prove powerplant performance in two respects.

turbojet airplane is of great importance be- First, an increase in altitude when below the cause no other single item can cause such large tropopause will provide lower inlet Gr tem- variations of specific range. If a given con- peratures which redqce the specific fuel con- figuration of airplane is operated at constant sumption (c~). Of course, above the tropo- gross weight and the lift coefficient for pause the specific fuel consumption tends to a change in altitude will produce increase. A; low altitude, the engine RPM (JCL/CDL, the following relationships: necessary to produce the required thrust is low and, generally, well below the normal rated vz - -= 3 value. Thus, a second benefit of altifude on J VI .Y* engine performance is due to the increased RPM required to furnish cruise thrust. An Tr=constant (neglecting compressibility increase in engine speed to the normal rated effects) value will reduce the specific fu,el consumption.

JR.2 - 3 (neglecting factors affecting en- The increase in specific range with altitude -= JR1 rJ* gine performance) J of the turbojet airplane can be attributed to these three factors: where (1) An increase in altitude will increase the proportion of (V/Tr) and provide a greater condition (I) applies some known condition TAS for the same TY.

of velocity, thrust required, and specific (2) An increase in altitude in the tropo- range for (&QCD),, at some original, sphere will produce lower inlet air temperature basic altitude.

which reduces the specific.fuel consumption.

condition (2) applies to some new values of (3) An increase in altitude requires in- velocity, thrust required, and specific creasedengine RPM to provide cruise thrust range for (fi/CD)mm at some different and the specific fuel consumption reduces as altitude.

normal rated RPM is approached.

and The combined effect of these three factors de- V= velocity, knots (TAX, of course) fines altitude as the one most important item Tr= thrust required, lbs.

affecting the specific range of the turbojet air- JR= specific range, nmi/lb.

ane. As an example of this combined’ effect, Pl a=altitude density ratio (sigma) the typical turbojet airplane obtains a specific range at 40,ooO ft. which is approximately 150 Thus, if flight is conducted at 40,000 ft.

percent greater than that obtained at sea leirel.

(u=O.246), the airplane will have: The increased TAS accounts for approxi- a 102 percent higher velocity mately two-thirds of this benefit while in- the same thrust required creased engine performance (reduced cJ ,~ ‘ ac- a 102 percent higher specific range counts for the other one-third of the benefit.

(even when the beneficial effects of altitude For example, at sea level the maximum spe- on engine performance are neglected) cific range of a turbojet airplane may be 0.1 than when operating at sea level. Of course, nmi/lb. but at 40,000 ft. the maximum specific the greater velocity is a higher TAJ and the range would be approximately 0.25 nmi/lb.

NAVWEPS OO-BOT-RO AIRPLANE PERFORMANCE From the previous analysis, it is apparent not restrained to a particular altitude, main- that the cruise altitude of the turbojet should taining the same lift coeAicient and engine be as high as possible within compressibility speed would allow the airplane to climb as the or thrust limits. Generally, the optimum alti- gross weight decreases. Since altitude gen- erally produces a beneficial effect on range, the tude to begin cruise is the highest altitude at which the maximum continuous thrust can climbing C&SC implies a more efficient flight path.

provide the optimum aerodynamic conditions.

The cruising flight of the turbojet airplane Of course, the optimum altitude is determined mainly by the gross weight at the begin of will begin usually at or above the tropopause cruise. For the majority of turbojet airplanes in order to provide optimum range conditions.

this altitude will be at or above the tropopause If flight is conducted at (a/&)-, optimum for normal cruise configurations. range will be obtained at specific values of lift Most turbojet airplanes which have rran- coefficient and drag coefficient. When the air- sonic or moderate supersonic performance will plane is fixed at these values of CL and C, and obtain maximum range with a high subsonic the TAS is held constant, both lift and drag are cruise. However, the airplane designed spe- directly proportional to the density ratio, (T.

cifically for high supersonic performance will Also, above the tropopause, the thrust is pro- portional to .J when the TAS and RPM are con- obtain maximum range with a supersonic stant. As a result, a reduction of gross weight cruise and subsonic operation will cause low by the expenditure of fuel would allow the lift-drag ratios, poor inlet and engine perform- airplane to climb but the airplane would re- ance and redute the range capability.

main in equilibrium because lift, drag, and The cruise control of the turbojet airplane thrust all vary in the same fashion. This re- is considerably ~different from that of the pro- lationship is illustrated by figure 2.26.

peller driven airplane. Since the specific range The relationship of lift, drag, and thrust is is so greatly affected by altitude, the optimum convenient for, in part, it justifies the condi- altitude for begin of cruise should be attained tion of a constant velocity. Above the tropo- as rapidly as is consistent with climb fuel re- pause, rhe speed of sound is constant hence a quirements. The range-climb program varies constant velocity during the cruise-climb considerably between airplanes and the per- would produce a constant Mach number. In formance section of the flight handbook will this case, the optimum values of (&,/CD), C, The de- specify the appropriate procedure.

and C, do not vary during the climb since the scent from cruise altitude will employ essen- Mach number is constant. The specific fuel tially the same feature, a rapid descent is consumption is initially constant above the necessary to minimize the time at low altitudes tropopause but begins to increase at altitudes where specific’range is low and fuel flow is high much above the tropopause. If the specific for a given engine speed.

fuel consumption is assumed to be constant During cruise flight of the turbojet airplane, during the cruise-climb, the following rela- the decrease of gross weight from expenditure tionships will apply: of fuel can result in two types of cruise control.

V, M, CL and C, are constant During a constant altitlrdc C&SC, a reduction in 62 wz gross weight will require a reduction of air- 61 w, speed and engine thrust ‘ to maintain the opti- FR 02 mum lift coefhcient of subsonic cruise. While FFI ~1 such a cruise may be necessary to conform to the flow of traffic, it constitutes a certain in- JR2-W, (cruise climb above tropopause, efficiency of operation. If the airplane were x-W9 constant M, c,) NAVWEPS oo-801-80 AIRPLANE PERFORMANCE where provide a comparison of the total range avail- able from a constant altitude or cruise-climb condition (1) applies to some known condi- tion of weight, fuel flow, and specific range at some original basic altitude during cruise climb.

0.0 Loo0 con&&r (2) applies to some new values of .I 1.026 weight, fuel flow, and specific range at .2 1.057 1.92 some different altitude along a partic- .3 .4 1.136 ular cruise path.

1.182 .5 and 1.248 .6 V= velocity, knots .7 1.331 M = Mach number For example, if the cruise fuel weight is 50 per- W= gross weight, lbs.

cent of the gross weight, the climbing cruise FF=fuel flow, lbs./hr.

flight path will provide a range 18.2 percent JR= specific range, nmi./lb.

greater than cruise at constant ,altitude. This e=altitude density ratio comparison does not include consideration of any variation of specific fuel consumption dur- Thus, during a cruise-climb flight, a 10 percent ing cruise or the effects of compressibility in decrease in gross weight from the consumption defining the optimum aerodynamic conditions of fuel would create: for cruising flight. However, the comparison no change in Mach number or ‘ TAS is generally applicable for aircraft which have a 5 percent decrease in EAS subsonic cruise.

a 10 percent decrease in C, i.e., higher When the airplane has a supersonic cruise for altitude maximum range, the optimum flight path is a 10 percent decrease in fuel flow generally one of a constant Mach number.

an 11 percent increase in specific range The optimum flight path is generally-but not An important comparison can be made between necessarily-a climbing cruise. In this case of the constant altitude cruise and the cruise- subsonic. or supersonic cruise, a Machmeter is climb with respect to the variation of specific of principal importance in cruise control of the range.

From the previous relationships, a jet airplane.

2 percent reduction in gross weight durmg The @ct of wind on nznge is of considerable importance in flying operations. Of course, a headwind will always reduce range and a tailwind will always increase range. The selection of a cruise altitude with the most favorable (or least unfa:vorable) winds is a rel- atively simple matter for the case of the cruise would create a 1 percent increase in propeller powered airplane. Since the range of specific range in a constant altitude cruise but the.propeller powered airplane is relatively un- a 2 percent increase in specific range in a cruise- affected by altitude, the altitude with the most climb at constant .Mach number. Thus, a favorable winds is selected for range. However, higher average specific range can.be maintained the range of the turbojet airplane is greatly during the expenditure of a given increment of affected by altitude so the selection of an op- fuel. If an airplane begins a cruise at optimum timum altitude will involve considering the conditions at or above the tropopause with a wind profile ‘ with the variation of range with given weight of fuel, the following data altitude. Since the turbojet range increases NAVWEPS 00-801-80 AIRPLANE PERFORMANCE TURBOJET CRUISE-CLIMB IF CL AND TAS ARE CONSTANT, LIFT IS PROPORTIONAL TOE t- I IF co AND T/h ARE CONSTANT, IF RPM AND TAS ARE CONSTANT, DRAG IS PROPORTIONAL TO a THRUST IS PROPORTIONAL TO” (APPROXIMATE) WEIGHT DECREASES AS FUEL IS CONSUMED t- EFFECT OF WIN0 ON RANGE (SPEEDS FOR MAXIMUM GROUNO NAUTICAL ,MlLES FUEL PER LB. OF FUEL) FLOW LBS/HR HEADWIND I I / -I- VELOCITY, KNOTS VELOCITY VELOCITY Figure 2.26. Range Performance NAVWEPS 00401-60 AIRPLANE PERFORMANCE greatly with altitude, the turbojet can tolerate The specific endurance is simply the reciprocal less favorable (or more unfavorable) winds of the fuel flow, hence maximum endurance with increased altitude. conditions would be obtained at the lowest In some cases, large values of wind may fuel flow required to hold the airplane in steady cause a significant change in cruise velocity to level flight. Obviously, minimum fuel flow maintain maximum ground nautical miles per will provide the maximum flying time from a lb. of fuel. As an example of an extreme con- given quantity of fuel. Generally, in subsonic dition, consider an airplane flying into a head- performance, the speed at which maximum en- wind which equals the cruise velocity.

In this durance is achieved is approximately 75 per- case, ““9 increase in velocity would improve cent of the speed for maximum range.

range.

While many different factors can affect the To appreciate the changes in optimum speeds specific endurance, the most important factors with various winds, refer to the illustration of at the control of the pilot are the configuration figure 2.26. When zero wind conditions exist, and operating altitude. Of course, for maxi- a straight line from the origin tangent to the mum endurance conditions the airplane must curve of fuel flow versus velocity will locate be in the clean configuration and operated at maximum range conditions. When a head- the proper aerodynamic conditions.

wind condition exists, the speed for maximum EFFECT OF ALTITUDE ON ENDUR- ground range is located by a line tangent drawn ANCE, PROPELLER DRIVEN AIRPLANES.

from a velocity offset equal to the headwind Since the fuel flow of the propeller driven air- velocity. This will locate maximum range at plane is proportional to power required, the some higher velocity and fuel flow. Of course, propeller powered airplane will achieve maxi- the range will be less than when at zero wind mum specific endurance when operated at mini- conditions but the higher velocity and fuel flow mum power required. The point of minimum will minimize the range loss due to the head- power required is obtained at a specific value wind. In a similar sense, a tailwind will re- of lift coefficient for a particular airplane con- duce the cruise velocity to maximize the figuration and is essentially independent of benefit of the tailwind.

weight or altitude. However, an increase in The procedure of employing different cruise altitude will increase the value of the minimum velocities to account for the effects of wind is power required as illustrated by figure 2.27.

necessary only at extreme values of wind If the specific fuel consumption were not in- velocity. It is necessary to consider the fluenced by altitude or engine power, the spe- change in optimum cruise airspeed when the cific endurance would be directly proportional wind velocities exceed 25 percent of the zero to ji, e.g., the specific endurance at 22,000 ft.

wind cruise velocity.

(a=O.498) would be approximately 70 percent of the value at sea level. This example is very ENDURANCE PERFORMANCE nearly the case of the airplane with the recipro- cat&g enginesince specific fuel consumption and The ability of the airplane to convert fuel propeller efficiency are not directly affected by energy into flying time is an important factor altitude. The obvious conclusion is that in flying operations. The “specific endurance” maximum endurance of the reciprocating en- of the airplane is defined as follows: gine airplane is obtained at the lowest practical specific endurance==1 altitude.

The variation with altitude of the maximum 1 endurance of the turboprop airplane requires specific endurance= fuel flow, Ibs. per hr. consideration of powerplant factors in addition im NAV’ iiEPS Oo-801-80 AIRPLANE PERFORMANCE EFFECT OF ALTlTUOE ON MINIMUM POWER REO’ D b AT ALTITUDE / SEA.LEVEL / / MINIMUM / / CONSTANT WEIGHT 8 CONFIGURATION lm- VELOCITY, KNOTS EFFECT OF ALTITUDE ON MINIMUM THRUST REO’ D t SEA LEVEL AT ALTITUDE T;;;g MINIMUM THRUST REO’ D /’ LBS A’ CONSTANT ,’ WEIGHT 8 -- CONFIGURATION I VELOCITY, KNOTS Figure 2.27. Endurance Performance NAVWEPJ OO-ROT-80 AIRPLANE PERFORMANCE airplane will have a maximum specific endur- to airplane factors. The turboprop power- ance at 35,ooO ft. which is at least 40 percent plant prefers operation at low inlet air tem- greater than the maximum value at sea level.

peratures and relatively high power setting to If the turbojet airplane is at low altitude and produce low specific fuel consumption.

While it is necessary to hold for a considerable time, an increase in altitude will increase the mini- maximum time in the air will be obtained by mum power required for the airplane, the beginning a climb to some optimum altitude powerplant achieves more efficient operation.

dependent upon the fuel quantity available.

As a result of these differences, maximum en- Even though fuel is expended during the climb, durance of the multiengine turboprop airplane the higher altitude will provide greater total at low altitudes may require shutting down endurance. Of course, the use of afterburner some of the powerplants in order to operate for the climb would produce a prohibitive re- the remaining powerplants at a higher, more duction in endurance.

efficient power setting.

EFFECT OF ALTITUDE ON ENDUR- OFl4X’ TIMUM RANGE AND ENDUR- ANCE, TURBOJET AIRPLANES. Since the ANCE fuel flow of the turbojet powered airplane is There are many conditions of flying oper- proportional to thrust required, the turbojet ations in which optimum range or endurance airplane will achieve maximum specific endur- conditions are not possible or practical. In ance when operated at minimum thrust re- the off-optimum conditions many instances, quired or (L/D),. In subsonic flight, result from certain operational requirements occurs at a specific value of lift or simplification of operating procedure. In (L/D)m~ coefBcient for a given airplane and is essentially addition, off-optimum performance may be the independent of weight or altitude.

If a given result of a powerplant malfunction or failure.

weight an~dconfiguration of airplane is oper- The most important conditions are discussed ated at various altitudes, the value of the for various airplanes by powerplant type.

minimum thrust required is unaffected by the RECIPROCATING POWERED AIR- curves of thrust required versus velocity shown PLANE. In the majority of cases, the recipro- in figure 2.27. Hence, it is apparent that the cating powered airplane is operated at’ an engine aerodynamic configuration has no prefeience dictated cruise. Service use will most probably for altitude (within compressibility limits) define some continuous power setting which and specific endurance is a function only of will give good service life and trouble-free engine performance.

When range or operation of the powerplant.

The specific fuel consumption of the turbojet endurance is of no special interest, the simple engine is strongly affected by operating RPM expedient is to operate the powerplant at the and altitude. Generally, the turbojet engine recommended power setting and accept what- prefers the operating range near normal rated ever speed, range, or endurance that results.

engine speed and the low temperatures of the While such a procedure greatly simplifies the stratosphere to produce low specific fuel con- matter of cruise control, the practice does not sumption. Thus, increased altitude provides provide the necessary knowledge required for the favorable lower inlet air temperature and operating a high performance, long range requires a greater engine speed to provide the airplane.

thrust required at (L/D)-. The typical The failure of an engine on the multiengine turbojet airplane experiences an increase in reciprocating powered airplane has interesting specific endurance with altitude with the peak ramifications. The first problem appearing is values occurring at or near the tropopausc. to produce sufficient power from the remaining For example, a typical single-engine turbojet engines to keep the airplane airborne. The NAVWEPS OO-ROT-RO AtRPLANE PERFORMANCE problem will be most .critical if the airplane is TURBOPROP POWERED AIRPLANE.

at high altitude, high gross weight, and with The turbine engine has the preference for gaps and gear extended. Lower altitude, relatively high power settings and high alti- jettisoning of weight items, and cleaning up tudes to provide low specific fuel consumption.

the airplane will reduce the power required for Thus, the off-optimum conditions of range or flight. Of course, the propeller on the in- endurance can be concerned with altitudes operative engine must be feathered or the less than the optimum. Altitudes less than power required may exceed that available from the optimum can reduce the range but the the remaining operating powerplants.

loss can be minimized on the multiengine The effect on range is much dependent on airplane by shutting down some powerplants the airplane configuration. When the pro- and operating the remaining powerplants at a peller on the’ inoperative engine is feathered, higher, more efficient output. In this case the added drag is at a minimum, but there is the change of range is confined to the variation added the trim drag ,required to balance of specific fuel consumption with altitude.

the unsymmetrical power. When both these Essentially the same situation exists in the sources of added drag are accounted for, the case of engine failure when cruising at optimum (L/D)- ,is reduced but not by significant altitude. If the propeller on the inoperative amounts. Generally, if the specific fuel con- engine is feathered, the loss of range will be sumption and propeller efficiency do not deteri- confined to the change in specific fuel con- orate, the maximum specific range is not greatly sumption from the reduced cruise altitude. If reduced. On the twin-engine airplane the a critical power situation exists due to engine power required must .be furnished by the one failure, a reduction in altitude provides im- remaining engine and this. usually requires mediate benefit because of the reduction of more than the,maximum cruise-rating of the power required and the increase in power powerplant.i As a result the powerplant can- available from the power plants. In addition, not be operated in the auto-lean or manual the jettisoning of expendable weight items will improve performance and, of course, the lean, power range and the specific ,fuel con- sumption increasesgreatly! Thus, noticeable clean configuration provides minimum parasite loss of range must be anticipated when one drag.

engine fails on the twin-engine airplane. The Maximum specific endurance of the turbo- failure of oneengine on the four (or more) prop airplane does not vary as greatly with engine airpla,W may allow the required, power altitude as the turbojet airplane. While each configuration has its own particular operating to be,develo,ped:by.the three remaining power- requirements, low altitude endurance of the plants operating in an economical power range.

turboprop airplane requires special considera- If the airplane is clean, at low altitude, and tion. The single-engine turboprop will gen- low gross weight, ,the failure of one engine is eraBy experience an increase in specific endur- not likely to cause a, loss of range. However, then loss. of ‘ two engines is likely ‘ to cause a ance with an increase in altitude from sea level.

considerable loss of range. However, if the airplane is at low altitude and When engine failure produces a critical must hold or endure for a period of time, the power or range situation, improved perform- decision to begin a climb or hold the existing altitude will depend on the quantity of fuel ance is possible with- theairplane in ;the clean configuration at low altitude. Also, jetti- available. The decision depends primarily on soning of expendable weight items will reduce the climb fuel,requirements and the variation of the power required and improve the specific specific endurance with altitude. A somewhat range. similar problem exists with the multiengine NAVWEPS OO-EOT-80 AIRPLANE PERFORMANCE turboprop airplane but additional factors are number, cruise-climb, or whatever the appro- available to influence the specific endurance at priate technique) will result in a loss of range low altitude. In other words, low altitude capability.

endurance can be improved by shutting down The failure of an engine during the optimum some powerplants and operating the remaining cruise of a multiengine turbojet airplane will powerplants at higher, more efbcient power cause a noticeable loss of range. Since the setting. Many operational factors could decide optimum cruise of the turbojet is generally a whether such procedure would be a suitable thrust-limited cruise, the loss of part of the technique.

total thrust means that the airplane must TURBOJET POWERED AIRPLANE. In- descend to a lower altitude.

For example, if a creasing altitude has a powerful effect on both twin-engine jet begins an optimum cruise at the range and endurance of the turbojet air- 35,000 ft. (e=O.31) and one powerplant fails, plane. As a result of this powerful effect, the the airplane must descend to a lower altitude typical turbojet airplane will achieve maxi- so that the operative engine can provide the mum specific endurance at or near the tropo- cruise thrust. The resulting altitude would be pause. Also, the maximum specific range will approximately 16,030 ft. (~=0.61). Thus, the be obtained at even higher altitudes since the airplane will experience a loss of the range peak specific range generally occurs at the remaining at the point of engine failure and highest altitude at which the normal rating of loss could be accounted for by the reduced the engine can sustain the optimum aero- velocity (TM) and the increase in specific fuel dynamic conditions. At low altitude cruise consumption (c~) from the higher ambient air conditions, the engine speed necessary to sus- temperature. In the case of the example air- tain optimum aerodynamic conditions is very plane, engine failure would cause a 30 to 40 low and the specific fuel consumption is rela- percent loss of range from the point of engine tively poor. Thus, at low altitude, the air- failure.

Of course, the jettisoning of expend- plane prefers the low speeds to obtain able weight items would allow higher altitude but the powerplant prefers the and would increase the specific range.

(&/CD)- higher speeds common to higher engine effi- Maximum endurance in the turbojet air- ciency. The compromise results in maximum plane varies with altitude but the variation is specific range at flight speeds well above the due to the changes in ‘ fuel flow necessary to optimum aerodynamic conditions. provide the thrust required at (I./D),...

In a sense, The low altitude cruise conditions are engine low inlet air temperature of the tropopause dictated. and the greater engine speed reduce the specific Altitude is the one most important factor fuel consumption to a minimum. If the single- affecting the specific range of the turbojet engine turbojet airplane is at low altitude airplane. Any operation below the optimum and must hold or endure for a period of time, altitude will have a noticeable effect on the a climb should begin to take advantage of the range capability and proper consideration higher specific endurance at higher altitude.

must be given to the loss of range. The altitude to which to climb will be deter- In addi- tion, turbojet airplanes designed specifically for mined by the quantity of fuel remaining.

In long range will have a large percent of the the case of the multiengine turbojet at low gross weight as fuel. The large changes in altitude, some slightly different procedure gross weight during cruise will require partic- may be utilized.

If all powerplants are oper- ular methods of cruise control to extract the ating, it is desirable to climb to a higher maximum flight range. A variation from the altitude which is a function of the remaining optimum flight path of cruise (constant Mach fuel quantity. An alternative at low altitude 17s NAVWEPS oo-80mo AIRPLANE PERFORMANCE the airplane were at a 60’ bank and lift were would be to provide the endurance thrust with not provided to produce the exact load factor some engine(s) shut down and the remaining of 2.0, the aircraft would be accelerating in the engine(s) operating at a more efficient power vertical direction as well as the horizontal di- output. This technique would cause a mmi- rection and the turn would not be steady.

mum loss of endurance if at low altitude. The Also, any sideforce on the aircraft due to feasibility of such a procedure is dependent sideslip, etc., would place the resultant aero- on many operational factors.

dynamic force out of the plane of symmetry In all cases, the airplane should be in the perpendicular to the lateral axis and the turn cleanest possible external configuration because would not be coordinated.

the specific endurance is directly proportional As a consequence of the increase lift re- to the (L/D).

quired to produce the steady turn in a bank, MANEUVERING PERFORMANCE ,...s’ .i :.,cyz’ ’ihe induced drag is increased above that in- When the airplane is’ in turning flight, the curred by steady, wing level, lift-equal-weight airplane is not in static equilibrium for there flight. In a sense, the increased lift required must be developed the unbalance of force to in a steady turn will increase the total drag or produce the acceleration of the turn. During power required in the same manner as increased a steady coordinated turn, the lift is inclined gross weight in level flight. The curves of to produce a horizontal component of force to figure 2.28 illustrate the general effect of turn- equal the centrifugal force of the turn. In ing flight on the total thrust and power re- addition, the steady turn is achieved by pro- quired. Of course, the change in thrust re- ducing a vertical component of lift which is quired at any given speed is due to the change equal to the weight of the airplane. Figure in induced drag and the magnitude of change 2.28 illustrates the forces which act on the depends on the value of induced drag in level airplane in a steady, coordinated turn.

flight and the angle of bank in .turning flight.

For the case of the steady, coordinatedturn, Since the induced drag generally varies as the the vertical component oft lift must equal the square of C,, the following data provide an weight of the aircraft so that there will be no illustration of the effect of various degrees of acceleration in the vertical direction. This bank : requirement leads to the following relation- ship: Load factor, Pcrccnt incrcaw in L n induced drag from *=- lcvcl flight W BE-- cos q5 n=sec $6 where rz= load factor or “G” L=lift, lbs.

W= weight, Ibs.

Since the, induced drag predominates at low += bank angle, degrees (phi) speeds, steep turns at low speeds can produce From this relationship it is apparent that the significant increases in thrust or power required steady, coordinated turn requires specific values to maintain altitude. Thus, steep turns must of load factor, n, at various angles of bank, 6. be avoided after takeoff, during approach, and For example, a bank angle of 60’ requires a especially during a critical power situation load factor of 2.0 (cos 60’ =0.5 or set 60’ =2.0) from failure or malfunction of a powerplant.

to provide the steady, coordinated turn. If The greatly increased induced drag is just as NAVWEPS 00-801-80 AIRPLANE PERFORMANCE CENTRIFUGAL FORCE iRUST TURNING FLIGHT& I I \ \

I VELOCITY, KNOTS

LEVEL FLIGHT VELOCITY, KNOTS Figure 2.28. Effect of Turning Flight NAVWEPS 00-8OT-80 AIRPLANE PERFORMANCE If the airplane were to hold the same angle of important-if not more important-as the bank at 500 knots (TAS), the turn radius increased stall speed in turning flight. It is important also that any turn be well coordi- would quadruple (r=22,200 ft.) and the turn rate would be one-half the original value nated to prevent the increased drag attendant (ROT=2.19 deg. per sec.).

to a sideslip.

Values of turn radius and turn rate versus TURNING PERFORMANCE. The hori- velocity are shown in figure 2.29 for various zontal component of lift will equal the centrif- angles of bank and the corresponding load ugal force of steady, turning flight. This fact factors. The conditions are for the steady, allows development of the following relation- coordinated turn at constant altitude but the ships of turning performance: results are applicable for climbing or descend- turn radius ing flight when the angle of climb or descent P is relatively small. While the effect of alti- r= 11.26 tan 6 tude on turning performance is not immediately where apparent from these curves, the principal effect r= turn radius, ft.

must be appreciated as an increased true air- I’ = velocity, knots (TAX) speed (TAX) for a given equivalent airspeed ti = bank angle, degrees (EAS).

ttrrn rate TACTICAL PERFORMANCE. Many tac- ROT= 1,091 tan rb tical maneuvers require the use of the maxi- V mum turning capability of the airplane. The where maximum turning capability of an airplane will ROT=rate of turn, degrees per sec.

be defined by three factors: $= bank angle, degrees

(1) Maximum lift capability. The combi-

v=velocity, knots, TAS nation of maximum lift coefIicient, C,,=, and wing loading, W/S, will define the These relationships define the turn radius, I, ability of the airplane to develop aero- and rate of turn, ROT, as functions of the two dynamically the load factors of maneuvering principal variables: bank angle, +, and velocity, flight.

I’ (TAX). Thus, when the airplane is flown (2) Optrating ftrcngth limits will define the in the steady, coordinated turn at specific upper limits of maneuvering load factors values of bank angle and velocity, the turn which will not damage the primary struc- rate and turn radius are fixed and independent ture of the airplane. These limits must not of the airplane type. As an example, an air- be exceeded in normal operations because of plane in a steady, coordinated turn at a bank the possibility of structural damage or angle of 45’ and a velocity of 250 knots (TAS) failure.

would have the following turn performance: (3) Thwt or power limits will define the ability of the airplane to turn at constant altitude. The limiting condition would al- low increased load factor and induced drag = 5,550 ft.

until the drag equals the maximum thrust available from the powerplant. Such a case and would produce the maximum turning capa- ROT=(I,091)(1.000) bility for maintaining constant altitude.

The first illustration of figure 2.30 shows -4.37 deg. per sec. how the aerodynamic and structural limits NAVWEPS 00-801-80 AIRPLANE PERFORMANCE define the maximum turning performance. and it produces the minimum turn radius The acrodynomic limir describes the minimum within aerodynamic and structural limitations.

turn radius available to the airplane when At speeds less than the maneuver speed, the When the airplane is at the limit load factor is not available aerodynami- operated at C,,,,.

stall speed in level flight, all the lift is neces- cally and turning performance is aerody- sary to sustain the aircraft in flight and none namically limited. At speeds greater than is available to produce a steady turn. Hence, the maneuver speed, CL- and maximum the turn radius at the stall speed is infinite. aerodynamic load factor are not available and As speed is increased above the stall speed, the turning performance is structurally limited.

is able to develop lift greater airplane at C,,, When the stall speed and limit load factor than weight and produce a finite turn radius. are known for a particular configuration, the For example, at a speed twice the stall speed, maneuver speed is related by the following the airplane at CL,,,,=is able to develop a load expression: factor of four and utilize a bank angle of 75.5’ (cos 75.~~ = 0.25). Continued increase in where speed increases the load factor and bank angle V,=maneuver speed, knots which is available aerodynamically but, be- V.=stall speed, knots cause of the increase in velocity and the basic n limit = limit load factor effect on turn radius, the turn radius approaches For example, an airplane with a limit load an absolute minimum value. When C,,, is factor of 4.0 would have a maneuver speed unaffected by velocity, the aerodynamic mini- which is twice the stall speed.

mum turn radius approaches this absolute The aerodynamic limit line of the first value which is a function of C,,,,,,,, W/S, and 6.

illustration of figure 2.30 is typical of an air- Actually, the one common denominator of which is invariant with aerodynamic turning performance is the wing plane with a CL, speed. While this is applicable for the ma- level stall speed.

The aerodynamic limit of turn radius requires jority of subsonic airplanes, considerable differ- ence would be typical of the transonic or that the increased velocity be utilized to pro- supersonic airplane at altitude. Compressi- duce increasing load factors and greater angles of bank. Obviously, very high speeds will bility effects and changes in longitudinal require very high load factors and the absolute control power may produce a maximum avail- aerodynamic minimum turn radius will require able CL which varies with velocity and an aerodynamic turn radius which is not an an infinite load factor. Increasing speed above absolute minimum at the maximum of velocity.

the stall speed will eventually produce the The second illustration of figure 2.30 describes limit load factor and continued increase in speed above this point will require that load the constant altitude turning performance factor and bank angle be limited to prevent of an airplane. When an airplane is at high When the load factor and structural damage. ,altitude, the turning performance at the high bank angle are held constant at the structural speed end of the flight speed range is more limit, the turn radius varies as the square of usually thrust limited rather than structurally the velocity and increases rapidly above the limited. In flight at constant altitude, the aerodynamic limit. The intersection of ‘ the thrust must equal the drag to maintain equilib- aerodynamic limit and structural limit lines rium and, thus, the constant altitude turn is the ‘ *maneuver speed.” The maneuver radius is infinite at the maximum level flight speed is the minimum speed necessary to speed. Any bank or turn at maximum level develop aerodynamically the limit load factor flight speed would incur additional drag and NAVWEPS 00-801-80 AIRPLANE PERFORMANCE EFFECT OF AERODYNAMIC AND STRUCTURAL LIMIT ON TURNING

A PERFORMANCE

TURN RADIUS F: ABSOLUTE MINIMUM

I

A--

t

VELOCITY, KNOTS (TAS) L CONSTANT ALTITUDE TURNING PERFORMANCE I ,-INCREASING BANK ANGLE TURN RADIUS THRUST OR F: t VELOCITY, KNOTS (TAS) figure 2.30. Maneuvering Performance NAVWEPS OO-EOT-80 AIRPLANE PERFORMANCE speed or minimum flying speed, e.g., 15 per- cause the airplane to descend. However, as cent above the stall speed.

speed is reduced below the maximum level (2) The accclcration during the takeoff or flight speed, parasite drag reduces and allows landing roll. The acceleration experienced increased load factors and bank angles and by any object varies directly with the un- reduced radius of turn, i.e., decreased parasite balance of force and inversely as the mass of drag allows increased induced drag to accom- the object.

modate turns within the maximum thrust (3) The takeoff or landing roll distance is available. Thus, the considerations of con- a function of both the acceleration and stant altitude will increase the minimum turn velocity.

radius above the aerodynamic limit and define In the actual case, the takeoff and landing dis- a particular airspeed for minimum turn radius.

tance is related to velocity and acceleration in Each of the three limiting factors (aero- a .very complex fashion. The main source of dynamic, structural, and power) may combine the complexity is that the forces acting on the to define the turning performance of an air- airplane during the takeoff or landing roll are ane. Generally, aerodynamic and structural Pl “difficult to define wit,h simple relationships.

limits predominate at low altitude while aero- Since the acceleration is a function of these dynamic and power limits predominate at high forces, the acceleration is difficult to define in altitude. The knowledge of this turning per- a simple fashion and it is a principal variable formance is particularly necessary for effective affecting distance. However, some simplifica- operation of fighter and interceptor types of tion can be made to study the basic relatiomhip airplanes.

of acceleration, velocity, and distance While the acceleration is not necessarily constant or TAKEOFF AND LANDING PERFORMANCE uniform throughout the takeoff or landing The majority of pilot caused airplane acci- roll, the assumption of uniformly acceler- dents occur during the takeoff and landing ated motion will facilitate study of the princi- phase of flight. Because of this fact, the pal variables. affecting takeoff and landing Naval Aviator must be familiar with all the distance.

many variables which influence the takeoff and From basic physics, the relationship of landing performance of an airplane and must velocity, acceleration, and distance for uni- strive for exacting, professional techniques of formly accelerated motion is defined by the operation during these phases of flight.

following equation: Takeoff and landing performance is a con- s=g dition of accelerated motion, For instance, during takeoff the airplane starts at zero veloc- where ity and accelerates to the takeoff velocity to S= acceleration distance, ft.

become airborne. During landing, the air- V= final velocity, ft. per sec., after accel- plane touches down at the landing speed and erating uniformly from zero velocity decelerates (or accelerates negatively) to the a= acceleration, ft. per sec.* zero velocity of the stop. In fact, the landing This equation ‘ could relate the takeoff distance performance could be considered as a takeoff in terms of the takeoff velocity and acceleration in reverse for purposes of study. In either when the airplane is accelerated uniformly case, takeoff or landing, the airplane is ac- from zero velocity to the final takeoff velocity.

celerated between zero velocity and the takeoff Also, this expression could relate the landing or landing velocity. The important factors of distance in terms of the landing velocity and takeoff or landing performance are: deceleration when the airplane is accelerated (1) The takeoff or landing velocity which (negatively) from the landing velocity to a will generally be a function of the stall complete stop. It is important to note that NAVWEPS 00-801-80 AIRPLANE PERFORMANCE NAVWEPS 00-801-80 AIRPLANE PERFORMANCE the distance varies directly as the square of the the runway requirements. The minimum take- velocity and inversely as the acceleration. off distance is obtained by takeoff at some As an example of this relationship, assume minimum safe velocity which allows sufficient margin above stall and provides satisfactory that during takeoff an airplane is, accelerated uniformly from zero velocity to a takeoff control and initial rate of climb. Generally, velocity of 150 knots (253.5 ft. per sec.) with the takeoff speed is some fixed percentage of an acceleration of 6.434 ft. per sec.* (or, 0.2g, the stall speed or minimum control speed for the airplane in the takeoff configuration. As since g=32.17 ft. per sec.*). The takeoff distance would be: such, the takeoff will be accomplished at some particular value of lift coefficient and angle of attack. Depending on the airplane character- istics, the takeoff speed will be anywhere from = (253.5)* 1.05 to 1.25 times the stall speed or minimum (2)(6.434) If the takeoff speed is specified control speed.

=5,ooo ft.

as 1.10 times the stall speed, the takeoff lift coefficient is 82.6 percent of CL- and the angle If the acceleration during takeoff were reduced of attack and lift coeticient for takeoff are 10 percent, the takeoff distance would increase fixed values independent of weight, altitude, 11.1 percent; if the takeoff velocity were wind, etc. Hence, an angle of attack indicator increased 10 percent, the takeoff distance can be a valuable aid during takeoff.

would increase 21 percent. These relation- To obtain minimum takeoff distance at the ships point to the fact that proper accounting specified takeoff velocity, the forces which act must be made of altitude, temperature, gross on the aircraft must provide the maximum weight, wind, etc. because any item affecting acceleration during the takeoff roll. The acceleration or takeoff velocity will have a various forces acting on the aircraft may or definite effect on takeoff distance.

may not be at the control of the pilot and If an airplane were to land at a velocity of various techniques may be necessary in certain 150 knots and be decelerated uniformly to a airplanes to maintain takeoff acceleration at stop with the same acceleration of 0.2g, the the highest value.

landing stop distance would be 5,000 ft.

Figure 2.32 illustrates the various forces However, the case is not necessarily that an which act on the aircraft during takeoff roll.

aircraft may have identical takeoff and landing The powerplant thrust is the principal force to performance but the principle illustrated is that provide the acceleration and, for minimum distance is a function of velocity and accelera- takeoff ,distance, the output thrust should be tion. As before, a 10 percent lower accelera- at a maximum. Lift and drag are produced as tion increases stop distance Il.1 percent, and a soon as the airplane has speed and the values 10 percent higher landing speed increases of lift and drag depend on the angle of attack landing distance 21 percent.

and dynamic .pressure. Rolling friction results The general relationship of velocity, accel- when there is a normal force on the wheels eration, and distance for uniformly accelerated and the friction force is the product of the motion is illustrated by figure 2.31. In this normal force and the coefficient of rolling illustration., acceleration distance is shown as friction. The normal force pressing the wheels a function of velocity for various values of against the runway surface is the net of weight acceleration.

TAKEOFF PERFORMANCE. The mini- and lift while the rolling friction coefficient is mum takeoff distance is of primary interest in a function of the tire type and runway surface texture.

the operation of any aircraft because it defines NAVWEPS 00-801-80 AIRPLANE PERFORMANCE The acceleration of the airplane at any The total retarding for& on the aircraft is instant during takeoff roll is a function of the the sum of drag and rolling friction (D+F) net accelerating force and the airplane mass. and, for the majority of configurations, this From Newton’ s second law of motion: sum is nearly Constant or changes only slightly during the takeoff roll. The net accelerating force is then the difference between the power- or plant thrust and the total retarding force, where Fn=T-D-F a=acceleration,~fr. per set Fn- net accelerating force, The variation of the net accelerating force W=weight, lbs.

throughout the takeoff roll is shown in figure g? gravitational accelerat 2.32. The typical propeller airplane demon- =32.17 ft. per sec.* strates a net accelerating force which decreases M= mass, slugb with velocity and the resulting acceleration is = WE initially high but decreases throughout the The riet aicelerating fdrce on ‘ the airplane, takeoff roll. The typical jet airplane demon- F,, is the net of thiust, T, drag, D, and rolling strates a net accelerating force which is essen- friction, F. Thus, the acceleration -at any tially constant throughout the takeoff roll.

instant during takeoff roll is: As a result, the takeoff performance of the typical turbojet airpiane will compare closely a=&T-D-F) with the case for uniformly accelerated motion.

The pilot technique required to achieve peak Figure 2.32 illustrates the typical variation of acceleration throughout takeoff roll can vary the various fbrces acting on the aircraft considerably between airplane configurations.

throughout the takeoff roll: In some instances, maximum acceleration will If ‘ it is assumed that the aircraft is at essentially constant be obtained by allowing the airplane to remain angle of attack during takeoff roll, CL and Co in the three-point attitude throughout the roll are constant and the forces of lift and drag until the airplane simply reaches lift-equal-to- vary as the square of the speed. weight and flies off the ground. Other air- For the case of uniformly accelerated motion, distance planes may require the three-point attitude along the takeoff roll is proportional also to until the takeoff speed is reached then rotation the square bf the velocity hence velocity to the takeoff angle of attack to become air- squared and distance can be used almost synon- borne. Still other configurations may require omously. partial or complete rotation to the takeoff Thus, lift and drag will vary lint arly with dyriamic pressure (4) or P from angle of attack prior to reaching the takeoff the point of beginning takeoff roll. As the speed. In this case, the procedure may be rolling friction coefficient -is esscnti&y un- necessary to provide a smaller retarding force affected by velocity, the rolling ftiction will (D+F) to achieve peak acceleration. When- vary as the normal force on the wheels. ever any form of pitch rotation is necessary the At zero velocity, the normal force on the wheels pilot must provide the proper angle of attack is equal to the airplane weight but, at takeoff since an excessive angle of attack will cause velocity, the lift is equal to the weight and excessive drag and hinder (or possibly pre- the normal force is zero. Hence, rolling fric- clude) a successful takeoff. Also, irisufficient tion decreases linearly with 4 or Vz from the rotation may provide added rolling resistance or require that the airplane accelerate to some beginning of takeoff roll and reaches zero at the point of takeoff. excessive speed prior to becoming airborne.

Revised January 1965 NAVWEPS O&601-80 AIRPLANE PERFORMANCE FORCES ACTING ON THE AIRPLANE DURING TAKEOFF ROLL LlFT,L7 /’ ,-THRUST (PROPELLER), T ,/ / THRUST (JETI,T / /’ ‘ \ ‘ 1 (T-D-F) / NET ACCELERATING CONSTANT /’ FORCE a (T;&F) (PROPELLER)- , I ’ ACCELERATING WHICH IS ESSENTIALLY POINT OFF INNING PROPORTIONAL TO DISTANCE TAKEOFF OF TAKEOFF IN UNIFORMLY ACCELERATED ROLL MOTION Figure 2.32. Forces Acting on the Airplane During Takeoff Roll NAVWEPS 00401-80 AIRPLANE PERFORMANCE mass to accelerate, and (3) increased retarding In this sense, an angle of attack indicator is especially useful for night or instrument takeoff force (D+F). If the gross weight increases, a greater speed is necessary to produce the conditions as well as. the ordinary day VFR takeoff conditions. Acceleration errors of the greater lift to get the airplane airborne at the attitude gyro usually preclude accurate pitch takeoff lift coefficient. The relationship of rotation under these conditions. takeoff speed and gross weight would be as FACTORS AFFECTING TAKEOFF PER- follows: FORMANCE. In addition to the important factors of proper technique, many other vari- ables affect the takeoff performance of an air- plane. Any item which alters the takeoff where velocity or acceleration during takeoff roll will VI= takeoff velocity corresponding to affect the takeoff distance. In order to evalu- some original weight, Wi ate the effect of the many variables, the prin- V2= takeoff velocity corresponding to cipal relationships of uniformly accelerated some different weight, W, motion,will be assumed and consideration will be given to those effects due to any nonuni- Thus, a given airplane in the takeoff configura- formity of acceleration during the process of tion at a given gross weight will have a specific takeoff. Generally, in the case of uniformly takeoff speed (EAS or CAS) which is invariant accelerated motion, distance varies directly with altitude, temperature, wind, etc. because with the square of the takeoff velocity and in- a certain value of 4 is necessary to provide lift versely as the takeoff acceleration. equal to weight at the takeoff CL.

As an ex- ample of the effect of a change in gross weight a 21 percent increase in takeoff weight will require a 10 percent increase in takeoff speed to where support the greater weight.

S= distance A change in gross weight will change the V= velocity, net accelerating force, Fn, and change the a= acceleration mass, M, which is being accelerated. If the ;’ con&&‘ (I) applies to some known takeoff airplane has a relatively high thrust-to-weight which was common to distance, Si, ratio, the change in the net accelerating force some original takeoff velocity, Vi, and is slight and the principal effect on accelera- acceleration, ai.

tion is due to the change in mass.

condition (2) applies to some new takeoff To evaluate the effect of gross weight on distance, Sa, which is the result of some takeoff distance, the following relationship different value of takeoff velocity, Vs, or are used : acceleration, aa.

the effect of weight on takeoff velocity is With xhis basic relationship, the effect of the many variables on takeoff ‘ distance can be approximated.

The effect of gross weight on takeoff distance is if the change in net accelerating force~is large and proper consideration of this item neglected, the effect of weight on accelera- must be made in predicting takeoff distance.

tion is Increased gross weight can be considered to produce a threefold effect on takeoff perform- ance: (1) increased takeoff velocity, (2) greater NAVWEPS 00-801-80 AIRPLANE PERFORMANCE the effect of these items on takeoff dis- the effect of a headwind is to reduce the tance is takeoff ground velocity by the amount of the headwind velocity, V W or the effect of wind on acceleration is

g+?)x(Z)

negligible,

J-2 WY2 a

-= -

J-1 W I

( )

the effect of these items on takeoff distance (ut 1eaJt this effect because weight will is alter the net accelerating force) This result approximates the e5ect of gross weight on takeoff distance for airplanes with relatively high thrust-to-weight ratios. In effect, the takeoff distance will vary at least as the square of the gross weight. For ex- ample, a 10 percent increase ,in takeoff gross weight would cause: where a 5 percent increase in takeoff velocity Xi= zero wind takeoff distance at least a, 9 percent decrease in acceleration Sa=takeoff distance into the head- at least a 21 percent increase in takeoff wind distance V,= headwind velocity For the airplane with a high thrust-to-weight VI= takeoff ground velocity with zero ratio, the increase in takeoff distance would wind, or, simply, the take05 be approximately 21 to 22 percent but, for airspeed the airplane with a relatively low thrust-to- *eight ratio, the increase in takeoff distance As a .result of this relationship, a headwind would be approximately 25 to 30 percent.

wh,ich is 10 percent of the takeoff airspeed will Such a powerful effect requires proper con- reduce the takeoff distance 19 percent. How- sideration of gross weight in predicting takeoff ever, a tailwind (or negative headwind) which distance.

is 10 percent of the take05 airspeed will in- The effect of wind on takeoff distance is large crease the takeoff distance 21 percent. In the and proper consideration also must be provided case where the headwind velocity is 50 percent when predicting takeoff distance.

The effect of the takeoff speed, the takeoff distance would of a headwind is to allow the airplane to reach be approximately 25 percent of the zero wind the takeoff velocity at a lower ground velocity takeoff distance (75 percent reduction).

while the effect of a tailwind is to require the The e5ect of wind on landing distance is airplane to achieve a greater ground velocity identical to the effect on takeoff distance.

to attain the takeoff velocity. The effect of Figure 2.33 illustrates the general dfect of the wind on acceleration is relatively small wind by the percent change in takeoff or land- and, for the most part, can be neglected. To evaluate the effect of wind on takeoff distance, ing distance as a function of the ratio of wind the following relationships are used: velocity to takeoff or landing speed.

NAVWEPS 00-801-80 AIRPLANE PEkFORMANCE Figure 2.33. Approximate Effect of Wind Velocity on Takeoff or Landing Distance NAVWEPS 00-8OT-80 AIRPLANE PERFORffANCE The cffcct of nrnzuay slope on takeoff distance “feel” of the airplane but will produce an un- is due to the component of weight along the desirable increase in takeoff distance.

Assum- inclined path of the airplane. A runway ing that the acceleration is essentially un- slope of 1 percent would provide a force com- affected, the takeoff distance varies as the ponent along the path of the airplane which is square of the takeoff velocity, 1 percent of the gross weight.

Of course, an s* vz.2 upslope would contribute a retarding force -= - 0 J-1 v, component while a downslope would contri- bute an accelerating force component. For Thus, 10 percent excess airspeed would increase the case of the upslope, the retarding force the takeoff distance 21 percent.

In most criti- component adds to drag and rolling friction to cal takeoff conditions, such an increase in reduce the net accelerating force.

Ordinarily, takeoff distance would be prohibitive and the a 1 percent runway slope can cause a 2’ tO 4 pilot must adhere to the recommended takeoff percent change in takeoff distance depending speeds.

on rhe airplane characrerisrics. The airplane

The effect of prcs~wc altitude and ambient

with the high thrust-to-weight ratio is least rcmpcraturc is to define primarily the density affected while the airplane with the low thrust- altitude and its effect on takeoff performance.

to-weight ratio is most affected because the While subsequent corrections are appropriate slope force component causes a relatively for the effect of temperature on certain items greater change in the net accelerating force.

of powerplant performance, density altitude The effect of runway slope must be consid- defines certain effects on takeoff performance.

ered when predicting the takeoff distance but An increase in density altitude can produce a the effect is usually minor for the ordinary run- way slopes and airplanes with moderate two-fold effect on takeoff performance: (I) in- thrust-to-weight ratios.

In fact, runway slope creased takeoff velocity and (2) decreased considerations are of great significance only thrust and reduced net accelerating force. If when the runway slope is large and the airplane a given weight and configuration of airplane is has an intrinsic low acceleration, i.e., low taken to altitude above standard sea level, the thrust-to-weight ratio. In the ordinary case, airplane will still require the same dynamic the selection of the takeoff runway will favor pressure to become airborne at the takeoff lift the direction with an upslope and headwind Thus, the airplane at altitude will coefficient.

rather than the direction with a downslope take 05 at the same equivalent airspeed (EAS) and tailwind.

as at sea level, but because of the reduced The effect of propertakeoff t&city is important density, the true airspeed (TAS) will be when runway lengths and takeoff distances are From basic aerodynamics, the rela- greater.

critical. The takeoff speeds specified in the tionship between true airspeed and equivalent flight handbook are generally the minimum airspeed is as follows: safe speeds at which the airplane can become airborne.

Any attempt to take 05 below the TAS 1 recommended speed may mean that the air- EAS=F craft may stall, be difficult to control, or have where very low initial rate of climb.

In some cases, TAS= true airspeed an excessive angle of attack may not allow EAS= equivalent airspeed the airplane to climb out of ground effect.

On the other hand, an excessive airspeed at takeoff n=altitude density ratio may improve the initial rare of climb and 0 = Plpo NAVWEPS 00-805-80 AIRPLANE PERFORMANCE combined effects would be approximated The effect of density altitude on powerplant for the case of the airplane with high in- thrust depends much on the type of power- trinsic acceleration by the following: plant. An increase in altitude above standard sea level will bring an immediate decrease in power output for the unsupercharged or ground g=(gyx(~) boosted reciprocating engine or the turbojet and turboprop engines.

However, an increase g=(i)x(;) in altitude above standard sea level will not cause a decrease in power output for the super- charged reciprocating engine until the altitude s2 12 -= - exceeds the critical altitude.

For those power- J-1 a plants which experience a decay in thrust with where an increase in altitude, the effect on the net S,= standard sea level takeoff distance accelerating force and acceleration can be ap- Ja= takeoff distance at altitude proximated by assuming a direct variation o=altitude density ratio with density. Actually, this assumed vari- ation would closely approximate the effect on As a result of these relationships, it should.

airplanes with high thrust-to-weight ratios.

be appreciated that density altitude will affect This relationship would be as follows: takeoff performance in a fashion depending Fm P a2 much on the powerplant type. The effect of -=-=-En al Frill PO density altitude on takeoff distance can be where appreciated by the following comparison: ai, Fn, = acceleration and net accelerating force corresponding to sea level aa, Fn, = acceleration and net accelerating - force corresponding to altitude P ~=altitude density ratio In order to evaluate the effect of these items on takeoff distance, the following relationships are used : if an increase in altitude does not alter ac- celeration, the principal effect would be drirude due to the greater TAS -- -- -- sealevel.... 1 ..om L.cca 0 0 0

;=(g,yxe)

I.cmft..... 1 .0?.98 L.oa5 2.98 6.05 9.8 Z,cmfC.....

I ..c605 1.125 6.05 12.5 19.9 ,,mfi..... I L.wls 1.191 9.28 19.5 30.1 f2 1 4.@JJfc..... L. 126 1.264 12.6 26.4 40.6 -=- 5.Ccnft..... 1 L. 1605 1.347 16.05 34.7 52.3 $1 (T 6.-xafC..... I 1.1965 1.431 19.65 0.1 65.8 where - - - Si=standard sea level takeoff distance St= takeoff distance at altitude From the previous table, some approximate o-altitude density ratio rules of thumb may be derived to illustrated if an increase in altitude reduces accelera- the differences between the various airplane tion in addition to the increase in TAS, the types.

A 1,ooo-ft. increase in density altitude NAVWEPS 00-801-80 AIRPLANE PERFORMANCE will cause these approximate increases in (2) Gross weight.

takeoff distance: (3) Temperature--an additional correc- 3% percent for the supercharged recipro- tion for nonstandard temperatures to ac- cating airplane when below critical count for the thrust loss associated with high compressor inlet air temperature.

altitude 7 percent for the turbojet with high thtust- For this correction the ambient tempera- ture at the runway conditions is appro- to-weight ratio 10 percent for the turbojet with low priate rather than the ambient temperature at some distant location.

thrust-to-weight ratio (4) Wind.

These approximate relationships show the In addition, corrections are necessary to ac- turbojet airplane to be much more sensitive to count for runway slope, engine power defi- density altitude than the reciprocating powered airplane, This is an important fact which ciencies, etc.

LANDING PERFORMANCE. In many must be appreciated by pilots in transition cases, the landing distance of an airplane will from propeller type to jet type airplanes.

define the runway requirements for flying Proper accounting of pressure altitude (field operations. This is particularly the case of elevation is a poor substitute) and temperature high speed ‘ jet airplanes at low altitudes where is mandatory for accurate prediction of takeoff landing distance is the problem rather than roll distance.

takeoff performance. The minimum landing The most critical conditions of takeoff distance is obtained by landing at some mini- performance are the result of somecombination mum safe velocity which allows sufficient mar- of high gross weight, altitude, temperature gin above stall and provides satisfactory, con- and unfavorable wind. In a11 cases, ir be- trol and capability for waveoff Generally, hooves the pilot to make an accurate prcdic- the landing speed is some fixed percentage of tion of takeoff’ distance from the performance the stall speed or minimum control speed for data of the Flight Handboo& regardless of the the airplane in the landing configuration. As runway available, and to strive for.2 polished, such, the landing will be accomplished at professional takeoff technique.

some particuIar value of ~lift coefficient and In the prediction of takeoff distance from angle of attack. The exact value of CL and the handbook data, the following primary P for landing will depend on the airplane considerations must be given: characteristics but, once defined, the values are Reciprocating poweredairplane independent of weight, altitude, wind, etc.

(1) Pressure altitude and temperature- Thus, an angle of attack indicator can be a to define the effect of density altitude on valuable aid during approach and landing.

distance.

To obtain minimum landing distance at the (2) Gross weight-a large effect on dis- specified landing velocity, the forces which tance.

act on the airplane must provide maximum (3) Specific humidity-to correct cake- deceleration (or negative.acceIeration) during off distance for the power loss associated the landing roll. The various forces actin~g.

with water vapor.

on the airplane during the landing roll may (4) Wind-a large effect due to the wind require various techniques to maintain landing or wind component along the runway.

deceleration at the peak value.

Turbine poweredairplane Figure 2.34 illustrates the forces acting on (I) Pressure altitude and temperature- the aircraft during landing roll. The power- to define the effect of density altitude.

plant thnrJt should be a minimum positive NAVWEPS OO-EOT-RO AtRPtANE PERFORMANCE Figure 2.34 illustrates the typical variation value, or, if reverse thrust is available, a maxi- of the various forces acting on the aircraft mum negative value for minimum landing dis- throughout the landing roll. If it is assumed tance. Lift and drag are produced as long as that the aircraft is at essentially constant angle the airplane has speed and the values of lift of attack from the point of touchdown, CL and and drag depend on dynamic pressure and CD are constant and the forces of lift and drag angle of attack. Braking friction results when there is a normal force on the braking wheel vary as the square of the velocity. Thus, lift and drag will decrease linearly with 4 or V’ surfaces and the friction force is the product of the normal force and the coe&cient of braking from the point of touchdown. If the braking coefficient is maintained at the maximum friction. The normal force on the braking value, this maximum value of coefficient of surfaces is some part of the net of weight and friction is essentially constant with speed and lift, i.e., some other part of this net may be the braking friction force will vary as the distributed to wheels which have no brakes.

normal force on the braking surfaces. As the The maximum coefficient of braking friction is airplane nears a complete stop, the velocity primarily a function of the runway surface con- and lift approach zero and the normal force on dition (dry, wet, icy, etc.) and rather inde- the wheels approaches the weight of the air- pendent of the type of tire for ordinary condi- plane. At this point, the braking friction tions (dry, hard surface runway). However, the operating coefficient of braking friction is force is at a maximum. Immediately after touchdown, the lift: is quite large and the controlled by the pilot by the use of brakes.

The acceleration of the airplane during the normal force on the wheels is small. As a re- sult, the braking friction force is small. A landing roll is negative (deceleration) and will common error at this point is to apply exces- be considered to be in that sense. At any in- sive brake pressure without sufficient normal stant during the landing roll the acceleration force on the wheels.

is a function of the net retarding force and the This may develop a skid with a locked wheel and cause the tire to blow airplane mass. From Newton’ s second law of out so suddenly that judicious use of the brakes motion: is necessary.

B = Fr/M The coefficient of braking friction can reach peak values of 0.8 but ordinarily values near or 0.5 are typical for the dry hard surface runway.

a=g 0+/W) Of course, a slick, icy runway can reduce the where maximum braking friction coefficient to values as low as 0.2 or 0.1: If the entire weight of a= acceleration, ft. per seca (negative) the airplane were the normal force on the brak- Fr=net retarding force, lbs.

ing surfaces, a coefficient of braking friction of g= gravitational acceleration, ft. per sec.’ 0.5 would produce a deceleration of %g, 16.1 ft.

W=weight, lbs.

per sec.a Most airplanes in ground effect M= mass, slugs rarely produce lift-drag ratios lower than 3 or = Wig 4. If the lift of the airplane were equal to the The net retarding force on the airplane, Fr, is weight, an L/D = 4 would produce a decelera- the net of drag, D, braking friction, F, and tion of xg, 8 ft. per sec.* By this comparison thrust, T. Thus, the acceleration (negative) it should be apparent that friction braking at any instant during the landing roll is : offers the possibility of greater deceleration than airplane aerodynamic braking. To this d=$ (Df F--T) end, the majority of airplanes operating from NAVWEPS 00-801-80 AIRPLANE PERFORMANCE FORCES ACTING ON THE AIRPLANE DURING LAUDING ROLL LIFT

I--

DRAG + BRAKING POINT FINAL STOP OF LANDING TOUCHDOWN Figure 2.34. Forces Acting on Airplane During Landing Roll NAVWEPS 00-ROT-80 AIRPLANE PERFORMANCE sufficient to cause deceleration of the airplane dry hard surface runways will require particular it can be used in deference to the brakes in the techniques to obtain minimum landing dis- early stages of the landing roll, i.e., brakes tance. Generally, the technique involves low- and tires suffer from continuous, hard use but ering the nose wheel to the runway and retract- airplane aerodynamic drag is free and does not 1 ing the flaps to increase the normal force on wear out with use. The use of aerodynamic the braking surfaces. While the airplane drag drag is applicable only for deceleration to 60 is reduced, the greater normal force can pro- ot 70 percent of the touchdown speed. At vide greater braking friction force to com- speeds less than 60 to 70 percent of the touch- pensate for the reduced drag and the net retard- ing force is increased. down speed, aerodynamic drag is so slight as to be of little use and braking must be utilized The technique necessary for minimum land- ing distance can be altered~ to some extent in to produce continued deceleration of the certain situations. For example, low aspect airplane.

ratio airplanes with high longitudinal control Powerplant thrust is not illustrated on figure 2.34 for there are so many possible power can create very high drag at the high speeds immediate to landing touchdown. If variations. Since the objective during the landing toll is to decelerate, the powerplant the landing gear configuration or flap or thrust should be the smallest possible positive incidence setting precludes a large reduction of CL, the normal force on the braking surfaces value or largest possible negative value. In and braking friction force capability are rela- the case of the turbojet aircraft, the idle tively small. Thus, in the initial high speed thrust of the engine is nearly constant with part of the landing roll, maximum deceleration speed throughout the landing roll. The idle thrust is of significant magnitude on cold days 1 would be obtained by creating the greatest because of the low compressor inlet air temper- possible aerodynamic drag. By the time the ature and low density altitude. Unfortu- aircraft has slowed to 70 or 80 percent of the nately, such atmospheric conditions usually touchdown speed, aerodynamic drag decays have the corollary of poor braking action be- but braking action will then be effective.

cause of ice or water on the runway. The Some form of this technique may be necessary thrust from a windmilling propeller with the to achieve minimum distance for some con- engine at idle can produce large negative thrust figurations when the coefficient of braking early in the landing roll but the negative force friction is low (wet, icy runway) and the decreases with speed. The .large negative braking friction force capability is reduced thrust at high speed is valuable in adding to relative to airplane aerodynamic drag.

drag and braking friction to increase the net A distinction should be made between the retarding force.

techniques for minimum landing distance and Various devices can be utilized to provide an ordinary landing roll with considerable greater deceleration-of the airplane or to mini- excess runway .available. Minimum landing mize the wear and teat on tires and brakes.

distance will be obtained from the landing ‘ The drag parachute can provide a large retatd- speed by creating a continuous peak decelera- ing force at high 4 and greatly increase the de- tion of the airplane. This condition usually celeration during the initial phase of landing requites extensive use of the brakes for maxi- toll. It should be noted that the contribution mum deceleration. On the other hand, an of the drag chute is important only during the ordinary landing roll with considerable excess high speed portion of the landing roll. For runway may allow extensive use of aero- maximum effectiveness, the drag chute must be dynamic drag to minimize wear and tear on deployed immediately after the airplane is in the tires and brakes. If aerodynamic drag is contact with the runway. Reverse thrust of Revised January 1965 NAVWEPS 00-EOT-80 AIRPLANE PERFORMANCE propellers is obtained by rotating the blade angle well below the low pitch stop and applying engine power. The action is to ex- where tract a large amount of momentum from the Si = landing distance resulting from certain airstream and thereby create negative thrust.

values of landing velocity, Vi, and The magnitude of the reverse thrust from pro- acceleration, 6zi pellets is very large, especially in the case of S2=landing distance resulting from some the turboprop where a very large shaft power different values of landing velocity, can be fed into the propeller. In the case of V2, or acceleration, a2 reverse propeller thrust, maximum effective- With this relationship, the effect of the many ness is achieved by use immediately after the variables on landing distance can be apptoxi- airplane is in contact with the runway. The mated.

reverse thrust capability is greatest at the The effect of gross wclght on landing distance high speed and, obviously, any delay in pro- is one of the principal items determining the ducing deceleration allows runway to pass by landing distance of an airplane One effect at a rapid rate. Reverse thrust of turbojet of an increased gross weight is that the airplane engines will usually employ some form of will require a greater speed to support the vanes, buckets, or clamshells in the exhaust to airplane at the landing angle of attack turn or direct the exhaust gases forward.

and lift coefficient. The relationship of land- Whenever the exit velocity is less than the in- ing speed and gross weight would be as let velocity (or negative), a negative momen- follows: tum change occurs and negative thrust is produced. The reverse jet thrust is valuable and effective but it should not be compared with the reverse thrust capability of a com- parable propeller powerplant which has the where high intrinsic thrust at low velocities. As Vi=landing velocity corresponding to with the propeller reverse thrust, jet reverse some original weight, W, thrust must be applied immediately after Vs = landing velocity corresponding to ground contact for maximum effectiveness in some different weight, W, reducing landing distance. Thus, a given airplane in the landing con- FACTORS AFFECTING LANDING PER- figuration at a given gross weight will have a FORMANCE. In addition to the important specific landing speed (MS ot CAS) which is factors of proper technique, many other vari- invariant with altitude, temperature, wind, ables affect the landing performance of an air- etc., because a certain value of 4 is necessary plane. Any item which alters the landing to provide lifr equal to weight at the landing velocity or deceleration during landing toll C,. As an example of the effect of a change in will affect the landing distance. As with gross weight, a 21 percent increase in landing takeoff performance, the relationships of uni- weight will require a 10 percent increase in formly accelerated motion will be assumed landing speed to support the greater weight.

applicable for studying the principal effects on When minimum landing distances are con- landing distance. The case of uniformly ac- sidered, braking friction forces predominate celerated motion defines landing distance as during the landing toll and, for the majority varying directly as the square of the landing of airplane configurations, braking friction is velocity and inversely as the acceleration dur- the main source of deceleration. In this case, ing landing toll.

an increase in gross weight provides a greater NAVWEPS OO-ROT-80 AIRPLANE PERFORMANCE braking friction will bring both airplanes to normal force and increased braking friction a stop in the same distance. The heavier ait- Also, force to cope with the increased mass.

plane will have the gteater mass to decelerate the higher landing speed at the same CL and but the greater normal force will provide a CD produce an average drag which increased in greater retarding friction force. As a result, the same proportion as the increased weight.

both airplanes would have identical accelera- Thus, increased gross weight causes like in- tion and identical stop distances from a given creasesin the sum of drag plus braking friction velocity. However, the heavier airplane and the acceleration is essentially unaffected.

would have a greater kinetic energy to be dis- To evaluate the effect of gross weight on sipated by the brakes and the principal differ- landing distance, the following relationships ence between the two airplanes as they reach are used: a stop would be that the heavier airplane the effect of weight on landing velocity is would have the hotter brakes. Therefore, one of the factors of braking performance is the ability of the brakes to dissipate energy with- out developing excessive temperatures and if the net retarding force increases in the losing effectiveness.

same proportion as the .weight, the accel- To appreciate the effectiveness of modern eration is unaffected.

brakes, a 30,000-lb. aircraft landing at 175 the effect of these items on landing dis- knots has a kinetic energy of 41 million ft.-lbs.

tance is, at the instant of touchdown. In a minimum distance landing, the brakes must dissipate most of this kinetic energy and sach brake must absotb an input power of approximately 1,200 or h.p. for 25 seconds. Such requirements for brakes are extreme but the example serves to $2 w* s,=w, illustrate the ptoblems of brakes for high performance airplanes.

In effect, the minimum landing distance will While a 10 percent increase in landing vary directly as the gross weight. For ex- weight causes: ample, a 10 percent increase in gross weight a 5 percent higher landing speed at landing would cause: a 10 percent greater landing distance, a 5 percent increase in landing velocity it also produces a 21 percent increase in the a 10 percent increase in landing distance kinetic energy of the airplane to be dissipated A contingency of the previous analysis is the during the landing roll. Hence, high landing relationship between weight and braking ftic- weights may approach the energy dissipating tion force. The maximum coefficient of brak- capability of the brakes.

ing friction is relatively independent of the The s&t of wind on landing distance is large usual range of normal forces and rolling speeds, and deserves proper consideration when pre- e.g., a 10 percent increase in normal force would dicting landing distance. Since the airplane create a like 10 percent increase in braking will land at a particular airspeed independent friction force. Consider the case of two air- of the wind, the principal effect of wind on planes of the same type and c.g. position but landing distance is due to the change in the of ~diffetent gross weights. If these two air- ground velocity at which the airplane touches planes are rolling along the runway at some down. The effect of wind on acceleration speed at which aerodynamic forces are negli- gible, the use of the maximum coefficient of duting the landing distance is identical to the NAVWEPS OO-ROLRO AIRPlANE PERFORMANCE effect on takeoff distance and is approximated TAS 1 by the following relationship: E-33=5 where

v 2

$2

..-.=

TAS= true airspeed

Sl c

EAS= equivalent airspeed where a=altitude density ratio Si= zero wind landing distance Since the airplane lands at altitude with the Sa=landing distance into a headwind same weight and dynamic pressure, the drag I’ , = headwind velocity and braking friction throughout the landing Vi=landing ground velocity with zero toll have the same values as at sea level. As wind or, simply, the landing airspeed long as the condition is within the capability of the brakes, the net retarding force is un- As a result of this relationship, a headwind changed and the acceleration is the same as which is 10 percent of the landing airspeed will with the landing at sea level.

reduce the landing distance 19 percent but a To evaluate the effect of density altitude on tailwind (or ‘ negative headwind) which is 10 landing distance, the following relationships percent of the landing speed will increase the are used : landing distance 21 percent. Figure 2.33 illus- since an increase in altitude does not alter trates this general effect.

acceleration, the effect would be due to

The effect of ranway slope on landing distance

the greater TAS is due to the component of weight along the inclined path of the airplane. The relation- ship is identical to the case of takeoff per- formance but the magnitude of the effect is not as great. While account must be made for the effect, the ordinary values of runway where slope do not contribute a large effect on landing distance. For this reason, the selection of the S1= standard sea level landing dis- landing runway will ordinarily favor the direc- tance tion with a downslope and’ headwind rather Sa=Ianding distance at altitude than an upslope and tailwind.

c=altitude density ratio The effect of pressurealtitude and ambient tem- From this relationship, the minimum land- perature is to define density altitude and its effect on landing performance. An increase in dens- ing distance at 5,OCOft. (u=O.8617) would be ity altitude will increase the landing velocity 16 percent greater than the minimum landing but will not alter the net retarding force. If distance at sea level. The approximate increase a given weight and configuration of airplane in landing distance with altitude is approxi- mately 3% percent for each 1,ooO ft. of altitude.

is taken to altitude above standard sea level, the airplane will still require the same 4 to Proper accounting of density altitude is neces- sary to accurately predict landing distance.

provide lift equal to weight at the landing C,.

The effect of proper landing velocity is impor- Thus, the airplane at altitude will land at the tant when runway lengths and landing dis- same equivalent airspeed (EAS) as at sea level tances are critical. The landing speeds specified but, because of the reduced density, the true airspeed (TM) will be greater. The relation- in the flight handbook ate generally the mini- ship between true airspeed and equivalent air- mum safe speeds at which the airplane can be landed. Any attempt to land at below the speed is as follows: NAVWEPS O&ROT-R0 AIRPLANE PERFORMANCE brakes. In all cases, it is necessary to make an specified speed may mean that the airplane may accurate prediction of minimum landing dis- stall, be difhcult to control, or develop high tance to compare with the available runway.

rates of descent. On the other hand, an exces- A polished, professional landing technique is sive speed at landing may improve the control- necessary because the landing phase of flight lability (especially in crosswinds) but will accounts for more pilot caused aircraft acci- cause an undesirable increase in landing dis- dents than any other single phase of flight.

tance. The principal effect of excess landing In the prediction of minimum landing dis- speed is described by: tance from the handbook data, the following

& v2 *

-= -

considerations must be given:

h

0VI

(1) Pressure altitude and temperature-to define the effect of density altitude.

Thus, a 10 percent excess landing speed would (2)’ Gross weight-which define the CAS cause a 21 percent increase in landing distance.

The excess speed places a greater working load or EAS for landing.

on the brakes because of the additional kinetic (3) Wind-a large effect due to wind or wind component along the runway.

energy to be dissipated. Also, the additional speed causes increased drag and lift in the nor- (4) Runway slope-a relatively small cor- mal ground attitude and the increased lift will rection for ordinary values of runway slope.

reduce the normal force on the braking sur- IMPORTANCE OF HANDBOOK PER- faces. The acceleration during this range of FORMANCE DATA. The performance sec- speed immediately after touchdown may suffer tion or supplement of the flight handbook con- and it will be more likely that a tire can be tains all the operating data for the airplane.

blown out from braking at this point. As a For example, all data specific to takeoff, climb, result, 10 percent excess landing speed will range, endurance, descent and landing are in- cause at JUJ; 21 percent greater landing dis- cluded in this section. The ordinary use of tance. these data in flying operations is mandatory The most critical conditions of landing per- and great knowledge and familiarity of the air- formance are the result of some combination of plane can be gained through study of this high gross weight, density altitude, and un- material. A complete familiarity of an air- favorable wind. These conditions produce the plane’ s characteristics can be obtained only greatest landing distance and provide critical through extensive analysis and study of the levels of energy dissipation required of the handbook data.

NAVWEPS 00-801-80 HIGH SPEED AERODYNAMICS

Chapter 3

HIGH SPEED AERODYNAMICS

Developments in aircraft and powerplants GENERAL CONCEPTS AND SUPERSONIC have produced high performance airplanes FLOW PATTERNS with capabilities for very high speed flight.

The study of aerodynamics at these very high NATURE OF COMPRESSIBILITY flight speeds has many significant differences from the study of classical low speed aero- At low flight speeds the study of aero- dynamics. Therefore, it is quite necessary dynamics is greatly simplified by the fact that the Naval Aviator be familiar with the that air may experience relatively small nature of high speed airflow and the charac- changes in pressure with only negligible teristics of high performance airplane changes in density. This airflow is termed configurations. incompressible since the air may undergo changes NAVWEPS 00-601-60 HIGH SPEED AERODYNAMICS in pressure without apparent changes in den- directions. Evidence of this “pressure warn- seeii in the typical subsonic flow sity. Such a condition of airflow is analogous ing’ ’ is pattern of figure 3.1 where there is upwash to the flow of water, hydraulic fluid, or any and flow direction change well ahead of the other incompressible fluid. However, at high leading edge. If the object is travelling at flight speeds the pressure changes that take some ,speed above the speed of sound the air- place are quite large and significant changes flow ahead of the object will not be influenced in air density occur. The study of airflow at by the pressure field on the object since pres- high speeds must account for these changes -sure disturbances cannot. be propagated ahead 1 in air density and must consider that the of the object.

1 air is compressible and that there will be Thus, as the flight speed nears the speed of sound a compression wave will “compressibility effects.” form at the leading edge and all changes in A factor of great importance in the study of velocity and pressure will take place quite high speed airflow is the speed of sound.

sharply and suddenly. The airflow, ahead of The speed of sound is the rate at which small the object is not influenced until the air par- pressure disturbances will be propagated through the air and this propagation speed ticles are suddenly forced out .of the way by is solely a function of air temperature. the concentrated pressure wave set up by the The accompanying table illustrates the variation object. Evidence of this phenomenon is seen in the typical supersonic flow pattern of of the speed of sound in the standard atmosphere. figure 3.1.

The analogy of surface waves on the water TABLE 3-I. V.r;afIm < ,I T< may help clarify these phenomena. Since a Altitude in the - surface wave is simply the propagation of a pressure disturbance, a ship moving at a speed -- much less than the wave speed will not form D F. - c. K?uI, a “bow wave.” As the. ship’ s speed nears 59.0 15.0 661.7 the wave pro$agation speed the bow wave 41.1 5.1 650.3 23.3 -4.8 6%.6 will form and become stronger as speed is 5.5 -14.7 6X6.7 increased beyond the wave speed.

--12., --24.6 614.6 At this point it should become apparent --30.2 -34.5 602.2 -48.0 -44.4 589.6 that all compressibility effects depend upon -65.8 --w.3 516.6 the relationship of airspeed to the speed of -69.7 -56.5 573:s -69.1 -56.5 573.8 sound. The term used to describe this rela- -69.7 -56.5 573.8 tionship is the Mach number, M, and this - term is the ratio of the true airspeed to the As an object moves through the air mass, speed of sound.

,-I velocity and pressure changes occur which M=; create pressure disturbances in the airflow sur- rounding the object. Of course, these pressure where disturbances are propagated through the air M=Mach number at the speed of sound. If the object is travel- V= true airspeed, knots ling at low speed the pressure disturbances are d= speed of sound, knots propagated ahead of the object and the airflow =a& immediately ahead of the object is influenced aO=speed of sound at standard sea level by the pressure field on the object.

Actually, conditions, 661 knots these pressure disturbances are transmitted in e= temperature ratio all directions and extend indefinitely in all = T/T, Revised January 1965 NAVWEPS OD-8OT-80 HIGH SPEED AERODYNAMICS TYPICAL SUBSONIC FLOW PATTERN FLOW DIRECTION CHANGES WELL AHEAD OF LEADING EDGE TYPICAL SUPERSONIC FLOW PATTERN APPARENT AHEAD OF LEADING EDGE Figure 3.1. Comparison of Subsonic and Supersonic Now Patterns NAVWEPS OCMOT-60 HIGH SPEED AERODYNAMICS exist in both compressible and incompressible It is important to note that compressibility cases.

effects are not limited to flight speeds at and The example of subsonic incompressible flow above the speed of sound. Since any aircraft is simplified by the fact that the density of will have some aerodynamic shape and will flow is constant throughout the tube. Thus, be developing lift there will be local flow as the flow approaches a constriction and the velocities on the surfaces which arc greater streamlines converge, velocity increases and than the flight speed. Thus, an aircraft can static pressure decreases. In other words, a experience compressibility effects at flight convergence of the tube requires an increasing speeds well below the speed of sound. Since velocity to accommodate the continuity of there is the possibility of having both subsonic flow. Also, as the subsonic incompressible and supersonic flows existing on the aircraft flow enters a diverging section of the tube, it is convenient to define certain regimes of velocity decreases and static pressure increases flight. These regimes are defined approxi- but density remains unchanged. The behavior mately as follows: of subsonic incompressible flow is that a con- Subsonic-Mach numbers below 0.75 Transonic-Mach numbers from 0.75 to vergence causes expansion (decreasing pressure) 1.20 while a divergence causes compression (in- Supersonic-Mach numbers from 1.20 to creasing pressure).

5.00 The example of supersonic compressible flow Hypersonic-Mach numbers above 5.00 is complicated by the fact that the variations While the flight Mach numbers used to define of flow density are related to the changes these regimes of flight are quite approximate, in velocity and static pressure. The behavior it is important to appreciate the types of flow of supersonic compressible flow is that a con- existing in each area. In the subsonic regime vergence causes compression while a divergence it is most likely that pure subsonic airflow causes expansion. Thus, as the supersonic exists on all parts of the aircraft. In the compressible flow approaches a constriction transonic regime it is very probable that flow and the streamlines converge, velocity dc- on the aircraft components may be partly sub- Con- creases and static pressure increases.

sonic and partly supersonic. The supersonic tinuity of mass flow is maintained by the and hypersonic’ flight regimes will provide increase in flow density which accompanies the definite supersonic flow velocities on all parts decrease in velocity. As the supersonic com- Of course, in supersonic flight of the aircraft.

pressible flow enters a diverging section of the there will be some portions of the boundary tube, velocity increases, static pressure de- layer which are subsonic but the predominating creases, and density decreases to accommodate flow is still supersonic.

the condition of continuity.

The principal differences between subsonic The previous comparison points out three 1 and supersonic flow are due to the cmprrs- significant differences between supersonic corn- 1 Jibi& of the supersonic flow.

Thus, any pressible and subsonic incompressible flow.

change of velocity or pressure of a supersonic (a) Compressible flow includes the addi- flow will produce a related change of density tional variable of flow density.

which must be considered and accounted for.

(b) Convergence of flow causes expansion Figure 3.2 provides a comparison of incom- of incompressible flow but compression of pressible and compressible flow through a compressible flow.

closed tube. Of course, the condition of con- (c) Divergence of flow causes compression tinuity must exist in the flow through the of incompressible flow but expansion of closed tube; the mass flow at any station along compressible flow.

the tube is constant. This qualification must Revised January 1965 NAVWEPS OD-8OT-80 HIGH SPEEO AERODYNAMICS INCOMPRESSIBLE (SUBSONIC) -- //------ --- -- ---- --- ------ -- --_-__-- __--__----- ------- ---_ --- ---- --- ----- ---_ -- _---- ---__- .,,,,,,,,,,l--~- CONVERGING DECREASING VELOCITY INCREASING VELOCITY INCREASING PRESSURE DECREASING PRESSURE CONSTANT DENSITY CONSTANT DENSITY COMPRESSIBLE (SUPERSONIC) DIVERGING CONVERGING DECREASING VELOCITY INCREASING VELOCITY INCREASING PRESSURE DECREASING PRESSURE DECREASING DENSITY JNCI~EASJ~~G DENSITY figure 3.2. Comparison of Compressible and lncomprossible Flow Through a Closed Tube NAVWEPS OD-SOT-80 HIGH SPEED AERODYNAMICS OBLIQUE SHOCK WAVE-, SUPERSONIC FLOW INTO A CORNER SERfES OFOBLIOUE SHOCK WAVES r\ SUPERSONIC FLOW INTO A ROUNDED CORNER Figure 3.3. Oblique Shock Wave Formotion NAVWEPS OD-807-80 HIGH SPEED AERODkNAMlCS ‘ I-YPICAL SUPERSONIC FLOW PATTERNS will form on each surface of the wedge and the inclination of the shock wave will be a func- When supersonic flow is clearly established, tion of the free stream Mach number and the all changes in velocity, pressure, density, flow wedge angle. As the free stream Mach number direction, etc., take place quite suddenly and increases, the shock wave angle decreases; as in relatively confined areas. The areas of flows the wedge angle increases the shock wave change are generally distinct and the phenom- angle increases, and, if the wedge angle is in- ena are referred to as “wave” formations. All creased to some critical amount, the shock compression waves occur suddenly and are wave will detach from the leading edge of the wasteful of energy. Hence, the compression wedge. It is important to note that detach- waves are distinguished by the sudden “shock” ment of the shock wave will produce sub$onic type of behavior. All expansion waves are not flow immediately after the central portion of so sudden in their occurrence and are not waste- the shock wave. Figure 3.4 illustrates these ful of energy like the compression shock waves.

typical flow patterns and the effect of Mach Various types of waves can occur in supersonic number and wedge angle.

flow and the nature of the wave formed depends The previous flow across a wedge in a upon the airstream and the shape of the object supersonic airstream would allow flow in ;UU causing the flow change. Essentially, there dimensions.

If a cone were placed in a super- are three fundamental types of waves formed sonic airstream the airflow would occur in in supersonic flow: (1) the oblip shock wave three dimensions and there would be some (compression), (2) the normal shock wave noticeable differences in flow characteristics.

(compression), (3) the expansion wave (no Three-dimensional flow for the same Mach shock).

number and flow direction change would pro- OBLIQUE SHOCK WAVE. Consider the duce a weaker shock wave with less change in case where a supersonic airstream is turned pressure and density. Also, this conical wave into the preceding airflow. Such would be formation allows changes in airflow that con- the case of a supersonic flow “into a comer” tinue to occur past the wave front and the as shown in figure 3.3. A supersonic airstream wave strength varies with distance away from passing through the oblique shock wave will the surface. Figure 3.5 depicts the typical experience these changes: three-dimensional flow past a cone.

(1) The airstream is slowed down; the Oblique shock waves can be reflected like velocity and Mach number behind the wave any pressure wave and this effect is shown in are reduced but the flow is still supersonic figure 3.5. This reflection appears logical and (2) The flow direction is changed to flow necessary since the original wave changes the along the surface flow direction toward the wall and the reflected (3) The static pressure of the airstrea:m wave creates the subsequent flow change to behind the wave is increased cause the flow to remain parallel to the wall (4) The density of the airstream behind surface. This reflection phenomenon places the wave is increased definite restrictions on the size of a model in a (5) Some of the available energy of the wind tunnel since a wave reflected back to the airstream (indicated by the sum of dynamic model would cause a pressure distribution not and static pressure) is dissipated and turned typical of free flight.

into unavailable heat energy. Hence, the NORMAL SHOCK WAVE. If a blunt- shock wave is wasteful of energy.

nosed object is placed in a supersonic airstream A typical case of oblique shock wave forma- tion is that of a wedge pointed into a super- the shock wave which is formed will be de- sonic airstream. The oblique shock wave tached from the leading edge. This detached NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS M = 3.0 \ M = 3.0 DETACHED Figure 3.4. Shock Waves Formed by Various Wedge Shapes NAVWEPS 00-BOT-80 HIGH SPEED AERODYNAMICS CONE IN SUPERSONIC FLOW CONICAL WAVE REF:LECTED OBLIOUE WAVES MODEL IN WIND TUNNEL WITH wows REFL\Cmg FROM Figure 3.5. Three Dimensional and Reflected Shock Waves Revised Januaty I%5 NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS OBLlOuE SHOCK WAVES NORMAL ,SHOCK WAVE / Figure 3.6. Normal ShockWave Formation NAVWEPS OD-EOT-80 HIGH SPEED AERODYNAMICS Mach number ahead of the wave is 1.25, wave also occurs when a wedge or cone angle the Mach number of the flow behind the exceeds some critical value. Whenever the wave is approximately 0.80.

shock wave forms perpendicular to the up- (2) The airflow direction immediately stream flow, the shock wave is termed a behind the wave is unchanged.

“normal” shock wave and the flow immediately (3) The static pressure of the airstream behind the wave is subsonic. Any relatively behind the wave is increased greatly.

blunt object in a supersonic airstream will form (4) The density of the airstream behind a normal shock wave immediately ahead of the the wave is increased greatly.

leading edge slowing the airstream to subsonic (5) The energy of the airstream (indi- SO the airstream may feel the presence of the cated by total pressure-dynamic plus static) blunt nose and flow around it. Once past the is greatly reduced. The normal shock wave blunt nose the airstream may remain subsonic is very wasteful of energy.

or accelerate back to supersonic depending on the shape of the nose and the Mach number of EXPANSION WAVE. If a supersonic air- the free stream. stream were turned away from the preceding In addition to the formation of normal flow an expansion wave would form. The shock waves described above, this same type flow “around a corner” shown in figure 3.7 of wave may be formed in an entirely different will not cause sharp, sudden changes in the manner when there is no object in the super- airflow except at the corner itself and thus is sonic airstream. It is particular that whenever not actually a “shock” wave. A supersonic a supersonic airscream is slowed to subsonic airstream passing through an expansion wave without a change in direction a normal shock will experience these changes: wave will form as a boundary between the (1) The airstream is accelerated; the ve- supersonic and subsonic regions. This is an locity and Mach number behind the wave important fact since aircraft usually encounter are greater.

some “compressibility effects” before the flight (2) The flow direction is changed to speed is sonic. Figure 3.6 illustrates the man- flow along the surface-provided separa- ner in which an airfoil at high subsonic speeds tion does not occur.

has local flow velocities which are supersonic.

(3) The static pressure of the airstream As the local supersonic flow moves aft, a behind the wave is decreased.

normal shock wave forms slowing the flow (4) The density of -the airstream behind to subsonic. The transition of flow from the wave is decreased.

subsonic to supersonic is smooth and is not (5) Since the flow changes in a rather accompanied by shock waves if the transition gradual manner there is no “shock” and is made gradually with a smooth surface. The no loss of energy in the airstream. The transition of flow from supersonic to subsonic expansion wave does not dissipate air- without direction change always forms a stream energy.

normal shock wave.

The expansion wave in three dimensions is A supersonic airstream passing through a a slightly different case and the principal normal shock wave will experience these difference is the tendency for the static pres- changes: sure to continue to increase past the wave.

(1) The airstream is slowed to subsonic; The following table is provided to summa- the local Mach number behind the wave is approximately equal to the reciprocal of the rize the characteristics of the three principal Mach number ahead of the wave-e.g., if wave forms encountered with supersonic flow.

21’ 1 NAVWEPS 00-807-80 HIGH SPEED AERODYNAMICS EXPANSION WAVE, SUPERSONIC FLOW AROUND A CORNER WAVES7 SERIES OF EXPANSION SUPERSONIC FLOW AROUND A SMOOTti CORNER Figure 3.7. Expansion Wove Formation NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS TABLE 3-P. Suprnonk Wave Charactwiltks - Typeof wave formation Oblique shock wave Normal shock wave. Expansion wwc.

‘ / //

- ,/$y

<

_- _- __ Flow direction change. “Flow into a corner,” No change. “Flow around a corner,” turned into preceding turned away from pre- flow. ceding flow.

__ -.

Efkct cm velociry and Mach Decreased but still supcr- Increased to higher super- number. sonic. sonic.

__ -.

Effect on static pressure and Great increase, DeCrWSe.

Increase. :.

density.

__ -.

DKICaSe Great decrease No change (no shock).

- - SECTIONS IN SUPERSONIC FLOW Parts (c) and (d) of figure 3.8 show the wave pattern and resulting pressure distribu- In order to appreciate the effect of these tion for a double wedge airfoil at zero lift.

various wave forms on the aerodynamic char- The airstream moving over the surface passes acteristics in supersonic flow, inspect figure 3.8.

through an oblique shock, an expansion wave, Parts (a) and (b) show the wave pattern and and another oblique shock. The resulting resulting pressure distribution for a thin flat pressure distribution on the surfaces produces plate at a positive angle of attack. The air- no net lift, but the increased pressure on the stream moving over the upper surface passes forward half of the chord along with the de- through an expansion wave at the leading edge creased pressure on the aft half of the chord and then an oblique shock wave at the trailing produces a “wave” drag. This wave drag is edge. Thus, a uniform suction pressure exists caused by the components of pressure forces over the upper surface. The airstream moving which are parallel to the free scream direction.

underneath the flat plate passes through an The wave drag is in addition to the drag due oblique shock wave at the leading edge then an to friction, separatien, lift, etc., and can be expansion wave at the trailing edge. This pro- a very considerable part of the total drag at duces a uniform positive pressure on the under- high supersonic speeds.

side of the section. This distribution of pres- Parts (e) and (f) of figure 3.8 illustrate the sure on the surface will produce a net lift and wave pattern and resulting pressure distribu- incur a subsequent drag due co lift from the in- tion for the double wedge airfoil at a small clination of the resultant lift from a perpen- dicular co the free stream. positive angle of attack. The net pressure NAVWEPS 00-8oT-80 HIGH SPEED. AERODYNAMlCS NOTE: CENTER OF PRESSURE IS AT 50% CHORD b FLAT PLATE PRESSURE DISTRIBUTION a FLAT PLATE WAVE PATTERN

v

NO NET LIFT BUT HAVE “WAVE DRAG” c DOUBLE WEDGE WAVE PATTERN d REDOUBLE WEDGE PRESSURE AT ZERO LIFT DISTRIBUTION AT ZERO LIFT DRAG DUE TO LIFT ANGLE ATTAC ‘ CLEFT L-WAVE DRAG f e DOUBLE WEDGE WAVE PATTERN DOUBLEWEDGEPRESSURE

O

AT POSITIVE ANGLE OF ATTACK DISTRIBUTION AT POSITIVE LIFT 9 CIRCULAR ARC TYPE AIRFOIL b CONVENTIONAL BLUNT NOSE AIRFOIL Figure 3.8. Typical Supersonic Flow Patterns and Distribution of Pressure NAWEPS 00-80T-80 HIGH SPEED AERODYNAMICS distribution produces an inclined lift with will be located approximately at the SO per- drag due to lift which is in addition to the cent chord position. As this contrasts with Part (g) of figure 3.8 wave drag at zero lift.

the subsonic location for the aerodynamic shows the wave pattern for a circular arc air- center of the 23 percent chord position, sig- foil. After the airflow traverses the oblique nificant changes in aerodynamic trim and shock wave at the leading edge, the airflow stability may be encountered in transonic undergoes a gradual but continual expansion flight.

until the trailing edge shock wave is en- countered. Part (h) of figure 3.8 illustrates the wave pattern on a conventional blunt nose CONFIGURATION EFFECTS airfoil in supersonic flow. When the nose is blunt the wave must detach and become a TRANSONIC AND SUPERSONIC PLIGHT normal shock wave immediately ahead of the leading edge. Any object in subsonic flight which has some Of course, this wave form produces an area of subsonic airflow at the finite thickness or is producing lift will have leading edge with very high pressure and local velocities on the surface which are density behind the detached wave. greater than the free stream velocity. Hence, The drawings of figure 3.8 illustrate the compressibility effects can be expected to typical patterns of supersonic flow and point occur at flight speeds less than the speed of sound. The transonic regime of flight pro- out these facts concerning aerodynamic surfaces in two dimensional supersonic flow: vides the opportunity for mixed subsonic and (1) All changes in velocity, pressure, supersonic flow and. accounts for the first 1 density and flow direction will take place significant effects of compressibility.

quite suddenly through the various. wave Consider a conventional airfoil shape as forms. The shape of the object and the shown in figure 3.9. If this airfoil is at a required flow ,direction change dictate the flight Mach number of 0.50 and a slight posi- type and strength of the wave formed. tive angle of attack, the maximum local (2) As always, lift results from the distri- velocity on the surface will be greater than bution of pressure on a surface and is the net the flight speed but most likely less than force perpendicular to the free stream direc- sonic speed. Assume that an increase in tion. Any component of the lift in a direc- flight Mach number to 0.72 would produce

tion parallel to the windstream will be lfrst cvidmc of local son@flow. This condition

drag due to lift. of flight would be the highest flight speed (3) In supersonic flight, the zero lift drag possible without supersonic flow and would be termed the “critical Mach number.” Thus, of an airfoil of some finite thickness will “wave drag.” critical Mach number is the bouodary between include a The thickness of subsonic and transonic flight and is an im- the airfoil will have an extremely powerful portant ~point of reference for all compressi- 1 effect on this wave drag since the wave drag bility effects encountered in transonic flight.

varies as the square of the thickness ratio- By delinition, critical Mach number is the if the thickness is reduced 50 percent, the “free stream Mach number which produces wave drag is reduced 73 percent. The lead- 6rst evidence of local sonic flow.” Therefore, ing edges of supersonic shapes must be sharp shock waves, buffet, airflow separation, etc., or the wave formed at the leading edge will take place above critical Mach number.

be a strong detached shock wave.

As critical Mach number is exceeded an (4) Once the flow on the airfoil is super- area of ~uprrronic airflow is created and a normal sonic, the aerodynamic center of the surface Revised January 1965 NAVWEPS 00-8OY-60 HIGH SPEED AERODYNAMICS MAXIMUM LOCALVELOCITY IS LESS THAN SONIC M=.50 MAXIMUM LOCAL VELOCITY EOUALTO SONIC M =.72 (CRITICAL MACH NUMB NORMAL SHOCK WAVE POSSIBLE SEPARATION

su

NORMAL SHOCK \\I NORMAL SHOCK NORMAL SHOCK Figure 3.9. Transonic Flow Patterns (sheet 1 of 2) NAVWEPS OD-801-80 HIGN SPEED AEQODYNAMICJ WING IN TRANSONIC FLOW M = .700 a= +2O CL= ,370 NO SHOCK WAVES

I

I M-.800 a=+2O CL=.442 SHOCK FORMATION IS APPARENT AT 25 TO 30 % CHORD POSITION

I

M=.075 a=+20 CL=.450 SHOCK INDUCED SEPARATION ALONG AFT PORTION OF WING PLAPJFORM

I

Figure 3.9. Transonic Flow Patterns (sheet 2 of 2) NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS value all oblique portions of the waves incline shock wave forms as the boundary between more greatly and the detached normal shock the supersonic flow and the subsonic flow on portion of the bow wave moves closer to the the aft portion of the airfoil surface. The leading edge.

acceleration of the airflow from subsonic to Of course, all components of the aircraft supersonic is smooth and unaccompanied by are affected by compressibility in a manner shock waves if the surface is smooth and the somewhat similar to that of basic airfoil.

transition gradual. However, the transition The tail, fuselage, nacelles, canopy, etc. and of airflow from supersonic to subsonic is the efkct of the interference between the always accompanied by a shock wave and, various surfaces of the aircraft must be when there is no change in direction of the considered.

airflow, the wave form is a normal shock FORCE DIVERGENCE. The airflow sepa- wave.

ration induced by shock wave formation can Recall that one of the principal effects of create significant variations in the aerody- th,e normal shock wave is to produce a large namic force coefficients.

increase in the static pressure of the airstream When the free stream If the shock wave is speed is greater than critical Mach number some behind the wave.

typical effects on an airfoil section are as strong, the boundary layer may not have follows : sufficient kinetic energy to withstand the large, adverse pressure gradient and separation (1) An increase in the section drag coeffi- will occur. At speeds only slightly beyond cient for a given section lift coe5cient.

critical Mach number the shock wave formed (2) A decrease in section lift coefficient is not strong enough to cause spearation or for a given section angle of attack.

any noticeable change in the aerodynamic (3) A change in section pitching moment force coefficients. However, an increase in coe5cient.

speed above critical Mach number sufhcient A reference point is usually taken by a plot of drag coe5cient versus Mach number for to form a strong shock wave can cause sepa- a constant lift coefficient. Such a graph is ration of the boundary layer and produce shown in figure 3.10. The Mach number sudden changes in the aerodynamic force coefficients. Such a flow condition is shown which produces a sharp change in the drag in figure 3.9 by the flow pattern for M=O.n. coe5cient is termed the “force divergence” Notice that a further increase in Mach number Mach number and, for most airfoils, usually to 0.82 can enlarge the supersonic area on the exceeds the critical Mach number at least 5 upper surface and form an additional area of to 10 percent. This condition is also referred supersonic flow and normal shock wave on the to as the “drag divergence” or “drag rise.” lower surface. PHENOMENA OF TRANSONIC FLIGHT.

Associated with the “drag rise” are buffet, As the flight speed approaches the speed of trim and stability changes, and a decrease sound the areas of supersonic flow enlarge and the shock waves move nearer the trailing in control surface effectiveness. Conventional edge. The boundary layer may remain sepa- aileron, rudder, and elevator surfaces sub rated or may reattach depending much upon jetted to this high frequency buffet may the airfoil shape and angle of attack. When “buzz,” and changes in hinge moments may the flight speed exceeds the speed of sound produce undesirable control forces. Of course, the “bow” wave forms at the leading edge and if the buffet is quite severe and prolonged, structural damage may occur if this operation this typical flow pattern is illustrated in is in violation of operating limitations. When figure 3.9 by the drawing for M= 1.05. If the speed is increased to some higher supersonic airflow separation occurs on the wing due to NAVWEPS OO-EOT-80 HIGH SPEED AERODYNAMICS FORCE DIVERGENCE MACH NUMBER CD DRAG CRITICAL COEFFICIENT MACH NUMBER.

I c I I 0.5 1.0 ht,MACH NUMBER Figure 3ilO. Compressibility Drag Rise downwash change can contribute to “pitch shock wave formation, there will be a loss of lift and subsequent loss of downwash aft of up.” Since most of the dificulties of transonic the affected area.

If the wings shock unevenly flight are associated with shock wave induced due to physical shape differences or sideslip, flow separation, any means of delaying or a rolling moment will be created in the alleviating the shock induced separation will direction of the initial loss of lift and con- improve the aerodynamic characteristics. An tribute to control difficulty (“wing drop”).

aircraft conhguration may utilize thin surfaces If the shock induced separation occurs sym- of low aspect ratio with sweepback to delay metrically near the wing root, a decrease in and reduce the magnitude of transonic force downwash behind this area is a corollary of divergence. In addition, various methods of the loss of lift. A decrease in downwash on boundary layer control, high lift devices, the horizontal tail will create a diving moment and the aircraft will “tuck under.” If these vortex generators, etc., may be applied to conditions occur on a swept wing. planform, improve transonic characteristics. For exam- the wing center of pressure shift contributes ple, the application of vortex generators to a surface can produce higher local surface veloci- to the trim change-root shock first moves the wing center of pressure aft and adds to the ties and increase the kinetic energy of the diving moment; shock formation at the wing boundary layer. Thus, a more severe pressure tips first moves the center of pressure forward gradient (stronger shock wave) will be neces- and the resulting climbing moment and tail sary to produce airflow separation.

NAVWEPS 00-801-80 HIGH SPEEO AERODYNAMICS Once the configuration of a transonic air- can be quite weak, the pressure waves can be craft is fixed, the pilot must respect the effect of sufficient magnitude to create an audible of angle of attack and altitude. The local flow disturbance. Thus, “sonic booms” will be a 1 velocities on any upper surface increase with an simple consequence of supersonic flight.

increase in angle of attack. Hence, local sonic The aircraft powerplant: for supersonic flight flow and subsequent shock wave formation must be of relatively high thrust output.

can occur at lower free stream Mach numbers. Also, in many cases it may be necessary to A pilot must appreciate this reduction of force provide the air breathing powerplant with divergence Mach number with lift coefficient special inlet configurations which will slow since maneuvers at high speed may produce the airflow to subsonic prior to reaching the compressibility effects which may not be en- compressor face or combustion chamber. Aero- countered in unaccelerated flight. The effect dynamic heating of supersonic flight can pro- of altitude is important since the magnitude vide critical inlet temperatures for the gas of any force or moment change due to com- turbine engine as well as critical structural pressibility will depend upon the dynamic temperatures.

pressure of the airstream. Compressibility The density variations in airflow may be effects encountered at high altitude and low shown by certain optical techniques. Schlieren dynamic pressure may be of little consequence photographs and shadowgraphs can define the in the operation of a transonic aircraft. various wave patterns and their effect on the How- the same compressibility effects en- airflow. The Schlieren photographs presented ever, countered at low altitudes and high dynamic in figure 3.11 define the flow conditions on an pressures will create greater trim changes, aircraft in supersonic flight.

I heavier buffet, etc., and perhaps transonic flight restrictions which are of principal inter- TRANSONIC AND SUPERSONIC CONFIGU- est only to low altitude.

RATIONS PHENOMENA OF SUPERSONIC FLIGHT.

While many of the particular effects of super- Aircraft configurations developed for high sonic flight will be presented in the detail of speed flight will have significant differences in later discussion, many general effects may be shape and planform when compared with air- anticipated. The airplane configuration must craft designed for low speed flight. One of have aerodynamic shapes which will have low the outstanding differences will be in the drag in compressible flow. Generally, this will selection of airfoil profiles for transonic or require airfoil sections of low thickness ratio supersonic flight.

and sharp leading edges and body shapes of AIRFOIL SECTIONS. It should be ob- high fineness ratio to minimize the supersonic vious that airfoils for high speed subsonic wave drag. Because of the aft movement of the flight should have high critical Mach num- aerodynamic center with supersonic flow, the bers since critical Mach number defines the increase in static longitudinal stability will lower limit for shock wave formation and demand effective, powerful control surfaces to subsequent force divergence. An additional achieve adequate controllability for super- complication to airfoil selection in this sonic maneuvering. speed range is that the airfoil should have As a corollary of supersonic flight the shock a high maximum lift coefficient and sufficient wave formation on the airplane may create thickness to allow application of high lift special problems outside the immediate vicinity devices. Otherwise an excessive wing area of the airplane surfaces. While the shock would be required to provide maneuverability waves a great distance away from the airplane and reasonable takeoff and landing speeds.

no NAVWEPS DG-RDT-RD HIGH SPEED AERODYNAMICS FE!4 MODEL AT VARIOUS MACH NUMBERS a-O0 pee M* 1.2 W 1.6 Figure 3.11. Schliemn Photographs of Supersonic Flight (sheet 1 of 2) Figure 3.7 1. Schlieren Photographs of Supersonic Flight (sheet 2 of 2) NAVWEPS 00-801-80 HIGH SPEED AERODYNAMICS However, if high speed flight is the primary Figure 3.13 shows the flow patterns for two basic supersonic airfoil sections and pro- consideration, the airfoil must be chosen to vides the approximate equations for lift,drag, have. the highest practical critical Mach and lift curve slope. Since the wave drag is number.

the only factor of difference between -the two Critical Mach number has been defined as airfoil sections, notice the configuration fac- the flight Mach number which produces first evidence of local sonic flow. Thus, the air- tors which affect the wave drag. For the same thickness ratio, the circular arc airfoil foil shape and lift coe&ient-which determine would have a larger wedge angle formed the pressure and velocity distribution-will have a profound effect on critical Mach number. between the upper and lower surfaces at the Conventional, low speed airfoil shapes have leading edge. At the same flight Mach num- relatively poor compressibility characteristics ber the larger angle at the leading edge would because of the high local velocities near the form the stronger shock wave at the nose and leading edge. These high local velocities are cause a greater pressure change on the circular arc airfoil.

inevitable if both the maximum thickness and This same principle applies when investigating the effect of airfoil thickness.

camber are well forward on the chord. An Notice that the wave drag coefficients for improvement of the compressibility character- istics can be obtained by moving the points of both airfoils vary as the SQUARE of the thickness ratio, e.g., if the thickness ratio maximum camber and thickness aft on the were doubled, the wave drag coefhcient would chord. This would distribute the pressure and he four times as great.

velocity more evenly along the chord and If the thickness were increased, the airflow at the leading edge will produce a lower peak velocity for the same experience a greater change in direction and lift coefficient. Fortunately, the airfoil shape a stronger shock wave will be formed. This to provide extensive lamiaar flow and low profile drag in low speed, subsonic flight will powerful variation of wave drag with thick- ness ratio necessitates the use of very thin air- provide a pressure distribution which is favor- foils with sharp leading edges for supersonic able for high speed flight. Figure 3.12 illustrates the pressure distributions and flight. An additional consideration is that thin airfoil sections favor the use of low aspect variation of critical Mach number with lift ratios and high taper to obtain lightweight coefficient for a conventional low speed airfoil and a high speed section. structures and preserve stiffness and rigidity.

In order to obtain a high critical Mach The parameter JMz-l appears in the number from an airfoil at some low lift denominator of each of the equations for the coefficient the section must have: aerodynamic coefficients and indicates a de- (u) Low thickness ratio. The point of crease in each of these coefficients with an maximum thickness should be aft to smooth increase in Mach number. Essentially, this the pressure distribution.

means that any aerodynamic surface becomes (6) Low camber. The mean camber line less sensitive to changes in angle of attack at should be shaped to help minimize the higher Mach numbers. The decrease in lift curve slope with Mach number has tremendous local velocity peaks.

implications in the stability and control of In addition, the higher the required lift high speed aircraft. The vertical tail becomes coefficient the lower the critical Mach number less sensitive to angles of sideslip and the and more camber is required of the airfoil.

directional stability of the aircraft will deteri- If supersonic flight is a possibility the thick- orate with Mach number. The horizontal ness ratio and leading edge radius must be tail of the airplane experiences the same small to decrease wave drag.

NAVWEPS DD-801-80 HIGH SPEED AERODYNAMICS SAME Cl LOW PEAK FOR -1.0 PRESSURE COEFFICIENT 0 PP, 1.0 HIGH SPEED SECTION (LAMINAR FLOW) SECTION LIFT COEFFICIENT Figure 3.72. High speed Section Characteristics NAVWEPS 00-BOT-80 HIGH SPEED AERODYNAMICS DOUBLE WEDGE SECTION CIRCULAR ARC SECTION WAVE DRAG COEFFICIENT: LIFT COEFFICIENT: DRAG DUE .TO LIFT: LIFT CURVE SLOPE: WHERE ( +/c ) = AIRFOIL THICKNESS RATIO a 2 ANGLE OF ATTACK (IN RADIANS) M = MACH NUMBER Figure 3.73. Approximate Equations for Supersonic Section Characteristics NAWEPS OD-ROT-RO HIGH SPEEO AERODYNAMICS In addition to the delay of the onset of com- general effect and contributes less damping to pressibility effects, sweepback will reduce the longitudinal pitching oscillations. These ef- magnitude of the changes in force coefficients fects can become so significant at high Mach due to compressibility. Since’the component numbers that the aircraft might require com- of velocity perpendicular to the leading edge is plete synthetic stabilization.

less than the free stream velocity, the magni- PLANFORM EFFECTS. The development of surfaces for high speed involves considera- tude of all pressure forces on the wing will be tion of many items in addition to the airfoil reduced (approximately by the square of the sections. Taper, aspect ratio, and sweepback cosine of the sweep angle). Since compressi- can produce major effects on the aerodynamic bility force divergence occurs due to changes in characteristics of a surface in high speed flight. pressure distribution, the use of sweepback will Sweepback produces an unusual effect on the “soften” the force divergence. This effect is high speed characteristics of a surface and has illustrated by the graph of figure 3.14 which basis in a very fundamental concept of aero- shows the typical variation of drag coeiIicient dynamics. A grossly simplified method of with Mach number for various sweepback visualizing the effect of sweepback is shown in angles. The straight wing shown begins drag figure 3.14. The swept wing shown has the rise at M=O.lO, reaches a peak near M=l.O, streamwise velocity broken down to a com- and begins a continual drop past M= 1.0. Note ponent of velocity perpendicular to the leading that the use of sweepback then deh+y~ the drag edge and a component parallel to the leading rise to some~higher Mach number and wdms edge. The component of speed perpendicular the magnitude of the drag rise.

to the leading edge is less than the free.stream In view of the preceding discussion, sweep- speed (by the cosine of the sweep angle) and back will have the following principal ad- it is this velocity component which determines vantages : the magnitude of the pressure distribution.

(1) Sweepback will delay the onset of all The component of speed parallel to the lead- compressibility effects. Critical Mach num- ing edge could be visualized as moving across ber and force divergence Mach number will constant sections and; in doing so, does not increase since the velocity component affect- contribute to the pressure distribution on the ing the pressure distribution is less than the Hence, sweep of a surface pro- swept wing.

free stream velocity. Also, the peak of drag duces a beneficial e&ct ‘ in high speed flight rise is delayed to some higher supersonic since higher flight speeds may be obtained be- speed-approximately the speed which pro- fore components of speed perpendicular to the duces sonic flow perpendicular to the leading leading edge produce critical conditions on the edge. Various sweeps applied to wings of wing. This is one of the most important ad- .moderate aspect ratio will produce these vantage of sweep since there is an increase in approximate effects in transonic flight: critical Mach number, force divergence Mach number, and the Mach number at which the drag rise will peak. In other words, sweep will Sweep angle(k) delay the onset of compressibility effects.

Generally, the effect of wing sweep will apply to either sweep back or sweep forward.

While the swept forward wing has been used 1 in rare instances, the aeroelastic instability of such a wing creates such a problem that sweep back is more practical for ordinary applica- tions.

Revised Jaanuar~ 1965 NAVWEPS 00-80T-80 HIGH SPEED AERODYNAMICS VELOCITY COhlPONENT PARALLEL TO LEADING EDGE FREE STREAM VELOCITY \ / SWEEP ANGLE, 11 VELOCITY COMPONENT PERPENDICULAR TO LEADING EDGE DFfAG COEFFICIENT cD c 0 3.0 I.0 2.0 MACH NUMBER, M UM MAXIM’ ,STRAIGHT t IlC.IT MACH NUMBER, M MACH NUMBER, M Figure 3.14. General Effects of Sweepbock NAVWEPS DD-ROT-80 HIGH SPEE’ D AERODYN,AMlCS EFFECT OF SWEEPBACK ON LOW SPEED LIFT CURVE LIFT SWEPT COEFFICIENT CL t ANGLE OF ATTACK,O / EFFECT OF SWEEPBACK ON YAW AND ROLL MOMENTS YAW MOMENT SWEPT WING IN A SWEPT WING AT SIDESLIP TO THE RIGHT ZERO SIDESLIP SWEPT WING IN A SWEPT WING S IDESLIP TOWARD IN LEVEL FLIGHT THE DOWN WING Figure 3.15. Aerodynamic Effects Due to Sweepbach NAVWEPS 00-801-80 HIGH SPEED AERODYNAMICS (1) The wing lift curve slope is reduced (2) Sweepback will reduce the magnitude of change in the aerodynamic force coeffi- for a given aspect ratio. This is illustrated by the lift curve comparison of figure 3.15 cients due to compressibility. Any change for the straight and swept wing. Any in drag, lift, or moment coefbcients will be reduction of lift curve slope implies the reduced by the use of sweepback. Various wing is less sensitive to changes in angle of sweep angles applied to wings of moderate attack. This is a beneficial effect only when aspect ratio will produce these approximate the effect of gusts and turbulence is con- effects in transonic flight.

sidered. Since the swept wing has the - lower lift curve slope it will be less sensitive to gusts and experience less “bump” due to gust for a given aspect ratio and wing loading. This is a consideration particular -_ to the aircraft whose structural design shows 00...............................

a predominating effect of the gust load 150.............. ................

spectrum, e.g., transport, cargo, and patrol types.

600..............................

(2) “Divergence” of a surface is an aero- - elastic problem which can occur at high These advantages of drag reduction and preser- dynamic pressures. Combined bending and vation of the transonic maximum lift coefficient twisting deflections interact with aerody- are illustrated in figure 3.14.

namic forces to produce sudden failure of Thus, the use of sweepback on a transonic the surface at high speeds. Sweep forward aircraft will reduce and delay the drag rise and will aggravate this situation by “leading” preserve the maneuverability of the aircraft the wing into the windstream and tends to in transonic flight. It should be noted that a lower the divergence speed. On the other small amount of sweepback produces very hand, sweepback tends to stabilize the little benefit. If sweepback is to be used at all, surface by “trailing” and tends to raise the at least 30’ to 33’ must be used to produce any divergence speed. By this tendency, sweep- significant benefit. Also note from figure 3.14 back may be beneficial in preventing di- that the amount of sweepback required to vergence within the anticipated speed range.

d&y drag rise in supersonic flight is very large, (3) Sweepback contributes slightly to the e.g., more than 60° necessary at M=2.0. By static directional-or weathercock-stability comparison of the drag curves at high Mach of an aircraft. This effect may be appre- numbers it will be appreciated that extremely ciated by inspection of hgure 3.13 which high (and possibly impractical) sweepback is shows the swept wing in a yaw or sideslip.

necessary to delay drag rise and that the lowest The wing into the wind has less sweep and drag is abtained with zero sweepback. There- a slight increase in drag; the wing away fore, the planform of a wing designed to operate from the wind has more sweep and less continuously at high Mach numbers will tend drag. The net effect of these force changes is to be very thin, low aspect ratio, and unswept.

to produce a yawing moment tending to An immediate conclusion is that sweepback is retarn the nose into the relative wind.

a device of greatest application in the regime of This directional stability contribution is transonic flight.

usually small and of importance in tailless A few of the less significant advantages of aircraft only. sweepback are as follows: Revised January l%S i NAVWEPS 00-801-80 HIGH SPEED AERODYNAMICS (4) Sweepback contributes to lateral sta- arated. The combined effect of taper and When bility in rhe same sense as dihedral. sweep present a considerable problem of tip the swept wing aircraft is placed in a side- stall and this is illustrated by the flow pat- slip, the wing into the wind experiences an terns of figure 3.16. Design for high speed increase in lift since the sweep is less and performance may dictate high sweepback, the wing away from the wind produces less while structural efficiency may demand a lift since rhe sweep is greater. As shown in highly tapered planform. When such is the figure 3.15, the swept wing aircraft in a case, the wing may require extensive aero- sideslip experiences lift changes and a sub- dynamic tailoring to provide a suitable stall sequent rolling moment which tends to pattern and a lift distribution at cruise condi- Wash- right the aircraft. This lateral stability tion which reduces drag due to lift.

conrribution depends on the sweepback and out of the tip, variation of section camber the lift coefficient of the wing. A highly throughout span, flow fences, slats, leading swept wing operating at high lift coeflicient edge extension, etc., are typical devices used to modify the stall pattern and minimize usually experiences such an excess of this lateral stability contribution that adequate drag due to lift at cruise condition.

controllability may be a significant problem. (2) As shown by the lift curve of figure As shown, the swept wing has certain im- 3.15 the use of sweepback will reduce the lift portant advantages. However, the use of curve slope and the subsonic maximum lift sweepback produces certain inevitable disad- coefficient. It is important to note this vantages which are important from the stand- case is definitely subsonic since sweepback point of both airplane design and flight oper- may be used to improve the transonic ma- ations. The most important of these disad- neuvering capability. Various sweep angles vantages are as follows: applied to wings of moderate aspect ratio (1) When sweepback is combined with produce these approximate effects on the taper there is an extremely powerful tendency subsonic lift characteristics: for the wing to stall tip first. This pattern of stall is very undesirable since there would be little stall warning, a serious reduction sweep Angle (A): in lateral control effectiveness, and the for- 300. 14 contribute to a nose up moment (“pitch up” or “stick force lightening”). Taper has its M)Q................................ yl own effect of producing higher local lift coefhcients toward the tip and one of the The reduction of the low speed maximum effects of sweepback is very similar. All lift coefficient (which is in addition to that outboard wing sections are affected by the lost due to tip stall) has very important upwash of the preceding inboard sections implications in design. If wing loading is and the lift distribution resulting from sweep- not reduced, stall speeds increase and sub- back alone is similar to that of high taper. sonic maneuverability decreases. On the An additional effect is the tendency to other hand, if wing loading is reduced, the develop a strong spanwise flow of the bound- increase in wing surface area may reduce ary layer toward the tip when the wing is at the anticipated benefit of sweepback in the high lift coefficients. This spanwise flow transonic flight regime. Since the require- produces a relatively low energy boundary ments of performance predominate, certain layer near the tip which can be easily sep- increases of stall speeds, takeoff speeds, NAVWEPS OO-EOT-80 NAVWEPS OO-EOT-80 HIGH SPEED AERODYNAMICS HIGH SPEED AERODYNAMICS SPANWISE LIFT O~STR~BUT~ON SPANWISE LIFT DISTRIBUTION WC TIP STALL TENDENCY TIP STALL TENDENCY OF UNMOOIFIEO WING OF UNMOOIFIEO WING ::G - - - - - - - - 1.0 1.0 g:: - I.0 - I.0 Ot+ ,s t ” 3 it WING MODIFIED BY WING MODIFIED BY zi WASHOUT, CAMBER, WASHOUT, CAMBER, OCJ SECTION VARIATION, ETC. SECTION VARIATION, ETC.

;$ v) 0 0 f ! 0 ROOT TIP TYPICAL STALLSEQUENCE SPANWISE FLOW OF BOUNDARY LAYER DEVELOPS AT HIGH CL STALL AREA Figure 3.16. Stall Characteristics of Tapered Swept Wing NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS STRAIGHT WING OF SAME AREA, ASPEC&ATIO, AN0 STRIJ;U;RAL I AEROD&AMIC WING BENDING PRODUCES -/TIP ROTATION --- TRAILING EDGE VIEW TIP VIEW figure 3.17. Structurd Complications Due to Sweephk NAVWEPS 00-ROT-80 HIGH SPEED AERODYNAMICS and landing speeds usually will be accepted. marginal control during crosswind takeoff While the reduction of lift curve slope may and landing where the aircraft must move in a controlled sideslip. Therefore, it is not be an advantage for gust considerations, the reduced sensitivity to changes in angle unusual to find swept wing aircraft with negative dihedral and lateral control de- of attack has certain undesirable effects in subsonic flight. The reduced wing lift vices designed principally to meet cross wind curve slope tends to increase maximum lift takeoff and landing requirements.

angles of attack and complicate the problem (5) The structural complexity and aero- of landing gear design and cockpit visi- elastic problems created by sweepback are of bility. Also, the lower lift curve slope great importance. First, there is the effect would reduce the contribution to stability shown in figure 3.17 that swept wing has a of a given tail surface area.

greater structural span than a straight wing (3) The use of sweepback will reduce of the same area and aspect ratio. This effect the effectiveness of trailing edge control increases wing structural weight since surfaces and high lift devices. A typical greater bending and shear material must be example of this effect is the application of distributed in the wing to produce the same a single slotted flap over the inboard 60 design strength. An additional problem is percent span to both a straight wing and a created near the wing root and “carry- wing with 35” sweepback. The flap applied through” structure due to the large twisting to the straight wing produces an increase loads and the tendency of the bending stress in maximum lift coefficient of approxi- distribution to concentrate toward the trail- mately 50 percent. The same type flap ing edge. Also shown in figure 3.17 is the applied to the swept wing produces an influence of wing deflection on the spanwise increase in maximum lift coefficient of lift distribution. Wing bending produces approximately 20 percent. To produce some tip rotation which tends to unload the tip reasonable maximum lift coefficient one a and move the center of pressure forward.

swept wing may require unsweeping the Thus, the same effect which tends to allay flap hinge line, application of leading edge divergence can make an undesirable contri- high lift devices such as slots or slats, and bution to longitudinal stability.

possibly boundary layer control. EFFECT OF ASPECT RATIO AND TIP (4) As described previously, sweepback SHAPE. In addition to wing sweep, plan- contributes to lateral stability by producing form properties such as aspect ratio, and tip stable rolling moments with sideslip. The shape, can produce significant effects on the lateral stability contribution of sweepback aerodynamic characteristics at high speeds.

varies with the amount of wing sweepback There is no particular effect of aspect ratio on and wing lift coefficient-large sweepback critical Mach number at high or medium and high lift coefficients producing large aspect ratios. The aspect ratio must be less While sta- contribution to lateral stability.

than four or five to produce any apparent bility is desirable, any excess of stability will change in critical Mach number. This effect reduce controllability. For the majority of is shown for a typical 9 percent thick sym- airplane configurations, high lateral sta- metrical airfoil in the graph of figure 3.18.

bility is neither necessary nor desirable, but Note that very low aspect ratios are required adequate control in roll is absolutely neces- to cause a significant increase in critical Mach An excess of sary for good flying qualities. number. Very low aspect ratios create the lateral stability from sweepback can aggra- extremes of three dimensional flow and sub- vate “Dutch roll” problems and produce sequent increase in free stream speed to create NAVWEPS 00-801-80 HIGH SPEED AERODYNAMICS APPROXIMATE VARIATION OF CRITICAL MACH NUMBER WITH ASPECT RATIO FOR i.oo- A 9% THICK AIRFOIL SECTION .95- .90- CRITICAL MACH .85- NUMBER .80- MCR .75 - .7od I 1 1 I 1 9 I II I2 01 2 3 4 5 6 7 8 9 IO ASPECT RATIO, AR MACH CONES FORMED AT TIPS OF RECTANGULAR WING IN SUPERSONIC FLOW \- PRESSURE DISTRIBUTION AT THE TIP OF THE RECTANGULAR WING MACH CONE

Y-

VORTEX CREATED WITHIN THE MACH CONE AT THE TIP OF THE RECTANGULAR WING WING WITH TIPS “RAKED” OUTSIDE THE TIP CONES Figure 3.18. Generd Pknform Effects NAVWEPS 00-ROT-80 HIGH SPEED AERODYNAMICS Actually, the extremely supersonic drag due to lift is a function of the local sonic flow.

low aspect ratios required to produce high section and angle of attack while the subsonic induced drag is a function of lift coefficient critical Mach number are not too practical.

and aspect ratio. This comparison makes it Generally, the advantage of low aspect ratio obvious that supersonic flight does not demand must be combined with sweepback and high the use of high aspect ratio planforms typical speed airfoil sections.

of low speed aircraft. In fact, low aspect The thin rectangular wing in supersonic ratios and high taper are favorable from the flow illustrates several important facts. AS standpoint of structural considerations if very shown in figure 3.18, Mach cones form at the thin sections are used to minimize wave drag.

tips of the rectangular wing and affect t~he pressure distribution on the area within the If sweepback is applied to the supersonic cone. The vortex develops within the tip wing, the pressure distribution will be affected cone due to the pressure differenti,al and the by the location of the Mach cone with respect resulting average pressure on the area within to the leading edge. Figure 3.19 illustrates the thecone is approximately one-half the pressure pressure distribution for the delta wing plan- between the cones. Three-dimensional flow form in supersonic flight with the leading edge on the wing is then confined to the area within behind or ahead of the Mach cone. When the the tip cones, while the area between the leading edge is behind the Mach cone the com- cones experiences pure two-dimensional flow.

ponents of velocity perpendicular to the leading It is important to realize that the three- edge are still subsonic even though the free dimensional flow on the rectangular wing in stream flow is supersonic and the resulting supersonic flight differs greatly from that of pressure distribution will greatly resemble the subsonic flight. A wing of finite aspect ratio subsonic pressure distribution for such a plan- in subsonic flight experiences a three-dimen- form. Tailoring the leading edge shape and sional flow which includes the tip vortices, camber can minimize the components of the downwash behind the wing, upwash ahead of high leading edge suction pressure which are the wing, and local induced velocities along inclined in the drag direction and the drag due the span. Recall that the local induced veloc- to lift can be reduced. If the leading edge ities along the span of the wing would incline is ahead of the h4ach cone, the flow over this the section lift aft relative to the free stream area will correspond to the two-dimensional and result in “induced drag.” Such a flow supersonic flow and produce constant pressure condition cannot be directly correlated with for that portion of the surface between the the wing in supersonic flow, ~ The flow pattern leading edge and the Mach cone.

for the rectangular wing of figure 3.18 dem- CONTROL SURFACES. The design of con- onstrates that the three-dimensional flow is trol surfaces for transonic and supersonic flight confined to the tip, and pure two-dimensional involves many important considerations. This flow exists on the wing area between the tip fact is illustrated by the typical transonic and cones. If the wing tips were to be “raked” supersonic flow patterns of figure 3.19. Trail- outside the tip cones, the entire wing flow ing edge control surfaces can be affected ad- would correspond to the two-dimensional (or versely by the shock waves formed in flight section) conditions. above critical Mach number. If the airflow Therefore, for the wing in supersonic flow, is separated by the shock wave the resulting no upwash exists ahead of the wing, three- buffet of the control surface can be very objec- dimensional effects are confined to the tip tionable. In addition to the buffet of the sur- cones, and no local induced velocities occur face, the change in the pressure distribution due along the span between the tip cones. The to separation and the shock wave location can NAVWEPS 00-801-60 HIGH SPEED AERODYNAMICS DELTA WING PLANFORM -PRESSURE DISTRIBUTION MACH CONE MACH CONE AHEAD OF LEADING EDGE CONTFOL SURFACE FLOW PATTERNS SONIC FLOW ON G EDGE CONTROLS M=.85 SUPERSONIC FLOW CONDITIONS TRAILING ED CONTROLSURFACE Figure 3.19. Planform Effects and Control Surfaces NAVWEPS 00-ROT-80 HIGH SPEED AERODYNAMICS create very large changes in control surface just above the speed of sound only slight modi- fications to ordinary subsonic inlet design pro- hinge moments. Such large changes in hinge duce satisfactory performance. However, at moments create very undesirable control forces supersonic flight speeds, the inlet design must and present the need for an “irreversible” con- slow the air with the weakest possible series-or trol system. An irreversible control. system combination of shock waves to minimize en- would employ powerful hydraulic or electric ergy losses and temperature rise. Figure 3.20 actuators to move the surfaces upon control by illustrates some of the various forms of super- the pilot and the airloads developed on the surface could not feed back to the pilot. Of sonic inlets or “diffusers.” course, suitable control forces would be syn- One of the least complicated types of inlet This thesized by bungees, “4” springs, bobweights, is the simple normal shock type diffuser.

etc. type of inlet employs a single normal shock Transonic and supersonic flight can cause a wave at the inlet with a subsequent internal noticeable reduction in the effectiveness of subsonic compression. At low supersonic Mach J trailing edge control surfaces. The deflection numbers the strength of the normal shock wave of a trailing edge control surface at low sub- is not too great and this type of inlet is quite sonic speeds alters the pressure distribution on practical. At higher supersonic Mach num- the fixed portion as well as the movable portion bers, the single normal shock wave is very of the surface. This is true to the extent that a strong and causes a great reduction in the total l-degree deflection of a 40 percent chord eleva- pressure recovered by the inlet. In addition, tor produces a lift change very nearly the it is necessary to consider that the wasted 1 equivalent of a l-degree change in stabilizer energy of the airstream will appear as an addi- setting. However, if supersonic flow exists on tional undesirable rise in temperature of the the surface, a deflection of the trailing edge captured inlet airflow.

control surface cannot influence the pressure If the supersonic’ airstream can be captured, distribution in the supersonic area ahead of the the shock wave formations tiill be swallowed movable control surface. This is especially and a gradual contraction will reduce the speed true in high supersonic flight where supersonic to just above sonic. Subsequent diverging flow 1 flow exists over the entire chord and the change section can then produce the normal shock in pressure distribution is limited to the area of wave which slows the airstream to subsonic.

the control surface. The reduction in effective- Further expansion continues to slow the air to ness of the trailing edge control surface at tran- lower subsonic speeds. This is the convergent- sonic and supersonic speeds necessitates the use divergent type inlet shown in figure 3.20. If Application of the of an all movable surface.

the initial contraction is too extreme for the all movable control surface to the horizontal inlet Mach number, the shock wave formation tail is most usual since the increase in longi- will not be swallowed and will move out in tudinal stability in supersonic flight requires a front of the inlet. The external location of the high degree of control effectiveness to achieve normal shock wave will produce subsonic flow required controllability for supersonic maneu- immediately at the inlet. Since the airstream vering.

is suddenly slowed to subsonic through the SUPERSONIC ENGINE INLETS. Air strong normal shock a greater loss of airstream which enters the compressor section of a jet energy wiIl occur.

engine or the combustion chamber of a ramlet Another form of diffuser employs an external usually must be slowed to subsonic velocity.

oblique shock wave which slows the super- This process must be accomplished with the sonic airstream before the normal shock occurs.

least possible waste of energy. At flight speeds Ideally, the supersonic airstream could be Revised January 1965 NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS CONVERGENT-DIVERGENT INLET NORMALSHOCKINLET IPLE OBLIOUE SHOCK SINGLEOBLIOUE SHOCK NORMAL SHOCK WAVE BELOW DESIGN RANGE NEAR DESIGN RANGE EFFECT OF DIFFUSER DESIGN AND MACH NUMBER ON DIFFUSER PERFORMANCE 1.00 .90 - .BO - .70 - .60 - .50 - - .40 - .30 - .20 - .I0 7 0 I I 1.5 2.5 3.5 1.0 2.0 3.0 4.0 MACH NUhl6ER Figure 3.20. Various Types of Supersonic Mets NAVWEPS 00-8OT-80 HIGH SPEED AERODYNAMICS airplane are developed, the most likely general slowed gradually through a series of very weak oblique shock waves to a speed just configuration properties will beas follows: above sonic velocity. Then the subsequent (1) The wing will be of low aspect ratio, normal shock to subsonic could be quite weak. have noticeable taper, and have sweepback depending on the design speed range. The Such a combination of the weakest possible wing sections will be of low thickness ratio waves would result in the least waste of energy and the highest pressure recovery. The ef- and require sharp leading edges.

ficiency of various types of diffusers is shown (2) The fmelagc and naceller will be of in figure 3.20 and illustrates this principle. high fineness ratio (long and slender). The An obvious complication of the supersonic supersonic pressure distribution may create inlet is that the optimum shape is variable with significant lift and drag and require con- inlet flow direction and Mach number. In sideration of the stability contribution of other words, to derive highest efficiency and these surfaces.

stability of operation, the geometry of the (3) The t&Z surfaces will be similar to inlet would be different at each Mach number the wing-low aspect ratio, tapered, swept and angle of attack of flight. A typical super- and of thin section with sharp leading edge.

sonic military aircraft may experience large The controls will be fully powered and ir- variations in angle of attack, sideslip angle, reversible with all movable surfaces the and flight Mach number during normal oper- most likely configuration.

ation. These large variations in inlet flow (4) In order to reduce interference drag conditions create certain important design in transonic and supersonic flight, the gross considerations. cross section of the aircraft may be “area (1) The inlet should provide the highest ruled” to approach that of some optimum practical efficiency. The ratio of recovered high speed shape.

total pressure to airstream total pressure is One of the most important qualities of high an appropriate measure of this efficiency. speed configurations will be the low speed (2) The inlet should match the demands flight characteristics. The low aspect ratio of the powerplant for airflow. The airflow swept wing planform has the characteristic captured by the inlet should match that of high induced drag at low flight speeds.

necessary for engine operation. Steep turns, excessively low airspeeds, and (3) Operation of the inlet at flight condi- steep, power-off approaches can then produce tions other than the design condition should extremely high rates of descent during landing.

not cause a noticeable loss of efficiency or Sweepback and low aspect ratio can cause excess drag. The operation of the inlet severe deterioration ‘ of handling qualities at should be stable and not allow “buzz” speeds below those recommended for takeoff conditions (an oscillation of shock location and landing. On the other hand, thin, swept wings at high wing loading will have rela- possible during off-design operation).

tively high landing speeds. Any excess of In order to develop a good, stable inlet design, this basically high airspeed can create an im- the performance at the design condition may possible requirement of brakes, tires, and arrest be compromised. A large variation of inlet ing gear. These characteristics require that flow conditions may require special geometric features for the inlet surfaces or a completely the pilot account for the variation of optimum variable geometry inlet design, speeds with weight changes and adhere to the SUPERSONIC CONFIGURATIONS. When procedures and techniques outlined in the all the various components of the supersonic flight handbook.

NAVWEPS Do-Sd-eD “,G” SPEED AERODYNAMICS EFFECT OF SPEED AND ALTITUDE ON AERODYNAMIC HEATING STAGNATION TEMPERATURE AT SEA LEVEL RAM TEMPERATURE ;;I STAGNATION Z w TEMPERATURE I- IN THE STRATOSPHERE 500- 0, --I 500 1000 1500 2000 2500 3000 TRUE AIRSPEED, KNOTS APPROXIMATE EFFECT OF TEMPERATURE ON TENSILE ULTIMATE STRENGTH, l/2 HR, EXPOSURE IOO- go- 00- 70- 60- 50- 40- 30- ,-ALUMINUM ALLOY 20- IO-

L

Or I 900 ~000 0 100 200 300 400 500 600 700 SO0 TEMPERATURE, “F Figure 3.21. Aerodynamic Heating NAVWEPS 00-BOT-80 H,lGH SPEED AERODYNAMICS Higher temperatures produce definite reduc- AERODYNAMIC HEATING tions in the strength of aluminum alloy and When air flows over any aerodynamic surface require the use of titanium alloys, stainless certain reductions in velocity occur with cor- steels, etc., at very high temperatures. Con- The responding increases in temperature.

tinued exposure at elevated temperatures effects greatest reduction in velocity and increase in further reductions of strength and magnifies the temperature will occur at the various stagna- problems of “creep” failure and structural tion points on the aircraft. Of course, similar stiffness.

changes occur at other points on the aircraft The turbojet engine is adversely affected by but these temperatures can be related to the high compressor inlet air temperatures. Since ram temperature rise at the stagnation point.

the thrust output of the turbojet is some func- While subsonic flight does not produce temper- tion of the fuel flow, high compressor inlet air atures of any real concern, supersonic flight temperatures reduce the fuel flow that can be can produce temperatures high enough to be used within turbine operating temperature of major importance to the airframe and power- limits. The reduction in performance of the plant structure. The graph of figure 3.21 il- turbojet engines with high compressor inlet 1 lustrates the variation of ram temperature rise air temperatures requires that the inlet design with airspeed in the standard atmosphere.

produce the highest practical efficiency and The ram temperature rise is independent of minimize the temperature rise of the air altitude and is a function of true .airspeed.

delivered to the compressor face.

Actual temperatures would be the sum of the High flight speeds and compressible flow temperature rife and the ambient air temper- dictate airplane configurations which are much ~Thus, low altitude flight at high Mach ature.

different from the ordinary subsonic airplane.

numbers will produce the highest temperatures.

To achieve safe and efficient operation, the pilot In addition to the effect on the crew member of the modern, high speed aircraft must under- environment, aerodynamic heating creates stand and appreciate the advantages and dis- special problems for the airplane structure A knowledge advantages of the configuration.

and the powerplant. The effect of tempera- of high speed aerodynamics will contribute ture on the short time strength of three typical structural materials is shown in figure 3.21. greatly to this understanding.

Revised January 1965

NAVWEPS 00-80T-80 STABILITY AND CONTROL

Chapter 4

STABILITY AND CONTROL

flight which provide the most critical require- An aircraft must have satisfactory handling ments of stability and control and these condi- qualities in addition to adequate performance.

tions must be understood and respected to ‘ lYhe aircraft must have adequate stability to maintain a uniform flight condition and recover accomplish safe and efficient operation of the from the various disturbing influences. It is aircraft.

necessary to provide sufficient stability to DEFINITIONS minimize the workload of the pilot. Also, the STATIC STABILITY aircraft must have proper response to the An aircraft is in a state of equilibrium when controls so that it may achieve the inherent the sum of all forces and all moments is equal performance. There are certain conditions of NAVWEPS 00-8OT-80 STABILITY AND CONTROL POSITIVE STATIC STABILITY TENDENCY TO RETURN TO EOUILIBRIUM

L

EOUILIBRIUM TENDENCY TO CONTINUE IN/DISPLACEMENT DIRECTION \ NEGATIVE STATIC STABILITY EOulLlBRlUM ENCOUNTERED AT ANY POINT OF DISPLACEMENT (-1 Figure 4.1. Static Stability NAVWEPS 00-802-80 STABILITY ,AND CONTROL to zero. When an aircraft is in equilibrium, aircraft from some trimmed angle of attack.

there are no accelerations and the aircraft If the aerodynamic pitching moments created continues in a steady condition of flight. If by this displacement tend to return the air- the equilibrium is disturbed by a gust or deflec- craft to the equilibrium angle of attack the tion of the controls, the aircraft will experi- aircraft has positive static longitudinal ence acceleration due to unbalance of moment stability.

or force.

The static stability of a system is defined by DYNAMIC STABILITY the initial tendency to return to equilibrium While static stability is concerned with the conditions following some disturbance from tendency of a displaced body to return to equilibrium. If an object is disturbed from equilibrium, dynamic stability is defined by equilibrium and has the tendency to return the resulting motion with time. If an object is to equilibrium, positive .rtatic Jtability exists.

disturbed from equilibrium, the time history If the object has a tendency to continue in the of the resulting motion indicates the dynamic direction of disturbance, negative static stability stability of the system. In general, the system or static instability exists. An intermediate will demonstrate positive dynamic stability condition could occur where an object dis- if the amplitude of motion decreases with placed from equilibrium remains in equilibrium time. The various condirions of possible in the displaced position. If the object subject dynamic behavior are illustrated by the time to a disturbance has neither the tendency to history diagrams of figure 4.2.

return nor the tendency to continue in the dis- The nonoscillatory modes shown in figure placement direction, ncutrnl Jtatic stability ex- 4.2 depict the time histories possible without ists. These three categories of static stability cyclic motion. If the system is given an initial are illustrated in figure 4.1. The ball in a disturbance and the motion simply subsides trough illustrates the condition of positive without oscillation, the mode is termed “sub- static stability. If the ball is displaced from sidence” or “deadbeat return.” Such a motion equilibrium at the bottom of the trough, the indicates positive static stability by the tend- initial tendency of the ball is to return to the ency to return to equilibrium and positive dy- equilibrium condition. The ball may roll namic stability since the amplitude decreases back and forth through the point of equilib- with time. Chart B illustrates the mode of rium but displacement to either side creates “divergence” by a noncyclic increase of ampli- the initial tendency to return. The ball on a tude with time. The initial tendency to con- hill illustrates the condition of static insta- tinue in the displacement direction is evidence bility. Displacement from equilibrium at the of static instability and the increasing ampli- hilltop brings about the tendency for greater tude is proof of dynamic instability. Chart C displacement. The ball on a flat, level surface illustrates the mode of pure neutral stability.

illustrates the condition of neutral static sta- If the original disturbance creates a displace- bility. The ball encounters a new equilibrium ment which remains constant thereafter, the at any point of displacement and has neither lack of tendency for motion and the constant stable nor unstable tendencies.

amplitude indicate neutral static and neutral The term “static” is applied to this form of dynamic stability.

stability since the resulting motion is not The oscillatory modes of figure 4.2 depict the considered. Only the tendency to return to time histories possible with cyclic motion.

1.

eqmlibrtum conditions is considered in static One feature common to each of these modes is stability. The static longitudinal stability of that positive static stability is demonstrated in an aircraft is appreciated by displacing the the cyclic motion by tendency to return to NAVWEPS 00-EOT-80 STABILITY AND CONTROL NON-OSCILLATORY MODES (OR DEAD BEAT RETURN) (NEGATIVE STATIC) (POSITIVE STATIC) (NEGATIVE DYNAMIC) (POSITIVE DYNAMIC) (NEUTRAL STATIC) (NEUTRAL DYNAMlc) E OSCILLATORY h UNDAMPED OSCILLATION

g

E

1: 0.

(POSITIVE STATIC) ; (POSITIVE DYNAMIC) (POSITIVE STATIC) (NEUTRAL DYNAMIC) (P0slTl~E STATIC) (NEGATIVE DYNAMIC) Figure 4.2. Dynamic Sfabihty NAVWEPS OO-ROT-80 STABILITY AND CONTROL quilibrium conditions. However, the dy- In any system, the existence of static sta- namic behavior may be stable, neutral, or un- bility does not necessarily guarantee the stable. Chart D illustrates the mode of a existence of dynamic stability. However, damped oscillation where the amplitude de- the existence of dynamic stability implies creases with time. The reduction of amplitude the existence of static stability.

with time indicates there is resistance to mo- Any aircraft must demonstrate the required tion and that energy is being dissipated. The degrees of static and dynamic stability. If dissipation of energy-or “damping’ ‘ -is nec- the aircraft were allowed to have static in- essary to provide positive dynamic stability. stability with a rapid rate of divergence, the If there is no damping in the system, the mode aircraft would be very difficult-if not impos- of chart E is the result, an undamped oscilla- sible-to fly. The degree of difficulty would tion. Without damping, the oscillation con- compare closely with learning to ride a uni- tinues with no reduction of amplitude with cycle. In addition, positive dynamic stability time. While such an oscillation indicates posi- is mandatory in certain areas to preclude tive static stability, neutral dynamic stability objectionable continued oscillations of the exists. Positive damping is necessary to elimi- aircraft.

nate the continued oscillation. As an example, TRIM AND CONTROLLABILITY an automobile with worn shock absorbers (or “dampers”) lacks sufficient dynamic stability An aircraft is said to be trimmed if all and the continued oscillatory motion is neither moments in pitch, roll, and yaw are equal to pleasant nor conducive to safe operation. In zero. The establishment of equilibrium at the same sense, the aircraft must have sufficient various conditions of flight is the function of damping to, rapidly dissipate any oscillatory the controls and may be accomplished by motion which would affect the operation of pilot effort, trim tabs, or bias of a surface the aircraft. When natural aerodynamic damp- actuator.

ing cannot be obtained, a synthetic damping The term “controllability” refers to the must be furnished to provide the necessary ability of the aircraft to respond to control positive dynamic stability.

surface displacement and achieve the desired Chart F of figure 4.2 illustrates the mode of condition of flight. Adequate controllability a divergent oscillation. This motion is stat- must be available to perform takeoff and ically stable since it tends to return to the landing and accomplish the various maneuvers equilibrium position. However, each subse- in flight. An important contradiction exists quent return to equilibrium is with increasing.

between stability and controllability since velocity such that amplitude continues to adequate controllability does not necessarily increase with time. Thus, dynamic insta- exist with adequate stability. In fact, a high bility exists. The divergent oscillation occurs degree of stability tends to reduce the controlla- when energy is supplied to the motion rather bility of the aircraft. The general relation- than dissipated by positive damping. The ship between static stability and controlla- most outstanding illustration of the divergent bility is illustrated by figure 4.3.

oscillation occurs with the short period pitch- Figure 4.3 illustrates various degrees of ing oscillation of an aircraft. If a pilot un- static stability by a ball placed on various knowingly supplies control functions which surfaces. Positive static stability is shown by are near the natural frequency of the airplane the ball in a trough; if the ball is displaced in pitch, energy is added to the system, nega- from equilibrium at the bottom of the trough, tive damping exists, and the “pilot induced there is an initial tendency to return to equilib- oscillation” results.

rium. If it is desired to “control” the ball NAVWEPS 00-ROT-80 STABILITY AND CONTROL POSITIVE STATIC STABILITY CREASED POSIT,VE TIC STABILITY NEUTRAL STATIC STABILITY NEGATIVE STATIC STABILITY Figure 4.3. Stability and Control/ability NAVWEPS DD-8OT-80 STABILITY AND CONTROL &ease the angle of attack, the aircraft would and maintain it in the displaced position, a be trimmed at the higher angle of attack by force must be supplied in rhe direction of a push force to keep the aircraft from con- displacement co balance the inherent tendency tinuing in the displacement direction.

to return to equilibrium. This same stable Such tendency in an aircraft resists displacement control force reversal would evidence the aii- from trim by pilot effort on the controls or plane instability; the pilot would be supply- atmospheric disturbances. ing the stability by his attempt to maintain The effect of increased stability on con- the equilibrium. An unstable aircraft can be trollabilicy is illustrated by rhe ball in a flown if the instability is slight with a low steeper trough. A greater force is required to rate of divergence. Quick reactions coupled “control” the ball to the same lateral dis- with effective controls can allow the pilot to placement when the stability is increased. cope with some degree of static instability.

In this manner, a large degree of stability tends Since such flight would require constant at- to make the aircraft less controllable. It is tention by the pilot, slight instability can be necessary to achieve the proper balance be- tolerated only in airships, helicopters, and tween stability and tontrollability during rhe certain minor motions of the airplane. How- design of an aircraft because the ~ppcr limits ever, the airplane in high speed flight will of stability arc set by the lower 1imitJ of controlla- react rapidly to any disturbances and any in- bility. stability would create unsafe conditions. Thus, The effect of reduced stability on .controlla- it is necessary to provide some positive static bility is illustrated by the ball on a flat surface. stability to the major aircraft degrees of When neutral static stability exists, the ball freedom.

may be displaced from equilibrium and there is no stable tendency to return. A new point AIRPLANE REFERENCE AXES of equilibrium is obtained and no force is In order to visualize the forces and moments required to maintain the displacement. As on the aircraft; it is necessary to establish a the static stability approaches zero, controlla- set of mutually perpendicular reference axes bility increases to infinity and the only resist- originating at the center of gravity. Figure ance to displacement is a resistance to the 4.4 illustrates a conventional right hand axis motion of displacement-damping. For this system. The longitudinal or X axis is located

reason, the lower Limits of stability may be Set

in a plane of symmetry and is given a positive

by the upper limits of controllability. If the

direction pointing into the wind. A moment stability of the aircraft is too low, control about this axis is a rolling moment, L, and the deflections may create exaggerated displace- positive direction for a positive rolling moment ments of the aircraft.

utilizes the right hand rule. The vertical or 2 The effect of static instability. on controlla- axis also is in a plane of symmetry and is estab- bility is illustrated by the ball on a hill. If lished positive downward. A moment about the ball is displaced from equilibrium at the the vertical axis is a yawing moment, N, and a top of the hill, the initial tendency is for the positive yawing moment would yaw the air- ball td continue in the displaced direction.

craft co the right (right hand rule). The In order to “control”~the ball to some lateral lateral or Y axis is perpendicular to the plane displacement, a force must be applied oppo& of symmetry and is given a positive direction to the direction of displacement. This effect out the right side of the aircraft.

A moment would be appreciated during flight of an un- about the lateral axis is a pitching moment, M, stable aircraft by an unstable “feel” of the air- and a positive pitching moment is in the nose- craft. If the controls were deflected co in- up dlrection.

NAVWEPS 00-8OT-80 STABELITY AND CONTROL _ CENTER OF ..-.. ,.-..

VERTICAL AXIS Figure 4.4. Airplane Rekre&e Axes LONGITUDINAL STABILITY AND and magnitude. Neutral static longitudinal CONTROL stability usually defines the lower limit of airplane stability since it ‘ is the boundary STATIC LONGITUDINAL STABILITY between stability and instability. The air- plane with neutral static stability’ may be GENERAL CONSIDERATIONS. An air- excessively responsive to controls and the craft will exhibit positive static Iongitudinal aircraft has no tendency to return to trim fol- stability if it tends to return to the trim angle lowing a disturbance. The airplane with of attack when displaced by a gust or control negative sradc longitudinal stability is in- The aircraft which is unstable will movement. herently divergent from any intended trim continue to pitch in the disturbed direction condition. If it is at all possible to fly the until the displacement is resisted by opposing aircraft, the aircraft. cannot be trimmed and control forces. If the aircraft is neutrally illogical control forces and deflections are rc- stable, it tends to remain at any displacement quired to provide equilibrium with a change to which it is disturbed. It is most necessary of attitude and airspeed.

to provide an airplane with positive staric Since static longitudinal stability depends longitudinal stability. The stable airplane is upon the relationship of angle of attack and safe and easy to fly since the airplane seeks and pitching moments, it is necessary to study the tends to maintain a trimmed condition of pitching moment contribution of each com- flight. It also follows that control deflec- ponent of the aircraft. In a manner similar tions and control “feel” are logical in direction to all other aerodynamic forces, the pitching NAVWE,PS OO-ROT-80 STABILITY AND CONTROL moment about the lateral axis is studied in B of figure 4.5 provides comparison of the the coefficient form. stable and unstable conditions. Positive sta- bility is indicated by the curve with negative M = C,qS(MAC) slope. Neutral static stability would be the or result if the curve had zero slope. If neutral M stability exists, the airplane could be dis- &= qS(MAC) turbed to some higher or lower lift coefficient without change in pitching moment coefficient.

where Such a condition would indicate that the air- M=pitching moment about the c.g., ft.- plane would have no tendency to return to lbs., positive if in a nose-up direction some original equilibrium and would not hold q= dynamic pressure, psf An airplane which demonstrates a posi- trim.

S= wing area, sq. ft.

tive slope of the C, versus C, curve would be MAC=mean aerodynamic chord, ft.

If the unstable airplane were subject unstable.

C,= pitching moment coefficient to any disturbance from equilibrium at the The pitching moment coefficients contributed trim point, the changes in pitching moment by all the various components of the aircraft When would only magnify the disturbance.

are summed up and plotted versus lift coeffi- the unstable airplane is disturbed to some cient. Study of this plot of C, versus C, higher CL, a positive change in C, occurs which will relate the static longitudinal stability would illustrate a tendency for continued, of the airplane.

greater displacement. When the unstable air- Graph A of figure 4.5 illustrates the variation plane is disturbed to some lower C,,, a negative of pitching moment coefficient, C,, with lift change in C, takes place which tends to create coefficient, C,, for an airplane with positive continued displacement.

static longitudinal stability. Evidence of Ordinarily, the static longitudinal stability static stability is shown by the tendency to re- of a conventional airplane configuration does ,t,urn to equilibrium-or “trim”- upon dis- In other words, not vary with lift coefficient.

The airplane described by graph A .,placement.

the slope of C, versus CL does not change with is in trim or equilibrium when C,=O and, if the CL. However, if the airplane has sweepback, ‘ airplane is disturbed to some different C,, the large contribution of power effects to stability, pitching moment change tends to return the or significant changes in downwash at the aircraft to the.point of trim. If the airplane horizontal tail, noticeable changes in static ‘ were disturbed to some higher C, (point Y), a stability can occur at high lift coefficients.

negative or nose-down pitching moment is de- This condition is illustrated by graph C of veloped which tends to decrease angle of attack figure 4.5. The curve of C, versus CL of this back to the trim point. If the airplane were illustration shows a good stable slope at low disturbed to some lower C,, (point X), a posi- values of CL. Increasing CL effects a slight tive, or nose-up pitching moment is developed decrease in the negative slope hence a decrease which tends to increase the angle of attack in stability occurs. With continued increase back to the trim point. Thus, positive static in C,, the slope becomes zero and neutral longitudinal stability is indicated by a negative stability exists. Eventually, the slope be- slope of C, versus C,, i.e., positive stability is comes positive and the airplane becomes un- evidenced by a decrease in CM with an increase stable or “pitch-up” results. Thus, at any in C,.

lift coefficient, the static stability of the air- The degree of static longitudinal stability is pl.ane is depicted by the slope of the curve of indicated by the slope of the curve of pitching moment coefficient with lift coefficient. Graph CM versus CL.

NAVWEPS 00-8OT-80 STABILITY AND CONTROL TRIM CM=0 LIFT COEFFICIENT CL

-I

+

b

CM ----

CL - - -NEUTRAL LESS STABLE Figure 4.5. Airphmc Static Longitudinal Stability NAVWEPS OO-BOT-BO STABILITY AND CONTROL CONTRIBUTION OF THE COMPONENT not vary with C, since all changes in lift would SURFACES. The net pitching moment about take place at the c.g. In this case, the wing the lateral axis is due to the contribution of contribution to stability would be neutral.

each of the component surfaces acting in their When the c.g. is located behind the a.c. the appropriate flow fields. By study of the con- wing contribution i,s unstable and the curve tribution of each component the effect of each of C, versus CL for the wing alone would have component on the static stability may be ap- a positive slope.

preciated. It is necessary to recall that the Since the wing is the predominating aero- pitching moment coefficient is defined as: dynamic surface of an airplane, any change in the wing contribution may produce a sig- M nificant change in the airplane stability. This ‘ “ =qS(MAC) fact would be most apparent in the case of the flying wing or tailless airplane where the wing Thus, any pitching moment coefficient-re- contribution determines the airplane stability.

gardless of source-has the common denomi- In order for the wing to achieve stability, the nator of dynamic pressure, q, wing area, S, and c.g. must be ahead of the a.c. Also, the wing wing mean aerodynamic chord, MAC. This must have a positive pitching moment about common denominator is applied to the pitch- the aerodynamic center to achieve trim at ing moments contributed by the fuselage and positive lift coefficients. The first chart of nacelles, horizontal tail, and power effects figure 4.7 illustrates that the wing which is as well as pitching moments contributed by stable will trim at a negative lift coefficient if the wing.

If the stable wing has a the C,,, is negative.

WING. The contribution of the wing to positive C,,, it will then trim at a useful posi- stability depends primarily on the location tive CL. The only means available to achieve of the aerodynamic center with respect to the trim at a positive CL with a wing which has a airplane center of gravity. Generally, the negative C,,, is an unstable c.g. position aft of aerodynamic center-or a.c.-is defined as the the ax. As a result, the tailless aircraft point on the wing mean aerodynamic chord cannot utilize high lift devices which incur where the wing pitching moment coefficient any significant changes in C,,,.

does not vary with lift coefficient. All changes WhiIe the trim lift coefficient may be altered in lift coefficient effectively take place at the by a change in c.g. position, the resulting wing aerodynamic center. Thus, if the wing change in stability is undesirable and is unsat- experiences some change in lift coefficient, the isfactory as a primary means of control. The pitching moment created will be a direct variation of trim CL by deflection of control function of the relative location of the a.c. and surfaces is usually more effective and is less c.g.

inviting of disaster. The early attempts at Since stability is evidenced by the develop- manned flight led to this conclusion.

ment of restoring moments, the c.g. must be When the aircraft is operating in subsonic forward of the a.c. for the wing to contribute flight, the a.c. of the wing remains fixed at the to positive static longitudinal stability. As 25 percent chord station. When the aircraft shown in figure 4.6, a change in lift aft of the is flown in supersonic flight, the ax. of the c,g. produces a stable restoring moment de- wing will approach the 50 percent chord sta- pendent npon the lever arm between the a.c.

tion. Such a large variation in the location and c.g. In this case, the wing contribution of the a.c. can produce large changes in the would be stable and the curve of CM versus CL wing contribution and greatly alter the air- for the wing alone would have a negative slope.

plane longitudinal stability. The second chart If the c.g. were located at the a.c., C, would NAVWEPS 00-801-80 STABILITY AND CONTROL t CHANGE IN LIFT ~AERODYNAMIC CENTER CENTER OF GRAVITY - CL Figure 4.6. Wing Contribution NAVWEPS 00-BOT-80 STABILITY AND CONTROL STABLE, POSITIVE CyAC CM .ICl-2A-rI\,C C~ I IDIIETAIPI e

ai*

I

STABLE, NEGATIVE f&AC ) =3=Ez.,.

CM

CL

+

SUBSONIC - \ \ SUPERSONIC C. G. Position and Mach Nimber Figure 4.7. Effect of CM~~ NAVWEPS DD-807-80 STABILITY AND CONTROL nacelles deserves consideration in several in- of figure 4.7 illustrates the change of wing stances. Body upwash and variation of local contribution possible between subsonic and Mach number can influence the wing lift while supersonic flight. The large increase in static lift carryover and downwash can effect the fu- stability in supersonic flight can incur high selage and nacelles forces and moments.

trim drag or require great control effectiveness to prevent reduction in maneuverability. HORIZONTAL TAIL. The horizontal tail usually provides the greatest stabilizing influ- FUSELAGE AND NACELLES. In most cases, the contribution of the fuselage and ence of all the components of the airplane. To nacelles is destabilizing. A symmetrical body appreciate the contribution of the horizontal of revolution in the flow field of a perfect fluid tail to stability, inspect figure 4.9. If the air- develops an unstable pitching moment when plane is given a change in angle of attack, a given an angle of attack. In fact, an increase change in tail lift will occur at the aerody- in angle of attack produces an increase in the namic center of the tail. An increase in lift unstable pitching moment without the devel- at the horizontal tail produces a negative opment of lift. Figure 4.8 illustrates the pres- moment about the airplane c.g. and tends to sure distribution which creates this unstable return the airplane to the trim condition.

In the While the contribution of the horizontal tail moment on the body of revolution.

actual case of real subsonic flow essentially to stability is large, the -magnitude of the the same effect is produced. An increase in contribution is dependent upon the change in angle of attack causes an increase in the tail lift and the lever arm of the surface. It is unstable pitching moment but a negligible obvious that the horizontal tail will produce a increase in lift.

stabilizing effect only when the surface is aft An additional factor for consideration is the of the c.g. For this reason it would be inap- influence of the induced flow field of the wing.

propriate to refer to the forward surface of a As illustrated in figure 4.8, the upwash ahead canard (tail&St) configuration as a horizontal of the wing increases the destabilizing influence “stabilizer.” In a logical sense, the horizontal from the portions of the fuselage and nacelles “stabilizer” must be aft of the c.g. and- ahead of the wing. The downwash behind generally speaking-the farther aft, the greater the wing reduces the destabilizing influence the contribution to stability.

from the portions of the fuselage and nacelles Many factors influence the change in tail aft of the wing. Hence, the location of the lift which occurs with a change in airplane fuselage and nacelles relative to the wing is angle of attack. The area of the horizontal important in determining the contribution to tail has the obvious effect that a large surface stability.

would generate a large change in lift. In a The body of revolution in supersonic flow similar manner, the change in tail lift would can develop lift of a magnitude which cannot depend on the slope of the lift curve for the be neglected. When the body of revolution in horizontal tail. Thus, aspect ratio, taper, supersonic flow is given an angle of attack, a sweepback, and Mach number would deter- pressure distribution typical of figure 4.8 is the mine the sensitivity of the surface to changes result. Since the center of pressure is well in angle of attack. It should be appreciated forward, the body contributes a destabilizing that the flow at the horizontal tail is not of influence.

AS is usual with supersonic con- the same flow direction or dynamic pressure as figurations, the fuselage and nacelles may be the free stream. Due to the wing wake, fuse- quite large in comparison with the wing area lage boundary layer, and power effects, the q and the contribution to stability may be large.

at the horizontal tail may be greatfy different Interaction between the wing and fuselage and from the 4 of the free stream. In most in- NAVWEPS oo-BDT-BD STABILITY AND CONTROL BODY OF REVOLUTION IN PERFECT FLUID INDUCED FLOW FIELD FROM WING BODY OF REVOLUTION INSUPERSONIC FLOW Figure 4.8. Body or Nacelle Contribution NAVWEPS 00-BOT-BO STABILITY AND CONTROL _--- -.

CHANGE IN LIFT ON HORIZONTAL TAlL OF HORIZONTAL TAIL DOWNWASH AT FUSELAGE CROSS FLOW SEPARATION VORTICES Figure 4.9. Contribution of Tail and Downwash Effects NAVWEPS OO-BOT-80 STABILITY AND CONTROL stances, the 4 at the tail is usually less and this stabilizing so that the complete configuration reduces the efficiency of the tail. will exhibit positive static stability at the When the airplane is given a change in angle anticipated c.g. locations. In addition, the tail of attack, the horizontal tail does not expe- and wing incidence must be set to provide a rience the same change in angle of attack as trim lift coefficient near the design condition.

When the configuration of the airplane is the wing. Because of the increase in down- fixed, a variation of c.g. position can cause wash behind, the wing, the horizontal tail will large changes in the static stability. In the experience a smaller change in angle of attack, e.g., if a 10" change in wing angle of attack conventional airplane configuration, the large causes a 4O increase in downwash at the hori- changes in stability with c.g. variation are zontal tail, the horizontal tail experiences primarily due to the large changes in the wing only a 6’ change in angle of attack. In this contribution. If the incidence of all surfaces manner, the downwash at the horizontal tail remains fixed, the effect of c.g. position on reduces the contribution to stability. static longitudinal stability is typified by the Any second chart of figure 4.10. As the cg. is factor which alters the rate of change of down- gradually moved aft, the airplane static sta- wash at the horizontal tail will directly affect bility’ decreases, then becomes neutral then the tail contribution and airplane stability.

unstable., The c.g. position which produces Power effects can alter the downwash at the zero ,slope and neutral static stability is re- horizontal tail and affect the tail contribution.

Also, the ~downwash at the tail is affected by ferred to aspthe ~“neutral point.” The neutral the lift distribution on the wing and the flow point may be imagined as the effective aerody- condition ,on the fuselage. The low aspect namic center of the entire airplane configura- ratio airplane requires large angles of attack ration, i.e., with the c.g. at this position, all to achieve high ,lift coefficients and this posi- changes in net lift effectively occur at this tions the fuselage at high angles of attack.

point and no change in pitching moment The change in the wing downwash can be results. The neutral point defines the most accompanied by crossflow separation vortices aft c.g. position without static instability.

on the fuselage. It is possible that the net POWER EFFECTS. The effects of power may effect obviates or destabilizes the contribu- cause significant changes in trim lift coefficient tion of the horizontal tail and produces air- and static. longitudinal stability. Since the plane instability.

contribution to stability is evaluated by the POWER-OFF STABILITY. When the in- change in moment coefficients, power effects trinsic stability of a configuration is of interest, will be most significant when the airplane power effects are neglected and the stability operates at high power and low airspeeds such is considered by a buildup of the contributing~ as the power approach or waveoff condition.

components. Figure 4.10 illustrates a typical The effects of power are considered in two buildup of the components of a conventional main categories. First, there are the direct airplane configuration. If the c.g. is arbi- trarily set at 30 percent MAC, the contribu- effects resulting from the forces created by the propulsion unit. Next, there are the indirect tion of the wing alone is destabilizing as indi- effects of the slipstream and other associated cated by the positive slope of CM versus C,.

The combination of the wing and fuselage flow which alter the forces and moments of the increases the instability. The contribution aerodynamic surfaces. The direct effects of of the tail alone is highly stabilizing from power are illustrated in figure 4.11. The ver- the large negative slope of the curve. The tical location of the thrust line defines one of the direct contributions to stability. If the contribution of the tail must be sufficiently NAVWEPS OD-BOT-80 STABILITY AND CONTROL TYPICAL GUILD-UP 0F tzci~m~ENTs ,-WING+ FUSELAGE CM WING ONLY/.

- - CL - C.G. @ 30% MAC .

EFFECT OF C.G. WsITION t CM 50% MAC 40% MAC (NEUTRAL pOlNn --- Figure 4.10. Stability Build-up and Effect of C.G. Positim NAVWEPS 00-BOT-80 STABILITY ,AND CONTROL slipstream creates a normal force at the plane thrust line is below the c.g., thrust produces a of the propeller similar to a wing creating lift positive or noseup moment and the effect is de- by deflecting an airstream. As this normal stabilizing. On the other hand, if the thrust force will increase with an increase in airplane line is ,located above the c.g., a negative angle of attack, the effect will be destabilizing moment is created and the effect is stabilizing.

when the propeller is ahead of the cg. The A propeller or inlet duct located ahead of magnitude of the unstable contribution de- the c.g. contributes a destabilizing effect. As pends on the distance from the c.g. to the shown in figure 4.11, a rotating propeller in- propeller and is largest at high power and low clined to the windstream causes a deflection dynamic pressure. The normal force created of the airflow. The momentum change of the NAVWEPS OD-BOT-80 S-lABlLlTY AND CONTROL EFFECT OF VERTICAL LOCATION OF THRUST LINE STABILIZING

d

DESTABILIZING DESTABILIZING INCRE IN NORMAL FORCE DESTABILIZING INCREASE IN DUCT INLET NORMAL FORCE Figure 4.11. Direct Power Effects NAVWEPS GO-BOT-BO STABILITY AND CONTROL WING.NACELLE,AND FUSELAGE

n f MOMENTS AFFECTED BY

SLIPSTREAM -DYNAMIC PRESSURE AT TAIL AFFECTED BY SLIPSTREAM WING LIFT AFFECTED BY SLIPSTREAM FLOW INDUCED BY JET EXHAUST DOWNWASH AT TAIL Figure 4.12. Indirect Power Effects.

NAVWEPS 00-8OT-90 STABHITY AND CONTROL at the inlet of a jet engine contributes a similar static stability at high power, high CL, and destabilizing effect when the inlet is ahead low 4. It is generally true that any airplane of the c,g. As with the propeller, the magni- will experience the lowest level of static longi- tude of the stability contribution is largest at tudinal stability under these conditions. Be- cause of the greater magnitude of both direct high thrust and low flight speed.

The indirect effects of power are of greatest and indirect power effects, the propeller pow- ered airplane usually experiences a greater concern in the propeller powered airplane effect than the jet powered airplane.

rather than the jet powered airplane. As shown in figure 4.12, the propeller powered An additional effect on stability can be from airplane creates slipstream velocities on the the extension of high lift devices. The high various surfaces which are different from the lift devices tend to increase downwash at the tail and reduce the dynamic pressure at the tail, flow field typical of power-off flight. Since the various wing, nacelle, and fuselage surfaces both of which are destabilizing. However, the high lift devices may prevent an unstable are partly or wholly immersed in this slip- stream, the contribution of these components contribution of the wing at high CL. While the effect of high lift devices depends on the to stability can be quite different from the airplane configuration, the usual effect is de- power-off flight condition. Ordinarily, the stabilizing. Hence, the airplane may experi- change of fuselage and nacelle contribution with power is relatively small. The added ence the most critical forward neutral point lift on the portion of the wing immersed in during the power approach or waveoff.

Dur- the slipstream requires that the airplane oper- ing these conditions of flight the static stability ate at a lower angle of attack to produce the is usually the weakest and particular attention must be given to precise control of the air- same effective lift coefficienr. Generally, this reduction in angle of attack to effect the same plane. The power-on neutral point may set the most aft limit of c.g. position.

CL reduces the tail contribution to stability.

CONTROL FORCE STABILITY.

However, the increase in dynamic pressure at The static longitudinal stability of an airplane is defined the tail tends to increase the effectiveness of by the tendency to return to equilibrium upon the tail and may be a stabilizing effect. The magnitude of this contribution due to the displacement. In otherwords, the stable air- slipstream velocity on the tail will depend on plane will resist displacement from the trim or the c.g. position and trim lift coefficient. equilibrium. The control forces of the air- The deflection of the slipstream by the nor- plane should reflect the stability of the air- mal force at the propeller tends to increase the plane and provide suitable reference for precise downwash at the horizontal tail and reduce control of the airplane.

the contribution to stability. Essentially the The effect of elevator deflection on pitching same destabilizing effect is produced by the moments is illustrated by the first graph of flow induced at the exhaust of the jet power- figure 4.13. If the elevators of the airplane are fixed at zero deflection, the resulting line of plant. Ordinarily, the induced flow at the horizontal tail of a jet airplane is slight and is CM versus C’ s for 0’ depicts the static stability destabilizing when the jet passes underneath and trim lift coefficient. If the elevators are the horizontal tail. The magnitude of the fixed at a deflection of 10” up, the airplane indirect power effects on stability tends to be static stability is unchanged but the trim lift greatest at high Cr, high power, and low flight coefficient is increased. A change in elevator speeds. or stabilizer position does not alter the tail The combined direct and indirect power contribution to stability but the change in effects contribute to a general reduction of pitching moment will alter the lift coeflicient NAVWEPS 00-SOT-80 STABILITY AND CONTROL EFFECT OF ELEVATOR DEFLECTION I ELEVATOR

CM

nre, CCTl,-..,

-L

TRIM FOR CG@20% MAC TRIM C, VERSUS ELEVATOR DEFLECTION TRIM AIRSPEED VS ELEVATOR DEFLECTION

A

z F ii UP ii ’ X~SLE : EQUIVALENT oz t / ~RSPEED / a 2 DOWN / / ii Figure 4.13. Longitudinal Control NAVWEPS 00-BOT-80 STABILITY AND CONTROL tail is subject to an increase in angle of attack at which equilibrium will occur. As the ele- and the elevators tend to float up, the change vator is fixed in various positions, equilibrium in lift on the tail is less than if the elevators (or trim) will occur at various lift coefficients remain fixed and the tail contribution to and the trim CL can be correlated with elevator stability is reduced. Thus, the “stick-free” deflection as in the second graph of figure 4.13.

stability of an airplane is usually less than the When the c,g. position of the airplane is stick-fixed stability. A typical reduction of fixed, each elevator position corresponds to a stability by free elevators is shown in figure particular trim lift coefficient. AS the c.g. is moved aft the slope of this line decreases and 4.14(A) where the airplane. stick-free demon- strates a reduction of the slope of CM versus Cs.

the decrease in stability is evident by a given control displacement causing a greater change While aerodynamic balance may be provided tu reduce control forces, proper balance of the in trim lift coefficient. This is evidence that decreasing stability causes increased controlla- surfaces will reduce floating and prevent great differences between stick-fixed and stick-free bility and, of course, increasing stability de- stability. The greatest floating tendency oc- creases controllability. If the c.g. is moved aft until the line of trim CL versus elevator de- curs when the surface is at a high angle of attack hence the greatest difference between flection has zero slope, neutral static stability is obtained and the “stick-fixed” neutral point stick-fixed and stick-free stability occurs when the airplane is at high angle of attack.

is determined.

If the controls are fully powered and actu- Since each value of lift coefhcient corresponds to a particular value of dynamic pressure re- ated by an irreversible mechanism, the sur- faces are not free to float and there is no differ- quired to support an airplane in level flight, uim airspeed can be correlated with elevator ace between the stick-fixed and stick-free deflection as in the third graph of figure 4.13.

static stability.

If the c.g. location is ahead of the stick-fixed The control forces in a conventional air- neutral point and control position is directly plane are made up of two components. First, related to surface deflection, the airplane will the basic stick-free stability of the airplane give evidence of stick podion mbility. In contributes an incremem of force which is other words, the airplane will require the independent of airspeed.. Next, there. is an stick to be moved aft to increase the angle increment of force dependent on the trim tab of attack and trim at a lower airspeed and to setting which varies with-the dynamic pres- be moved forward to decrease the angle of sure or the square of ‘ equivalent airspeed.

attack and trim at a higher airspeed. To be Figure 4.14(B) indicates the variation of sure, it is desirable to have an airplane demon- stick force with airspeed and illustrates the strate this feature. If the airplane were to effect of tab setting on stick force. In order have stick position instability, the airplane te trim the airplane at point (1) a certain would require the stick to be moved aft to trim amount of up elevator is required and zero at a higher airspeed or to be moved forward to stick force is obtained~ with’ the nse of the tab.

trim at a lower airspeed.

To trim the airplane for higher speeds corre- There may be slight differences in the static sponding to points (2) and (3) less and less longitudinal stability if the elevators are nose-up tab is required. Note that when the allowed to float free. If the elevators are airplane is properly trimmed, a push force is allowed to float free as in “hands-off” flight, required to increase airspeed and a pull force the elevators may have a tendency to “float” is required to decrease airspeed. In this man- or streamline when the horizontal tail is given ner, the airplane would indicate positive stick a change in angle of attack.

If the hot&ma1 force stability with a stable “feel” for air- NAVWEPS 00-BOT-80 STABILITY AND CONTROL STICK -FIXED ) a,,, I, -- F TAB FORCE INCREMENT EQUIVALENT INCREMENT CG AT 20% MAC I CG POSITION 10% MAC PULL

p-z; ,/’EQUlV

PUSH PULL w E T ,o D - FRICTION FORC BAND Figure 4.74. Control Force Stability NAVWEPS 00-801-80 STABILITY AND CONlRO’ L the pitch motion which adds to the restoring speed, If the airplane were given a large nose moment from the basic static stability. The down tab setting the pull force would in- principal source of this additional pitching crease with airspeed. This fact points out the moment is illustrated in figure 4.15.

possibility of “feel” as not being a true indi- During a pull-up the airplane is subject to cation of airplane static stability.

an angular rotation about the lateral axis and If the c.g. of the airplane were varied while the horizontal tail will experience a component maintaining trim at a constant airspeed, the effect of c.g. position on stick force stability of wind due to the pitching velocity. The vector addition of this component velocity to could be appreciated. As illustrated in figure the flight velocity provides a change in angle 4,14(C), moving the c,g. aft decreases the of attack for the tail and the change in lift on slope of the line of stick force through the the tail creates a pitching moment resisting trim speed. Thus, decreasing stick force stability is evident in that smaller stick forces the pitching motion. Since the pitching mo- ment opposes the pitching motion but is due are necessary to displace the airplane from to the pitching motion, the effect is a damping the trim speed. When the stick force gradient in pitch. Of course, the other components of (or slope) becomes zero, the c.g. is at the the airplane may develop resisting moments stick-free neutral point and neutral stability and contribute to pitch damping but the exists. If the c.g. is aft of the stick-free neutral point, stick force instability will horizontal tail is usually the largest contri- bution. The added pitching moment from exist, e.g. the airplane will require a push force at a lower speed or a pull force at a higher pitch damping will effect a higher stability speed. It should be noted that the stick force in maneuvers than is apparent in steady flight.

gradient is low at low airspeeds and when From this consideration, the neutral point for the airplane is at low speeds, high power, maneuvering flight will be aft of the neutral and a c.g. position near the aft limit, the point for unaccelerated flight and in most cases “feel” for airspeed will be weak. will not be a critical item. If the airplane Control system friction can create very un- demonstrates static stability in unaccelerated desirable effects on control forces. Figure flight, it will most surely demonstrate stability 4.14(D) illustrates that the control force in maneuvering flight.

versus airspeed is a band rather than a line. The most direct appreciation of the ma- A wide friction force band can completely neuvering stability of an airplane is obtained mask the stick force stability when the stick from a plot of stick force versus load factor force stability is low. Modern flight control such as shown in figure 4.15. The airplane systems require precise maintenance to mini- with positive maneuvering stability should mize the friction force band and preserve demonstrate a steady increase in stick force proper feel to the airplane. with increase in load factor or “G”. The MANEUVERING STABILITY. When an maneuvering stick force gradient-or stick airplane is subject to a normal acceleration, force per G-must be positive but should be the flight path is curved and the airplane is The stick force of the proper magnitude.

subject to a pitching velocity. Because of gradient must not be excessively high or the the pitching velocity in maneuvering flight, airplane will be difficult and tiring to maneuver.

the longitudinal stability of the airplane is Also, the stick force gradient must not be too slightly greater than in steady flight condi- low or the airplane may be overstressed in- tions. When an airplane is subject to a pitch- advertently when light control forces exist.

1 ing velocity at a given lift coefficient, the air- A maneuvering stick force gradient of 3 to 8 plane develops a pitching moment resisting lbs. per G is satisfactory for most fighter and NAVWEPS 00-801-80 STABILITY AND CONTROL CHANGE IN TAIL LIFT RELATIVE WIND FROM ANGULAR ROTATION CHANGE IN TAIL ANGLE OF ATTACK DUE TO PITCHING VELOCITY co !!I 30 ; 20 MANEUVERING STICK :: FORCE GRADIENT g IO w I 2 3 4 5 6 7 8 LOAD FACTOR, n (OR G) CG POSITION % MAC / LOAD FACTOR Figure 4.15. Maneuvering Stability NAVWEPS 00-8’ X-60 STABILITY AND CONTROL leading edge (unshielded) or partway to the attack airplanes. A large patrol or transport leading edge (shielded). Aerodynamic balance type airplane would ordinarily show a much can be achieved by the provision of- a hinge higher maneuvering stick force gradient be- line aft of the control surface leading edge.

cause of the lower limit load factor.

When the airplane has high static stability, The resulting overhang of surface area ahead of the hinge line will provide a degree of the maneuvering stability will be high and a high stick force gradient will result. A balance depending on the amount of overhang.

possibility exists that the forward c.g. limit Another variation of aerodynamic balance is could be set to prevent an excessively high an internal balance surface ahead of the hinge maneuvering stick force gradient. As the line which is contained within ,the surface.

A flexible seal is usually incorporated to in- c.g. is moved aft, the stick force gradient de- creases with decreasing maneuvering stability crease the effectiveness of the balance area.

Even the bevelling of the trailing edge..of the and the lower limit of stick force gradient may be reached. control surface is effective also as a balancing technique. The choice of the type of aerody- The pitch damping of the airplane is obvi- ously related to air density. namic balance will depend on many factors At high altitudes, the high true airspeed reduces the change in such as required degree of balance, simplicity, tail angle of attack for a given pitching velocity drag, etc.

and reduces the pitch damping. Thus, a de- Many devices can be added to a control crease in maneuvering stick force stability can system to modify or tailor the stick force be expected with increased altitude. stability to desired levels. If a spring is added TAILORING CONTROL FORCES. The to the control system as shown in figure 4.16, control forces should reflect the stability of it will tend to center the stick and provide a the airplane but, at the same time, should be force increment depending on stick displace- of a tolerable magnitude. The design of the ment. When the control system has a fixed surfaces and control system may employ an gearing between stick position and surface infinite variety of techniques to provide satis- deflection, the centering spring will provide a factory control forces. contribution to stick force stability according Aerodynamic balance must be thought of in to stick position. The contribution to stick two different senses. First, the control surface force stability will be largest at low flight must be balanced to reduce hinge moments due speeds where relatively large control deflec- to changes in angle of attack. tions are required. The contribution will be This is necessary to reduce the floating tendency of the surface smallest at high airspeed because of the smaller which reduces the stick-free stability. Next, control deflections required. Thus, .the stick aerodynamic balance can reduce the hinge centering bungee will increase the airspeed moments due to deflection of the control sur- and maneuvering stick force stability but the face. Generally, it is difficult to obtain a high contribution decreases at high airspeeds. A degree of deflection balance without incurring variation of this device would be a spring stiffness which would be controlled to vary a large overbalance of the surface for changes in angle of attack.

with dynamic pressure, 4. In this case, the Some of the types of aerodynamic balance contribution of the spring to stick force are illustrated in figure 4.16. Thesimple horn stability would, not diminish with. speed.

type balance employs a concentrated balance A “downspring” added to a control system area located ahead of the hinge line.

The is~a means ~of increasing airspeed stick force balance area may extend completely to the stability without a change in airplane static 2,70 NAVWEPS 00-8OT-80 STABILITY AND CONTROL TYPES OF AERODYNAMIC BALANCE OVERHANGORLEADINGEDGE BALANCE BY OFFSET HINGE 7 INTERNAL BALANCE WITH FL’ XlBLESE& <I HORN TYPE BALANCE ---‘ I “1G EDGE BEVEL -, EFFECT LaF STICK CENTERING SPRING TICK CENTERING RING OR BUNGEE

A

PULL FORCE INCREMENTADDED BY SPRING y EQUIVALENT E e \ AIRSPEED i5 I= m PUSH LOAD FACTOR figure 4.16. loiloring Control forces NAVWEPS 00-801-80 STABILITY AND CONTROL EFFECT OF DOWNSPRING P*RELO+DED SPRING u PULL EQUIVALENT lRSPEED EFFECT OF BOBWEIGHT PULL EQUIVALENT PUSH RETRIMMED FORCE INCREMENT PROVIDED BY BOBWEIGHT c LOAD FACTOR Figure 4.77. Tailoring Control Forces NAVWEPS 00-EOT-80 STABILITY AND CONTROL stability. As shown in figure 4.17, a down- Various control surface tab devices can be spring consists of a long preloaded spring at- utilized to modify control forces.

Since the de- tached to the control system which tends to flection of a tab is so powerful in creating hinge rotate the elevators down. The effect of the moments on a control surface, the possible downspring is to contribute an increment of application of tab devices is almost without pull force independent of control deflection or limit, The basic trim tab arrangement is airspeed. When rhe downspring is added to shown in figure 4.18 where a variable linkage the control system of an airplane and the air- connects the tab and the control surface. Ex- plane is retrimmed for the original speed, the tension or contraction of this linkage will de- airspeed stick force gradient is increased and flect the tab relative to the control surface and there is a stronger feel for airspeed. The down- create a certain change in hinge mon~ent coef- spring would provide an “ersatz” improve- ficient. The use of the trim tab will allow the ment to an airplane deficient in airspeed stick pilot to reduce the hinge moment to zero and force stability, Since the force increment from trim the control forces to zero for a given flight the downspring is unaffected by stick position condition. Of course, the trim tab should have or normal acceleration, the maneuvering stick adequate effectiveness so that control forces force stability would be unchanged. can be trimmed out throughout the flight speed The bobweight is an effective device for im- range.

proving stick force stability. As shown in The lagging tab arrangement shown in figure figure 4.17, the bobweight consists of an eccen- 4.18 employs a linkage between the fixed sur- tric mass attached to the control system face and the tab surface. The geometry is which-in unaccelerated flight--contributes such that upward deflection of the control an increment of pull force identical to the surface displaces the tab down relative to the downspring. In fact, a bobweight added to control surface. Such relative displacement the control system of an airplane produces an of the tab will aid in deflection of the control effect identical to the downspring. The bob- surface and thus reduce the hinge moments due weight will increase the airspeed stick force to deflection. An obvious advantage of this device is the reduction of deflection hinge gradient and increase the feel for airspeed.

moments without a change in aerodynamic A bobweighr will have an effect on the maneuvering stick force gradient since the bob- balance.

The leading tab arrangement shown in figure weight mass is subjected to the same accelera- 4.18 also employs a linkage between the fixed tion as the airplane. Thus, the bobweight will provide an increment of stick force in direct surface and the tab surface. However, the geometry of the linkage is such that upward proportion to the maneuvering acceleration of deflection of the control surface displaces the the airplane. Because of the linear contribu- This tion of the bobweight, the bobweight can be tab up relative to the control surface.

relationship serves to increase the control sur- applted to Increase the maneuvering stick force face hinge moments due to deflection of the stability if the basic airplane has too low a surface.

value or develops a decreasing gradient at high The servo tad shown in figure 4.18 utilizes a lift coefficients.

The example of the bobweight is useful to horn which has no direct connection to the point out the effect of the control system dis- control surface and is free to pivot about the tributed masses. All carrier aircraft must have hinge axis. However, a linkage connects this free horn to the tab surface.

the control system mass balanced to prevent Thus, the control undesirable control forces from the longi- system simply deflects the tab and the resulting tudinal accelerations during catapult launching. hinge moments deflect the control surface.

NAVWEPS 00-EOT-80 STABILITY AND CONTROL TRIM TAB VARIABLE LINKAGE LAGGING TAB LEAOING TAB SERVO TAB HORN FREE TO PIVOT ON HINGE 13X6 SPRING TAB ON HINGE AXIS FIXED TO SURFACE SPRING LLADED TAB ROTATES TAB UP Figure 4.18. Various Tab Devices NAVWEPS OtWOT-80 STABILITY AND CONTROL stability. Ati airplane with high static longi- Since the only control forces are those of the tudinal stability will exhibit great resistance tab, this device makes possible the deflection to displacement from equilibrium. Hence, of large surfaces with relatively small control the most critical conditions of controllability forces.

will occur when the airplane has high sta- A variation of the basic servo tab layout is the sprirzg tab arrangement of figure 4.18. bility, i.e., the lower limits of controllability will set the upper limits of stability.

When the control horn is connected to the There are three principal conditions of control surface by springs, the function of the tab is to provide a given portion of the required fli~ght which provide the critical requirements control forces. The spring tab arrangement of longitudinal control power. Any one can then function as a boost to reduce control or combination of these conditions can de- forces. The servo tab and spring tab are termine the longitudinal control power and usually applied to large or high speed subsonic set a limit to forward c.g. position.

airplanes to provide tolerable stick forces. MANEUVERING CONTROL REQUIRE- The spring Zoadcdtab of figure 4.18 cotisists MENT. The airplane should have sufficient longitudinal control power to attain the maxi- of a free tab preloaded with a spring which furnishes a constant moment about the tab mum usable lift coefficient or limit load factor during maneuvers. As shown in figure 4.19, hinge line. When the airplane is at zero air- speed, the tab is rotated up to the limit of forward movement of the c.g. increases the deflection. As airspeed is increased, the aero- longiturjinal stability of an airplane and requires larger control deflections to produce dynamic hinge moment on the tab will finally changes in trim lift coefficient. For the equal the spring torque and the tab will begin example shown, the maximum effective de- to streamline. The effect of this arrangement is to provide a constant hinge moment to the flection of the elevator is not capable of trim- ing the airplane ‘ at C,,,, for c.g. positions control system and contribute a constant push force requirement at speeds above the preload ahead of 18 percent MAC.

This particular control requirement can be speed. Thus, the spring loaded tab can im- most critical for an airplane in supersonic prove the stick force gradient in a manner flight. Supersonic flight is usually accom- similar to the downspring. Generally, the .

panied by large increases in static longltu- spring loaded tab may be more desirable dinal stability and a reduction in the effective- because of greater effectiveness and the lack of ness of control surfaces. In order to cope with undesirable control forces during ground these trends, powerful all-movable surfaces operation.

must be used to attain limit load factor or The various tab devices have almost un- maximum usable C, in supersonic flight. This limited possibilities for tailoring control forces.

requirement is so important that once satis- However, these devices must receive proper fied, the supersonic configuration usually has care and maintenance in order to function sufficient longitudinal control power for all properly. In addition, much care must be other conditions of flight.

taken to ensure that no slop or play exists in TAKEOFF CONTROL REQUIREMENT.

the joints and fittings, otherwise destructive At takeoff, the airplane must have sufficient flutter may occur.

control power to assume the takeoff attitude prior to reaching takeoff speed. Generally, LONGITUDINAL CONTROL for airplanes with tricycle landing gears, it To be satisfactory, an airplane must have is desirable to have at least sufficient control adequate controllability as well as adequate power to attain the takeoff attitude at 80 NAVWEPS 00-80’ 1-80 SlABILITY AND CONTROL MAXIMUM MOST FORWARD DEFLECTION CG FOR MANEUVERING CONTROLLABILITY DOWN POSITION TAIL LOAD !'.',i:'.

WEIGHT TAKE OFF CONTROL REDUCED DOWNWASH DUE TO GROUND EFFECT . .:,.,. ‘ ,:::.;,y ,;,,.,,>: ::..‘ ~~,‘ i;,:,‘ ,,:.~,,‘ : y::, ,: ,/.:“ ‘ J.:;:‘ j:~!,.: : :., :, .‘ .

;. ~.. i... .,-: -, :,.: ~, :,., :.:, :~’ LANDING CONTROL Figure 4.19. Longitudinal Control Requirements NAVWEPS 00-BOT-80 STABILITY AND CONTROL percent of the stall speed for propeller air- flaps are fully extended, and power is set at planes or 90 percent of the stall speed for jet idle. This configuration will provide the airplanes. This feat must be accomplished on most stable condition which is most demand- ing of controllability. The full deflection of a smooth runway at all normal service takeoff loading conditions. flaps usually provides the greatest wing diving Figure 4.19 illustrates the principal forces moment and idle power will produce the most acting on an airplane during takeoff toll. critical (least) dynamic pressure at the hoti- When the airplane is in the three point attitude zontal tail.

at some speed less than the stall speed, the The landing control requirement has one wing lift will be less than the weight of the particular difference from the maneuvering airplane. As the elevators must be capable control requirement of free flight. As the of rotating to the takeoff attitude, the critical airplane approaches the ground surface, there condition will be with zero load on the nose will be a change in the three-dimensional flow wheel and the net of lift and weight supported of the airplane due to ground effect. A wing in on the main gear. Rolling friction resulting proximity to the ground plane will experience from the normal force on the main gear creates a decrease in tip vortices and downwash at an adverse nose down moment. Also, the a given lift coefficient. The decrease in down- center of gravity ahead of the main gear wash at the tail tends to increase the static contributes a nose down moment and this stability and produce a nosedown moment from consideration could decide the most aft loca- the reduction in download on the tail. Thus, tion of the main landing gear during design. the airplane just off the runway surface will The wing may contribute a large nose down requite additional control deflection to trim moment when flaps are deflected but this at a given lift coefficient and the landing con- effect may be countered by a slight increase trol requirement may be critical in the design in downwash at the tail. To balance these of longitudinal control power.

nose down moments, the horizontal tail As an example of ground effect, a typical should be capable of producing sufficient nose propeller powered airplane may requite as up moment to attam the takeoff attitude. at much as 15” more up elevator to trim at CL- the specified speeds. in ground effect than in free flight away from The propeller airplane at takeoff power may the ground plane. Because of this effect, many induce considerable slipstream velocity at the aitplaneshavesufIicientcontrolpowertoachieve horizontal tail which can provide an increase full stall out of ground effect but do not have in the e&iency of the surface. The jet the ability to achieve full stall when in close airplane does not experience a similar magni- proximity to the ground.

tude of this effect since the induced velocities In some cases the effectiveness of the control from the jet are relatively small compared surface is adversely affected by the use of trim to the slipstream velocities from a propeller. tabs. If trim tabs are used to excess in ttim- LANDING CONTROL REQUIREMENT ming stick forces, the effectiveness of the At landing, the airplane must have suthcient elevator.may be reduced to hinder landing or control power to ensure adequate control at takeoff control.

Each of the three principal conditions re- specified landing speeds. Adequate landing control is usually assured if the elevators are quiting adequate longitudinal control are ctit- capable of holding the airplane just off the ical for high static stability. If the forward runway at 105 percent of the stall speed. Of c.g. limit is exceeded, the airplane may en- course, the most critical requirement will exist counter a deficiency of controllability in any when the c.g. is in the most forward position, of these conditions. Thus, the forward c.g.

NAVWEPS DD-801-80 STABILITY AND CONTROL (4) The displacement or deflection of the limit is set by the minimum permissible con- elevator when the stick-free condition is trollability while the aft c.g. limit is set by the minimum permissible stability. considered.

LONGITUDINAL DYNAMIC STABILITY. The longitudinal dynamic stability of an airplane generally consists of three basic modes All previous considerations of longitudinal stability have been concerned with the initial (or manners) of oscillation. While the longi- tendency of the airplane to return to equilib- tudinal motion of the airplane may consist of a rium when subjected to a disturbance. combination of these modes, the characteristics The considerations of longitudinal dynamic sta- of each mode are sufficiently distinct that each bility ate concerned with time history response oscillatory tendency may be studied separately.

of the airplane to these disturbances, i.e., the The first mode of dynamic longitudinal sta- variation of displacement amplitude with time bility consists of a very long period oscillation following a disturbance. From previous deli- referred to as the phagoid. The phugoid or long nition, dynamic stability will exist when the period oscillation involves noticeable vatia- amplitude of motion decreases with time and tions in pitch attitude, altitude, and airspeed dynamic instability will exist if the amplitude but nearly constant angle of attack. Such an increases with time. oscillation of the airplane could be considered Of course, the airplane must demonstrate as a gradual interchange of potential and positive dynamic stability for the major longi- kinetic energy about some equilibrium airspeed tudinal motions. In addition, the airplane and altitude.

Figure 4.20 illustrates the char- must demonstrate a certain degree of longitu- acteristic motion of the phugoid.

dinal stability by reducing the amplitude of The period of oscillation in the phugoid is motion at a certain rate. quite large, typical values being from 20 to 100 The requited degree of dynamic stability is usually specified by seconds. Since the pitching rate is quite low the time necessary for the amplitude to reduce and only negligible changes in angle of attack to one-half the original value-the time to take place, damping of the phugoid is weak and damp to half-amplitude.

possibly negative. However, such weak or The airplane in free flight has six degrees of negative damping does not necessarily have any freedom: rotation in roll, pitch, and yaw and great consequence.

Since the period of oscilla- translation in the horizontal, vertical, and tion is so great, the pilot is easily able to lateral directions. In the case of longitudinal counteract the oscillatory tendency by very dynamic stability, the degrees of freedom can slight and unnoticed control movements. In be limited to pitch rotation, vertical and most cases, the necessary corrections ate so horizontal translation. Since the airplane is slight that the pilot may be completely un- usually symmetrical from port to starboard, aware of the oscillatory tendency.

there will be no necessity for consideration of Due to the nature of the phugoid, it is not coupling between longitudinal and lateral- necessary to make any specific aerodynamic directional motions. Thus, the principal vari- provisions to contend with the oscillation.

ables in the longitudinal motion of an airplane The inherent long period of the oscillation al- will be: lows study to be directed to more important (1) The pitch attitude of the airplane. oscillatory tendencies. Similarly, the diffet- (2) The angle of attack (which will differ ences between the stick-fixed and stick-free from the pitch attitude by the inclination of phugoid are not of great importance.

the flight- path).

The secondmodeof longitudinal dynamic sta- (3) The flight velocity. bility is a relatively short period motion that NAVWEPS OO-BOT-80 STABILITY AND CONTROL IST MODE OR PHUGOID ANGLE OF ATTACK AT EACH INS%; ,,“L&blSG$~,lGH~ &

LoNG PERIOD ------I

kw

a0

f 2

- g: *a 2ND MODE OR SHORT PERIOD OSCILLATION MOTION OCCURS AT ESSENTIALLY CONSTANT SPEED L TIME TO DAMP TO HALF AMPLITUDE TIME Lb-- / / -6.HORT PERIOD - UNSTABLE OSCILLATION Figure 4.20. Longiitudinal Dynamic Sttxbility NAVWEPS 00-BOT-80 STABILITY AND CONTROL can be assumed to take place with negligible control system is greatly magnified. In addi- changes in velocity.

The second mode consists tion, response lag of the controls may add to of a pitching oscillation during which the air- the problem of attempting to forceably damp plane is being restored to equilibrium by the the oscillation. In this case, should an oscilla- static stability and the amplitude of oscillation tion appear, the best rule is to release the con- decreased by pitch damping. The typical mo- trols as the airplane stick-free will demonstrate tion is of relatively high frequency with a the necessary damping, Even an attempt to period of oscillation on the order of 6.5 to 5 fix the controls when the airplane is oscillating seconds.

may result in a small unstable input into the For the conventional subsonic airplane, the control system which can reinforce the oscilla- second mode stick-fixed is characterized by tion to produce failing flight loads. Because heavy damping with a time to damp to half of the very short period of the oscillation, the amplitude of approximately 0.5 seconds. IJsu- amplitude of an unstable oscillation can reach ally, if the airplane has static stability stick- dangerous proportions in an extremely short fixed, the pitch damping contributed by the period of time.

horizontal tail will assume sufficient dynamic The third mode occurs in the elevator free case stability for the short period oscillation. How- and is usually a very short period oscillation.

ever, the second mode stick-free has the possi- The motion is essentially one of the elevator bility of weak damping or unstable oscilla- flapping about the hinge line and, in most tions. This is the case where static stability cases, the oscillation has very heavy damping.

does not automatically imply adequate dy- A typical flapping mode may have a period of namic stability.

The second mode stick-free is 0.3 to 1.5 seconds and a time to damp to half- essentially a coupling of motion between the amplitude of approximately 0.1 second.

airplane short period pitching motion and ele- Of all the modes of longitudinal dynamic vator in rotation about the hinge line. Ex- stability, the second mode or porpoising oscil- treme care must be taken in the design of the lation is of greatest importance. The por- control surfaces to ensure dynamic stability for poising oscillation has the possibility of this mode. The elevators must be statically damaging flight loads and can be adversely balanced about the hinge line and aerodynamic affected by pilot response lag. It should be balance must be within certain limits.

Control remembered that when stick-free the airplane system friction must be minimized as it con- will demonstrate the necessary damping.

tributes to the oscillatory tendency. If insta- The problems of dynamic stability are acute bility were to exist in the second mode, “por- Low static under certain conditions of flight.

poising” of the airplane would result with stability generally increases the period (de- possibility of structural damage. An oscilla- creases frequency) of the short period oscil- tion at high dynamic pressures with large lations and increases the time to damp to half- changes in angle of attack could produce severe amplitude. High altitude-and consequently flight loads. low density-reduces the aerodynamic damp- The second mode has relatively short periods ing. Also, high Mach numbers of supersonic flight produce a decay of aerodynamic damping.

that correspond closely with the normal pilot response lag time, e.g., 1 or 2 seconds or less.

There is the possibility that an attempt to MODERN CONTROL SYSTEMS forceably damp an oscillation may actually re- inforce the oscillation and produce instability.

In order to accomplish the stability and This is particularly true in the case of powered control objectives, various configurations of control systems are necessary. Generally, the controls where a small input energy into the ?Bl NAVWEPS 00-BOT-BO STABILITY AND CONTROL type of flight control system is decided by the by the actuator and none of the hinge moments size and flight speed range of the airplane. are fed back through the controls. In such The conventional control system consists of a control system, the control position decides direct mechanical linkages from the controls the deflection of the control surfaces regardless to the control surfaces. For the subsonic of the airloads and hinge moments. Since the airplane, the principal means of producing power-operated control system has zero feed- proper control forces utilize aerodynamic bal- back, control feel must be synthesized other- wise an infinite boost would exist.

ance and various tab, spring, and bobweight The advantages of the power-operated COR- devices. Balance and tab devices are capable trol system are most apparent in transonic and of reducing control forces and will allow the use of the conventional control system on large supersonic flight. In transonic flight, none of airplanes to relatively high subsonic speeds. the erratic hinge moments are fed back to the When the airplane with a conventional pilot. Thus, no unusual or erratic control control system is operated at transonic speeds, forces,will be encountered in transonic flight.

the great changes in the character of flow Supersonic flight generally requires the use of can produce great aberrations in control sur- an all-movable horizontal surface to achieve the necessary control effectiveness. Such con- face hinge moments and the contribution of tab devices. Shock wave formation and trol surfaces must then be actuated and posi- tively positioned by an irreversible device.

separation of flow at transonic speeds will The most important item of an artificial feel limit the use of the conventional control system is the stick-centering spring or bungee.

system to subsonic speeds.

The bungee develops a stick force in proportion The power-boostedcontrol system employs a ‘ mechanical actuator in parallel with the to stick displacement and thus provides feel for airspeed and maneuvers. A bobweight mechanical linkages of a conventional control system. The principle of operation is to pro- may be included in the feel system to develop vide a fixed, percentage of the required control a steady positive maneuvering stick force forces thus reducing control forces at high gradient which is independent of airspeed for speeds. The power-boosted control system ordinary maneuvers.

requires a hydraulic actuator with a control The gearing between the stick position and valve which supplies boost force in fixed control surface deflection is not necessarily a proportion to control force. Thus, the pilot linear relationship. The majority of powered is given an advantage by the boost ratio to control systems will employ a nonlinear gear- assist in deflecting the control surface, e.g., ing such that relatively greater stick deflection with a boost ratio of 14, the actuator provides per surface deflection will occur at the neutral 14 lbs. of force for each 1 lb. of stick force. stick position. This sort of gearing is to The power-boosted control system has the advantage for airplanes which operate at flight obvious advantage of reducing control forces conditions of high dynamic pressure. Since at high speeds. However, at transonic speeds, the airplane at high 4 is very sensitive to small the changes in control forces due to shock deflections of the control surface, the nonlinear waves and separation still take place but to a gearing provides higher stick force stability lesser degree. The “feedback” of hinge with less sensitive control movements than moments is reduced but the aberrations in the ‘ system with a linear gearing. Figure 4.21 stick forces may still exist.

illustrates a typical linear and nonlinear control The power-opsrdted, irreversible control system system gearing.

consists of mechanical actuators controlled The second chart of figure 4.21 illustrates by the pilot. The control surface is deflected the typical control system stick force variation NAVWEPS 00-ROT-80 STABILITY AND CONTROL CONTROL SYSTEM GEARING CONTROL SYSTEM STICK FORCE -40 STICK FORCE LBS.

-30 PULL -20 -10 STABILIZER DEFLECTION LEADING EDGE UP LEADING EDGE DOWN 25O 200 I50 100 50 50 I00 Figure 4.27. Longitudinal Control System NAVWEPS OO-ROT-80 STABILITY AND CONTROL moments which tend to restore the airplane with control surface deflection. While it is to equilibrium.

desirable to have a strong centering of the DEFINITIONS. The axis system of an air- stick near the neutral position, the amount of plane will define a positive yawing moment, force required to create an initial displacement N, as a moment about the vertical axis which must be reasonable. If the control system tends to rotate the nose to the right. As in “break-out” forces are too high, precise control other aerodynamic considerations, it is con- of’ the airplane at high speeds is diflicult. As venient to consider yawing moments in the the solid friction of the control system con- coefficient form so that static stability can be tributes to the break-out forces, proper mainte- evaluated independent of weight, altitude, nance of the control system is essential. Any speed, etc. The yawing moment, N, is de- increase in control system friction can create fined in the coefficient form by the following unusual and undesirable control forces.

equation: The trim of the powered control system is essentially any device to produce zero control N = C,qSb force for a given control surface deflection.

or One system may trim off bungee force at a

C,=N

given stick position while another system may trim by returning the stick to neutral position.

where Flight at high supersonic Mach numbers might require a great variety of devices in the N=yawing moment, ft.-lbs; longitudinal control system. The deteriora- positive to the right tion of pitch damping with Mach-number may q= dynamic pressure, psf require that dynamic stability be obtained S=wing area, sq. ft.

synthetically by pitch dampers in the control b=wing span, ft.

system. The response of the airplane to C,=yawing moment coefficient, positive longitudinal control may be adversely affected to the right by flight at high dynamic pressures. In such The yawing moment coefficient, C,, is based on conditions of flight stick forces must be ade- the wing dimensions $ and 6 as the wing is the quate to prevent an induced oscillation. Stick characteristic surface of the airplane.

forces must relate the transients of flight as The yaw angle of an airplane relates the dis- well as the steady state conditions. Such a placement of the airplane centerline from some contribution to control system forces may be reference azimuth. and is assigned the short- provided by a pitching acceleration bobweight ,hand notation I& (psi). A positive yaw angle and a control system viscous damper.

occurs when the nose of the airplane is dis- placed to the right of the azimuth direction.

DIRECTIONAL STABILITY AND CONTiOL The definition of sideslip angle involves a sig- DIRECTIONAL STABILITY nificant difference. Sides&p angle relates the The directional stability of an airplane is displacement of the airplane centerline from essentially the “weathercock” stability and the relative wind rather than some reference involves moments about the vertical axis and azimuth., Sideslip angle is’ provided the short- their relationship with yaw or sideslip angle. hand notation p (beta) and is positive when An airplane which has static directional sta- ihe rela&e wind is displaced to the right of bility would tend to return to an equilibrium the,airplane centerline. Figure 4.22 illustrates when subjected to some disturbance from equi- the definitions of sideslip and yaw angles.

librium. Evidence of static directional sta- The sideslip angle, 8, is essentially the di- bility would be the development of yawing rectional angle of attack of the airplane and NAVWEPS 00-ROT-80 STABILITY AND CONTROL Static directional stability must be in evi- is the primary reference in lateral stability as well as directional stability considerations. dence for all the critical conditions of flight.

The yaw angle, #, is a primary reference for Generally, good directional stability is a ftm- damental quality directly affecting the pilots’ wind tunnel tests and time history motion of an airplane. From the definitions there is no impression of an airplane.

CONTRIBUTION OF THE AIRPLANE direct relationship between @ and # for an COMPONENTS. The static directional sta- airplane in free flight, e.g., an airplane flown through a 360° turn has yawed 360” but side- bility of the airplane is a result of contribution of each of the various airplane components.

slip may have been zero throughout the entire turn. Since the airplane has no directional While the contribution of each component is sense, static directional stability of the air- somewhat dependent upon and related to other plane is appreciated by response to sideslip. components, it is necessary to study each The static directional stability of an airplane component separately.

can be illustrated by a graph of yawing moment The vertical tail is the primary source of coe&cient, C., versus sideslip angle, 8, such as directional stability for the airplane. As shown in figure 4.23, when the airplane is in shown in figure 4.22. When the airplane is subject to a positive sideslip angle, static direc- a sideslip the vertical tail will experience a change in angle of attack. The change in tional stability will be evident if a positive lift-or side force-on the vertical tail creates yawing moment coefficient results. Thus, a yawing moment about the center of gravity when the relative wind comes from the right which tends to yaw the airplane into the (+p), a yawing moment to the right (+C.)

relative wind.

should be created which tends to weathercock The magnitude of the vertical the airplane and return the nose into the wind. tail contribution to static directional stability Static directional stability will exist when the then depends on the change in tail lift and the tail moment arm.

curve of C,, versus fi has a positive slope and the Obviously, the tail moment degree of stability will be a function of.the arm is a powerful factor but essentially dic- tated by the major configuration properties of slope of this curve. If the curve has zero slope, there is no tendency to return to equilibrium the airplane.

and neutral static directional stability exists. When the location of the vertical tail is set,, When the curve of C. versus /3 has a negative the contribution of the surface to directional slope, the yawing moments developed by side- stability depends on its ability to produce slip tend to diverge rather than restore and changes in lift-or side force-with changes in static directional instability exists. sideslip.

The surface area of the vertical tail The final chart of figure 4.22 illustrates the is a powerful factor with the contribution of fact that the instantaneous slope of the curve of the vertical tail being a direct function of the C,, versus @ will describe the static directional area. When all other possibilities are ex- stability of the airplane. At small angles of hausted, the required directional stability may sideslip a strong positive slope depicts strong be obtained by increases in tail area. How- directional stability. Large angles of sideslip ever, increased surface area has the obvious produce zero slope and neutral stability. At disadvantage of increased drag.

very high sideslip the negative slope of the The lift curve slope of the vertical tail curve indicates directional instability. This relates how sensitive the surface is to changes decay of directional stability with increased in angle of attack. While it is desirable to sideslip is not an unusual condition.

However, have a high lift curve slope for the vertical directional instability should not occur at the surface, a high aspect ratio surface is not angles of sideslip of ordinary flight conditions.

necessarily practical or desirable. The stall NAVWEPS 00-ROT-80 STABILITY AND CONTROL +N,YAWlNG MOMENT YAWING MOMENT COEFFICIENT,Cn t +Cn p SIDESLLANGLE, Figure 4.22. Static Directional Stability NAVWEPS OO-ROLRO STARIUTY AND CONTROL angle of the surface must be sufficiently great greater aerodynamic force and, generally, a to prevent stall and subsequent loss of effec- continued destabilizing influence.

tiveness at ordinary sideslip angles. Figure 4.23 illustrates a typical buildup of The high Mach numbers of supersonic flight produces a the directional stability of an airplane by decrease in lift curve slope with the consequent separating the contribution of the fuselage reduction in tail contribution to stability. and tail. As shown by the graph of C. versus In order to have sufficient directional stability at 6, the contribution of the fuselage is de- high Mach numbers, the typical supersonic stabilizing but the instability decreases at large sideslip angles.

configuration will exhibit relatively large Tbe contribution of the vertical tail surfaces. vertical tail alone is highly stabilizing up to the point where the surface begins to stall.

The flow field in which the vertical tail operates is affected by the othei components The contribution of the vertical tail must be large enough so that the complete airplane of the airplane as well as powe; effects.

The (wing-fuselage-tail combination) exhibits the dynamic pressure at the vertical tail could required degree of stability.

depend on the slipstream of a propeller or the The dorsal fin has a powerful effect on pre- boundary layer of the fuselage. Also, the serving the directional stability at large angles local flow direction at the vertical tail is in- of sideslip wliich would produce stall of the fluenced by the wing wake, fuselage crossflow, vertical tail. The addition of a dorsal fin to induced flow of the horizontal tail, or the the airplane will allay the decay of directional direction of slipstream from a propeller.

Each stability at high sideslip in two ways. The of these factors must be considered as possibly least obvious but most important effect is a affecting the contribution of the vertical tail large increase in the fuselage stability at large to directional stability.

sideslip angles. In addition, the effective The contribution of the wing tb %tatic direc- aspect rario of the vertical tail is reduced tional stability is tisually small: The swept which increases the stall angle for the surface.

wing provides a stable contribution’ depending By this twofold effect, the addition of the on the amount of sweepback but the contribu- dorsal fin is a v useful’ device.

tion is relatively weak when compared with other components. Poluer effects on static directional stability :.

The contribution of the fuselage andnacelles are similar to the power effects on static

is of primary importance since these compo- longitudinal stability. The direct effects are nents furnish rhe greatest destabilizing in- confined to the normal force at the propeller fluence. The contribution of the fuselage and plane or the jet inlet and, of course, are de- nacelles is similar to the longitudinal case stabilizing when the propeller or inlet is with the exception that there is no large in- located ahead of the c.g. The indirect effects fluence of the induced flow field of the wing.

of power induced velocities and flow dirkccion The subsonic center of pressure of the fuselage changes at the vertical tail are quite significant will be located at or forward of the quarter- for the propeller driven airplane and can pro- length point and, since the airplane c.g. is duce large directional trim changes. As in usually considerably aft of this point, the the lontitudinal case, the indirect effects are fuselage contribution will be destabilizing.

negligible for the jet powered airplane.

However, at large angles of sideslip the large The contribution of the direct and indirect destabilizing contribution of the fuselage di- power effects to static directional stability is minishes which is some relief to the problem greatest for the propeller powered airplane of maintaining directional stability at large and usually slight for the jet powered airplane.

displacements. The supersonic pressure,. dis- tribution on the body provides a relatively In either case, the general effect of power is NAVWEPS oO-801-80 STABILITY AND CONTROL CONTRIBUTION OF VERTICALTAIL CHANGE IN TAIL LIFT TYPICAL DIRECTIONAL STABILITY BUILD-UP AIRPLANE WITH DORSAL FIN STALL ,-ADDED Figure 4.23. Contribution of Components to Directional Stability NAVWEPS Oe8OT-80 STABILITY AND CONTROL EFFECT OF RUDDER FLOAT ON STATIC DIRECTIONAL STABILITY

\

RUDDER-FIXED

t

RUDDER-FREE RUDDER FLOAT -e ANGLE t SIDESLIP ANGLE, p EFFECT OF ANGLE OF ATTACK HIGH ANGLE OF ATTACK w SIDESLIP ANGLE, fla EFFECT OF MACH NUMBER A SIDESLIP ANGLE, p Figure 4.24. Factors Affecting Direcfional Stability NAVWRPS DD-807-80 STABILITY AND CONTROL destabilizing and the greatest contribution because of increase in the fuselage boundary layer at the vertical tail location. The decay of will occur at high power and low dynamic dir&ctional stability with angle of attack is pressure as during a waveoff.

As in the case of longitudinal static stability, most significant for the low aspect ratjo air- freeing the controls will reduce the effective- plane with sweepback since this configuration ness of the tail and alter the stability. requires such high angles of attack to achieve While Such decay in directional the rudder must be balanced to reduce control high lifr coefficients.

pedal forces, the rudder will tend to float or stability can have a profound effect on the re- streamline and reduce the contribution of the sponse of the airplane to adverse yaw and spin vertical tail to static directional stability. The characteristics.

High Mach ntrmbersof supersonic flight reduce floating tendency is greatest at large angles of sideslip where large angles of attack for the the contribution of the vertical tail to direc- vertical tail tend to decrease aerodynamic bal- tional stability because of the reduction of lift ante. Figure 4.24 illustrates the difference be- cnrve slope with Mach number. The third tween rudder-fixed and rudder-free static di- chart of figure 4.24 illustrates the typical decay of directional stability with Mach number. To rectional stability.

produce the required directional stability at CRITICAL CONDITIONS. The most criti- high Mach numbers, a viziy large vertical tail cal conditions of,staric directional stability are usually the combination of several separate area may be necessary. Ventral fins may be added as an additional contribution to direc- effects. The combination which produces the tional stability but landing clearance require- most critical condition is much dependent upon In addi- ments may limir their size or require the fins to the type and mission of the airplane.

be retractable.

tion, there exists a coupling of lateral and di- Hence, the most critical demands of static rectional effects such that the required degree directional stability will occur from some of static directional stability may be deter- combination of the following effects: mined by some of these coupled conditions.

Center of gravity position has a relatively (1) high angle of sideslip negligible effect on static directional stability. (2) high power at low airspeed The usual range of c.g. position on any air- (3) high angle of attack plane is set by the Jinits of long&d&a/ stability (4) high Mach number and control. Within this limiting range of The propeller powered airplane may have such c.g. position, no significant changes take place considerable power effects that the critical in the contribution of the vertical tail, fuselage, conditions may occur at low speed while the nacelles, etc. Hence, the static directional effect of high Mach numbers may produce the stability is essentially unaffected by the varia- critical conditions for the typical supersonic tion of c.g. position within the longitudinal airplane. In addition, the coupling of lateral limits. and directional effects may require prescribed degrees of directional stability.

When the airplane is at a high angle of a$tack

a decrease in static directional stability can be DIRECTIONAL CONTROL anticipated. As shown by the second chart of figure 4.24, a high angle of attack reduces the In addition to directional stability, the air- The stable slope of the curve of C,, versus 8, plane must have adequate directional control decrease in static directional stability is due in to coordinate turns, balance power effects, great part to the reduction in the contribution create sideslip, balance unsymmetrical power, of the vertica1 tail. At high angles of attack, etc. The principal source of directional con- the effectiveness of the vertical tail is reduced trol is the rudder and the rudder must be NAVWEPS 00-SOT-80 STABIUTY AND CONTROL have a stable rudder pedal feel through the capable of producing sufhcient yawing moment available range of sideslip.

for the critical conditions of flight.

DIRECTIONAL CONTROL REQUIRE- The effect of rudder deflection is to produce MENTS. The control power of the rudder a yawing moment coefficient according to must be adequate to contend with the many control deflection and produce equilibrium at unsymmetrical conditions of flight. Gener- some angle of sideslip. For small deflections ally, there are five conditions of flight which of the rudder, there is no change in stability provide the most criticalrequirements of di- but a change in equilibrium. Figure 4.25 shows the effect of rudder deflection on yawing ‘ rectional control power. The type and mission of the airplane will decide which of these moment coefficient curves with the change in equilibrium sideslip angle. conditions is most important.

ADVERSE YAW. When an airplane is If the airplane exhibits static directional stability with rudder lixed, each angle of side- rolled into a turn yawing moments are pro- duced which require rudder deflection to main- slip requires a particular deflection of the tain zero sideslip, i.e., coordinate the turn.

rudder to achieve equilibrium. Rudder-free The usual source of adverse yawing moment is directional stability will exist when the float illustrated in figure 4.26. When the airplane angle of the rudder is less than the rudder shown is subject to a roll to the left, the down- deflection required for equilibrium. However going port wing will experience a new relative at high angles of sideslip, the floating tend- ency of the rudder increases. This is illus- wind and an increase in angle of attack. The inclination of the lift vector produces a com- trated by the second chart of figure 4.25 where ponent force forward on the downgoing wing.

the line of rudder float angle shows a sharp The upgoing starboard wing has its lift in- increase at large values of sideslip. If the clined with a component force aft. The re- floating angle of the rudder catches up with sulting yawing moment due to rolling motion the required rudder angle, the, rudder pedal is in a direction opposite to the roll and is force will decrease to zero and rudder lock will hence “adverse yaw.” The yaw due to roll is occur. Sideslip angles beyond this point pro- primarily a function of the wing lift coefficient duce a floating angle greater than the required and is greatest at high C,.

rudder deflection and the rudder tends to float In addition to the yaw due to rolling motion to the limit of deflection.

there will be a yawing moment contribution Rudder lock is accompanied by a reversal of due to control surface deflection.

Conventional pedal force and rudder-free instability will ailerons usually contribute an adverse yaw exist. The dorsal fin is a useful addition in while spoilers may contribute a favorable or this case since it will improve the directional “proverse” yaw. The high wing airplane stability at high angles of sideslip. The re- with a large vertical tail may encounter an sulting increase in stability requires larger influence from inboard ailerons. Such a con- deflections of the rudder to achieve equilibrium figuration may induce flow directions at the at high sideslip and the tendency for rudder vertical tail to cause proverse yaw.

lock is reduced.

Since adverse yaw will be greatest at high Rudder-free directional stability is appre- C, and full deflection of the ailerons, coordi- ciated by the pilot as the rudder pedal force to nating steep turns at low speed may produce maintain a given sideslip. If the rudder pedal a critical requirement for rudder control power.

force gradient is too low near zero sideslip, it SPIN RECOVERY. In the majority of air- will be difficult to maintain zero sideslip dur- planes, the rudder is the principal control for ing various maneuvers. The airplane should spin recovery. Powerful control of sideslip at NAVWEPS 00-807-80 STABILITY AND CONTROL EFFECT OF RUDDER DEFLECTION ON EOlJlLlSRlUM SIDESLIP ANGLE RUDDER DEFLECTION RUDDER LOCK.

RUDDER DEFLECTION FLOAT ANGLE / + SIDESLIP ANGLE, p EFFECT DF RUDDER LOCK ON PEDAL FORCE RUDDER LOCK w +P --- DORSAL FIN ADDED Figure 4.25. Directional Control NAVWEPS 00-8OT-30 STABILITY AND CONTROL ADVERSE YAW DUE TO ROLL ,IRPLANE.IN ROLL TO LEFT FORCE FORWARD DOWNGOING PORT WING / \FOR SAKE OF CLARITY.

SLIPSTREAM SWIRL ON THE PROPFLLER POWERED AIRPLANE YAWING MOMENT DUE TO ASYMMETRICAL THRUST YAWING MOMENT COEFFICIENT FROM ASYMMETRICAL / THRUST I w I EQUIVALENT AIRSPEED, KNOTS Figure 4.26. Requirements for Directional Control NAVWEPS 00-8OT-80 STABILITY AND CONTROL speed of the airplane in the lightest practical high angles of attack is required to effect re- covery during a spin. Since the effectiveness takeoff configuration. This will provide ade- quate directional control for the remaining of the vertical tail is reduced at large angles of attack, the directional control power neces- conditions of flight.

Once defined, the minimum directional con- sary for spin recovery may produce a critical trol speed is not a function of weight, altitude, requirement of rudder power.

SLIPSTREAM ROTATION. A critical di- etc., but is simply the equivalent airspeed (or dynamic pressure). to produce a required yaw- rectional control requirement may exist when ing moment with the maximum rudder deflec- the propeller powered airplane is at high tion. If the airplane is operated in the critical power and low airspeed. As shown in figure unbalance of power below the minimum con 4.26, the single rotation propeller induces trol speed, the airplane will yaw uncontrolla- a slipstream swirl which causes a change in bly into the inoperative engine. In order to flow direction at the vertical tail. The rudder regain directional control below the minimum must furnish sufficient control power to balance speed certain alternatives exist: reduce power this condition and achieve zero sideslip.

on the operating engines or sacrifice altitude CROSSWIND TAKEOFF AND LANDING.

for airspeed. Neither alternative is satisfac- Since the airplane must make a true path down tory if the airplane is in a marginal condition the runway, a crosswind during takeoff or of powered flight so due respect must be given landing will require that the airplane be.con- to the minimum control speed.

trolled in a sideslip. The rudder must have Due to the side force on the vertical tail, a sufficient control power to create the required slight bank is necessary to prevent turning sideslip for the expected crosswinds.

flight at zero sideslip. The inoperative engine ASYMMETRICAL POWER. The design will be raised and the inclined wing lift will of a multiengine airplane must account for the provide a component of force to balance the 1 possibility of an engine failure at low airspeed.

The unbalance of thrust from a condition of side force on the tail.

In each of the critical conditions of required unsymmetrical power produces a yawing mo- directional control, high directional stability ment dependent upon the thrust unbalance is desirable as it will reduce the displacement and the lever arm of the force.

The deflection of the aircraft from any disturbing influence.

of the rudder will create a side force on the tail Of course, directional control must he sufficient and contribute a yawing moment to balance to attain zero sideslip. The critical control the yawing moment due to the unbalance of requirement for the multiengine airplane is thrust. Since the yawing moment coefficient the condition of asymmetrical power since from the unbalance of thrust will be greatest spinning is not common to this type of airplane.

at low speed, the critical requirement will be at a low speed with the one critical engine The single engine propeller airplane may have out and the remaining engines at maximum either the spin recovery or the slipstream rota- power. Figure 4.26 compares the yawing tion as a critical design condition.

The single moment coeflicient for maximum rudder deflec- engine jet airplane may have a variety of tion with the yawing moment coefficient for critical items but the spin recovery require- the unbalance of thrust. The intersection of ment usually predominates.

the two lines,determines the minimum speed for directional control, i.e., the lowest speed LATERAL STABILITY AND CONTROL at which the rudder control moment can equal LATERAL STABILITY It is usually the moment of unbalanced thrust, specified that the minimum directional control The static lateral stability of an airplane speed be no greater than 1.2 times the stall involves consideration of rolling moments due Revised January 1965 NAVWEPS 00-8OT-80 STABILITY AND COI’ ITROL to sideslip. moment coefficient results. Thus, when the If an airplane has favorable rolling moment due to sideslip, a lateral displacement relative wind comes from the right (+-a>, a rolling moment to the left (-Cl> should be from wing level flight produces sideslip and the sideslip creates rolling moments tending created which tends to roll the airplane to the left. Lateral stability will exist when to return the airplane to wing level flight.

the curve of C1 versus p has a negative slope By this action, static lateral stability will be evident. Of course, a sideslip will produce and the degree of stability will be a function yawing moments depending on the nature of of the slope of this curve. If the slope of the curve is zero, neutral lateral stability exists; the static directional stability but the consid- if the slope is positive lateral instability is rations of static lateral stability will involve present.

only the ‘ relationship of rolling moments and It is desirable to have lateral stability or sideslip.

DEFINITIONS. The axis system of an favorable roll due to sideslip. However, the required magnitude of lateral stability is deter- airplane defines a positive rolling, L, as a moment about the longitudinal axis which mined by many factors. Excessive roll due to tends to rotate the right wing down. As in sideslip complicates crosswind takeoff and landing and may lead to undesirable oscil- other aerodynamic considerations, it is con- latory coupling with the directional motion of venient to consider rolling moments in the the airplane. In addition, a high lateral sta- coefficient form so that lateral stability can bility may combine with adverse yaw to hinder be evaluated independent of weight, altitude, rolling performance. Generally, favorable han- speeds, etc. The rolling moment, L, is defined dling qualities are obtained with a relatively in the coeflicient form by the following equa- light-or weak positive-lateral stability.

tion : L=C,qSb CONTRIBUTION OF THE AIRPLANE or COMPONENTS. In order to appreciate the * development of lateral stability in an airplane, +I each of the contribution components must be where inspected.

Of course, there will be interference between the components which will alter the L=rolling moment, ft.-lbs., positive to contribution to stability of each component on the right 4 = dynamic pressure, psf. the airplane.

The principal surface contributing to the S=wing area, sq. ft.

lateral stability of an airplane is the wing.

b = wingspan, ft. The effect of the geometric dihedral of a wing is a C,=rolling moment coeflicient, positive powerful contribution to lateral stability. As to the right shown in figure 4.28, a wing with dihedral will The angle of sideslip, 8, has been defined develop stable rolling moments with sideslip.

previously as the angle between the airplane If the relative wind comes from the side, the centerline and the relative wind and is positive wing into the wind is subject to an increase in when the relative wind is to the right of the angle of attack and develops an increase in lift.

centerline.

The wing away from the wind. is subject to a The static lateral stability of an airplane can decrease in angle of attack and develops a de- be illustrated by a graph of rolling moment crease in lift. The changes in lift effect a rolling coefficient, Cl, versus sideslip angle, 8, such moment tending to raise the windward wing as shown in figure 4.27. When the airplane is subject to a positive sideslip angle, lateral hence dihedral contributes a stable roll due to stability will be evident if a negative rolling sideslip.

NAVWEPS DD-8OT-80 STABILITY AND CONTROL RELATIVE WIND +L, ROLLING MOMENT ROLLING MOMENT COEFFICIENT UNSTABLE 7, -I SIDESLIP ANGLE, /3 TABLE ROLL DUE TO SIDESLIP NEUTRAL Figure 4.27. Static Lateral Stability NAVWEPS CID-8OT-80 STABILITY AND CONTROL EFFECT OF DlilEDRAL EFFECTIVE INCREASE IN --SE IN LIFT DUE TO SIDESLIP EFFECT OF SWEEPBACK R~~;~~~p CONTRIBUTION OF VERTICAL TAIL SIDESLIP CONTRIBUTES ROLLING MOMENT Figure 4.28. Contribution of Components to Lateral Stability N A V W E P S OO-BOT-80 STABILITY AND CONTROL Since wing dihedral is so powerful in pro- there is no wing lift to change.

Thus, the ducing lateral stability it is taken as a common dihedral effect due to sweepback is zero at zero denominator of the lateral stability contribu- lift and increases directly with wing lift coefficient. When the demands of high speed tion of all other components. Generally, the contribution of wing position, flaps, power, flight require a large amount of sweepback, the etc., is expressed as an equivalent amount of resulting configuration may have an excessive- “effective dihedral” or “dihedral effect.” ly high dihedral effect at low speeds (high CL)

The contribution of the fadage alone is while the dihedral effect may be satisfactory

usually quite small depending on the location in normal flight (low or medium C,).

of the resultant aerodynamic side force on the The vertical tail of modern configurations fuselage. However, the effect of the wing- can provide a sign&ant-and, at times, un- fuselage-tail combination is significant since desirable-contribution to the effective dihe- the vertical placement of the wing on the fuse- dral. If the vertical tail is large, the side force lage can greatly affect the stability of the com- produced by sideslip may produce a noticeable bination. A wing located at the mid wing rolling moment as well as the important yaw- position will generally exhibit a dihedral effect ing moment contribution. Such an effect is no different from that of the wing alone. A usually small for the conventional airplane low wing location on the fuselage may con- configuration but the modern high speed tribute an effect equivalent to 3’ or 4’ of nega- airplane configuration induces this effect to a tive dihedral while a high wing location may great magnitude. It is difficult then to obtain contribute a positive dihedral of 2’ or 3’ . The a large vertical tail contribution to directional magnitude of dihedral effect contributed by stability without incurring an additional con- vertical position of the wing is large and may tribution to dihedral effect.

necessitate a noticeable dihedral angle for the The amount of effective dihedral necessary low wing configuration. to produce satisfactory flying qualities varies The contribution of wccpback to dihedral ef- greatly with the type and purpose of the air- fect is important because of the nature of the plane. Generally, the effective dihedral should contribution. As shown in figure 4.28, the not be too great since high roll due to side- swept wing in a sideslip has the wing into slip can create certain problems. Excessive wind operating with an effective decrease in dihedral effect can lead to “Dutch roll,” sweepback while the wing out of the wind difficult rudder coordination in rolling maneu- is operating with an effective increase in vers, or place extreme demands for lateral sweepback. If the wing is at a positive lift control power during crosswind takeoff and coefficient, the wing into the wind has less landing. Of course, the effective dihedral sweep and an increase in lift and the wing out should not be negative during the predominat- of the wind has more sweep and a decrease in ing conditions of flight, e.g., cruise, high lift. In this manner the swept back wing speed, etc. If the airplane demonstrates satis- would contribute a positive dihedral effect and factory dihedral effect for these conditions of the swept forward wing would contribute a flight, certain exceptions can be considered negative dihedral effect.

when the airplane is in the takeoff and landing The unusual nature of the contribution of configuration. Since the effects of flaps and sweepback to dihedral effect is that the con- power are destablizing and reduce the dihedral tribution is proportional to the wing lift effect, a certain amount of negative dihedral coefficient as well as the angle of sweepback.

effect may be possible due to these sources.

It should be clear that the swept wing at zero The deflection of flaps causes the inboard lift will provide no roll due to sideslip since sections of the wing to become relatively more NAVWEPS, OO-ROT-80 STABILITY AND CONTROL (2) Yawing moment due to sideslip or effective and these sections have a small spanwise moment arm. Therefore, the changes static directional stability.

in wing lift due to sideslip occur closer in- (3) Yawing moment due to rolling veloc- board and the dihedral effect is reduced. The ity or the adverse (or proverse) yaw.

effect of power on dihedral effect is negligible (4) Rolling moment due to yawing ve- for the jet airplane but considerable for the locity-a cross effect similar to (3). If the propeller driven airplane. The propeller slip- aircraft has a yawing motion to the right, stream at high power and low airspeed makes the left wing will move forward faster and the inboard wing sections much more effective momentarily develop more lift than the and reduces the dihedral effect. The reduction right and cause a rolling moment to the in dihedral effect is most critical when the right.

flap and power effects are combined, e.g., the (3) Aerodynamic side force due to side- propeller driven airplane in the power approach slip.

or waveoff. (6) Rolling moment due to rolling ve- locity or damping in roll.

With certain exceptions during the condi- (7) Yawing moment due yawing velocity tions of landing and takeoff, the dihedral or damping in yaw.

effect or lateral stability should be positive but light. The problems created by excessive (8) The moments of inertia of the air- plane about the roll and yaw axes.

dihedral effect are considerable and difficult to contend with. Lateral stability will be The complex interaction of these effects pro- evident to a pilot by stick forces and displace- duces three possible types of motion of the ments required to maintain sideslip. Positive airplane: (a) a directional divergence, (b) a spiral divergence, and (c) an oscillatory stick force stability will be evident by stick forces required in the direction of the controlled mode termed Dutch roll.

sideslip.

Directional divergence is a condition which cannot be tolerated. If the reaction to a small LATERAL DYNAMIC EFFECTS initial sideslip is such as to create moments which tend to increase the sideslip, directional Previous discussion has separated the lateral divergence will exist. The sideslip would in- and directional response of the airplane to sideslip. This separation is convenient for crease until the airplane is broadside to the detailed study of each the airplane static Of course, wind or structural failure occurs.

lateral stability and the airplane static direc- increasing the static directional stability re- tional stability. However, when the airplane duces the tendency for directional divergence.

in free flight is placed in a sideslip, the lateral Spiral divergencewill exist when the static and directional response will be coupled, i.e., directional stability is very large when com- simultaneously the airplane produces rolling pared with the dihedral effect. The character moment due to sideslip and yawing moment of spiral divergence is by no means violent, due to sideslip. Thus, the lateral dynamic The airplane, when disturbed from the equilib- motion of the airplane in free flight must rium of level flight, begins a slow spiral which consider the coupling or interaction of the gradually increases to a spiral dive. When a lateral and directional effects.

small sideslip is introduced, the strong direc- The principal effects which determine the tional stability tends to restore the nose into lateral dynamic characteristics of an airplane the wind while the relatively weak dihedral are : effect lags in restoring the airplane laterally, (1) Rolling moment due to sideslip or In the usual case, the rate of divergence in the dihedral effect (lateral stability).

N A V W E P S DGROT-50 STABBITY AND CONTROL spiral motion is so gradual that the pilot can The contribution of sweepback to the lateral dynamics of an airplane is significant. Since control the tendency without difficulty.

the dihedral effect from sweepback is a function Dutch roll is a coupled lateral-directional of lift coefficient, the dynamic characteristics oscillation which is usually dynamically stable but is objectionable because of the oscillatory may vary throughout the flight speed range.

When the swept wing airplane is at low C,, the nature. The damping of this oscillatory mode may be weak or strong depending on the prop- dihedral effect is small and the spiral tendency may be apparent. When the swept wing air- erties of the airplane. The response of the air- plane is at high C,, the dihedral effect is in- plane to a disturbance from equilibrium is a creased and the Dutch Roll oscillatory tendency combined rolling-yawing oscillation in which is increased.

the rolling motion is phased to precede the An additional oscillatory mode is possible yawing motion. Such a motion is quite unde- in the lateral dynamic effects with the rudder sirable because of the great havoc it would free and the mode is termed a “snaking” oscil- create with a bomb, rocket, or gun platform.

lation. This yawing oscillation is greatly Generally, Dutch roll will occur when the affected by the aerodynamic balance of the dihedral effect is large when compared to static rudder and requires careful consideration in directional stability. Unfortunately, Dutch design to prevent light or unstable damping roll will exist for relative magnitudes of dihe- of the oscillation.

dral effect and static directional stability be- tween the limiting conditions for directional divergence and spiral divergence. When the CONTROL IN ROLL dihedral effect is large in comparison with static directional stability, the Dutch roll The lateral control of an airplane is ac- motion has weak damping and is objectionable. complished by producing differential lift on When the static directional stability is strong the wings. The rolling, moment created by in comparison with the dihedral effect, the the differential lift can be used to accelerate Dutch roll motion has such heavy damping the airplane to some rolling motion or control that it is not objectionable. However, these the airplane in a sideslip by opposing dihedral qualities tend toward spiral divergence. effect. The differential lift for control in The choice is then the least of three evils. roll is usually obtained by some type of ailerons or spoilers.

Directional divergence cannot be tolerated, Dutch roll is objectionable, and spiral diver- ROLLING MOTION OF A N AIRPLANE.

gence is tolerable if the rate of divergence is / When an airplane is given a rolling motion in low. For this reason the dihedral effect should flight, the wing tips move in a helical path be no more than that required for satisfactory through the air. As shown in figure 4.29, a lateral stability. If the static directional sta- rolling velocity to the right gives the right bility is made adequate to prevent objection- wing tip a downward velocity component and able Dutch roll, this will automatically be the left wing tip an upward velocity com- sufficient to prevent directional divergence, ponent. By inspection of the motion of the Since the more important handling qualities left wing tip, the velocity of the tip due to roll combines with the airplane flight path are a result of high static directional stability velocity to define the resultants motion. The and minimum necessary dihedral effect, most airplanes demonstrate a mild spiral tendency. resulting angle between the flight path vector and the resultant path of the tip is the helix As previously mentioned, a weak spiral tend- angle of roll. From the trigonometry of small ency is of little concern to the pilot and cer- tainly preferable to Dutch roll.

angles, the helix angle of roll can be defined as: NAVWEPS 00-6OT-60 STABILITY AND CONTROL If the airplane is unrestrained and sideslip is Roll helix angle=&; (radians) allowed, the affect of the directional stability and dihedral effect can be appreciated. The where conventional airplane will develop adverse p=rate of roll, radians per second yawing moments due to aileron deflection and 6=wing span, ft. rolling motio6. Adverse yaw tends to produce yawing displacements and sideslip but this is V=airplane flight velocity, ft. per sec.

resisted by the directional stability of the air- plane. If adverse yaw produces sideslip, di- and, one radian=S7.3 degrees hedral effect creates a rolling moment opposing the roll and tends to reduce the roll rate. The pb Generally, the maximum values of rVobtained typical transient motions (A) and (B) of the by control in roll are approximately 0.1 to 0.07.

time history diagram of figure 4.29 show that high directional stability with low dihedral The helix angle of roll, $i, is, actually a com- effect is the preferable combination. Such a mon denominator of rolling performance.

combination provides an airplane which has The deflection of the lateral control surfaces no extreme requirement of coordinating aileron creates the differential lift and the rolling and rudder in order to achieve satisfactory moment to accelerate the airplane in roll.

The rolling performance. While the coupled mo- roll rate increases until an equal and opposite tion of the airplane in roll is important, moment is created by the resistance to rolling further discussion of lateral control will be motion or “damping in roll.” The second directed to pure uncoupled rolling performance.

illustration of figure 4.29 defines the source ROLLING PERFORMANCE. The required of the damping in roll. When the airplane rolling performance of an airplane is generally is given a rolling velocity to the right, the specified as certain necessary values of the roll 1 downgoing wing experiences an increase in angle of attack due to the helix angle of roll.

However, in certain condi- helix angle, &I$ Of course, the upgoing wing experiences a tions of flight, it may be more appropriate to decrease in angle of attack.

In flight at angles specify minimum times for the airplane to of attack less than that for maximum lift, the accelerate through a given angle of roll.

downgoing wing experiences an increase in lift and the upgoing wing experiences a de- Usually, the maximum value of 2% should be crease in lift and a rolling moment is developed Of course, fighters and on the order of 0.10.

which opposes the rolling motion. Thus, the attack airplanes have a more specific require- steady state rolling motion occurs when the ment for high rolling performance and 0.09 damping moment equals the control moment.

Pb The response of the airplane to aileron deflec- may be considered a minimum necessary 2v.

tion is shown by the time history diagram of Patrol, transport, and bomberairplaneshaveless figure 4.29. When the airplane is restrained requirement for high rolling performance and a so that pure rolling motion is obtained, the Pb initial response to an aileron deflection is a 2-V of 0.07 may be adequate for these types.

steady increase in roll rate. As the roll rate The ailerons or spoilers must be powerful increases so does the damping moment and the Pb enough to provide the required rV’ While roll acceleration decreases. Finally, the damping moment approaches the control mo- the size and effectiveness of the lateral control ment and a steady state roll rate is achieved. devices is important, consideration must be Revised January 1965 NAVWEPS OO-80T-80 STABILITY AND CONTROL HELIX ANGLE OF ROLL IP VELOCITY,$ RCUING VELOCITY, P TIP VELOCITY WE TO ROLL RESULTANT PATH ( RADIANS 1 DAMPING IN ROLL STARBOARD WING AIRPLANE RESPONSE TO AILERON DEFLECTION PIRPLANE RESTRAINED TO ROLLING MOTION ONLY HIGH DlRECTlCNAL STABILITY ------(A) m DIHEDRAL EFFECT AIRPLANE UNRESTRAINED \ AND FREE TO SIDESLIP \ (RUDDER FIXED) ( B ) LOW DIRECTIONAL STABIUTY HIGH MHEDRAL EFFECT .---A w TIME, SECONDS Figure 4.29. Rolling Performance NAVWEPS OO-BOT-BO STABILIJY AND CONTROL given to the airplane size. For geometrically the critical speed, with some limited amount similar airplanes, a certain deflection of the of force applied by the pilot (usually the limit of lateral force is assumed to be 30 lbs.), the I!!.

ailerons will produce a fixed value of zlr mde- Pb ailerons cannot be held at full deflection, ~~ pendent of the airplane size. However, the roll rate of the geometrically similar airplanes drops, and rate of roll decreases. In this exam- at a given speed will vary inversely with the ple, the rolling performance at high speeds is limited by the ability of the pilot to maintain span, b.

full deflection of the controls.

In an effort to If reduce the aileron hinge moments and control Pb - forces, extensive application is made of aerody- ~-constant namic balance and various tab devices. How- p=(constant) 7 ever, 100 percent aerodynamic balance is not ( ) always feasible or practical but a sufficient Thus, the smaller airplane will have an ad- Pb value of - must be maintained at high speeds.

ZV vantage in roll rate or in time to accelerate Rather than developing an extensive weight through a prescribed angle of roll. For ex- lifting program mandatory for all Naval ample, a one-half scale airplane will develop Aviators, mechanical assistance in lateral con- twice the rate of roll of the full scale airplane.

trol can be provided. If a power boost is This relationship points to the favor of the provided for the lateral control system, the small, short span airplane for achieving high rolling performance of the airplane may be roll performance.

extended to higher speeds since pilot effort An important variable affecting the rate of will not be a limiting factor. The effect of a roll is the true airspeed or flight velocity, V.

power boost is denoted by the dashed line If a certain deflection of the ailerons creates a extensions of figure 4.30. A full powered, Pb specific value of -7 the rate of roll varies irreversible lateral control system is common 2V for high speed airplanes. In the power oper- directly with the true airspeed. Thus, if the ated system there is no immediate limit to the roll helix angle is held constant, the rate of deflection of the control surfaces and none of roll at a particular true airspeed will not be the aberrations in hinge moments due to com- affected by altitude. The linear variation of pressibility are fed back to the pilot. Control roll rate with airspeed points out the fact that forces are provided by the stick centering high roll rates will require high airspeeds.

lateral bungee or spring.

The low roll rates at low airspeeds are simply A problem particular to the high speed is a consequence of the low flight speed and this condition may provide a critical lateral con- due to the interaction of aerodynamic forces trol requirement for satisfactory handling and the elastic deflections of the wing in qualities. torsion. The deflection of ailerons creates Figure 4.30 illustrates the typical rolling twisting moments on the wing which can cause significant torsional deflections of the wing.

paformance of a low speed airplane. When the ailerons are at full deflection, the maximum At the low dynamic pressures of low flight speeds, the twisting moments and twisting roll helix angle is obtained. The rate of roll increases linearly with speed until the control deflections are too small to be of importance.

forces increase to limit of pilot effort and full However, at high dynamic pressures, the control deflection cannot be maintained. deflection of an aileron creates significant Past NAVWEPS 00-807-80 STABILITY AND CONTROL P, RAl ^, ,/ <EiECT 0 OF ADDED r%“LL POWER O/SEC. BOOST V. KNOTS ROLL .lD HELIX ANGLE pb TT - V, KNOTS A AILERON ----- DEFLECTlON 8, V.KNOTS SPEED CORRESPONDING TO LIMIT OF PILOT EFFORT TO MAINTAIN MAXIMUM DEFLECTION

A

(3

z

1.0 is ELASTIC WING c TWISTING REVERSAL Figure 4.30. Control in Roll NAVWEPS OO-UOT-80 STABILITY AND CONTROL twisting deflections which reduce the effec- trolled in a sideslip to accomplish crosswind tiveness of the aileron, e.g., downward deflec- takeoff and landing. The lateral control dur- tion of an aileron creates a nose down twist of ing crosswind takeoff and landing is a par- the wing which reduces the rolling moment ticular problem when the dihedral effect is due to aileron deflection. At very high speeds, high. Since the sweepback contributes a large the torsional deflection of the wing may be dihedral effect at high lift coefficients, the so great than a rolling moment is created problem is most important for the airplane with considerable sweepback. The limiting opposite to the direction controlled and “aile- ron reversal” occurs. Prior to the speed for crosswind components must be given due re- spect especially when the airplane is at low aileron reversal, a serious loss of roll helix gross weight. At low gross weight the speci- angle may be encountered. The effect of this fied takeoff and landing speeds will be low and aeroelastic phenomenon on rolling perform- the controlled angle of sideslip will be largest ance is illustrated in figure 4.30.

To counter the undesirable inceractiuo be- for a given crosswind velocity.

tween aerodynamic forces and wing torsional deflections, the trailing edge ailerons may be MISCELLANEOUS STABILITY PROBLEMS moved inboard to reduce the portion of the span subjected to twisting moments. Of There are several general problems of flying course, the short span, highly tapered wing which involve certain principles of stability as planform is favorable for providing relatively well as specific areas of longitudinal, direc- high stiffness. In addition, various configura- tional and lateral stability. Various condi- tions of spoilers may be capabIe of producing tions of flight will exist in which certain the required rolling performance without the problems of stability (or instability) are un- development of large twisting moments.

avoidable for some reason or another.

any CRITICAL REQUIREMENTS, The critical of the following items deserve consideration conditions for requiring adequate lateral con- because of the possible unsafe condition of flight trol power may occur at either high speed or and the contribution to an aircraft accident.

low speed depending on the airplane configura- tion and intended use. In transonic and super- LANDING GEAR CONFIGURATIONS sonic flight, compressibility effects tend to reduce the effectiveness of lateral control de- There are three general configurations for the vices to produce required roll helix angles. aircraft landing gear: the tricycle, bicycle, and These effects are most significant when com- “conventional” tail wheel arrangement. At bined with a loss of control effectiveness due to low rolling speeds where the airplane aerody- aeroelastic effects. Airplanes designed for namic forces are negligible, the “control-fixed” high speed flight must maintain suflicient static stability of each of these configurations lateral control effectiveness at the design dive is determined by the side force characteristics speed and this is usually the predominating of the tires and is not a significant problem.

requirement. The instability which allows ground loops During landing and takeoff, the airplane in an aircraft with a conventional tail wheel must have adequate lateral control power to landing gear is quite basic and can be appre- contend with the ordinary conditions of flight. ciated from the illustration of figure 4.31. Cen- The lateral controls must be capable of achiev- trifugal force produced by a turn must be ing required roll helix angles and acceleration balanced and the aircraft placed in equilibrium.

through prescribed roll dispIacements. Also, The greatest side force is produced at the main the airplane must be capable of being con- wheels but to achieve equilibrium with the NAVWEPS oo-SOT-80 STABILITY AND CONTROL “CONVENTIONAL’ TAIL WHEEL CONFIGURATION - SIDE FORCE ON MAIN WHEELS CENTRIFUGAL FORCE TRICYCLE CONFIGURATION \\ --BALANCING NOSE WHEEL SIDE FORCE CENTRIFUGAL FORCE BICYCLE CONFIGURATION FORCE Figure 4.31. Landing Gear Configurations NAVWEPS DD-BDT-80 STABILITY AND CONTROL center of gravity aft of the main wheels a bal- The bicycle configuration of landing gear has stability characteristics more like the ancing load on the tail wheel must be produced toward the center of turn. When the tail automobile. If directional control is ac- wheel is free to swivel, the equilibrium of the complished with the front wheels operated turn requires a control force opposite to the by power controls, no stability problem exists direction of turn-i.e.. control force insta- at low speeds. A problem can exist when the bility. The inherent stability problem exists airplane is at high speeds because of a distribu- because the center of gravity is aft of the point tion of normal force being different from the where the main side forces are developed. This ordinary static weight distribution. If the condition is analogous to the case of static airplane is held onto the runway at speeds longitudinal stability with the center of well above the normal takeoff and landing gravity aft of the neutral point. speeds, the front wheels carry a greater than The conventional tail wheel configuration ordinary amount of normal force and a tend- has this basic instability or ground loop tend- ency for instability exists. However, at these same high speeds the rudder is quite powerful ency which must be stabilized by the pilot.

At high rolling speeds where aerodynamic and the condition is usually well within control.

forces are significant, the aerodynamic direc- tional stability of the airplane resists the The basically stable nature of the tricycle and bicycle landing gear configurations is best ground looping tendency. The most likely appreciated by the ease of control and ground times for a ground loop exist when rolling maneuvering of the airplane. Operation of speeds are not high enough to provide a con- a conventional tail wheel configuration after tribution of the aerodyhamic forces. When the tail wheel is free to swivel or when the normal considerable experience with tricycle cohfigu- rations requires careful consideration af the force on the tail wheel is small, lack of pilot stability that must be furnished by the pilot attention can allow the ground loop to take during ground maneuvering.

place.

The tricycle landing gear configuration has SPINS AND PROBLEMS OP SPIN an inherent stability d,ue to the relative posi- RECOVERY tion of the main wheels and the center of The motion of an airplane in a spin can gravity. Centrifugal force produced by a involve many complex aerodynamic and in- turn is balanced by the side force on the main ertia forces and moments. However, there are wheels and a side force on the nose wheel in certain fundamental relationships regarding the direction of turn. Note that the freeing spins and spin recoveries with which all aviators should be familiar. The spin differs the nose wheel to swivel produces moments from a spiral dive in that the spin always which bring the aircraft out of the turn. Thus, involves flight at high angle of attack while the tricycle configuration has a basic stability the spiral dive involves a spiral motion of which.is given evidence by control displace- the airplane at relatively low angle of attack.

ment and a wheel side force in the direction The stall characteristics and stability of of turn. Because of the contrast in stability, the airplane at high lift coefficients are im- the tricycle configuration is much less difficult portant in the initial tendencies of the airplane.

to maneuver than the tail wheel configuration As previously mentioned, it is desirable to and does not provide an inherent ground loop have the wing initiate stall at the root first tendency. However, a steerable nose wheel rather than tip first. Such a stall pattern is usually necessary to provide satisfactory prevents the undesirable rolling moments at maneuvering capabilities.

high lift coeGients, provides suitable stall _~.

,, .

NAVWEPS OO-BOY-BO STABIUTY AND CoMml warning, and preserves lateral control effec- damping in roll is generally referred to as tiveness at high angles of attack. Also, the “autorotation.” airplane must maintain positive static longi- When the conventional airplane is stalk4 tudinal stability at high lift coe&ients and and some rolling-yawing displacement takes place, the resulting autotiotation rolling mo- should demonstrate satisfactory stall recovery characteristics. ments and yawing moments start the airplane In order to visualize the principal effects of into a self-sustaining rolling-yawing motion.

The autorotation rolling and yawing tenden- an airplane entering a spin, suppose the air- plane is subjected to the rolling and yawing cies of the airplane at high angles of attack velocities shown in figure 4.32. The yawing are the principal prospin moments of the velocity to the right tends to produce higher conventional airplane configuration and these local velocities on the left wing than on the tendencies accelerate the airplane into the right wing. The rolling velocity tends to spin until some limiting condition exists.

increase the angle of attack for the downgoing The stabilized spin is not necessaray a simple right wing (a,) and. decrease the angle of steady vertical spiral but may involve some coupled unsteady oscillatory motion.

attack for the upgoing left wing (al). At An important characteristic of the mote airplane angles of attack below the stall this relationship produces roll due to yaw, damping conventional airplane configuration is that the in roll, etc., and some related motion of the spin shows a predominating contribution of airplane in unstalled flight. However, at the autorotation tendency. Generally, the conventional configuration has a spin motion angles of attack above the stall, important changes take place in the aerodynamic char- which is primarily rolling with moderate yaw.

acteristics. High directional stability is favorable since it Figure 4.32 illustrates the aerodynamic will limit or minimize the yaw displacement characteristics typical of a conventional air- of the spinning airplane.

plane configuration, i.e., moderate or high The fundamental requirement of the spin is aspect ratio and little-if any-sweepback. that the airplane be placed at an excessive Ifs this airplane is provided a rolling displace- angle of attack to produce the autorotation ment when at some angle of attack above rolling and yawing tendencies. Generally the stall, the upgoing wing experiences a speaking, the conventional airplane must be decrease in angle of attack with a correspond- stalled .before a spin can take place. This ing increase in C, and decrease in C,,. In other relationship establishes a fundamental p&r- words, the upgoing wing becomes less stalled. ciple of recovery-the airplane must be un- Similarly, the downgoing wing experiences stalled by decreasing the wing angle of attack.

an increase in angle of attack with a corre- The most dfective procedure for the conven- sponding decrease in CL and increase in CD. Es- tional configuration is to use opposite rudder sentially, the downgoing wing becomes more to stop the sideslip, then lower the angle of stalled. Thus, the rolling motion is aided attack with the elevators. With sufficient rather than resisted and a yawing moment is rudder power this procedure will produce a produced in the direction of roll. At angles positive recovery with a minimum loss of of attack below stall the rolling motion is altitude. Care should be taken during pullout resisted by damping in roll and adverse yaw from the ensuing dive to prevent excessive is usually present. At angles of attack above angle of attack and entry into another spin.

the stall, the damping in roll is negative and It should be appreciated that a spin is always a rolling motion produces a rolling moment a possible corollary of a stall and the self- in the direction of the roll. This negative sustaining motion of a spin will take place at NAVWEPS OO-BOT-80 STABILITY AND CONTROL YAWING VELOCITY ROLLING VELOCITY AERODYNAMIC CHARACTERISTICS TYPICAL OF AERODYNAMIC CHARACTERISTICS TYPICAL OF A CONVENTIONAL CONFIGURATION A CONVENTIONAL CONFIGURATION STALL STALL I--- I--- CL CL AND AND CD CD I 0, ANGLE OF ATTACK QL OR CD AERODYNAMIC CHARACTERISTICS

TYPICAL Q ’ . ..I,.” cncrn A

lr H “lU” a-LL” co NFIGURATION

t

I a, ANGLE OF ATTACK OL aR Figure 4.32. Spin Characteristics NAWWEPS DO-BOT-BO STABILITY AND CONTROL attack is capable of producing pro-spin mo- excessive angles of attack. Of course, a low ments of considerable magnitude which con- speed airplane could be: designed to be spin- tribute to the self-sustaining nature of the proof by making it stallproof. By limiting spin. Also, the large distributed mass of the the amount of control deflection, the airplane fuselage in rolling-yawing rotation contributes may not have the longitudinal control power to inertia moments which flatten the spin and to trim to maximum lift angle of attack. Such place the aircraft at extreme angles of attack.

a provision may be possible for certain light The spin recovery of the modern high speed planes and commercial aircraft but would airplane involves principles which are similar create an unrealistic and impractical limita- to those of the spin recovery of the conven- tion on the utility of a military airplane.

tional airplane. However, the nature of the The modern high speed airplane configura- spin for the modern configuration may involve tion is typified by low aspect ratio, swept wing planforms with relatively large yaw and pitch specific differences in technique necessary to inertia. The aerodynamic characteristics of reduce the sideslip and angle of attack. The such a configuration are shown in figure 4.32. use of opposite rudder to control the sideslip The lift curve (C, versus U) is quite shallow at and effect recovery will depend on the effective- high angles of attack and maximum lift is not ness of the rudder when the airplane is in the clearly defined. When this type of airplane is spin. At high positive angles of attack and provided a rolling motion at high angles of high sideslip the rudder effectiveness may be attack, relatively small changes in C, take reduced and additional anti-spin moments must place. When this effect is combined with the be provided for rapid recovery. The deflection relatively short span of this type airplane, it is of ailerons into the spin reduces the autorota- apparent that the wing autorotation contribu- tion rolling moment and can produce adverse tion will be quite weak and will not be a pre- yaw to aid the rudder yawing moment in dominating pro-spin moment. The relatively effecting recovery.

large changes in drag coefficient with rolling There may be many other specific differences motion imply .a predominance of yaw for the in the technique necessary to effect spin re- spin of the high speed airplane configuration. covery . The effectiveness of the rudder during Actually, various other factors contribute recovery may be altered by the position of to the predominating yaw tendency for the elevators or horizontal tail. Generally, full spin of the modern airplane configuration. aft stick may be necessary during the initial The static directional stability deteriorates at phase of recovery to increase the effectiveness high angles of attack and may be so weak that of the rudder. The use of power during the extemely large yaw displacements result. In spin recovery of a propeller powered airplane certain instances, very high angles of attack may or may not aid recovery depending on the may bring such a decay in directional stability specific airplane and the particular nature of the slipstream effects. The use of power during that a “slice” or extreme yaw displacement the spin recovery of a jet powered airplane takes place before a true spin is apparent. At induces no significant or helpful flow but does these high angles of attack, the adverse yaw offer the possibility of a severe compressor due to roll and aileron deflection can be very stall and adverse gyroscopic moments. Since strong and create large yaw displacements of the airplane is at high angle of attack and the airplane prior to realizing a stall.

sideslip, the flow at the inlet may be very The aircraft with the relatively large, long poor and the staI1 limits considerably reduced.

fuselage can exhibit a significant moment con- These items serve to point out possible dif- The cross tribution from the fuselage alone.

ferences in technique required for various con- flow pattern on the fuselage at high angles of figurations. The spin recovery specific for 31.1 NAVWEPS woT-80 STABILITY AND CONTROL -UNSTABLE I w CL v PITCH-UP NEUTRAL SEPARATION OR STALLTIP FIRST RD SHIFT OF VORTEX INCREASE IN LOCAL DDWNWAM AT TAIL : : FUSELAGE CROSS- 4b FLOW SEPARATION VORTICES INCREASE LOCAL DOWNWASH AT TAIL Figure 4.33. Pitch-up NAWEPS DD-EDT-89 STABILITY AND CQNROL the wing flow field where higher relative each airplane is outlined in the pilot’ s hand- downwash exists. Thus, a decrease in stability book and it is impcrativc that the specific tech- would take place.

nique be followed for successful recovery.

Certain changes in the flow field behind the wing at high angles of attack can produce large PITCH-UP changes in the tail contribution to stability.

The term of “pitch-up” generally applies to If the wing tips stall first, the vortices shift in- the static longitudinal instability encountered board and increase the local downwash at the by certain configurations at high angle of tail for a given airplane C,. Also, the fusel~age attack. The condition of pitch-up is illustrated at high angle of attack can produce strong by the graph of CM versus C, in figure 4.33.

cross flow separation vortices which increase Positive static longitudinal stability is evident the local downwash for a horizontal tail placed at low values of Cs by the negative slope of the above the fuselage. Either one or a combiua- curve. At higher values of Cs the curve changes tion of these downwash influences may provide to a positive slope and large positive pitching a large unstable contribution of the horizontal moments are developed. This sort of in- tail.

stability implies that an increase in angle of The pitch-up instability is usually conlined attack produces nose up moments which tend to the high angle of attack range and may be to bring about further increases in angle of a consequence of a configuration that otherwise attack hence the term “pitch-up” is applied.

has very desirable flying qualities. In such a There are several items which may con- case it would be necessary to provide some Sweepback tribute to a pitch-up tendency.

automatic control function to prevent entry of the wing planform can contribute unstable into the pitch-up range or to provide synthetic moments when separation or stall occurs at stability for the condition. Since the pitch-up the tips first. The combination of sweepback is usually a strong instability with a high1 and taper alters the lift distribution to produce rate of divergence, most pilots would not be high local lift coefficients and low energy At capable of contending with the condition.

boundary layer near the tip. Thus, the tip high 4, pitch-up would be of great danger in stall is an inherent tendency of such a plan- that structural failure could easily result. At form. In addition, if high local lift coefficients low q, failing flight loads may not result but exist near the tip, the tendency will be to incur the strong instability may preclude a successful the shock induced separation first in these recovery from the ensuing motion of the, air- areas. Generally, the wing will contribute plane.

to pitch-up only when there is large sweepback.

Of course, the wing is not the only item con- EFFFCTS OF HIGH MACH NUMBFB tributing to the longitudinal stability of the airplane. Another item important as a source Certain stability problems are particular to supersonic flight. While most of the problem of pitch-up is the downwash at the horizontal areas have been treated in particular in previous tail. The contribution of the tail to stability discussion, it is worthwhile to review the depends on the change in tail lift when the air- plane is given a change in angle of attack. effects of supersonic flight on the various items of stability.

Since the downwash at the tail reduces the The static longitudinal stability of an air- change in angle of attack at the tail, any in- plane increases during the transition from sub- crease in downwash at the tail is destabilizing.

sonic to supersonic flight. Usually the prin- For certain low aspect ratio airplane configura- cipal source of the change in stability is due to tions, an increase in airplane angle of attack the shift of the wing aerodynamic center with may physically locate the horizontal tail in NAVWEPS oo-s01-80 STABILITY AND CONTROL deflection when subject to load, the tendency Mach number. As a corollary of this increase may be to lower the contribution to static in stability is a decrease in controllability and stability and reduce the damping contribution.

an increase in trim drag.

Thus, the problem of adequate stability of the The static directional stability of an air- various airplane motions is aggravated.

plane decreases with Mach number in super- sonic flight. The influence of the fuselage and the decrease in vertical tail lift curve slope PILOT INDUCED OSCILLATIONS bring about this condition.

The dynamic stability of the airplane The pilot may purposely induce various generally deteriorates with Mach number in motions to the airplane by the action of the supersonic flight. Since a large part of the controls. In additron, certain undesirable damping depends on the tail surfaces, the motions may occur due to inadvertent action decrease in lift curve slope with Mach number on the controls. The most important con- will account in part for the decrease in damp dition exists with the short period longitu- ing. Of course, all principal motions of the dinal motion of the airplane where pilot- aircraft must have satisfactory damping and control system response lag can produce an if the damping is not available aerodynami- unstable oscillation. The coupling possible cally it must be provided synthetically to in the pilot-control system-airplane combi- obtain satisfactory flying qualities. For many nation is most certainly capable of producing high speed configurations the pitch and yaw damaging flight loads and loss of control of dampers, flight stabilization systems, etc., the airplane.

are basic necessities rather than luxuries.

When the normal human response lag and Generally, flight at high Mach number will control system lag are coupled with the air- cake place at high altitude hence the effect of plane motion, inadvertent control reactions high altitude must be separated for study.

by the pilot may furnish a negative damping All of the basic aerodynamic damping is due to the oscillatory motion and dynamic in- stability exists.

to moments created by pitching, rolling, or Since the short period motion is of relatively high frequency, the amplitude yawing motion of the aircraft. These moments of the pitching oscillation can reach dangerous are derived from the changes in angles of proportions in an unbelievably short time.

attack on the tail surfaces with angular When the pilot induced oscillation is en- rotation (see fig. 4.15). The very high true airspeeds common to high altitude flight countered, the most effective solution is an immediate release of the controls. Any at- reduce the angle of attack changes and reduce the aerodynamic damping. In fact, the aero- tempt to forcibly damp the oscillation simply dynamic damping is proportional to & continues the excitation and amplifies the similar to the proportion of true airspeed to oscillation. Freeing the controls removes the unstable (but inadvertent) excitation and equivalent airspeed. Thus, at the altitude of 4O,C00 ft., the aerodynamic damping would allows the airplane to recover by virtue of be reduced to one-half the sea level value and its inherent dynamic stability.

The pilot induced oscillation is most likely at the altitude of 100,000 ft. the aerodynamic under certain conditions, damping would be reduced to one-tenth the Most obvious is the case of the pilot unfamiliar with the “feel” sea level value.

of the airplane and likely to overcontrol or High dynamic pressures (high $I can be common to flight at high Mach number and have excessive response lag.

High speed flight at low. altitude (high 4) is most likely to adverse aeroelastic effects may be encountered.

If the aircraft surfaces, encounter significant provide low stick-force gradients and periods NAVWEPS OO-SOT-80 STABILITY AND CONTROL of oscillation which coincide with the pilot- and pitch inertia and each inertia is a measure Also, the high 4 control system response lag.

of the resistance to rolling, yawing, or pitching flight condition provides the aerodynamic acceleration of the airplane. The long,slender, capability for failing flight loads during the high-density fuselage with short, thin wings oscillation.

produces a roll inertia which is quite small in If a pilot induced oscillation is encountered comparison to the pitch and yaw inertia.

the pilot must rely on the inherent dynamic These characteristics are typical of the modern stability of the airplane and immediately airplane configuration. The more conventional release the controls. If the unstable excitation low speed airplane may have a wingspan is continued, dangerous oscillation amplitudes greater than the fuselage length. This type of will develop in a very short time.

configuration produces a relatively large roll inertia. A comparison of these configurations is shown in figure 4.34.

ROLL COUPLING Inertia coupling can be illustrated by con- sidering the mass of the airplane to be con- The appearance of “inertia coupling” prob- centrated in two elements, one representing the lems in modern airplanes was the natural result mass ahead of the c.g. and one representing the of the progressive change in aerodynamic and mass behind the c.g. There are two principal inertia characteristics to meet the demands of axis systems to consider: (1) the aerodynamic, high speed flight. Inertia coupling problems or wind axis is through the c.g. in the relative were unexpected only when dynamic stability wind direction, and (2) the inertia axis is analyses did not adequately account for the through the c.g. in the direction of the two rapid changes in aerodynamic and inertia element masses. This axis system is illus- characteristics of airplane configurations. The trated in figure 4.34.

The term of “intertia coupling” is somewhat If the airplane shown in figure 4.34 were in misleading because the complete problem is some flight condition where the inertia axis one of aerodynamic as well as inertia coupling.

and the aerodynamic axis are alined, no inertia “Coupling” results when some disturbance coupling would result from rolling motion.

about one airplane axis causes a disturbance However, if the inertia axis is inclined to the about another axis. An example of uncoupled aerodynamic axis, rotation about the aero- motion is the disturbance provided an airplane dynamic axis will create centrifugal forces and when subjected to an elevator deflection. The cause a pitching moment. In this case, a resulting motion is restricted to pitching motion without disturbance in yaw or roll. rolling motion of the aircraft induces a pitch- An example of, coupled motion could be the ing moment through the action of inertia disturbance provided an airplane when sub- forces. This is “inertia coupling” and is jected to rudder deflection. The ensuing mo- illustrated by part B of figure 4.34.

tion can be some combination of yawing and When the airplane is rotated about the rolling motion. Hence, the rolling motion is inertia axis no inertia coupling will exist but coupled with the yawing motion to define the aerodynamic coupling will be present. Part resulting motion. This sort of interaction C of figure 4.34 shows the airplane after rolling results from aerodynamic characteristics and is 90” about the inertia axis. The inclination termed “aerodynamic coupling.” which was initially the angle of attack (a) is A separate type of coupling results from the now the angle of sideslip (-6). Also the inertia characteristics of the airplane conligura- original zero sideslip has now become zero tion. The inertia characteristics of the com- angle of attack. The sideslip induced by this plete airplane can be divided into the roll, yaw, 90° displacement will affect the roll rate NAVWEPS OD-3OT-80 STABILITY AND CONTROL RELATIVELY HIGH cc > -I ROLL INERTIA

y$z>

RELATIVELY A /7 ROLL MASS MOTION ROLL MOTION WSITIVE ANGLE OF ATTACK.

ZERO SIDESLIP FUSELAGE fh SIDEFORCE AERODYNAMIC AXIS FINITE SIDESLIP

u pgq

ROLL MOTION Figure 4.34. Roll Coupling NAVWEPS 00-8OT-80 STABILITY AND CONTROL pitch frequency and yaw frequency. Gen- depending on the nature of the dihedral effect erally, the greater the static longitudinal and of the airplane.

directional stability, the higher will be the It should be noted that initial inclination of the inertia axis above the aerodynamic axis coupled pitch-yaw frequency. When the air- will cause the inertia couple to provide adverse plane is subject to roiling motion, the inertia yaw with rolling motion. If the inertia axis couple disturbs the airplane in pitch and yaw with each roll revolution and provides a dis- were initially inclined below the aerodynamic axis (as may happen at high 4 or negative load turbing forcing function.’ If the airplane is factors), the roll induced inertia couple would rolled at a rate equal to the coupled pitch-yaw provide proverse yaw. Thus, roll coupling frequency, the oscillatory motion will either diverge or stabilize at some maximum ampli- may present a problem at both positive and negative inclination of the inertia axis depend- tude depending on the airplane characteristics.

ing on the exact aerodynamic and inertia The longitudinal stability of the typical high speed configuration is much greater than the characteristics of the configuration.

directional stability and results in a pitch fre- As a result of the aerodynamic and inertia coupling, rolling motion can induce a great quency higher than the yaw frequency. In- creasing the directional stability by increasing variety of longitudinal, directional, and lateral forces and moments. The actual motion of the vertical tail area, addition of ventral hns, the airplane is a result of a complex combina- or use of stabilization systems will increase the tion of the aerodynamic and inertia coupling. coupled pitch-yaw frequency and raise the roll Actually, all airplanes exhibit aerodynamic rate at which a possible divergent condition and inertia coupling but of varying degrees. could exist. Increasing directional stability The roll coupling causes no problem when the by the addition of ventral fins rather than by moments resulting from the inertia couple are addition to the vertical tail has an advantage easily counteracted by the aerodynamic re- of not contributing to the positive dihedral storing moments. The very short span, high effect at low or negative angles of attack.

speed modern aircraft has the capability for High dihedral effect makes higher roll rates the high roll rates which cause large magni- more easily attainable in roll motion where tudes of the inertia couple. The low aspect proverse yaw occurs.

ratio planform and flight at high Mach number Since the uncoupled yawing frequency is allow large inclination of the inertia axis with lower than the pitching frequency, a divergent respect to the aerodynamic axis and also add condition would lirst reach critical proportions to the magnitude of the inertia couple. In in yaw, closely followed by pitch. Of course, addition, the aerodynamic restoring moments whether the airplane motion becomes divergent deteriorate as a result of high Mach number directionally or longitudinally is of academic and angle of attack and can create the most interest only.

serious roll coupling conditions. There is one additional type of coupling Since the roll coupling induces pitching and problem that is referred to as “autorotative yawing motion, the longitudinal and direc- rolling.” A rolling airplane which has a high tional stability is important in determining the positive dihedral effect may reach a large pro- overall characteristics of the coupled motion.

verse sideslip as a result of the inertia couple and A stable airplane, when disturbed in pitch and the rolling moment due to sideslip may exceed yaw, will return to equilibrium after a series that available from lateral control. In such of oscillations. For each flight condition, the a case it would not be possible to stop the air- airplane will have a coupled pitch-yaw fte- plane from rolling although lateral control quency between the uncoupled and separate was held full against the roll direction. The NAVWEPS DD-EOT-80 STABMTY AND CONTROL design features which result in a large positive The first four items can be effected,only during dihedral effect are high sweepback, high wing design or by design changes. Some roll per- position, or large, high vertical tail, When formance restriction is inevitable since all of the inertia axis is inclined below the aero- the desirable characteristics are difficult to dynamic axis at low or negative angles of obtain without serious compromise elsewhere attack, the roll induced inertia couple results in the airplane design. The typical high in proverse yaw. speed airplane will have some sort of roll pet- Depending on the flight condition where the formance limitation provided by flight restric- roll coupling problem exists, four basic types tions or automatic control devices to prevent of airplane behavior are possible: reaching some critical condition from which recovery is impossible. Any roll restriction (1) Coupled motion stable but unacceptabk.

In this case the motion is stable but proves provided an airplane must be regarded as a principal flight operating limitation since the unacceptable because of poor damping of the motion. Poor damping would make it more severe motions can cause complete loss dificult to track a target or the initial am- of control and structural failure.

plitudes of the motion may be great enough to cause structural failure of loss of control. HELICOPTER STABILITY AND CONTROL (2) Coupled motion stable and acceptable.

In discussing many of the problems of sta- The behavior of the airplane is stable and bility and control that occur in high speed adequately damped to allow acceptable airplanes, one might be prone to believe that target tracking. The amplitudes of motion the slow flying helicopter does not have any are too slight to result in structural failure such problems. Unfortunately, this is not or loss of control.

the case. Flying qualities that would be con- (3) Coupledmotion divergentand unacceptable.

sidered totally unsatisfactory by fixed-wing The rate of divergence is too rapid for the standards ate normal for helicopters. Heli- pilot to recognize the condition and recover copter pilots are living evidence that an un- prior’ to structural failure or complete loss stable aircraft ca. k‘ .: controlled. Also, they of control.

are evidence ~a. control without stability (4) Coupled.motion divergent but acceptable.

requires constant attention and results in con- For such a condition the rate of divergence siderable pilot fatigue.

is quite slow and considerable roll displace- “Inertia coupling” problems are relatively ment is necessary to produce a critical ampli- new to fixed-wing aircraft but a similar effect tude. The condition can be recognized in the helicopter rotor has resulted in some easily in time to take corrective action.

of its most important characteristics. This There are available various means to cope aerodynamic-dynamic coupling effect is so im- with the problem of roll coupling. The fol- portant that it must be considered in discussing lowing items can be applied to control the both stability and control. The helicopter problem of roll coupling: derives both longitudinal and lateral control (ZZ) Increase directional stability.

by tilting the main rotor and thus producing (b) Reduce dihedral effect.

a pltchmg or rolling moment as indicated in (c) M ’ h 1‘ mnmze t e mc mation of the inertia figure 4.35. The magnitude of the rotor thrust axis at normal flight conditions.

the angle of tilt, and the height of the rotor (d) Reduce undesirable aerodynamic coupling. hub above the c.g. determine the control (e) Limit roll rate, roll duration, and moment produced. It should be noted that angle of attack or load factor for performing low control effectiveness would result when rolling maneuvers. the rotor thrust is low. Some helicopters NAWWEPS 00-8OT-80 STABILITY AND CONTROL THRUST C.G.

A

ROTOR GYROSCOPIC ACTION THESE FORCES PRODUCE THIS MOMEPdT AND DISPLACEMENT Figure 4.35. Rotor Forces and Moments NAVWEPS DO-80T-80 STABILITY AND CONTROL Adequate pitch and lateral control effective- employ an offset flapping hinge to increase the ness are easy to obtain in the typical helicopter control effectiveness by creating a centrifugal and usually present no problems. The more force couple when the rotor is tilted.

This is usual problem is an excess of control effective- shown in figure 4.35.

ness which results in an overly sensitive heli- The rotor is tilted by taking advantage of The helicopter control specifications copter.

the gyroscopic effect of the rotor system. This attempt to assure satisfactory control charac- effect causes a rotating mass which is disturbed teristics by requiring adequate margins of con- about one axis to respond about another axis, trol travel and effectiveness without objection- as shown in figure 4.35.

A forward tilt to the able sensitivity.

rotor is obtained by decreasing the pitch of the Directional control in a single rotor heli- blade when at the starboard position and in- copter is obtained by a tail rotor (antitorque creasing the pitch of the blade when at the rotor) since a conventional aerodynamic sur- port position. The lateral dissymmetry of face would not be effective at low speeds or lift which results causes the rotor to tilt for- hovering. The directional control require- ward by the gyroscopic effect.

ments of the tail rotor on a typical shaft-driven A differential blade pitch change like this helicopter are quite demanding since it must is called a cyclic.pitch change since each blade counteract the engine torque being supplied to goes thr0ugh.a complete cycle of varying pitch the main rotor as well as provide directional angles as it completes one revolution of rota- control. Being a rotor in every respect, the tion about the hub. A cyclic pitch change is tail rotor requires some of the engine power to accomplished by the pilot by the use of the generate its control forces. Unfortunately, the cyclic stick. The control arrangement is such maximum demands of the tail rotor occur at that the rotor tilts in the same direction that conditions when engine power is also in great the cyclic stick is deflected.

demand. The most critical condition is while A variation in rotor thrust is accomplished hovering at maximum gross weight. The tail by increasing>sthe pitch of the blades simul- rotor effectiveness is determined by the rotor taneously or collectively. This type of control characteristics and the distance the tail rotor action is called “collective pitch” and is ac- is behind the c.g. The control specifications complished by the use of the collective pitch require the helicopter to be able to turn in the stick. In operation, the cyclic stick is an- most critical direction at some specified rate alogous to the control stick of an airplane, while hovering at maximum gross weight in a and the collective stick is analogous to the specified wind condition. Also, it is required throttle ~of an ,airplane.

that the helicopter have sufficient directional There are several possibilities for longi- control to fly sideways up to 30 knots, an tudinal control of a tandem-rotor helicopter.

important requirement for plane guard duties.

A pitching moment can be produced by tilting The directional control requirements are both rotors by a cyclic pitch change in each easily met by a tip-driven helicopter since the rotor, by a differential collective pitch change directional control does not have to counter that increases the thrust on one rotor and de- the engine torque.

creases it on the other, or by some combination Directional control of a tandem-rotor heli- of these methods. The two basic methods are copter is accomplished by differential cyclic illustrated in figure 4.36. Obviously, a change control of the main rotors. For a pedal turn in fuselage attitude must accompany the dif- to the starboard, the forward rotor is tilted ferential collective method of longitudinal to the starboard and the rear rotor is tilted to control.

port, creating a turning moment as shown in NAVWEPS DD-80T-80 STABILITY AND CONTROL TANDEM ROTOR LONGITUDINAL CONTROL TANDEM ROTOR DIRECTIONAL CONTROL AFT ROTOR F”&%iD *JR Fig&e 4.36. longitudinal and Directional Control NAVWEPS 00-801-80 STABILITY AND CONTROL retreating blade since the relative wind veloci- figure 4.36. The directional control require- ties are greater on the advancing blade. This ments are easily met in a tandem-rotor heli- lateral dissymmetry of lift causes the rotor to copter because the engine torque from one rotor is opposed by the torque of the other tilt back due to the gyroscopic effect of the rotor, further increasing the rotor angle of rotor thereby eliminating one directional mo- ment. Of course, some net unbalance of torque attack. Thus, the rotor is unstable with changes in angle of attack at forward flight may have to be overcome if the engine torque on the two rotors is different. speeds. Since the magnitude of the unstable When a tandem-rotor helicopter is rotated moment is affected by the magnitude of rapidly about one of the rotors rather than the rotor thrust as well as the tilt of about the cg., the other rotor picks up the thrust force, a greater instability exists “translational lift” as a result of the velocity for increases in angle of attack than for due to rotation and an increase in rotor thrust decreases in angle of attack. In addition, the This causes pitch-up or pitch-down instability is greater for increases in angle of results.

attack when the rotor thrust also increases.

depending on which rotor the helicopter is If the rotor angle of attack is held constant being rotated about. Rotation about the forward rotor, which is more common, re- and the rotor is given a translational velocity, sults in pitch-down. a dissymmetry of lift results since the velocity The overall stability of a helicopter results of the advancing blade is increased while the from the individual stability contributions of velocity of the retreating blade is decreased.

the various components just as in the case of This dissymmetry of lift causes the rotor to the fixed-wing airplane. The stability con- tilt in a direction to oppose the change in tributions can be divided as follows: velocity due to the gyroscopic effect of the (1) Rotor rotor. Hence, the rotor has velocity stability.

(2) Fuselage A hovering helicopter exhibits some degree (3) Stabilizers of apparent stability by virtue of its velocity (4) Mechanical devices stability although it has neutral angle of The destabilizing contribution of the fuselage attack stability. This type of hovering sta- and the stabilizing contribution of a stabilizing bility is analogous to the apparent lateral- surface are similar in effect to an airplane and directional stability an airplane exhibits due will not be discussed here. The principal to dihedral effect. Additional hovering sta- stability characteristics that make the heli- bility can be obtained by the use of mechanical copter different from an airplane are those of stabilizers such as th,e Bell stabilizer bar, by the rotor. the use of offset flapping hinges, or by syn- Two types of stability are important in the thetic or artificial stabilization devices.

rotor: (1) angle of attack stability and (2) The total static stability of a helicopter is velocity stability. In hovering flight the determined by combining the stability con- relative wind velocity, angle of attack, and tributions of all the components. The usual lift on each blade of the rotor is the same. If result for a typical helicopter is instability the rotor is displaced through some angle, no with angle of attack and a variable velocity changes in forces result. Therefore, the rotor stability which becomes neutral or unstable has neutral angle of attack stability when at high speeds. Of course, the helicopter hovering. However, in forward flight, an could be made stable with angle of attack by increase in rotor angle of attack increases the providing a large enough horizontal stabilizer.

lift on the advancing blade more than on the Unfortunately, adverse effects at low speed or NAVWEPS 00-801-80 STABILITY AND CONTROL greatly to improving the flying qualities of hovering and large trim moments upon entering the helicopter.

autorotation will limit the stabilizer size to This dynamic instability characteristic is a relatively small surface. Usually the hori- particularly important if the helicopter is zontal stabilizer is used only to give the fuse- expected to be used for instrument flight in lage the desired moment characteristics.

all-weather operations. In fact, a seriously The angle of attack stability of a tandem- divergent phugoid mode would make instru- rotor helicopter is adversely affected by the ment flight impractical. For this reason, the downwash from the forward rotor reducing the angle of attack and thrust of the rear flying qualities specification requires that rotor. This reduction of thrust behind the helicopters with an instrument capability cg. causes the helicopter to pitch up to a exhibit varying degrees of stability or insta- bility depending on the period of the oscilla- higher angle of attack, thereby adding to the angle of attack instability. tion. Long period oscillations (over 20 sec- As in the airplane, several oscillatory modes onds) must not double in amplitude in less of motion are characteristic of the dynamic than 15 seconds whereas short period oscil- lations (under 10 seconds) must damp to half stability of a helicopter. The phugoid is the amplitude in two cycles.

most troublesome for the helicopter. The The only immediate solution for the dynamic phugoid mode is unstable in the majority of instability is an attitude stabilization system helicopters which operate without the assist- which is essentially an autopilot. Other ance of artificial stabilization devices. The solutions to the dynamic instability problem dynamic instability of the helicopter is given involve mechanical, aerodynamic, or elec- evidence by the flying qualities specification for tronic control feedback of pitch attitude, helicopters. These specifications essentially pitch velocity, normal acceleration, or angle limit the rate of divergence of the dynamic oscil- of attack. The improvement of the heli- lations for the ordinary helicopter. Although copter’ s stability is mandatory to fully utilize this dynamic instability can be controlled, it its unique capability. As more of the heli- requires constant attention by the pilot and copter problems are analyzed and studied, the results in pilot fatigue. The elimination of flying qualities of helicopters wiI1 improve the dynamic instability would contribute and be comparable to the fixed wing aircraft.

NAVWEPS 00-801-80 OPERATING STRENGTH LIMITATIONS

Chapter 5

OPERATING STRENGTH

LIMITATIONS

The weight of the structural components of order to obtain the required service life from an aircraft is an extremely important factor in his aircraft, the Naval Aviator must undet- the development of an efficient aircraft con- stand, appreciate, and observe the operating figuration. In no other field of mechanical strength limitations. Failure to do so will design is there such necessary importance incur excessive maintenance costs and a high assigned to structural weight. The efficient incidence of failure during the service life of aircraft and powerplant structure is the zenith of highly reined rknimum weight design.

in an aircraft.

NAVWEPS oo-EOT-80 OPERATING STRENGTH LIMITATIONS GENERAL DEFINITIONS AND STRUC- permanent deformation when subjected to the TURAL REQUIREMENTS limit load. In fact, the components must with- stand this load with a positive margin. This There are strength requirements which ate requirement implies that the aircraft should common to all aircraft. In general, these re- withstand successfully the limit load and then quirements can be separated into three particu- return to the original unstressed shape when lar areas. These are detailed in the following the load is removed. Obviously, if the air- discussion.

craft is subjected to some load which is in excess of the limit load, the overstress may STATIC STRENGTH incur an objectionable permanent deformation of the primary structure and require replace- The static strength requirement is the con- ment of the damaged parts.

sideration given to the effect of simple static Many different flight and ground load condi- loads with none of the ramifications of the tions must be considered to define the most repetition or cyclic variation of loads. An critical conditions for the structural com- important reference point in the static strength ponents. In addition to positive lift flight, requirement is the “limit load” condition.

negative lift flight must be considered. Also, When the aircraft is at the design conligura- the effect of flap and landing gear configura- tion, there will be some maximum of load tion, gross weight, flight Mach,number, sym- which would be anticipated from the mission requirement of the airplane. For example, a metry of loading, c.g. positions, etc., must be studied to account for all possible sources of fighter or attack type aircraft, at the design critical loads.

configuration, may encounter a very peak load To verify the capability of the factor of 7.5 in the accomplishment of its mis- structure, ground static tests are conducted sion. Of course, such an aircraft may be sub- and flight demonstrations ate required.

ject to load factors of 3, 4, 5, 6, 1, etc., but no To provide for the rare instances of flight more than 7.5 should be required to accom- when a load greater than the limit is required plish the mission. Thus, the limit load condi- to prevent a disaster, an “ultimate factor of tion is the maximum of loads anticipated in is provided. Experience has shown safety” normal operation of the aircraft, that an ultimate factor of safety of 1.5 is suf- Various types of aircraft will have different limit load ficient for piloted aircraft. Thus, the aircraft factors according to the primary mission of must be capable of withstanding a load which the aircraft. is 1.3 times the design limit load.

Typical values are tabulated The primary below: structure of the aircraft must withstand the hbi”< Type of aircraft: “ultimate load” (1.5 times limit) without limi,hi,orror failure. Of course, permanent deformation Fighter or attack.

7.5 Trainer. may be expected with this “overstress” but 7.5 T ransport, patrol, antisubmarine. 3.0 or 2.5 no actual failure of the major load-carrying components should take place at ultimate load Of course, these examples are quite general and Ground static tests are necessary to verify this it is important to note that there may be varia- capability of the structure.

tions according to specific mission require- An appreciation of the static strength re- ments.

quirements may be obtained by inspection of Since the limit load is the maximum of the the basic properties of a typical aircraft metal.

normally anticipated loads, the aircraft struc- ture must withstand this load with no ill Figure 3.1 illustrates the typical static strength effects.

Specilicallv, the primary structure of properties of a metal sample by a plot of applied the aircraft should experience no objectionable stress versus resulting strain. At low values 3,26 NAVWEPS 00-EOT-80 OPERATING STRENGTH LIMITATIONS STATIC STRENGTH OF TYPICAL AIRCRAFT METAL ULTIMATE STRENGTH -Cc Q FAILURE STRESSES APPLIED ABOVE THIS POINT RESULT IN OBJECTIONABLE PERMANENT DEFORMATION -I STRAIN (IN/IN) PERMANENT II: SET

-I I--

FATIGUE STRENGTH OF TYPICAL AIRCRAFT METAL HIGH CYCLIC STRESS VERY FEW CYCLES REQUIRED TO CAUSE FAILURE MODERATE CYCLIC STRESS RELATIVELY LARGE NUMBER OF CYCLIC APPLICATIONS NECESSARY TO STRESS CAUSE FAILURE LOW CYCLIC STRESS (PSI) ALMOST INFINITE CYCLES TO CREATE FATIGUE FAILURE NUMBER OF APPLICATIONS TO CAUSE FATIGUE FAILURE Egu,e 5.1. Strength Chomctorirfics NAVWEPS oo-8oT-80 OPERATING STRENGTH LIMITATIONS of stress the plot of stress and strain is essen- FATIGUE CONSIDERATIONS. The fa- tigue strength requirement is the considera- tially a straight line, i.e., the material in this range is elastic. A stress applied in this range tion given the cumulative effect of repeated or cyclic !oads during service. While there is incurs no permanent deformation and the ma- a vague relationship with the static strength, terial returns to the original unstressed shape repeated cyclic loads produce a completely when the stress is released. At higher values of stress the plot of stress versus strain develops separate effect. If a cyclic, tensile stress is applied to a metal sample, the part is subject a distinct curvature in the strain direction and to a “fatigue” type loading. After a period the material incurs disproportionate strains.

of time, the cyclic stressing will produce a High levels of stress applied co the part and minute crack at some critical location in the then released produce a permanent deforma- sample. With continued application of the tion. Upon release of some high stress, the varying stress, the crack will enlarge and metal snaps back-but not all the way. The propagate into the cross section. When the stress defining the limit of tolerable permanent crack has progressed sufficiently, the remaining strain is the “yield stress” and stresses applied cross section is incapable of withstanding the above this point produce objectionable per- imposed stress and a sudden, final rupture manent deformation. The very highest stress occurs. In this fashion, a metal can be failed the material can withstand is the “ultimate at stresses much lower than the static ultimate stress.” Noticeable permanent deformation strength.

usually occurs in this range, but the material Of course, the time necessary to produce does have the capability for withstanding one fatigue failure is related to the magnitude of application of the ultimate stress.

the cyclic stress. This relationship is typified The relationship between the stress-strain by the graph of figure 5.1. The fatigue diagram and operating strength limits should be obvious. If the aircraft is subjected to a strength of a material can be demonstrated by a plot of cyclic stress versus cycles of stress load greater than the limit, the yield stress As might may be exceeded and objectionable permanent required to produce fatigue failure.

deformation may result. If the aircraft is be expected, a very high stress level requires relatively few cycles to produce fatigue failure.

subject to a load greater than the ultimate, Moderate stress levels require a fairly large failure is imminent.

number of cycles to produce failure and a very low stress may require nearly an infinite num- SERVICE LIFE ber of cycles to produce failure. The very The various components of the aircraft and certain implication is that the aircraft must powerplant structure must be capable of oper- be capable of withstanding the gamut of ating without failure or excessive deformation service loads without producing fatigue failure throughout the intended service life. The of the primary structure.

repetition of various service loads can produce For each mission type of aircraft there is fatigue damage in the structure and special a probable spectrum of loads which the air- attention must be given to prevent fatigue craft will encounter. That is, various loads failure within the service life, Also, the sus- will be encountered with a frequency particular taining of various service loads can produce to the mission profile. The fighter or attack creep damage and special attention must ‘ be type of aircraft usually experiences a pre- given to prevent excessive deformation or dominance of maneuver loads while the trans- creep failure within the service life, This is a particular feature of components which are port or patrol type usually encounters a pre- subjected to operation at high temperatures.

dominance of gust loads. Since fatigue damage SNOIlVlIWll HlOM3US ONllVU3dO 08-108-00 Sd3MAVN NAVWEPS 00-8OT-80 OPERATING STRENGTH LIMITATIONS is cti~n&zti~e during cyclic stressing, the useful relationships for aircraft and powerplant service life of the aircraft must be anticipated structures.

to predict the gross effect of service loads. CREEP CONSIDERATIONS. By definition, creep is the structural deformation which oc- Then, the primary structure is required to curs as a function of time. If a part is subjected sustain the typical load spectrum rhrough the anticipated service life without the occurrence to a constant stress of sufficient magnitude, the part will continue to develop plastic strain and of fatigue failure. To prove this capability deform with time. Eventually, failure can of the structure, various major components must be subjected to an accelerated fatigue occur from the accumulation of creep damage.

test to verify the resistance to repeated loads. Creep conditions are most critical at high stress and high temperature since both factors The design of a highly stressed or long life increase the rate of creep damage. Of course, structure emphasizes the problems of fatigue.

any structure subject to creep conditions should Great care must be taken during design and manufacture to minimize stress concentrations not encounter excessive deformation or failure which enhance fatigue. When the aircraft within the anticipated service life.

enters service operation, care must be taken in The high operating temperatures of gas tur- the maintenance of components to insure proper bine components furnish a critical environment adjustment, torquing, inspection, etc., as proper for creep conditions. The normal operating maintenance is a necessity for achieving full temperatures and stresses of gas turbine com- service life. Also, the structure must not be ponents create considerable problems in design for service life. Thus, operating limitations subjected to a load spectrum more severe than deserve very serious respect since excessive was considered in design or fatigue failures engine speed or excessive turbine temperatures may occur within the anticipated service life.

will cause a large increase in the rate of creep With this additional factor in mind, any pilot damage and lead to premature failure of com- should have all the more respect for the oper- ponents. Gas turbines require high operating ating strength limits-recurring overstress causes a high rate of fatigue damage. temperatures to achieve high performance and efficiency and short periods of excessive tem- There are many examples of the detrimental effect of repeated overstress on service life. peratures can incur highly damaging creep One major automobile manufacturer adver- rates.

tised his product as “guaranteed to provide Airplane structures can be subject to high 100,000 miles of normal driving without me- temperatures due to aerodynamic heating at chanical failure.” The little old lady from high Mach numbers. Thus, very high speed airplanes can be subject to operating limita- Pasadena-the original owner of ALL used cars tions due to creep conditions.

-will probably best the guaranteed mileage by many times. On the other hand, the hot- AFROELASTIC EFFECTS rod artist and freeway Grand Prix contender The requirement for structural stiffness and do not qualify for the guarantee since their rigidity is the consideration given to the inter- manner of operation could not be considered action of aerodynamic forces and deflections of normal. The typical modern automobile may the structure. The aircraft and its components be capable of 60,000 to l~,OOO miles of normal must have sufficient stiffness to prevent or operation before an overhaul is necessary.

minimize aeroelastic influences in the normal However, this same automobile may encounter flight range, Aileron reversal, divergence, catastrophic failures in a few hundred miles if flutter, and vibration should not occur in the operated continually at maximum torque in range of flight speeds which will be normal low drive range. Obviously, there are similar operation for the aircraft.

NAVWEPS 00-EOT-80 OPERATING STRENGTH LIMITATIONS airplane may encounter depend in great part It is important to distinguish between strength and stiffness. Strength is simply the on the mission type of the airplane. However, resistance to load while stiffness is the resist- the maximum maneuvering capability is of interest because of the relationship with ance to deflection or deformation. While strength and stiffness are related, it is necessary strength limits.

to appreciate that adequate structural strength The flight load factor is defined as the pro- does not automatically provide adequate stiff- portion between airplane lift and weight, ness. Thus, special consideration is necessary where to provide the structural components with n=L/W specific stiffness characteristics to prevent un- n= load factor desirable aeroelastic effects during normal L=lift, Ibs.

operation.

W= weight, Ibs.

An obvious solution to the apparent prob- lems of static strength, fatigue strength, MANEUVERING LOAD FACTORS. The stiffness and rigidity would be to build the maximum lift attainable at any airspeed occurs airplane like a product of an anvil works, when the airplane is at CLmU. With the use capable of withstanding all conceivable loads.

of the basic lift equation, this maximum lift However, high performance airplane con- is expressed as: figurations cannot be developed with inefi- cient, lowly stressed structures. The effect of additional weight is best illustrated by pre- liminary design studies of a very long range, Since maximum lift must be equal to the high altitude bomber. In the preliminary weight at the stall speed, phases of design, each additional pound of any weight would necessitate a 25-pound increase in gross weight to maintain the same If the effects of compressibility and viscosity performance. An increase in the weight of are neglected for simplification, the on Ch any item produced a chain reaction-more maximum load factor attainable is determined fuel, larger tanks, bigger engines, more fuel, by the following relationship.

heavier landing gear, more fuel, etc. In the competitive sense of design, no additional structural weight can be tolerated to provide more strength than is specified as necessary

v.2

for the design mission requirement.

V*

=(-)

Thus, if the airplane is flying at twice the AIRCRAFT LOADS AND OPERATING stall speed and the angle of attack is increased LIMITATIONS to obtain maximum lift, a maximum load FLIGHT LOADS-MANEUVERS AND factor of four will result. At three times the GUSTS stall speed, nine “g’ s” would result; four The loads imposed on an aircraft in flight times the stall speed, sixteen g’ s result; five are the result of maneuvers and gusts. The times the stall speed, twenty-five g’ s result; maneuver loads may predominate in the etc. Therefore, any airplane which has high design of fighter airplanes while gust loads speed performance may have the capability of may predominate in the design of the large high maneuvering load factors. The airplane multiengine aircraft. The maneuver loads an which is capable of flight speeds that are N A V W E P S 00-801-80 OPERATING STRENGTH LIMITATIONS Operation in this region of high load factors many times the stall speed will require due at .low gross weight may create the impression consideration of the operating strength limits.

that the airplane has great excess strength The structural design of the aircraft must capability. This effect must be understood and consider the possibility of negative load factors from maneuvers. Since the pilot cannot com- intelligently appreciated since it is not uncom- fortably tolerate large prolonged negative “g”, mon to have a modern airplane configuration the aircraft need not be designed for negative with more than SO percent of its gross weight load factors as great as the positive load factors. as fuel.

The effect of airplane gross weight during GUST LOAD FACTORS. Gusts are asso- ciated with the vertical and horizontal velocity maneuvers must be appreciated because of the gradients in the atmosphere. A horizontal particular relation to flight operating strength limitations. During flight, the pilot appre- gust produces a change in dynamic pressure on the airplane but causes relatively small and ciates the degree of a maneuver from the inertia forces produced by various load factors; unimportant changes in flight load factor.

the airplane structure senses the degree of a The more important gusts are the vertical gusts maneuver principally by the airloads involved. which cause changes in angle of attack. This Thus, the pilot recognizes loadfactor while the process is illustrated in figure 5.2. The vec- To better structure recognizes only load. torial addition of the gust velocity to the air- understand this relationship, consider an ex- plane velocity causes the change in angle of ample airplane whose basic configuration gross attack and change in lift. The change in angle weight is 20,000 lbs. At this basic configura- of attack at some flight condition causes a tion assume a limit load factor for symmetrical change in the flight load factor. The incre- flight of 5.6 and an ultimate load factor of 8.4. ment change in load factor due to the vertical If the airplane is operated at any other con- gust can be determined from the following figuration, the load factor limits will be al- equation: tered. The following data illustrate this fact by tabulating the load factors required to produce identical airloads at various gross weights.

where Grass weight, Ibs. Limit load Ultimate An=change in load factor due to gust factor load factor m=lift curve slope, unit of C, per degree of 01 20,wO (basic).

5.60 8.40 o=altitude density ratio 30,003(max. rakcoff).

3.73 5.60 13,333(min. f”cl):. 8.40 12.60 W /S= wing loading, psf V. = equivalent airspeed, knots As illustrated, at high gross weights above the KU=equivalent sharp edged gust velocity basic configuration weight, the limit and ulti- ft. per sec.

mate load factors may be seriously reduced.

For the airplane shown, a 5-g maneuver im- As an example, consider the case of an air- mediately after a high gross weight takeoff plane with a lift curve slope m=O.OB and wing could be very near the “disaster regime,” loading, (W/S)=60 psf.

If this airplane were especially if turbulence is associated with the flying at sea level at 350 knots and encountered maneuver. In the same sense, this airplane an effective gust of 30 ft. per sec., the gust at very low operating weights below that of would produce a load factor increment of 1.61.

the basic configuration would experience great- This increment would be added to the flight ly increased limit and ultimate load factors. load factor of the airplane prior to the gust, NAVWEPS OO-80T-80 OPERATING STRENGTH LIMITATIONS CHANGE IN LIFT AIRPLANE VELOCITY, V GUST RESULTANT VELOCITY VELOCITY KU figure 5.2. Effect of Vertical Gust e.g., if in level flight before encountering the of the airplane and the gradient of the gust.

gust, a final load factor of 1.0+1.61=2.61 A gust factor, K (usually on the order of 0.6), would result. As a general requirement all reduces the actual gust to the equivalent sharp edged gust velocity, KU.

airplanes must be capable of withstanding an approximate effective f30 ft. per sec. gust The properties of the airplane exert a power- when at maximum level flight speed for normal ful influence on the gust increment. The lift rated power. Such a gust intensity has rela- curve slope, m, relates the sensitivity of the tively low frequency of occurrence in ordinary airplane to changes in angle of attack. An flying operations. aircraft with a straight, high aspect ratio The equation for gust load increment pro- wing would have a high lift curve slope and vides a basis for appreciating many of the would be quite sensitive to gusts. On the variables of flight. The gust load increment other hand, the low aspect ratio, swept wing varies directly with the equivalent sharp airplane has a low lift curve slope and is com- edged gust velocity, KU, since this factor paratively less sensitive to turbulence. The effects the change in angle of attack.’ The apparent effect of wing loading, W/S, is at highest reasonable gust velocity that may be times misleading and is best understood by anticipated is an actual vertical velocity, U, considering a particular airplane encountering of 50 ft. per sec. This value is tempered by a fixed gust condition at various gross weights.

the fact that the airplane does not effectively If the airplane encounters the gust at lower encounter the full effect because of the response than ordinary gross weight, the accelerations NAVWEPS 00-ROT-80 OPERATING STRENGTH LIMITATIONS due to the gust condition are higher. This is THE V-B OR V-g DIAGRAM explained by the fact that essentially the The operating flight strength limitations of same lift change acts on the lighter mass.

an airplane are presented in the form of a The high accelerations and inertia forces V-‘ -n or V-g diagram. This chart usually is magnify the impression of the magnitude of included in the aircraft flight handbook in the turbulence. If this same airplane encounters section dealing with operating limitations.

the gust condition at higher than ordinary A typical V-n diagram is shown in figure 5.3.

gross weight, the accelerations due to the gust The V-n diagram presented in figure 5.3 is condition are lower, i.e., the same lift change intended to present the most important general acts on the gteatet mass. Since the pilot features of such a diagram and does not neces- primarily senses the degree of turbulence by sarily represent the characteristics of any par- the resulting accelerations and inertia forces, ticular airplane. Each airplane type has its this effect can produce a very misleading own particular V-n diagram with specific V’ s impression.

and n’ s, The effect of airspeed and altitude on the The flight operating strength of an airplane gust load factor is important from the stand- is presented on a graph whose horizontal scale point of flying operations. The effect of alti- is airspeed (V) and vertical scale is load factor tude is related by the term &, which would (n). The presentation of the airplane strength related that an airplane flying at a given EAS is contingent on four factors being known: at 40,000 ft. (c=O.25) would experience a (I) the aircraft gross weight, (2) the configura- gust load factor increment only one-half as tion of the aircraft (clean, external stores, flaps great as at sea level. This effect results be- and landing gear position, etc.), (3) symmetry cause the true airspeed is twice as great and of loading (since a rolling pullout at high speed only one-half the change in angle of attack can reduce the structural limits to approxi- occurs for a given gust velocity. The effect of mately two-thirds of the symmetrical load airspeed is illustrated by the linear variation limits) and (4) the applicable altitude. A of gust increment with equivalent airspeed.

change in any one of these four factors can Such a variation emphasizes the effect of gusts cause important changes in operating limits.

at high flight speeds and the probability of For the airplane shown, the positive limit structural damage at excessive speeds in turbu- load factor is 7.5 and the, positive ultimate lence.

load factor is Il.25 (7.5x1.5)- For negative The operation of any aircraft is subject to lift flight conditions the negative’ limit load specific operating strength limitations. A factor is 3.0 and the negative ultimate load single large overstress may cause structural factor is 4.5 (3.0x1.5). The limrt airspeed is failure or damage severe enough to require stated as 575 knots while the wing level stall costly overhaul. Less severe overstress re- speed is apparently 100 knots.

peated for sufficient time will cause fatigue Figure 5.4 provides supplementary informa- cracking and require replacement of parts to tion to illustrate the significance of the V-n prevent subsequent failure. A combat airplane diagram of figure 5.3.

The lines of maximum need not be operated in a manner like the “little lift capa’ bility are the first points of importance old lady from Pasadena” driving to church on on the’ V-n diagram. The subject aircraft is Sunday but each aircraft type has strength capable bf developing no more than one posi- capability only specific to the mission require- tive “g” at 100 knots, the wing level stall speed ment. Operating limitations must be given of the airplane. Since the maximum load due regard.

faztor varies with the square of the aitspeed, GROSS WEIGHT - 16.000 LBS CLEAN CONFIGURATION SEA LEVEL ALTITUDE SYMMETRICAL LOADING 12- I ,.,/,,.~A~~‘ ~,, FACTOR i II- IO- 9- B- ~/POSlT,VE LlMlT LOAD FACTOR i 7- LOAD 6- FACTOR, n 5- LIMIT LIMIT 4- AIRSPEED AIRSPEED 3 575 575 KNOTS KNOTS 2- I-.

INDICATED AIRSPEED - KNOTS INDICATED AIRSPEED - KNOTS -o-.

200 300 400 400 500 500 I 600 600 -I- -2- NEGATIVE LIMIT LOAO FACTOR -3- STALL -4- NEGATIVE ULTIMATE LOAD FACTOR \ -5- Figure 5.3. Flight Strength Diagram STRUCTURAL FAILURE 12- II- IO- 9- a- 7.5 7- UP !

6- 5- 4- MAXIMUM IN,,lCATF . . I -. . - - - - NEGATIVE LIFT CAPABILITY Figure 5.4. Signikance o\ the V-n Diagram NAVWEPS 00-SOT-80 OPERATING STRENGTH LIMITATIONS the maximum positive lift capability of this The occurrence of any one of these items could airplane is 4 “g” at 200 knots, 9 g at 300 knots, cause structural damage or failure of the pri- 16 g at 400 knots, etc. Any load factor above mary structure. A reasonable accounting of this line is unavailable aerodynamically, i.e., these items is required during the design of an the subject airplane cannot fly above the line of airplane to prevent such occurrences in the re- quired operating regions. The limit airspeed maximum lift capability. Essentially the same of an airplane may be any value between termi- situation exists for negative lift flight with the exception that the speed necessary to produce a nal dive speedand 1.2 times the maximum level flight speed,depending on the aircraft type and given negative load factor is higher than that mission requirement. Whatever the resulting to produce the same positive load factor. Gen- limit airspeed happens to be, it deserves due erally, the negative CL,., is less than the posi- respect.

tive CL,., and the airplane may lack sufficient Thus, the airplane in flight is limited to a control power to maneuver in this direction.

regime of airspeeds and g’ s which do not If the subject airplane is flown at a positive exceed the limit (or redline) speed, do not load factor greater than the positive limit load’ exceed the limit load factor, and cannot exceed factor of 7.5, structural damage will be possi- the maximum lift capability. The airplane ble. When the airplane is operated in this region, objectionable permanent deformation must be operated within this “envelope” to prevent structural damage and ensure that of the primary structure may take place and a the anticipated service life of the airplane is high rate of fatigue damage is incurred. Opera- obtained. The pilot must appreciate the tion above the limit load factor must be avoided in normal operation. If conditions of V-n diagram as describing the allowable extreme emergency require load factors above combination of airspeeds and load factors for the limit to prevent an immediate disaster, the safe operation. Any maneuver, gust, or gust airplane should be capable of withstanding the plus maneuver outside the structural envelope can cause sttuctural damage and effectively ultimate load factor without failure. The same situation exists in negative lift flight shorten the service.life, of the airplane.

with the exception that the limit and ultimate There are two points of great importance on load factors are of smaller magnitude and the the V-n diagram of figure 5.4. Point B is negative limit load factor may not be the same the intersection of the negative limit load value at all airspeeds. At speeds above the factor and line of maximum negative lift maximum level flight airspeed the negative capability. Any airspeed greater than point limit load factor may be of smaller magnitude. B provides a negative lift capability sufficient The limit airspeed (or redline speed) is a de- to damage the airplane; any airspeed less sign reference point for the airplane-the sub- than point B does not provide negative lift ject airplane is limited to 575 knots. If flight capability sufficient to damage the airplane is attempted beyond the limit airspeed struc- from excessive flight loads. Point A is the tural,idamage or structural failure may result intersection of the positive limit load factor from a variety of phenomena. The airplane in and the line of maximum, positive lift capa- flight above the limit airspeed may encounter: bility. The airspeed at this point is the (u) critical gust minimum airspeed at which the limit load (6) destructive flutter can be developed aerodynamically. Any air- (c) aileron reversal speed greater than pomt A provides a positive (d) wing or surface divergence lift capability sufficient to damage the air- (e) critical compressibility effects such as stability and control problems, plane; any airspeed less than point A does damaging buffet, etc.

not provide Positive lift capability sufficient to NAVWEPS 00-801-80 OPERATING STRENGTH LIMITATIONS cause damage from excessive flight loads. The is also an important consideration for an air- plane with a high limit load factor if the gust usual term given to the speed at point A is the should be superimposed 00 a maneuver. Since “maneuver speed,” since consideration of the gust Ioad factor increment varies directly subsonic aerodynamics wouId predict mini- mum usable turn radius to occur at this con- with airspeed and gust intensity, high airspeeds must be avoided in turbulent conditions.

dition. The maneuver speed is a valuable When it is impossible to avoid turbulent reference point since an airplane operating conditions and the airplane must be subject to below this point cannot produce a damaging gusts, the flight condition must be properly positive flight load. Any combination of controlled to minimize the effect of turbulence.

maneuver and gust cannot create damage due If possible, the airplane airspeed and power to excess airload when the airplane is below should be adjusted prior to entry into turbu- the maneuver speed.

The maneuver speed can be computed from lence to provide a stabilized attitude. Ob- viously, penetration of turbulence should not the following equation: be accomplished at an excess airspeed because of possible structural damage. On the other hand, an excessively low speed should not be where chosen to penetrate turbulence for the gusts may cause stalling of the aircraft and difficulty VP= maneuver speed of control. To select a proper penetration V,= stall speed airspeed the speed should not be excessively high or ‘ low-the two extremes must be n limit = limit load factor tempered. The “maneuver” speed is an im- portant reference point since it is the highest Of course, the stall speed and limit load factor speed that can be taken to alleviate stall due must be appropriate for the airplane gross to gust and the lowest speed at which limit weight. One notable fact is that this speed, load factor can be develoPed aerodynamically.

once properly computed, remains a constant The optimum penetration speed occurs at or value if no significant change takes place in very near the maneuver speed.

the spanwise weight distribution. The ma- Aileron rever& is a phenomenon particular neuver speed of the subject aircraft of figure to high speed flight. When in flight at very 5.4. would be high dynamic pressures, the wing torsional deflections which occur with aileron deflection v,= loo&3 are considerable and cause noticeable change = 274 knots in aileron effectiveness. The deflection of an aileron on a rigid wing creates a change in lift EFFECT OF HIGH SPEED FLIGHT and produces a rolling moment. In addition the deflection of the control surface creates a Many different factors may be of structural twisting moment on the wing. When the importance in high speed flight. Any one or actual elastic wing is subject to this condition combination of these factors may be encount- at high dynamic pressures, the twisting mo- ered if the airplane is operated beyond the ment produces measurable twisting deforma- limit (or redline) airspeed.

tions which affect the rolling performance of At speeds beyond the limit speed the air- the aircraft. Figure 5.5 illustrates this process plane may encounter a critical gust. This is especially true of a high aspect ratio airplane and the effect of airspeed on aileron effective- with a low limit load factor. Of course, this ness. At some high dynamic pressure, the N A V W E P S OO-SOT-80 OPERATING STRENGTH LIMITATIONS - ELASTIC WING RIGID WING

A

AILERON 1.0 EFFECTIVENESS AILERON REVERSAL C, ELASTIC SPEED C, RIGID -3 w -0.

EQUIVALENT AIRSPEED DIVERGENCE A+ LELASTIC AXIS Figure 5.5. Aeroelastic Effects (Sheet I of 2) NAVWEPS 00-SOT-80 OPERATING STRENGTH LIMITATIONS WING ROOT’ /-TRAILING EDGE 9- LEADING EDGE Figure 5.5. Aeroelastic Effects (Sheet 2 of 2) NAVWEPS 00-ROT-80 OPERATING STRENGTH LIMITitTIONS twisting deformation will be great enough to buildup may overpower the resisting torsional stiffness and “divergence” will occur.

The nullify the effect on aileron deflection and the aileron effectiveness will-be zero. Since speeds divergence speed of the surfaces must be suf- above this point create rolling moments op- ficiently high that the airplane does not en- posite to the direction controlled, this point counter this phenomenon within the normal is termed the “aileron reversal speed.” Oper- operating envelope. Sweepback, short span, ation beyond the reversal speed would create and high taper help raise the divergence speed.

an obvious control difficulty. Also, the ex- F/titter involves aerodynamic forces, inertia tremely large twisting moments which produce forces and the elastic properties of a surface.

loss of aileron effectiveness create large twist- The distribution of mass and stiffness in a structure determine certain natural frequencies ing moments capable of structural damage.

In order to prevent loss of aileron effective- and modes of vibration. If the structure is sub- ness at high airspeeds, the wing must have ject to a forcing frequency near these natural high torsional stiffness. This may be a feature frequencies, a resonant condition can result difficult to accomplish in a wing of very thin with an unstable oscillation. The aircraft is section and may favor the use of inboard ailer- subject to many aerodynamic excitations while ons to reduce the twisted span length and in operation and the aerodynamic forces at effectively increase torsional stiffness. The use various speeds have characteristic properties of spoilers for lateral control minimizes the for rate of change of force and moment. The twisting moments and alleviates the reversal aerodynamic forces may interact with the problem. structure in a fashion which may excite or Divergcm is another phenomenon common negatively damp the natural modes of the Like to flight at high dynamic pressures.

structure and allow flutter. Flutter must not aileron reversal, it is an effect due to the inter- occur within the normal flight operating en- action of aerodynamic forces and elastic deflec- velope and the natural modes must be damped tions of the structure. However, it differs if possible or designed to occur beyond the from aileron reversal in that it is a violent limit speed. A’ typical flutter mode is illus- instability which produces immediate failure.

‘ trated in figure 5.5.

Figure 5.5 illustrates the process of instability.

Since the problem is one of high speed flight, If the surface is above the divergence speed, it is generally desirable to have ‘ very high any disturbance precipitates this sequence.

natural frequencies and flutter speeds well Any change in lift takes place at the aerody- above the normal operating speeds.

namic center of the section. The change in Any change of stiffness or mass distribution will lift ahead of the elastic axis produces a twist- alter the modes and frequencies and thus allow ing moment and a consequent twisting deflec- tion. The change in angle of attack creates a change in the flutter speeds. If the aircraft is not properly maintained and excessive play greater lift at the ac., greater twisting deflec- tion, more lift, etc., until failure occurs. and flexibility exist, flutter could occur at At low flight speeds where the dynamic flight speeds below the limit airspeed.

Compres&ility pmblems may define the limit pressure is low, the relationship between aero- dynamic force buildup and torsional deflection airspeed for an airplane in terms of Mach num- ber. The supersonic airplane may experience is ‘ stable. However, the change in lift per angle of attack is proportional to ‘ vz but the a great decay of stability at some high Mach structural torsional stiffness of the wing re- number or encounter critical structural or mains constant. This relationship implies engine inlet temperatures due to aerodynamic that at some high speed, the aerodynamic force heating. The transonic airplane at an excessive NAVWEPS 00-801-80 OPERATING STRENGTH LIMITATIONS speed may encounter a variety of stability, con- oil is forced through an orifice at high velocity trol, or buffet problems associated with tran- and the energy of the aircraft is absorbed. To sonic flight. Since the equivalent airspeed for have an efficient strut the orifice size must be a given Mach number decreases with altitude, controlled with a tapered pin to absorb the the magnitude of compressibility effects at energy with the most uniform force on the strut.

high altitude may be negligible for the tran- The vertical landing loads resulting at touch- sonic airplane. In this sense, the airplane may down can be simplified to an extent by assum- ing the action of the strut to produce a uni- not be able to fly at high enough dynamic pressures within a certain range of Mach num- formly accelerated motion of the aircraft. TV landing load factor for touchdown at a consta bers to create any significant stability or control problem. rate of descent can be expressed by the follow- The transonic airplane which is buffet lim- ing equation: ited requires due consideration of the effect of n= F/W load factor on the onset of buffet,. Since critical Mach number decreases with lift coef- n = (ROD)’ ficient, the limit Mach number will decrease w with load factor. If the airplane is subject to where prolonged or repeated buffet for which it was a=landing load factor-the ratio of not designed, structural fatigue will be the the load in the strut, F, to the certain result.

weight, W The limit airspeed for each type aircraft is set sufficiently high that full intended appli- ROD=rate of descent, ft. per sec.

cation of the aircraft should be possible. Each of the factors mentioned about the effect of g= acceleration due to gravity excess airspeed should provide due respect for the limit airspeed. = 32 ft. per sec.’ S= effective stroke of the strut, ft.

LANDING AND GROUND LOADS The most critical loads on the landing gear As an example, assume that an aircraft touches down at a constant rate of descent of 18 ft. per occur at high gross weight and high rate of sec. and the effective stroke of the strut is 18 descent at touchdown. Since the landing inches (I.5 ft.). The landing load factor for gear has requirements of static strength and the condition would be 3.37; the average force fatigue strength similar to any other com- would be 3.37 times the weight of the aircraft.

ponent, overstress must be avoided to prevent (NOTE: there is no specific correlation between failure and derive the anticipated service life the landing load factor and the indication of from rhe components.

a cockpit mounted flight accelerometer. The The most significant function of the landing gear is to absorb the vertical energy of the air- response of the instrument, its mounting, and the onset of landing loads usually prevent craft at touchdown. An aircraft at a given weight and rate of descent at touchdown has direct correlation.)

a certain kinetic energy which must be dis- This simplified equation points out two im- sipated in the shock absorbers of the landing portant facts.

The effective stroke of the strut gear. If the energy were not absorbed at should be large to minimize the loads since a touchdown, the aircraft would bounce along greater distance of travel reduces the force similar to an automobile with faulty shock necessary to do the work of arresting the ver- absorbers. As the strut deflects on touchdown, tical descent of the aircraft. This should NAVWEPS 00-EOT-80 OPERATING STRENGTH LIMITATIONS life of any structural component. This fact emphasize the necessity of proper maintenance of the struts. An additional fact illustrated is is certain and irreversible. Thus, the opera- tion of the airplane, powerplant, and various that the landing load factor varies as the square systems must be limited to design values to of the touchdown rate of descent. Therefore, prevent failure or excessive maintenance costs a 20 percent higher rate of descent increases early in the anticipated service life. The the landing load factor 44 percent.

This fact operating limitations presented in the hand- should emphasize the need for proper landing book must be adhered to in a very strict technique to prevent a hard landing and over- stress of the landing gear components and fashion.

In many cases of modern aircraft structures associated structure.

it is very difficult to appreciate the effect of a The effect of landing gross weight is two- moderate overstress. This feature is due in fold. A higher gross weight at some landing load factor produces a higher force in the great part to the inherent strength of the landing gear. The highe: gross weight re- materials used in modern aircraft construction.

quires a higher approach speed and, if the same As a general airframe static strength require- glide path is used, a higher rate of descent ment, the primary structure must not expe- results. In addition to the principal vertical rience objectionable permanent deformation at loads on the landing gear, there are varied side limit load or ~failure at 150 percent of limit loads, wheel spin up and spring back loads, load (ultimate load is 1.5 times limit load).

To satisfy each part of the requirement, limit etc., all of which tend to be more critical at load must not exceed the yield stress and ulti- high gross weight, high touchdown ground mate load must not exceed the ultimate stress speed, and high rate of descent.

The function of the landing gear as a shock capability of the parts.

absorbing device has an important application Many of the high strength materials used in when a forced landing must be accomplished aircraft construction have stress-strain dia- grams typical of figure 5.6. One feature of on an unprepared surface. If the terrain is rough and the landing gear is not extended, these materials is that the yield point is at some stress much greater than two-thirds of initial contact will be made with relatively solid structure and whatever energy is ab- the ultimate stress. Thus, the critical design sorbed will be accompanied by high vertical condition is the ultimate load. If 150 percent accelerations. These high vertical accelera- of limit load corresponds to ultimate stress of tions encountered with a gear-up landing on the material, 100 percent of limit load corre- an unprepared surface are the source of a very sponds to a stress much lower than the yield incapacitating type injury-vertical compres- stress. Because of the inherent properties of sion fracture of the vertebrae. Unless some the high strength material and the ultimate peculiarity of the configuration makes it factor of safety of 1.5, the limit load condition inadvisable, it is generally recommended that is rarely the critical design point and usually the landing gear be down for forced landing on possesses a large positive margin of static an unprepared surface. (NOTE: for those prone strength. This fact alone implies that the to forget, it is also recommended that the gear structure must be grossly overstressed to pro- be down for landing on prepared surfaces.)

duce damage easily vidble to the naked eye.

This lack of immediate visible damage with EFFECT OF OVERSTRESS ON SERVICE “overstress” makes it quite diflicult to recog- LIFE nize or appreciate the long range effect.

Accumulated periods of overstress can create A reference point provided on the stress a very detrimental effect on the useful service strain diagram of figure 5.6 is a stress termed NAVWEPS 00-8OT-80 OPERATING STRENGTH LIMITATIONS - i\ ULTIMATE STRENGTH STRESS, PSI LIMIT LOAD 100% LIMIT LOAD :NDURANCE LIMIT

I-

STRAIN, lN/,N Figure 5.6. Typical Stress Strain Diagram for a High Strength Aluminum Alloy the “endurance limit.” inherent high yield strength and low ductility If the operating cyclic stressesnever exceed this “endurance limit” an of typical aircraft metals. These same over- infinite (,or in some cases “near infinite”) num- stresses cause high rate of fatigue damage and ber of cycles can be withstood without fatigue create premature failure of parts in service.

failure. No significant fatigue damage accrues The effect of accumulated overstress is rhe from stresses below the endurance limit but formation and propagation of fatigue cracks.

While it is sure that fatigue crack always will the value of this endurance limit is approxi- be formed before final failure of a part, accumu- mately 30 to 50 percent of the yield strength for the light alloys used ia airkraft construc- lated overstress is most severe and fatigue provoking at the inevitable stress coticentra- tion. The rate of fatigue damage caused by stresses only &g/&y above the endurance limit tions. Hence, disassembly and detailed’ inspec- is insignificant. Even stresses near the limit tion is both costly and time-consuming. To load do not cause a significant accumulation of prevent in-service failures of a basically sound fatigue damage if the frequency of applicatibn structure, the part must be properly maintained is reasonable and within the intended mission and operated within the design “envelope.” Examples of in-service fatigue failures are requirement. However, stresses above the shown in figure 5.7.

limit load-and especially stresses well above The operation of any aircraft and powerplant the limit load-create a very rapid rate of must be conducted withm the operating limita- fatigue damage.

A puzzling situation then exists. “Over- tions prescribed in the flight handbook. No stress” is difficult to recognize because of the hearsay or rumors can be substituted for chc NAVWEPS 00-80T-80 OPERATING STRENGTH LIMITATIONS FATIGUE CRACKS IN STRUCTURAL SAMPLE ATTACHMENT FITTING FATiGUE FAILURES Figure 5.7. Examples of Fatigue Failures N A V W E P S 00-801-80 OPi?RATlNG STRENGTH LIMITATIONS accepted data presented in the aircraft hand- operated past the specified time, speed, or book. All of the various static ‘ strength, temperature limits without immediate appar- service life, and aeroelastic effects must be ent damage. In each case. the cumulative effect will tell at some later tim e when in- given proper respect. An airplane can be over- stressed with the possibility that no immediate service failures occur and maintenance costs damage is apparent. A powerplant may be increase.

SNOllVlIWll H13N3US ONllVU3dO 08-108-00 Sd3MAVN

NAVWEPS OD-8OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING

Chapter 6

APPLICATION OF AERODYNAMICS TO SPECIFBCPROW

OF FLYING

PRIMARY CONTROL OF AIRSPEED AND While the previous chapters have presented ALTITUDE the detailed parts of the general field of aero- dynamics, there remain various problems of For the conditions of steady flight, the air- flying which require the application of princi- plane must be in equilibrium. Equilibrium ples from many parts of aerodynamics. The will be achieved when there is no unbalance of application of aerodynamics to these various force’ or moment acting on the airplane.

If it is problems of flying will assist the Naval Aviator assumed that the airplane is trimmed so that in understanding these problems and develop- no unbalance of pitching, yawing, or rolling moments exists, the principal concern is for ing good flying techniques.

NAVWE,PS OD-80T-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING the forces acting on the airplane, i.e., lift, lent airspeed to provide lift equal to weight.

thrust, weight, and drag. Hence, angle of attack is the primary .control of

ANGLE OF ATTACK VERSUS AIRSPEED. airspeed in mad3 fright. If an airplane is es- In order to achieve equilibrium in the vertical tablished in steady, level flight at a particular direction, the net lift must equal the airplane airspeed, any increase in angle of attack will weight. This is a contingency of steady, level result in some reduced airspeed common to the flight or steady climbing and descending flight increased C,. A decrease in angle of attack when the flight path inclination is slight. A will result in some increased airspeed com- refinement of the basic lift equation defines the mon to the decreased CL. As a result of the relationship of speed, weight, lift coefficient, change in airspeed, the airplane may climb or etc., for the condition of lift equal to weight.

descend if there is no change in powet setting but the change in airspeed was provided by the change in angle of attack. The state of V=17.2 y J TP the airplane during the change in speed will or be some transient condition between the original and final steady state conditions.

Primary control of airspeed in steady flight by angle of attack is an important principle.

where With some configurations of airplanes, low speed flight will bring about a low level of V=velocity, knots (TAX) longitudinal stick force stability and possi- VE=equivalent airspeed, knots (EAS) airplane static longitudi- W=gross weight, lbs. bility of low S= wing surface area, sq. ft. nal stability. In such a case, the “feel” for W/S= wing loading, psf airspeed will be light and may not furnish g=altitudc density ratio a ready reference for easy control of the air- C,= lift coefficient plane. In addition, the high angles of attack common to low speed flight are likely to pro- From this relationship it is appreciated that a vide large position errors to the airspeed indi- given configuration of airplane with a specific cating system. Thus, proper control of air- wing loading, W/S, will achieve lift equal to speed will be enhanced by good “attitude” weight at particular combinations of velocity, flying or-when the visual t;eference field is V, and lift coefficient, C,. In steady flight, each poor-an angle of attack indicator.

equivalent airspeed demands a particular vaIue RATE OF CLIMB AND .DESCENT. In of C,, and each value of C, demands a particular order for an airplane to achieve ‘ equilibrium at equivalent airspeed to provide lift equal to constant altitude, lift must be equal to weight weight. Figure 6.1 illustrates a typical lift and thrust must be equal to drag. Steady, curve for an airplane and shows the relation- level flight requires equilibrium in both the ship between C, and OL,angle of attack. For For the vertical and horizontal directions.

this relationship, some specific value of a will case of climbing or descending flight condi- create a certain value of C, for any given aero- tions, a component of weight is inclined along dynamic configuration.

the flight path direction and equilibrium is For the conditions of steady flight with achieved when thrust is not equal to the drag.

a given airplane, each angle of attack corre- When the airplane is in a steady climb or sponds to a specific airspeed. Each angle of descent, the rate of climb is related by the attack produces a specific value of CL and each value of C, requires a specific value of equiva- following expression: NAVWEPS OO-80T-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING LIFT COEFFICIENT \ CL FOR LIFT EQUAL TO WEIGHT, “= 17.2J$- gs a ANGLE OF ATTACK FOR A STEADY CLIMB, ROC = 33,000 POWER REQ’ D- FPM

t

POWER EXCESS

POWER \ A

REQUIRED

7-

IER AVAILABLE PO’ lh AVAILABLE ‘ HIGH WILL ESTABLISH w...-.. ..-- -_... - -.-.

HI?

LEVEL FLIGHT AT -- SNCY

t

VELOCITY, KNOTS A

I

Figure 6.1. Primary Control of Airspeed and Altitude NAVWEPS DO-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING (2) Power setting is the primary control RC,,= 33,ooo pa;pr of altitude, i.e., rate of cl&b/descent.

( 1 With the exception of the transient conditions where of flight which occur during maneuvers and RC=rate of climb, ft: per min.

acrobatics, the conditions of steady flight will Pn=propulsive power available, h.p.

be applicable during such steady flight condi- Pr=power required for level flight, h.p.

tions as cruise, climb, descent, takeoff, ap- W=gross weight, Ibs.

proach, landing, etc. A clear understanding From this relationship it is appreciated that of these two principles will develop good, safe the rate of climb in steady flight is a direct flying techniques applicable to any sort of function of the difference between power avail- airplane.

able and power required. If a given airplane The primary control of airspeed during configuration is in lift-equal-to-weight flight steady flight conditions is the angle of attack.

at some specific airspeed and altitude, there However, changes in airspeed will necessitate is a specific power required to maintain these changes in power setting to maintain altitude conditions. If the power available from the because of the variation of power required with powerplant is adjusted LO equal the power velocity. The primary control of altitude required, the rate of cl&b is zero (Pa--Pr=O).

(rate of climb/descent) is the power setting.

This is illustrated in figure 6.1 where the power If an airplane is being flown at a particular available is ser equal to the power required at airspeed in level flight, an increase or decrease velocity (A). If rhe airplane were in steady in power setting will result in a rate of climb level flight at velocity (A), an increase in or descent at this airspeed. While the angle power available would create an excess of of attack must be maintained to hold airspeed power which will cause a rate of climb. Of in steady flight, a change in power setting will course, if the speed were allowed to increase necessitate a change in nttitude;to.accommodate by a decreased angle of attack, the increased the new flight path direction. These princi- power setting could simply maintain altitude ples form the basis for “attitude” flying tech- at some higher airspeed. However, if the nique, i.e., “attitude plus, power equals per- original aerodynamic conditions arc maintain- formance,” and provide .a background for ed, speed is maintained at (A) and an increased good instrument flying technique as well as power available results in a rate of climb.

good flying technique for all ordinary flying Also, a decrease in power available at point (A) conditions.

will produce a deficiency in power and result One of the most important phases of flight in a negative rate of climb (or a rate of descent).

is the landing approach and it is during this For this reason, it is apparenr. that pomr phase of flight that the principles of steady

setting is the primary control of altitude in Jtcady

flight are so applicable. If, during the landing Bight. There is the direct correlation between approach, it is realized that ithe airplane is the excess power (Pa-P,>, and rhe airplane below the desired glide path, an increase in rate of climb, RC.

nose up attitude will not insure that the FLYING TECHNIQUE, Since the condi- airplane will climb to the desired glide path.

tions of steady flight predominate during a In fact, an increase in nose-up attitude may majority of all flying, the fundamentals of produce a greater race of descent and cause flying technique are the principles of steady the airplane co sink more below the desired flight: glide path. At a given airspeed, only an (1) Angle of attack is the primary control increase in power setting can cause a rate of of airspeed. climb (or lower rate of descent) and an in- NAVWEPS DCI-ROT-RD APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYl,NG crease in nose up attitude without the appro- which increase with a decrease in speed. Since the increase in required power setting with priate power change only controls the airplane decreased velocity is contrary to the normal to a lower speed.

command of flight, the regime of flight speeds REGION 0~ REVERSED COMMAND between the speed for minimum required The variation of power or thrust required power setting and, the stall speed (or minimum with velocity defines the power settings neces- control speed) is termed the “region of re- In this regime of flight, sary to maintain steady level flight at various versed command. ” airspeeds. To simplify the situation, a gener- a decrease in airspeed ‘ must be accompanied ality could be,assumed that the airplane con- by an increased power setting in order to main- figuration and. altitude define a variation of tain steady flight. Obviously, induced drag power setting required (jet thrust required or or induced power required predominates in prop power required) versus velocity. This this regime to produce the increased power general variation of required power setting setting required with decreased velocity. One versus velocity is illustrated by’ the first graph fact should be made clear about the region of of figure 6.2. This curve illustrates the fact reversed command: flight in the “reversed” that at low speeds near the stall or minimum region of command does not imply that a control speed the power setting required for decreased power setting will bring about a steady level flight is quite high. However, higher airspeed or an increased power setting at low speeds, ant increase in speed reduces the will produce a lower airspeed. To be sure, required power setting until some minimum the primary control of airspeed is not the value is reached.at the conditions for maximum power setting. Flight in the region of re- endurance. Increased speed beyond the con- versed command only implies that a higher ditions for maximum endurance will then airspeed will repire a lower power setting and in&ease the power setting required for steady a lower airspeed will require a higher power level flight. setting to hold altitude.

REGIONS OF NORMAL AND REVERSED Because of the variation of required power COMMAND. This .typical variation of re- setting throughout the range of flight speeds, quired power setting with speed allows a it is possible that one particular power setting sort of terminology to be assigned to specific may be capable of achieving steady, level flight regimes of velocity. Speeds greater than the at two different, airspeeds. As shown on the speed for maximum endurance require increas- first curve of figure 6.2, one given power setting ingly greater power settings to achieve steady, would meet the power requirements and allow level flight. Since the normal command of steady, level flight at both points 1 and 2. At flight assumes a higher power setting will speeds lower than point 2, a deficiency of power 1 achieve a greater speed, the regime of flight would exist and a rate of descent would be in- speeds greater than the speed for minimum curred. Similarly, at speeds greater than point required power setting is termed the “region 1, a deficiency of power would exist and the 1 of normal command.” Obviously, parasite airplane would descend. The speed range be- drag or parasite power predominates in this tween points 1 and 2 would provide an excess regime to produce the increased power setting of power and climbing flight would be pro- required with increased velocity. Of course, duccd the major items of airplane flight performance FEATURES OF FLIGHT IN THE NOR- take place in the region of normal command.

MAL AND REVERSED REGIONS OF COM- Flight speeds below the sperd for maximum MAND. The majority of all airplane flight is endurance produce required power settings conducted in the region of normal command, Revised January 1965 NAVWEPS 00-6OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING REGION OF REVERSED COMMA POWER REGION OF= SETTING NORMAL COMMAND REQUIREt REQUIRED AND AVAILABL

I

- -.

SETTING

L-

-SPEED FOR MINIMUM ,REQUlRED POWER SETTING.ie MAX.ENDURANCE - VELOCITY, KNOTS

I

REGION OF REVERSED COMMAND REGION OF REOUIRED NORMAL COMMAND

-I-- 1

POWER -POWER SETTING, DEFICIENCY REOUIRED AND AVAILABLE VELOCITY, KNOTS Figure 6.2. Region of Reversed Command Revised January 1965 NAVWEPS OD4OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING e.g., cruise, climb, maneuvers, etc. The region angle of attack is changed rapidly, may lead to the impression thal rate of climb and descent of reversed command is encountered primarily in the low speed phases of flight during takeoff can be controlled by changes in angle of attack.

While such is true in the region of normal com- and landing. Because of the extensive low speed flight during carrier operations, the mand, for the conditions of stead’ flight, pri- mary control of altitude remains the power Naval Aviator will be more familiar with the setting and the primary control of airspeed re- region of reversed command than the ordinary mains the angle of attack. The impressions pilot.

The characteristics of flight in the region’ of and habits that can be developed in the region of normal command can bring about disastrous normal command are illustrated at point A on the second curve of figure 6.2. If the airplane consequences in the region of reversed com- mand is established in steady, level flight at point A, lift is equal to weight and the power available The characteristics of flight in the region of is set equal to the power required. When the reversed command are illustrated at point B airplane is disturbed to some airspeed slightly on the second curve of figure 6.2. If the air- greater than point ‘ A, a power deficiency exists plane is established in steady, level flight at and, wheq,:the &+la&is disturbed to some air- point B, lift is equal to weight and the power available is set equal to the. power required.

speed slightly lower than point A, a power When the airplane is disturbed to some air- excess exists. This relationship provides a speed slightly greater than point B, an excess tendency for the airplane to return to the equili- of power exists and, when the airplane is dis- brium of point A and resume the original flight turbed to some airspeed slightly lower than condition following a disturbance. Also, the point B, a deficiency of power exists. This static longitudinal stability of the airplane relationship is basically unstable because the tends to return the airplane to the original variation of excess power to either side of trimmed CL and velocity corresponding to this C,. The phugoid usually has most satisfactory point B tends to magnify any original dis- qualities at low values of C,. so the high speed turbance. While the static longitudinal sta- bility of the airplane tends to maintain the of the region ‘ of normal command provides little tendency of. the airplane’ s, airspeed to original trimmed C, and airspeed correspond- ing to that CL, the phugoid usually has the vary or wander abom.

With all factors considered, flight in Lhe least satisfactory qualities at the high values region of noi& command is characterized by of CL corresponding to low speed flight.

a relatively strong tendency of the airplane to When all factors are considered, flight in the maintain the trim speed quite naturally. How- region of reversed command is characterized ever, flight in the region of normal command by a relatively weak tendency of the airplane can lead to some unusual and erroneous impres-, to maintain the trim speed naturally. In fact it is likely that the airplane will exhibit no sions regarding proper flying technique. For example, if the airplane is established at point inherent tendency to maintain the trim speed in this regime of flight.

A in steady level flight, a controlled increase in For this reason, the pilot inust give particular attention to precise airspeed without a change in power setting control of airspeed when operating in the low will create a deficiency of power and cause the airplane to descend. Similarly, a controlled flight speeds of the region of reversed command.

decrease in airspeed without a change in power While flight in the region of normal com- setting will create an excess of power and cause mand may create doubt as to the primary con- the airplane to climb. This fact, coupled with trol of airspeed and altitude, operation in the Lhe transient motion of the airplane when the region of reversed command should leave little ‘: -.- * ,-.

. :,,.

_,: .-,A* NAVWEPS 00-807-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING doubt about proper flying techniques. For sitate special landing techniques, particularly example, if the airplane is established at point in the case of a flameout landing.

B in level flight, a controlled increase in air- Operation in the region of reversed command speed (by reducing angle of attack) without does not imply that great control difficulty and change in power setting will create an excess dangerous conditions will exist. However, of power at the higher airspeed and cause the flight in the region of reversed command does airplane to climb. Also, a controlled decrease amplify any errors of basic flying technique.

Hence, proper flying technique and precise in airspeed (by increasing angle of attack) control of the airplane are most necessary in without a change of power setting will create the region of reversed command.

a deficiency of power at the lower airspeed and cause the airplane to descend. This rela- THE ANGLE OF ATTACK INDICATOR tionship should leave little doubt as to the AND THE MIRROR LANDING SYSTEM primary control of airspeed and altitude.

The usual errors during the takeoff and The transient conditions during the changes landing phases of flight involve improper con- in airspeed in the region of reversed command trol of airspeed and altitude along some desired are of interest from the standpoint of landing flight path.

flare characteristics. Suppose the airplane is Any errors of technique are ampli- fied when an adequate visual reference is not in steady flight at point B and the airplane available to the pilot. It is necessary to angle of attack is increased to correspond with provide the pilot with as complete as possible the value for the lower airspeed of point C (see visual reference field to minimize or eliminate fig. 6.2). The airplane would not instanta- any errors in perception and orientation.

neously dPvelop the lower speed and rate of The descent common to point C but would approach angle of attack indicator and the mirror land- ing system assist the pilot during the phases of the conditions of point C through some tran, takeoff and landing and allow more consistent, sient process depending on the airplane char.

precise control of the airplane.

acteristics. If the airplane characteristics are low wing loading, high L/D, and high lift curve THE A.NGLE OF ATTACK INDICATOR.

slope, the increase in angle of attack at point B Many specific aerodynamic conditions exist at particular angles of attack for the airplane.

will produce a transient motion in which Generally, the conditions of stall, landing ap- curvature of the flight path demonstrates a proach, takeoff, range, endurance, etc., all definite flare. That is, the increase in angle occur at specific values of lift coefficient and of attack creates a momentary rate of climb (or reduction of rate of descent) which would specific airplane angles of attack. Thus, an instrument to indicate or relate airplane angle be accompanied by a gradual loss of airspeed.

Of course, the speed eventually decreases to of attack would be a valuable reference to aid point C and the steady state rate of descent is the pilot.

achieved. If the airplane characteristics are When the airplane is at high angles of attack high wing loading, low L/D, and low lift curve it becomes difficult to provide accurate indica- tion of airspeed because of the possibility of slope, the increase in angle of attack at point B large position errors. In fact, for low aspect may produce a transient motion in which the ratio airplane configurations at high angles of airplane does not flare. That is, the increase in angle of attack may produce such rapid re- attack, it is possible to provide indications of duction of airspeed and increase in rate of angle of attack which are more accurate than indications of airspeed.

descent that the airplane may be incapable of As a result, an angle a flaring flight path without an increase in of attack indicator can be of greatest utility ar power setting. Such characteristics may neces- the high angles of attack.

NAVWEPS 00-BOT-80 APPLICATION OF AERODYNAMKS TO SPECIFIC PROBLEMS OF FLYl,NG A particular advantage of an angle of attack airplane is operated at the proper approach speed-not too low or too high an airspeed.

indicator is that the indicator is not directly In addition to the tise of the angle of attack affected by gross weight, bank angle, load indicator during approach and landing, the or density altitude. The factor, velocity, instrument may te used as a principal reference typical lift curve of figure 6.3 illustrates the during takeoff.

variation of lift coefficient, C,, with angle of The use of the angle of attack indicator to assume the proper takeoff angle attack. a. When a particular aerodynamic configuration is in subsonic flight, each angle of attack will prevent both over-rotation and excess takeoff speed. Also, the angle of at- of attack produces a particular value of lift tack indicator may be applicable to assist in coefficient. Of course, a point of special control of the airplane for conditions of range, interest on the lift curve is the maximum lift Angles of attack greater endurance, maneuvers, etc.

coefficient, C,,,,.

produce a decrease in lift THE MIRROR LANDING SYSTEM. A than that for C,,,, well planned, stabilized approach is a funda- coefficient and constitute the stalled condition occurs at a particular mental requirement for a good landing.

of flight. Since Cz,., How- ever, one of the more difficult problems of angle of attack, any device to provide a stall warning should be predicated on the function perception and orientation is the positioning of this critical angle of, attack. Under these of the airplane along a proper flight path dur- conditions, stall of the airplane may take place ing approach to landing. While various de- at various airspeeds depending on gross weight, vices are possible, the most successful form of load factor, etc., but always the same angle of glide path indicator applicable to both field attack. and shipboard operations is the mirror landing In order to reduce takeoff and landing dis- system. The function of the mirror landing tances and minimize arresting loads, takeoff system is to provide the pilot with an accurate and landing wil! be accomplished at minimum visual reference for a selected flight path which practical speeds. The takeoff and landing has the desired inclination and point of touch- speeds inust provide suficient margin above down. Utilization of the mirror system will the stall speed (or minimum control speed) allow the pilot to position the airplane along and are usually specified at some fixed per- the desired glide path and touch down at the centages of the stall speed. As such, takeoff, desired point. When the proper glide path approach, and landing will be accomplished inclination is set, the pilot can be assured that at specific values of lift coefficient and, thus, the rate of descent will not be excessive and particular angles of attack. For example, a foundation is established for a successful assume that point A on the lift curve is defined landing.

as the proper aerodynamic condition for the The combination of the angle of attack in- landing approach. This condition exists as dicator and the mirror landing system can a particular lift coefficient and angle of attack provide an excellent referetice for a landing for a specific aerodynamic configuration. technique. The use of the angle of attack When the airplane is flown in a steady flight indicator will provide the airplane with the path at the prescribed angle of attack, the proper airspeed while the mirror system refer- resulting airspeed will be appropriate for the ence will provide the desired flight path.: When airplane gross weight. Any variation in gross shipboard operations are conducted without weight will Simply alter the airspeed necessary the mirror system and angle of attack indicator, The use of an angle to provide suificient lift.

the landing signal officer must provide the of attack indicator to maintain the recom- immediate reference of airspeed and flight path.

mended angle of attack will insure that the The LSO must perceive gnd judge the angle of NAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING CL MAX - A - STALL LIFT COEFFICIENT CL ANGLE OF ATTACK, 0 3s9 NAVWEPS DD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING attack (and, hence, airspeed) and the flight and stall speed in the turn. Figure 6.4 illus- path of the landing aircraft and signal correc- trates the typical change in thrust required caused by a steep turn.

tions to be made in order to achieve the desired A steep turn may cause the airplane to stall or the large increase in in- flight path and angle of attack. Because of the field of orientation available to the LSO, duced drag may create an excessive rate of descent. In either case, there may not be suf- he is able to perceive the flight path and angle ficient altitude to effect recovery. If the .air- of attack more accurately than the pilot with- out an angle of attack indicator and mirror plane is not properly lined up on the final ap- proach, it is certainly preferable to take a landing system.

waveoff and go around rather than “press on regardless” and attempt to salvage a decent THE APPROACH AND LANDING landing from a poor approach.

The specific techniques necessary during the The proper coordination of the controls is phase of approach and landing may vary con- an absolute necessity during the approach. In siderably between various types of airplanes this sense, due respect must be given to the and various operations. However, regardless primary control of airspeed and race of descent of the airplane type or operation, there are for the conditions of the steady approach.

certain fundamental principles which will de- Thus, the proper angle of attack will produce fine the basic techniques of flying during ap- the desired approach airspeed; too low an proach and landing. The specific procedures angle of attack will incur an excess speed while recommended for each airplane type must be an excessive angle of attack will produce a followed exactly to insure a consistent, safe deficiency of speed and may cause stall or con- landing technique. trol problems. Once the proper airspeed and THE APPROACH. The approach must be angle of attack are attained the primary control conductrd to provide a stabilized, steady flight of rate of descent during the steady approach path to the intended point of touchdown. The will be the power setting. For example, if it approach speed specified for an airplane must is realized that the airplane is above the de- provide sufficient margin above the stall speed sired glide path, a more nose-down attitude or minimum control speed to allow satisfactory without a decrease in power setting will result control and adequate maneuverability. On the in a gain in airspeed. On the other hand, if it other hand, the approach speed must not be is realized that the airplane is below the desired greatly in excess of the touchdown speed or a glide path, a more nose-up attitude without an large reduction in speed would be necessary increase in power setting will simply allow the prior to ground contact. Generally, the ap- airplane to fly more slowly and-in the region proach speed will be from 10 to 30 percent of reversed command-eventually produce a above the stall speed depending on the air- greater rate of descent.

For the conditions of plane type and the particular operation.

steady flight, angle of attack is the primary During the approach, the pilot must attempt control of airspeed and power setting is the to maintain a smooth flight path and prepare primary control of rate of climb and descent.

for the touchdown. A smooth, steady ap- This is especially true during the steady ap- proach to landing will minimize the transient proach to landing. Of course, the ability of items of the flight path and provide the pilot the powerplant to produce rapid changes in better opportunity to perceive and orientate thrust will affect the specific technique to be the airplane along the desired flight path. used. If the powerplant is not capable of pro- Steep turns must be avoided at the low speeds ducing immediate controlled changes in thrust, of the approach because of the increase in drag the operating technique must’ account for this NAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING EFFECT OF STEEP TURNS ON THRUST REQ’ D THRUST REO’ D LBS.

WING LEVEL FLIGHT APPROACH PATHS VARloUS TYPICAL LIFT n CURVES LIFT COEFFICIENT CL ANGLE OF ATTACK, a Figure 6.4. The Approach and Landing NAVWEPS OD-BOT-BO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYI’ NG deficiency. It is most desirable that the power- to judge and control the point of touchdown.

plant be capable of effecting rapid changes in The LSO, mirror landing system, and various thrust to allow precise control of the airplane approach lighting systems will aid the pilot during approach. in achieving the desired approach flight path.

The type of approach path is an important THE LANDING FLARE AND TOUCH- factor since it affects the requirement of the DOWN. The specific techniques of landing flare and touchdown will vary considerably flare, the touchdown rate of descent, and-to between various types of airplanes. In fact, some extent-the ability to control the point of touchdown. Approach path A of figure for certain types of airplanes, a flare from a properly executed approach may not be de- 6.4 depicts the steep, low power approach.

Such a flight path generally involves a low sirable because of the possibility of certain critical dynamic landing loads or because of power setting near idle conditions and a high rate of descent. Precise control of the air- the necessity for a certain standard of tech- nique when aerodynamic flare characteristics plane is difficult and an excess airspeed usually results from an approach path similar to A. are critical. The landing speed should be the lowest practical speed above the stall or mini- Waveoff may be difficult because of the re- mum control speed to reduce landing distances quired engine acceleration and the high rate of descent. In addition, the steep approach and arresting loads. Generally, the landing speed will be from 5 to 25 percent above the path with high rate of descent requires con- siderable flare to reduce the rate of descent at stall speed depending on the airplane type touchdown. This extreme flare requirement and the particular operation.

will be di,fficult to execute with consistency The technique required for the landing will and will generally result in great variation be determined in great part by the aerodynamic If the airplane in the speed, rate of descent, and point of characteristics of the airplane.

touchdown. characteristics are low wing loading, high LID, and relatively high lift curve slope, the airplane Approach path C of figure 6.4 typifies the long, shallow approach with too small an usually will have good landing flare charac- teristics. If the airplane characteristics are inclination of the flight path.. Such a flight path requires a relatively high power setting high wing loading, low L/D, and relatively low and a deficiency of airspeed is a usual conse- lift curve slope, the airplane may not possess quence. This extreme of an approach path desirable flare characteristics and landing tech- is not desirable because it is difficult to control nique may require a minimum of flare to the point of touchdown and the low speed touchdown. These extremes are illustrated by may allow the airplane to settle prematurely the lift curves of figure 6.4.

In preparation for the landing, several factors short of the intended landing touchdown.

Some approach path between the extremes must be accounted for because of their effect on landing distance, landing loads, and arrest- of A and C must be selected, e.g., flight path B. The desirable approach path must not ing loads. These factors are: incur excessive speed and rate of descent or (1) Landing gross weight must be con- require excessive flaring prior to touchdown. sidered because of its effect on landing speed Also, some moderate power setting must be and landing loads. Since the landing is required which will allow accurate control accomplished at a specific angle of attack or of the flight path and provide suitable waveoff margin above the stall speed, gross weight characteristics. will define the landing speed. In addition, The approach flight path cannot be too shallow for excessive power the gross weight is an important factor in setting may be required and it may be difficult determining the landing distance and energy NAVWEPS OD-BOT-BO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING dissipating requirements of the brakes.

course, the landing is not completed until the There will be a maximum design landing airplane is slowed to turn off the runway.

weight specified for each airpIane and this Control of the airpIane must be maintained limitation must be respected because of after the touchdown and proper technique must critical landing loads, arresting loads, or be used to decelerate the airplane.

brake requirements. Of course, any air- TYPICAL ERRORS. There are many un- plane will have a limiting touchdown rate desirable consequences when basic principles of descent specified with the maximum land- and specific procedures are not followed during ing weight and the principal landing load the approach and landing.

Some of the typical limitations will be defined by the combina- errors involved in landing accidents are out- tion. of gross weight and rate of descent at lined in the following discussion.

touchdown. The steep, low power approach leads to an (2) The surface winds must be considered exce.rsive rate of descentand the possibility of a because of the large effect of a headwind or hard landing. This is particularly the case tailwind OR the landing distance. In the for the modern, low aspect ratio, swept wing case of the crosswind, the component of airplane configuration which incurs very large wind along the runway will be the effective induced drag at low speeds and does not have headwind or tailwind velocity. Also, the very conventional flare characteristics. For crosswind component across the runway will this type of airplane in a steep, low power define certain requirements of lateral control approach, an increased angle of attack without The airplane which exhibirs large power. a change of power setting may not cause a dihedral effect at high lift coefficients is reduction of rate of descent and may even in- quite sensitive to crosswind and a limiting crease the rate of descent at touchdown. For crosswind component will be defined for the this reason, a moderate stabilized approach is configuration.

necessary and the principal changes in rate of (3) Press.w~ dtitsde and tmpma~e will descent must be controlled by changes in power affect the landing distance because of the setting and principal changes in airspeed must effect on the true airspeed for landing.

be controlled by changes in angle of attack.

Thus, pressure altitude and temperature must

‘ An excessiveangle of attack during the ap-

be considered to define the density altitude.

proach and landing implies that the airplane is (4) The runway condition must be con- being operated at too low an airspeed. Of sidered for its effect on landing distances.

course, excessive angle of attack may cause the Runway slope of ordinary values will ordi- airplane to stall or spin and the low altitude narily favor selection of a runway for a may preclude recovery. Also, the low aspect favorable headwind at landing.

The surface ratio configuration at an excessively low air- condition of the runway will determine speed will incur very high induced drag and braking effectiveness and ice or water on the will necessitate a high power setting or other- runway may produce a considerable increase wise incur an excessive rate of descent. An in the minimum landing distance.

additional problem is created by an excessive Thus, preparation for the landing must in- angle of attack for the airplane which exhibits clude determination of the landing distance of a large dihedral effect at high lift coefficients.

the airplane and comparison with the runway In this case, the airplane would be more sensi- length available. Use of the angle of attack tive to crosswind.s and adequate lateral control indicator and the mirror landing system will may not be available to effect a safe landing at assist the pilot in effecting touchdown at the a critical value of crosswind.

desired location with the proper airspeed.

Of MAVWEPS OO-BOLBO APPLICA’ IIOM OF AERODYNAMICS 10 SPECIFIC PROBLEMS OF FLYI~NG MAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING Excess airspeed at landing is just as undesira- insure a consistent, safe takeoff flying tech- ble as a deficiency of airspeed. An cxccssivc nique.

airspeedat landing will produce an undesirable TAKEOFF SPEED AND DISTANCE. The increase in landing distance and the energy to takeoff speed of any airplane is some mini- be dissipated by the brakes for the field landing mum practical airspeed which allows sufficient or excessive arresting loads for theshipboard margin above stall and provides satisfactory landing. In addition, the excess airspeed is a control and initial rate of climb.. Depending corollary of too low an angle of attack and the on the airplane characteristics, the takeoff airplane may contact the deck or runway nose speed will be some value 5 to 25 percent above wheel first and cause damage to the nose wheel the stall or minimum control speed. As such, or begin a porpoising of the airplane. During the takeoff will be accomplished at a certain a flare to landing, any excess speed will be value of lift coefficient and angle of attack difficult to dissipate due to the reduction of specific to each airplane configuration. As drag due to ground effect. Thus, if the air- a result, the takeoff airspeed (FAX or CM) of plane is held off with excess airspeed the air- any specific airplane configuration is a function plane will “float” with the consequence of a of the gross weight at takeoff. Too low an barrier engagement, barricade engagement, airspeed at takeoff may cause stall, lack of bolter, or considerable runway distance used adequate control, or poor initial climb per- before touchdown. formance. An excess of speed at takeoff may A fundamental requirement for a good land- provide better control and initial rate of climb ing is a well planned and executed approach. but the higher speed requires additional dis- The possibility of errors during the landing tance and may provide critical conditions for process is minimized when the airplane is the tires.

brought to the point of touchdown with the The takeoff distance of an airplane is affected proper glide path and airspeed. With the by many different factors other than technique proper approach, there is no need for drastic and, prior to takeoff, the takeoff distance changes in the flight path, angle of attack, or must be determined and compared with the power setting to accomplish touchdown at the runway length available. The principal factors intended point on the deck or runway. affecting the takeoff distance are as follows: Late corrections to line up with the deck or diving (1) The gross weight of the airplane has for the deck are common errors which eventu- a considerable effect on takeoff distance be- ally result in landing accidents. cause it affects both takeoff speed and ac- Accurate celeration during takeoff roll.

control of airspeed and glide path are ab- solutely necessary and the LSO, angle of attack (2) The surface winrls must be considered because of the powerful effect of a headwind indicator, and the mirror landing system pro- or tailwind on the takeoff distance. In the vide great assistance in accurate control of the case of the crosswind, the component of airplane.

wind along the runway will be the effective THE TAKEOFF headwind or tailwind velocity. In addi- As in the case of landing, the specific tech- tion, the component of wind across the run- niques necessary may vary greatly between way will define certain requirements of lateral various types of airplanes and various oper- control power and the limiting compo- ations but certain fundamental principles will nent wind must not be exceeded.

be common to all airplanes and all operations.

(3) Pressure altitude and temperature can The specific procedures recommended for each cause a large effect on takeoff distance, es- airplane type must be followed exactly to pecially in the case of the turbine powered NAVWEPS OD-SOT-80 APPLICATION OF AERODYNAMICS, TO SPECIFIC PROBLEMS OF FLYING airplane. Density altitude will determine length. Familiarity with the airplane hand- the true airspeed at takeoff and can affect book performance data and proper accounting of weight, wind, altitude, temperature, etc., the takeoff acceleration by altering the are necessary parts of flying. Conditions of powerplant thrust. The effect of tempeta- high gross weight, high pressure altitude and ture alone is important in the case of the turbine powered aircraft since inlet air tem- temperature, and unfavorable winds create the perature will affect powerplant thrust. Ic extreme requirements of runway length, espe- should be noted that a typical turbojet ait- cially for the turbine powered airplane. Under plane may he approximately twice as sensi- these conditions, use of the handbook data is tive to density altitude and five to ten times mandatory and no guesswork can be tolerated.

as sensitive to temperature as a representa- One typical.etror of takeoff technique is the cive reciprocating engine powered airplane.

premature or excess pitch rotation of the air- (4) Specific humidity must be accounted plane. Premzture or excm pitch rotation of the for in the case of the reciprocating engine airplane may seriously reduce the takeoff accel- powered airplane. A high water vapor eration and increase the takeoff distance. In content in the air will cause a definite reduc- addition, when the airplane is placed at an tion in takeoff power and takeoff acceler- excessive angle of attack during takeoff, the ation.

airplane may become airborne at too low a (5) The runluay condition will deserve con- speed and the result may be a stall, lack of ade- sideration when the takeoff acceleration is quate control (especially in a crosswind), or basically low. The runway slope must be poor initial climb performance. In fact. there compared carefully with the surface winds are certain low aspect ratio configurations of because ordinary values of runway slope will airplanes which, at an excessive angle of ar- usually favor choice of the runway with tack, will not fly out of ground effect. Thus, headwind and upslope rather than down- over-rotation of the airplane ,during takeoff slope and tailwind. The surface condition may hinder takeoff acceleration or the.initial of the runway has little bearing on takeoff climb. It is quite typical for an airplane to be distance as long as the runway is a hard placed at an excess angle of attack and become surface.

airborne prematurely then settle back fo rhe Each .of these factors must be accounted When the proper angle of attack is runway.

for and the takeoff distance properly com- assumed, the airplane simply accelerates to the puted for the existing conditions. Since takeoff speed and becomes airborne wirh suf- obstacle clearance distance is generally a ficient initial rate of climb. In this sense, the function of the same factors which affect appropriate rotation and takeoff speeds or an takeoff distance, the obstacle clearance dis- angle of attack indicator must be used.

tance is usually related as some proportion If the airplane is subject to a sudden pull-up of the takeoff distance. Of course, the take- or Jteep tzzra after becoming airborne, rhe,resulr off and obstacle clearance distances related may be a stall, spin, or reduction in initial rate by the handbook data will be obtained by of climb. The increased angle of attack may the techniques and procedures outlined in the exceed the critical angle of attack or the in- handbook.

For crease in induced drag may be quite large.

TYPICAL ERRORS. The takeoff distance this reason, any clearing turns made immedi- of an airplane should be computed for each ately after takeoff or deck launch must be slight A most inexcusable error would be to takeoff. and well within the capabilities of the air- attempt takeoff from a runway of insufficient plane.

NAVWEPS DD-BOT-BD APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING while a negative (down) gust causes a de- In order to obviate some of the problems crease in angle of attack. Of course, a change of a deficiency of airspeed at takeoff, usual in angle of attack will effect a change in lift result can be an excess of airspeed at takeoff.

and, if some critical combination of high gust The principal effect of an BXCBJS takeoff air@pssd intensity and high flight speed is encountered, is the greater takeoff distance which results.

the change in lift may be large enough to The general effect is that each 1 percent excess cause structural damage.

takeoff velocity incurs approximately 2 per- At low flight speeds during approach, land- cent additional takeoff distance. Thus, excess ing, and takeoff, the effect of the vertical gust speed must be compared with the additional is due to the same mechanism of the change runway required to produce the higher speed.

in angle of attack. However, at these low In addition, the aircraft tires may be subject flight speeds, the problem is one of possible to critical loads when the airplane is at very incipient stalling and sinking rather than high rolling speeds and speeds in excess of a overstress. When the airplane is at high basically high takeoff speed may produce angle of attack, a further increase in angle of damage or failure of the tires.

attack due to a gust may exceed the critical As with the conditions of landing, excess angle of attack and cause an incipient stalling velocity or deficiency of velocity at takeoff of the airplane. Also, a decrease in angle is undesirable. The proper takeoff speeds and of attack due to a gust will cause a loss of lift angle of attack must be utilized to assure For this and allow the airplane to sink.

satisfactory takeoff performance.

reason, any deficiency of airspeed will be quite critical when operating in gusty conditions.

GUSTS AND WIND SHEAR The effect of the hori<oonral gust differs from The variation of wind velocity and direction the effect of the vertical gust in that the im- throughout the atmosphere is important be- mediate effect is a change of airspeed rather cause of its effect on the aerodynamic forces than a change in angle of attack. In this and moments on an airplane. As the airplane sense, the horizontal gust is of little conse- traverses this variation of wind velocity and quence in the major airplane airloads and direction during flight, the changes in airflow strength limitations. Of greater significance direction and velocity create changes in the is the response of the airplane to horizontal aerodynamic forces and moments and produce gusts and wind shear when operating at low a response of the airplane. The variation of flight speeds. The possible conditions in airflow velocity along a given direction exists which an airplane may encounter horizontal with shear parallel to the flow direction.

gusts and wind shear are illustrated in figure Hence, the velocity gradients are often re- 6.5. As the airplane traverses a shear of wind ferred to as the wind “shear.” direction, a change in headwind component The effect of the vertical gust has important will exist. Also, a climbing or descending effects on the airplane at high speed because airplane may traverse a shear of wind velocity, of the possibility of damaging flight loads.

i.e., a wind profile in which the wind velocity The mechanism of vertical gust is illustrated varies with altitude.

in figure 6.5 where the vertical gust velocity The response of an airplane is much de- is added vectorially to the flight velocity to pendent upon the airplane characteristics but produce some resultant velocity. The principal certain basic effects are common to all ait- effect of the vertical gust is to produce a change planes. Suppose that an airplane is estab- in airplane angle of attack, e.g., a positive lished in steady, level flight with lift equal to weight, thrust equal to drag, and trimmedso (up) gust causes an increase in angle of attack NAVWEPS OG-8OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING EFFECT OF VERTICAL GUST CHANGE IN ANGLE OF ATTACK OF WIND -1 VERTICAL VARll STEADY TRANSIENT LEVEL LIFT CONDITION FROM FLIGHT WIND SHEAR OR HORIZONTAL GUST 1 LIFT I Figure 6.5. Effect of Wind Shear NAVWEPS O&ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING there is no unbalance of pitching, yawing, or in the case of powerplant failure or malfunc- When a powerplant failure or malfunc- rolling moment. If the airplane traverses a tion.

sharp wind shear equivalent to a horizontal tion occurs, it is usually of interest to obtain a gust, the resulting change in airspeed will gliding flight path which results in the mini- disturb such an equilibrium. For example, if mum glide angle. The minimum glide angle the airplane encounrers a sharp horizontal will produce the greatest proportion of glide gust which reduces the airspeed 20percent,the distance to altitude loss and will result in new airspeed (80 percent of the original value) maximum glide range or minimum expendi- produces lift and drag at the same angle of ture of altitude for a specific glide distance.

attack which are 64 percent of the original GLIDE ANGLE AND LIFT-DRAG RATIO.

value. The change in these aerodynamic forces In the study of climb performance, the forces would cause the airplane to accelerate in the acting on the airplane in a steady climb (or direction of resultant unbalance of force. glide) produce the following relationship: That is, the airplane would accelerate down and forward until a new equilibrium is achieved. In addition, there would be a where change in pitching moment which would Y=: angle of climb, degrees produce a response of the airplane in pitch.

T-thrust, lbs.

The response of the airplane to a horizontal D-drag, lbs.

gust will differ according to the gust gradient W=: lbs.

and airplane characccristics. Gmcrally, if the In the case of power-off glide performance, the airplane encounters a sharp wind shear which thrust, T, is zero and the relationship reduces reduces the airspeed, the airplane tends to sink to: and incur a loss of altitude ‘ before equilibrium D sin y= -- conditions are achieved. Similarly, if the W airplane encounters a sharp wind shear which By this relationship it is evident that the mini- increases the airspeed, the airplane tends to mum angle of glide-or minimum negative float and incur a gain of altitude before equilib- climb angle-is obtained at the aerodynamic rium conditions are achieved.

conditions which incur the minimum total Significant vertical and horizontal gusts may drag. Since the airplane lift is essentially equal be due to the terrain or atmospheric conditions.

to the weight, the minimum angle of glide The proximity’ of an unstable front or thunder- will be obtained when the airplane is operated storm activity’ in the vicinity of the airfield is at maximum lift-drag ratio, (L/D)ma,. When likely to create significant wind shear and gust the angle of glide is relatively small, the ratio activity at low altitude. During gusty condi- of glide distance to glide altitude is numeri- tions every effort must be made for precise con- cally equal to the airplane lift-drag ratio.

trol of airspeed and flight path and any changes due to gusts must be corrected by proper con- glide distance, ft.

glide ratio= trol action. Under extreme gusts conditions, glide altitude, ft.

it may be advisable to utilize approach, land- glide ratio = (L/D) ing, and takeoff speeds slightly greater than Figure 6.6 illustrates the forces acting on the normal to provide margin for adequate control.

The equilibrium airplane in a power-off glide.

POWER-OFF GLIDE PERFORMANCE of the steady glide is obtained when the sum- The gliding performance of an airplane is of mation of forces in the vertical and horizontal special interest for the single-engine airplane directions is equal to zeta.

N A V W E P S 00-801-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING

l--J-@ $ !?e

+Y

DRAG

I

SIN 7 =- j

\

WEIGHT GLIDE RATIO * L/o i LIFT-OR&G RATIO -CLEAN CONFIGURATION )M r

L4l

A <LANDING CONFIGURATION

!

LIFT COEFFICIENT, CL RATE OF CLEAN CONFIGURATION DESCENT, F P M P O W E R OFF VELOCITY, KNOTS Figure 6.6. Glide Performance NAVWEPS W-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING speed will not cause any significant reduction In order to obtain maximum glide ratio, the of glide ratio. This is fortunate and allows the airplane must be operated at the angle of at- specifying of convenient glide speeds which tack and lift coefficient which provide maxi- will be appropriate for a range of gross weights mum lift-drag ratio. The illustration of figure at which power-off gliding may be encoun- 6.6 depicts a variation of lift-drag ratio, L/D, tered, e.g., small quantities of fuel remaining. with lift coeficient, C,, for a typical airplane An attempt to stretch a glide by flying at in the clean and landing configurations. Note speeds above or below the best glide speed will for each configuration will occur that (LID),,, prove futile. As shown by the illustration of at a specihc value of lift coefficient and, hence, figure 6.6, any C, above or below the optimum a specific angle of attack. Thus, the maximum will produce a lift-drag ratio less than the glide performance of a given airplane configu- maximum. If the airplane angle of attack is ration will be unaffected by gross weight and increased above the value for (L/D),,, a tran- altitude when the airplane is operated at sient reduction in rate of descent will take place (L/D),az. Of course, an exception occurs at but this process must be reserved for the land- very high altitudes where compressibility ef- fects may alter the aerodynamic characteristics.

ing phase. Eventually, the steady-state condi- The highest value of (L/D) will occur with the tions would be achieved and the increased airplane in the clean configuration.

angle of attack would incur a lower airspeed As the airplane is changed to the landing configura- and a reduction in (L/D) and glide ratio.

The effect of gross weight on glide performance tion, the added parasite drag reduces (L/D)_nz and the C, which produces (L/D),, will be in- may be difficult to appreciate. Since (L/D)- creased. Thus, the best glide speed for the of a given airplane configuration will occur at a landingconhguration generallywill be lessthan specific value of C,, the gross weight of the air- the best glidespeed .for theclean configuration.

plane will not affect the glide ratio if the air- The power-off glide performance may be plane is operated at the optimum C,. Thus, appreciated also by the graph of rate of descent two airplanes of identical aerodynamic con- versus velocity shown in figure 6.6. When a figuration but different gross weight could straight line is drawn from the origin tangent glide the same distance from the same altitude.

to the curve, a point is located which produces Of course, this fact would be true only if both airplanes are flown at the specific C, to produce the maximum proportion of velocity to rate of descent. Obviously, this condition provides (L/D),,. The principal difference would be that the heavier airplane must fly at a higher maximum glide ratio. Since the rate of descent is proportional to the power required, the airspeed to support the greater weight at the optimum C,. In addition, the heavier airplane points of tangency define the aerodynamic condition of (L/D)m.z.

flying at the greater speed along the same flight FACTORS AFFECTING GLIDE PER- path would develop a greater rate of descent.

FORMANCE. In order to obtain the mini- The relationship which exists between gross mum glide angle through the air, the airplane weight and velocity for a particular C, is as follows: must be operated at (L/D)mor. The subsonic of a given airplane configuration will (LIDL VT- w, (constant C,> occur at a specific value of lift coefficient and VI w,

-4

angle of attack. However, as can be noted where from the curves of figure 6.6, small deviations VI= best glide speed corresponding to from the optimum C, will not cause a drastic some original gross weight. WI reduction of (L/D) and glide ratio. In fact, a V,=best glide speed corresponding to 5 percent deviation in speed from the best glide some new gross weight, IV2 NAVWEPS OD-ROT-80 APPLICATION OF AERODYNAMICS TO ‘ SPECIFIC PROBLEMS OF FLYl,NG The eficct aj wind on gliding performance is As a result of this relationship, a IO percent similar to the effect of wind on cruising range.

increase in gross weight would require a 5 per- That is, a headwind will always reduce the cent increase in glide speed to maintain glide range and a tailwind will always increase (L/D),,. While small. variations in gross the glide range. The maximum glide range weight may produce a measurable change in of the airplane in still air will be obtained by best glide speed, the airplane can tolerate small flight at (L/D),,,,. However, when a wind is deviations from the optimum C, without signif- icant change in (L/D) and glide ratio. For this present, the optimum gliding conditions may not be accomplished by operation at (L/D)ma.

reason, a standard, single value of glide speed For example, when a headwind is present, may be specified for a small range of gross the optimum glide speed will be increased to weights at which glide performance can be of importance. A gross weight which is con- obtain a maximum proportion of ground dis- siderably different from the normal range will tance to altitude. In this sense, the increased require a modification of best glide speed to glide speed helps to minimize the detrimental maintain the maximum glide ratio. effect of the headwind. In the case of a tail- The effect a! &it.& on glide performance is wind, the optimum glide speed will be reduced insignificant if there is no change in (L/D),.,. to maximize the benefit of the tailwind. For Generally, the glide performance of the major- ordinary wind conditions, maintaining the ity of airplanes is subsonic and there is no glide speed best for zero wind conditions will noticeable variation of (L/D),, with altitude.

suffice and the loss or gain in glide distance Any specific airplane configuration at a partic- must be accepted. However, when the wind ular gross weight will require a specific value conditions are extreme and the wind velocity of dynamic pressure to sustain flight at the is large in comparison with the glide speed, C, for (L/D),,. Thus, the airplane will have e.g., wind velocity greater than 25 percent of a best glide speed which is a specific value of the glide speed, changes in the glide speed must equivalent airspeed (EAS) independent of be made to obtain maximum possible ground altitude. For convenience and simplicity, this distance.

best glide speed is specified as a specific value THE FLAMEOUT PATTERN. In the case of indicated airspeed (IAS) and compressibility of failure of the powerplant, every effort and position errors are neglected. The prin- should be made to establish a well-planned, cipal effect of altitude is that at high altitude stabilized approach if a suitable landing area the true airspeed (TAX) and rate of descent is available. Generally a 360’ overhead ap- along the optimum glide path are increased proach is specified with the approach begin- above the low altitude conditions. However, ning from the “high key” point of the flameout is maintained, the glide angle and if WD),.z pattern. The function of a standardized glide ratio are identical to the low altitllde pattern is to provide a flight path well within conditions.

the capabilities of the airplane and the abilities The effect of configura+~n has been noted pre- of the pilot to judge and control the flight viously in that the addition of parasite drag by path. The flight handbook will generally flaps, landing gear, speed brakes, external specify the particulars of the flameout pattern stores, etc. will reduce the maximum lift-drag such as the altitude at the high key, glide In ratio and cause a reduction of glide ratio.

speeds, use of flaps, etc. Of course, the par- the case where glide distance is of great im- ticulars of the flameout pattern will be de- portance, the airplane must be maintained in termined by the aerodynamic characteristics the clean configuration and flown at (L/D),=, of the airplane. A principal factor is the NAVWEPS OD-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING effect of glide ratio, or (L/D),,, on the alti- low aspect ratio, sweepback, and high wing tude required at the high key point at the loading. Since these airplane characteristics ~ _ beginning of the flameour pattern. The air- also produce marginal flare capability in power- plane with a low value of (L/D),,* will require off flight, great care should be taken to follow a high altitude at the high key point.

the procedure recommended for the specific The most favorable situation during a airplane.

flameout would be for the airplane to in posi- As an example of the power-off glide per- tion to arrive over the intended landing area formance of an airplane with low aspect ratio, the altitude for the high key point. In this sweepback, and high wing loading, a best case, the standard flameout pattern could be glide speed of 220 knots and a glide ratio of 6 utilized. If the airplane does not have s&i- may be typical. In such a case, the rate of cient glide range to arrive at the landing descent during the glide at low altitude would area with the altitude for the high key point, be on the order of 3,700 FPM. Any deviations it is desirable to fit the approach into the from the recommended landing technique can- lower portions of the standard flameout ap- not be tolerated because of the possibility of an proach. If it is not possible to arrive at the excessive rate of descent. Either premature intended landing area with sufficient altitude flare or delayed flare may allow the airplane to to “play” the approach, serious considera- touch down at a rate of descent which would tion should be given to ejection while suffi- cause structural failure. Because of the mar- cient altitude remains.

Deviations from a ginal flare characteristics in power-off flight, well-planned approach such as the standard the best glide speed recommended for the land- flameout pattern may allow gross errors in ing configuration may be well above the speed judgment. A typical error of a non-standard corresponding to the exact maximum lift-drag or poorly executed flameout approach is the ratio. The greater speed reduces induced drag use of excessive angles of bank in turns to and provides a greater margin for a successful correct the approach. Because of the great power-off landing flare.

increase ‘ in induced drag at large angles of In the extreme case, the power-off glide and bank, excessive rates of descent will be incurred landing flare characteristics may be very criti- and there will be further deviations from a cal for certain airplane configurations. Thus, desirable flight path.

a well-planned standard flameout pattern and The power-off gliding characteristics of the precise flying technique are necessary and, if airplane can be simulated in power on flight by very suitable conditions are not available, the certain combinations of engine power setting recommended alternative is simple: eject!

and position of the speed brake or dive Rap.

EFFECT OF ICE AND FROST ON AIRPLANE This will allow the pilot to become familiar PERFORMANCE with the power-off glide performance and the flameopt landing pattern. In addition, the Without exception, the formation of ice or simulated flameout pattern is useful during a frost on the surfaces of an airplane will cause a precautionary landing when the powerplant is detrimental effect on aerodynamic performance.

malfunctioning and there is the possibility of The ice or frost formation on the airplane sur- an actual flarneout. faces will alter the aerodynamic contours and The final approach and landing flare will be affect the nature of the boundary layer. Of particularly critical for the airplane which has* course, the most important surface of the air- a low glide ratio but a high best glide speed. plane is the wing and the formation of ice or frost can create significant changes in the aero- These airplane characteristics are typical of the modern configuration of airplane which has dynamic characteristics.

N A V W E P S DO-80T-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING EDGE ICE FOR_“ATlON UPPER SURFACE FROST

A

BASIC SMOOTH WING WING WITH FROST LIFT COEFFICIENT WITH ICE CL t ANGLE OF ATTACK, a Figure 6.7. Effect of ice and Frost NAVWEPS OD-BOT-80 APP,LlCATlON OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING on the lift characteristics is typified by the il- A large formation of ice on the leading edge of the wing can produce large changes in the lustration of figure 6.7.

The effect of ice or frost on takeoff and land- local contours and severe local pressure gra- dients. The extreme surface roughness common ing performance is of great importance. The to some forms of ice will cause high surface effects are so detrimental to the landing and friction and a considerable reduction of bound- takeoff that no effort should be spared to keep ary layer energy. As a result of these effects, the airplane as free as possible from any ac- If any ice remains the ice formation can produce considerable in- cumulation of ice or frost.

crease in drag and a large reduction in maxi- on the airplane as the landing phase approaches mum lift coefficient. Thus, the ice formation it must be appreciated that the ice formation will cause an increase in power required and will have reduced CL,., and incurred an increase in stall speed. Thus, the landing speed will be stall speed. In addition, the added weight of the ice formation on the airplane will provide greater. When this effect is coupled with the an undesirable effect. Because of the detri- possibility of poor braking action during the It is mental effects of ice formation, recommended landing roll, a critical situation can exist.

anti-icing procedures must be followed to obvious that .great effort must be made to preserve the airplane performance. prevent the accumulation of ice during flight.

The effect of frost is perhaps more subtle In no circumstances should a formation of ice than the effect of ice formation on the aero- or frost be allowed to remain on the airplane dynamic characteristics of the wing. The ac- wing surfaces prior to takeoff. The undesir- cumulation of a hard coat of frost on the wing able effects of ice are obvious but, as previously upper surface will provide a surface texture of mentioned, the effects of frost are more subtle.

considerable roughness. While the basic shape If a heavy coat of hard frost exists on the wing and aerodynamic contour is unchanged, the upper surface, a typical reduction in CL,..

increase in surface roughness increases skin- would cause a 5 to 10 percent increase in the Because of this magnitude friction and reduces the kinetic energy of the airplane stall speed.

boundary layer. As a result, there will be an of effect, the effect of frost on takeoff per- increase in drag but, of course, the magnitude formance may not be realized until too late.

of drag increase will not compare with the The takeoff speed of an airplane is generally considerable increase due to a severe ice forma- some speed 5 to 25 percent greater than the tion. The reduction of boundary layer kinetic stall speed, hence the takeoff lift coefficient energy will cause incipient stalling of the wing, will be value from 90 to 65 percent of C1,,.., i.e., separation will occur at angles of attack Thus, it is possible that the airplane with frost cannot become airborne at the specified take- and lift coefficients lower than for the clean, Even off speed because of premature stalling.

smooth wing. While the reduction in C,,,, if the airplane with frost were to become air- due to frost formation ordinarily is not as great borne at the specified takeoff speed, the air- as that due to ice formation, it is usually un- plane could have insufficient margin of air- expected because it may be thought that large speed above stall and turbulence, gusts, turning changes in the aerodynamic shape (such as flight could produce incipient or con plete due to ice) are necessary to reduce CL,az. How- stalling of the airplane.

ever, the kinetic energy of the boundary layer The increase in drag during takeoff roll due is an important factor influencing separation to frost or ice is not considerable and there of the airflow and this energy is reduced by an will not be any significant effect on the initial increase in surface roughness.

acceleration during takeoff. Thus, the effect The general effects of ice and frost formation of frost or ice will be most apparent during the NAVWEPS DD-8OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING later portions of takeoff if the airplane is un- speed but of greater importance is the reduc- able to become airborne or if insufficient margin tion in excess thrust. Since the acceleration above stall speed prevents successful initial and climb performance is a function of the climb, In no circumstances should a formation excess thrust and power, the failure of a power- of ice or frost be allowed to remain on the air- plant will be most immediately appreciated in plane wing surfaces prior to takeoff. this area of performance. As illustrated in figure 6.8, loss of one-half the maximum avail- ENGINE FAILURE ON THE MULTIENGINE able thrust will reduce the excess thrust to less AIRPLANE than half the original value. Since some In the case of the single-engine airplane, thrust is required to sustain flight, the excess power-plant failure leaves only the alternatives which remains to accelerate and climb the of effecting a successful power-off landing or airplane may be greatly reduced. The most abandoning the airplane. In the case of the critical conditions will exist when various multiengine airplane, the failure of a power- factors combine to produce a minimum of plant does nor necessarily constitute a disaster excess thrust or power when engine failure since flight may be continued with the remain- occurs. Thus, critical conditions will be com- ing powerplants functioning. However, the mon to high gross weight and high density altitude performance of the multiengine airplane with (and high temperatures in the case of the a powerplant inoperative may be critical for turbine powered airplane) as each of these certain conditions of flight and specific tech- factors will reduce the excess thrust at any niques and procedures must be observed to specific flight condition.

obtain adequate performance. The asymmetrical power condition which The effect of a powerplant failure on the results when a powerplant fails can provide multiengine turbojet airplane is illustrated by critical control requirements. First consid- the first chart of figure 6.8 with the variation eration is due the yawing moment produced of required and available thrust with velocity.

by the asymmetrical power condition. Ade- If half of the airplane powerplants are inoper- quate directional control will be available ative, e.g., single-engine operation of a twin- only when the airplane speed is greater than engine airplane, the maximum thrust available the minimum directional control speed. Thus, at each velocity is reduced to half that avail- the pilot must insure that the flight speed never able prior to the engine failure. The variation falls below the minimum directional control of thrust required with velocity may be speed because the application of maximum affected by the failure of a powerplant in that power on the functioning powerplants will there may be significant increases in drag if produce an uncontrollable yaw if adequate directional control is unavailable. A second specific procedures are not followed. The inoperative powerplant may contribute addi- consideration which is due the propeller tional drag and the pilot must insure that the powered airplane involves the rolling moments additional drag is held to a minimum. In the caused by the slipstream velocity. Asym- case of the propeller powered airplane, the metrical power on the propeller airplane will propeller must be feathered, cowl flaps closed.

create a dissymmetry of the slipstream veloc- as the increased drag will detract con- etc., ities on the wing and create rolling moments siderably from the performance.

which must be controlled. These slipstream The principal effects of the reduced available induced rolling moments will be greatest at thrust are pointed out by the illustration of high power and low velocity and the pilot figure 6.6. Of course, the lower available must be sure of adequate lateral control, thrust will reduce the maximum level flight especially for the crosswind landing.

NAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING The previous table of values illustrates the The effect of an engine failure on the remain- fact that coordinated turns with less than 15” ing range and endurance is specific to the air- of bank .cause no appreciable effect on stall plane type and configuration. If an engine fails during optimum cruise of the turbojet speed or induced drag. However, note that 30” airplane, the airplane must descend and experi- of bank will increase the induced drag by 33.3 ence a loss of range. Since the turbojet air- percent. Under critical conditions, such an in- plane is generally overpowered at (L/D),,, crease in induced drag (and, hence, total drag) a loss of a powerplant will not cause a signi- would be prohibitive causing the airplane to ficant change in maximum endurance. If an descend rather than climb. The second graph engine fails during cruise of a reciprocating of figure 6.7 illustrates the case where the steep powered airplane, there will be a significant turn causes such a large increase in required loss of range only if the maximum range condi- thrust that a deficiency of thrust exists. When- tion cannot be sustained with the remaining ever engine failure produces critical perform- powerplants operating within the cruise power ance conditions it is wise to limit all turns to rating. If a power greater than the maximum II0 of bank wherever possible.

cruise rating is necessary to sustain cruise, the Another factor to consider in turning flight specific fuel consumption increases and causes is the effect of sideslip. If the turn is not coor- a reduction of range. Essentially the same dinated to hold sideslip to a minimum, addi- relationship exists regarding maximum endur- tional drag will be incurred due to the sideslip.

ance of the reciprocating powered airplane. The use of the flaps and landing gear can When critical conditions exist due to failure greatly affect the performance of the multi- engine airplane when a powerplant is inopera- of a powerplant, the pilot must appreciate the tive. Since the extension of the landing gear reduced excess thrust and operate the airplane and flaps increases the parasite drag, maximum within specific limitations. If the engine-out performance of the airplane will be obtained performance of the airplane is marginal, the with airplane in the clean configuration. In pilot must be aware of the very detrimental effect of steep turns.. Due to the increased load certain critical conditions, the extension of the factor in a coordinated turn, there will be an landing gear and full flaps may create a defi- increase in stall speed and-of greater import- ciency of thrust at any speed and commit the ance to engine-out performance-an increase airplane to descend. This condition is illus- in induced drag. The following table illus- trated by the second graph of figure 6.8. Thus, trates the effect of bank angle on stall speed judicious use of the flaps and landing gear is and induced drag.

necessary in the case of an engine failure.

TABLE 6.1 In the case of engine failure immediately after takeoff, it is important to maintain air- speed in excess of the minimum directional con- Bank mglc, 6, dcgrccs Load factor trol speed and accelerate to the best climb After the engine failure, it will be fa- speed.

0 0 vorable to climb only as necenary to clear obstacles 0.8 0.2 Of until the airplane reachesthe best climb speed.

0.7 3.1 1.7 7.2 course, the landing gear should be retracted as 3.2 13.3 soon as the airplane is airborne to reduce para- 21.7 5.0 site drag and, in the case of the propeller pow- 7.5 33.3 10.5 4% 0 ered airplane, it is imperative that the wind 70.4 14.3 milling propeller be feathered. The flaps should IS. 9 loo. 0 41.4 303.0 be retracted only as rapidly as the increase in NAVWEPS 00-801-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING THRUST AVAJLABLE WJTH ALL ENGINES OPERATING THRUST REQ’ D AND AVAILABLE LBS.

THRUST AVAILABLE WITH NES OPERATING VELOCITY, KNOTS

I

THRUST REP’ D THRUST REO’ D CLEAN LANDING CONFIGURATION CONFIGURATION WING LEVEL FLIGHT , BUT TURNING FLIGHT THRUST WING LEVEL FLIGHT REO’ U AND AVAILABLE LB.% AVAILABLE DUE TO ENGINE FAILURE VELOCITY, KNOTS Figure 6.8. Engine Failure on Multi-engine Aircraft NAVWEPS OO-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING GROUND EFFECT airspeed will allow. If full flap deflection is utilized for takeoff it is important to recall that When an airplane in flight nears the ground the last 50 percent of flap deflection creates (or water) surface, a change occurs in the more than half the total drag increase but less three dimensional flow pattern because the than half the total change in CL,-. Thus, for local airflow cannot have a vertical component some configurations of airplanes, a greater re- at the ground plane. Thus, the ground plane duction in drag may be accomplished by partial will furnish a restriction to the flow and alter retraction of the flaps rather than retraction of the wing upwash, downwash, and tip vortices.

the landing gear. Also, it is important that no These general effects due to the presence of steep turns be attempted because of the unde- the ground plane are referred to as “ground sirable increase in induced drag.

effect. ‘ * During the landing with an engine inopera- AERODYNAMIC INFLUENCE OF tive, the same fundamental precautions must GROUND EFFECT. While the aerodynamic be observed as during takeoff, i.e., minimum characteristics of the tail and fuselage are directional control speed must be maintained altered by ground effects, the principal effects (or exceeded), no steep turns should be at- due to proximity of the ground plane are the tempted, and the extension of the flaps and changes in the aerodynamic characteristics landing gear must be well planned. In the case of the wing. As the wing encounters ground of’ a critical power condition it may be neces- effect and is maintained at a constant lift sary to delay the extension of the landing gear coefficient, there is a reduction in the upwash, and full flaps until a successful landing is as- downwash, and the tip vortices. These effects sured. If a waveoff is necessary, maximum per- are illustrated by the sketches of figure 6.9.

formance will be obtained cleaning up the air- As a result of the reduced tip vortices, the wing plane and accelerating to the best climb speed in the presence of ground effect will behave as before attempting any gain in altitude.

if it were of a greater aspect ratio. In other At all times during flight with an engine words, the induced velocities due to the tip inoperative, the pilot must utilize the proper (or trailing) vortices will be reduced and the techniques for control of airspeed and altitude, wing will incur smaller values of induced e.g., for the conditions of steady flight, angle drag coefficient, C,<, and induced angle of of attack is the primary control of airspeed attack, OL;,for any specific lift coefhcient, C,.

and excess power is the primary control of In order for ground effect to be of a signifi- rate of climb. For example, if during approach cant magnitude, the wing must be quite close to landing the extension of full flaps and to the ground plane. Figure 6.9 illustrates landing gear creates a deficiency of power at one of the direct results of ground effect by all speeds, the airplane will be committed to the variation of induced drag coefficient with descend. If the approach is not properly wing height above the ground plane for a planned and the airplane sinks below the representative unswept wing at constant lift desired glide path, an increase in angle of coefficient. Notice that the wing must be quite close to the ground for a noticeable attack will only allow the airplane to fly more reduction in induced drag. When the wing slowly and descend more rapidly. An attempt is at a height equal to the span (h/b=l.O), to hold altitude by increased angle of attack the reduction in induced drag is only 1.4 when a power deficiency exists only causes a percent. However, when the wing is at a continued loss of airspeed. Proper procedures height equal to one-fourth the span (b/b= and technique are an absolute necessity for 0.25), the reduction in induced drag is 23.5 safe flight when an engine failure occurs.

NAVWEPS 00-802-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYtNG AIRPLANE OUT OF TIP VORTEX GROUND EFFECT REDUCED DOWNWASH REDUCED t-- SFkAN’ --I AND UPWASH- / CL CONSTANT PERCENT REDUCTION IN INDUCED DRAG COEFFICIENT IO RATIO OF WING HEIGHT TO SPAN, h/b AIRPLANE IN THRUST REQ’ D AIRPLANE OUT OF / LIFT LBS.

COEFFICIEN’ r

CL AIRPLANE OUT OF GROUND EFFECT < (-,’ AIRPLANE IN GROUND EFFECT

w - w

VELOCITY, KNOTS ANGLE OF ATTACK, 0 Figure 6.9. Ground Effect NAVWEPS CKLBOT-BO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING percent and, when the wing is at a height thus, a constant dynamic pressure and equiva- equal to one-tenth the span (h/b=O.l), the lent airspeed. As the airplane descends into reduction in induced drag is 47.6 percent. ground effect, the following. effects will take Thus, a large reduction in induced drag will place: take place only when the wing is very close (1) Because of the reduced induced angle to the ground. Because of this variation, of attack and change in lift distribution, a ground effect is most usually recognized during smaller wing angle of attack will be required the liftoff of takeoff or prior to touchdown on to produce the same lift coefficient. If a landing.

constant pitch attitude is maintained as The reduction of the tip or trailing vortices ground effect is encountered, an increase in due to ground effect alters the spanwise lift lift coefficient will be incurred.

distribution and reduces the induced angle of (2) The reduction in induced flow due to attack. In this case, the wing will require ground effect causes a significant reduction a lower angle of attack in ground effect to in induced drag but causes no direct effect on produce the same lift coefficient. This effect parasite drag. As a result of the reduction is illustrated by the lift curves of figure 6.9 in induced drag, the thrust required at low which show that the airplane in ground effect speeds will be reduced.

will develop a greater slope of the lift curve. (3) The reduction in downwash due to For the wing in ground effect, a lower angle of ground effect will produce a change in longi- attack is necessary to produce the same lift tudinal stability and trim. Generally, the coefficient or, if a constant angle of attack is reduction in downwash at the horizontal maintained, an increase in lift coefficient will tail increases the contribution to static longi- result.

tudinal stability. In addition, the reduction Figure 6.9 illustrates the manner in which of downwash at the tail usually requires ground effect will alter the curve of thrust re- a greater up elevator to trim the airplane at quired versus velocity. Since induced drag a specific lift coefficient. For the conven- predominates at low speeds, the reduction of tional airplane configuration, encountering induced drag due to ground effect will cause ground effect will produce a nose-down the most significant reduction of thrust re- change in pitching moment. Of course, the quired (parasite plus induced drag) only at increase in stability and trim change associ- low speeds. At high speeds where parasite ated with ground effect provide a critical re- drag predominates, the induced drag is but quirement of adequate longitudinal control a small part of the total drag and ground power for landing and takeoff.

effect causes no significant change in thrust re- (4) Due to the change in upwash, down- quired. Because ground effect involves the wash, and tip vortices, there will be a change induced effects of airplane when in close prox- in position error of the airspeed system, as- imity to the ground, its effects are of greatest In the majority sociated with ground effect.

concern during the takeoff and landing. Ordi- of cases, ground effect will cause an increase narily, these are the only phases of flight in in the local pressure at the static source and which the airplane would be in close proximity produce a lower indication of airspeed and to the ground. altitude.

GROUND EFFECT ON SPECIFIC FLIGHT During the landing pha~c of flight, the effect CONDITIONS. The overall influence of of proximity to the ground plane must be ground effect is best realized by assuming that understood and appreciated. If the airplane the airplane descends into ground effect while is brought into ground effect with a constant maintaining a constant lift coefficient and, angle of attack, the airplane will experience 3&l NAVWEPS OD-8OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYfNG an increase in lift coeflicient and reduction in moment, and (4) usually a reduction in static thrust required. Hence, a “floating” sensa- source pressure and increase in indicated air- tion may be experienced. Because of the re- speed. These general effects should point out duced drag and power-off deceleration in the possible danger in attempting takeoff prior to achieving the recommended takeoff ground effect, any excess speed at the point of flare may incur a considerable “float” distance. speed. Due to the reduced drag in ground As the airplane nears the point of touchdown effect the airplane may seemcapable of takeoff on the approach, ground effect will be most below the recommended speed. However, as realized at altitudes less than the wing span. the airplane rises out of ground effect with a An exact appreciation of the ground effect may deficiency of speed, the greater induced drag be obtained during a PcZd approach with the may produce marginal initial climb perform- mirror landing system furnishing an exact ance. In the extreme conditions such as high reference of the flight path. During the final gross weight, high density altitude, and high phases of the field approach as the airplane temperature, a deficiency of airspeed at takeoff nears the ground plane, a reduced power may permit the airplane to become airborne setting is necessary or the reduced thrust re- but be incapable of flying’ out of ground effect.

quired would allow the airplane to climb In this case, the airplane may become airborne above the desired glide path. During ship- initially with a deficiency of speed, but later board operations, ground effect will be delayed settle back to the runway. It is imperative until the airplane passes the edge of the deck that no attempt be made to force the airplane and the reduction in power setting that is to become airborne with a deficiency of speed; common to field operations should not be the recommended takeoff speed is necessary to encountered. Thus, a habit pattern should provide adequate initial climb performance.

not be formed during field landings which In fact, ground effect can be used to advantage would prove dangerous during carrier oper- if no obstacles exist by using the reduced drag ations. to improve initial acceleration.

An additional factor to consider is the aero- The results of the airplane leaving ground dynamic drag of the airplane during the land- effect can be most easily realized during the ing roll. Because of the reduced induced drag deck launch of a heavily loaded airplane. As when in ground effect, aerodynamic braking the airplane moves forward and passes over the will be of greatest significance only when edge of the deck, whatever ground effect exists partial stalling of the wing can be accom- will be lost immediately. Thus, proper rota- plished. The reduced drag when in ground tion of the airplane will be necessary to main- effect accounts for the fact that the brakes tain the same lift coefficient and the increase are the most effective source of deceleration in induced drag must be expected.

for the majority of airplane configurations.

The rotor of the helicopter experiences a During the takeoff pharc of flight ground similar restraint of induced flow when in prox- effect produces some important relationships.

imity to the ground plane. Since the induced Of course, the airplane leaving ground effect rotor power required will predominate at low encounters just the reverse of the airplane flight speeds, ground effect will produce a con- entering ground effect, i.e., the airplane leaving siderable effect on the power required at low ground effect will (1) require an increase in speeds. During hovering and flight at low angle of attack to maintain the same lift speeds, the elevation of the rotor above the coefficient, (2) experience an increase in in- ground plane will be an important factor de- duced drag and thrust required, (3) experience a decrease in stability and a nose-up change in termining the power required for flight.

NAVWEPS D&ROT-R0 APPLICATION OF AERODYNAMICS TO SPECIFIC ‘ PROBLEMS OF FLYING The range sf the reciprocating powered air- One example of interference between air- plane can be augmented by the use of ground planes in flight is shown first in figure 6.10 with effect. When the airplane is close to the the effect of lateral separation of two airplanes ground or water surface the reduction of in- flying in line abreast. A plane of symmetry duced drag increases the maximum lift-drag would exist halfway between two identical air- ratio and causes a corresponding increase in planes and would furnish a boundary of flow range. Of course, the airplane must be quite across which there would be no lateral com- close to the surface to obtain a noticeable in- ponents of flow. As the two airplane wing creasein (L/D),., and range. The difficulty in tips are in proximity, the effect is to reduce the holding the airplane at the precise altitude strength of the tip or trailing vortices and re- without contacting the ground or water will duce the induced velocities in the vicinity of preclude the use of ground effect during ordi- wing tip. Thus, each airplane will experience a local increase in the lift distribution as the nary flying operations. The use of ground effect to extend range should be reserved as tip vortices are reduced and a rolling moment is Because developed which tends to roll each airplane a final measure in case of emergency.

of the very detrimental effect of low altitude away from the other. This disturbance may on the range of the turbojet, ground effect will provide the possibility of collision if other air- not be of a particular advantage in an attempt planes are in the vicinity and there is delay in to augment range. control correction or overcontrol. If the wing The most outstanding examples of the use tips are displaced in a fore-and-aft direction, of ground effect are shown in the cases of multi- the same effect exists but generally it is of a engine airplanes with some engines inoperative. lower magnitude.

When the power loss is quite severe, the air- The magnitude of the interference effect due plane may not be capable of sustaining altitude to lateral separation of the wing tips depends and will descend. As ground effect is en- on the proximity of the wi.ig tips and the ex- countered, the reduced power required may tent of induced Pov;. This implies that the interference v-r 1 allow the airplane to sustain flight at extremely e grealest when the tips low altitude with the remaining powerplants are very close AL-L the airplanes are operating An interesting ramifi- functioning. In ground effect, the recipro- at high lift coefficients.

cating powered airplane will encounter a cation of this effect is that several airplanes in greater (L/D),, which occurs at a lower air- line abreast with the wing tips quite close will speed and power required and the increase in experience a reduction in induced drag.

An indirect form of interference can be en- range may be quite important during emer- gency conditions. countered from the vortex system created by a preceding airplane along the intended flight The vortex sheet rolls up a considerable path.

INTERFERENCE BETWEEN AIRPLANES IN distance behind an airplane and creates consid- FLIGHT erable turbulence for any closely following air- During formation flying and inflight refuel- plane. This wake can prove troublesome if air- ing, airplanes in proximity to one another will planes taking off and landing are not provided produce a mutual interference of the flow pat- adequate separation. The rolled-up vortex terns and alter the aerodynamic characteristics sheet will be strongest when the preceding air- The principal effects of this of each airplane.

planes is large, high gross weight, and operat- interference must be appreciated since certain ing at high lift coefhcients. At times this tur- factors due to the mutual interference may bulence may be falsely attributed to propwash enhance the possibility of a collision.

or jetwash.

NAVWBPS OO-BOT-BO APPLICATION OF AERODYNAMlCS TO SPECIFIC PROBLEMS OF FLYING LIFT DISTRIBUTION LBWFT OF SPAN TIP VORTEX PLANE OF SYMMETRY REDUCED CHANGE IN LIFT DISTRIBUTION - DOCASH -- \’ %SH TRIM CHANGE figure 6.10. Interference 8etween Airplanes in Flight NAVWEPS OO-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING and greater power changes required to hold Another important form of direct inter- ference is common when the two airplanes are position.

A common collision problem is the case of in a trail position and stepped down. As shown an airplane with a malfunctioning landing in figure 6.10, the single airplane in flight de- gear. If another”airpIane is called to inspect velops upwash ahead of the wing and down- the malfunctioning landing gear, great care wash behind and any restriction accorded the must be taken to maintain adequate separation flow can alter the distribution and magnitude of and preserve orientation. Many instances the upwash and downwash. When the trailing such as this have resulted in a collision when airplane is in close proximity aft and below the the pilo: of the trailing airplane became dis- leading airplane a mutual interference takes place betweetrthe two airplanes. The leading oriented and did not maintain adequate sepa- ration.

airplane above will experience an effect which would be somewhat similar to encountermg During inflight refueling, essentially the ground effect, i.e., a reduction in induced drag, same problems of interference exist. AS the a reduction in downwash at the tail, and a receiver approaches the tanker from behind change in pitching moment nose down. The and below, the receiver will encounter the trailing airplane below will experience an effect downwash from the tanker and require a which is generally the opposite of the airplane slight, gradual increase in power and pitch above. In other words, the airplane below attitude to continue approach to the receiving will experience an increase in induced drag, an position. While.‘ the .receiver may not be increase in downwash at the tail, and a change visible to the pilot ‘ of the tanker, he will in pitching moment nose up. Thus, when anticipate the receiver coming into position the airplanes are in close proximity, a definite by the slight reduttion in power required and collision possibility exists because of the trim nose down changein pitching moment. Ade- change experienced by each airplane. The quate clearance and, proper position must be magnitude of the trim change is greatest maintained by the pilot of the receiver for a when the airplanes are operating at high lift collision possibility is enhanced by the rela- coefficients, e.g., low speed flight, and when tive positions of the airplanes. A hazardous the airplanes are in close proximity. condition exists if the pilot of the receiver In formation flying, this sort of interference has excessive speed and runs under the tanker must be appreciated and anticipated. In cross- in close proximity.* ‘ The trim change expe- ing under another airplane, care must be rienced by both airphines may be large and taken to anticipate the trim change and unexpected and it may be difficult to avoid a adequate clearance must be maintained, other- collision.

wise a collision may result. The pilot of the In addition to the forms of interference leading aircraft will know of the presence of previously mentioned, there exists the possi- the trailing airplane by the trim change bility of strong interference between airplanes experienced. Obviously, some anticipation is in supersonic flight. In this case, the shock necessary and adequate separation is necessary waves from one airplane may strongly affect to prevent a disturbing magnitude of the the pressure distribution and rolling, yawing, trim change. In a close diamond formation and pitching moments of an adjacent air- the leader will be able to “feel” the presence ane. It is difficult to express general rela- Pl of the slot man even though the airplane is tionships of the effect except that magnitude not within view. Obviously, the slot man of the effects will be greatest when in close will have a difficult job during formation proximity at low altitude and high 4. General- maneuvers because of the unstable trim changes ly, the trailing airplane will be most affected.

NAVWEPS O&ROT-R0 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING BRAKING PERFORMANCE rolling friction is of an approximate magnitude of 0.015 to 0.030 for dry, hard runway surface.

For the majority of airplane configurations The application of brakes supplies a torque and runways conditions, the airplane brakes to the wheel which tends co retard wheel rota- furnish the most powerful means of deceler- tion. However, the initial application of ation. While specific techniques of braking brakes creates a braking torque but the initial are required for specific situations, there retarding torque is balanced by the increase in are various fundamentals which are common friction force which produces a driving or to all conditions.

rolling torque. Of course, when the braking

Solid ftictim is the resistance to relative

torque is equal to the rolling torque, the wheel motion of two surfaces in contact. When experiences no acceleration in rotation and the relative motion exists between the surfaces, equilibrium of a constant rotational speed is the resistance to relative motion is termed maintained. Thus, the application of brake “ kinetic” or “ sliding” friction; when no develops a retarding torque and causes an relative motion exists between the surfaces, increase in friction force between the tire and the resistance to the impending relative mo- runway surface. A common problem of brak- tion is termed “ static” friction. The minute ing technique is application of excessive brake discontinuities of the surfaces in contact are pressure which creates a braking torque greater able to mate quite closely when relative than the maximum possible rolling torque.

motion impends rather than exists, so static In this case, the wheel loses rotational speed friction will generally exceed kinetic friction.

and decelerates until the wheel is stationary The magnitude of the friction force between and the result is a locked wheel with the tire two surfaces will depend in great part on the surface subject to a full slip condition.

types of surfaces in contact and the magnitude The relationship of friction force, normal of force pressing the surfaces together. A force, braking torque, and rolling torque is convenient method of relating the friction illustrated in figure 6.11.

charactersitics of surfaces in contact is a The effect of slip velocity on the coefficient proportion of the friction force to the normal of friction is illustrated by the graph of figure (or perpendicular) force pressing the surfaces 6.11. The conditions of zero slip corresponds together. This proportion defines the coeffi- to the rolling wheel without brake application cient of friction, ~1.

while the condition of full, 100 percent slip ,L= F/N corresponds to the locked wheel where the relative velocity between the tire surface and where the runway equals the actual velocity. With p =coefFicient of friction (mu) the application of brakes, the coefficient of F =friction force, Ibs.

N = normal force, lbs. friction increases but incurs a small but meas- urable apparent slip. Continued increase in The coefficient of friction of tires on a runway friction coefficient is obtained until some max- surface is a function of many factors. Runway imum is achieved then decreases as the slip surface condition, rubber composition, tread, increases and approaching the 100 percent slip inflation pressure, surface friction shearing condition. Actually, the peak value of co- stress, relative slip speed, etc., all are factors efficient of friction occurs at an incipient skid which affect the coefficient of friction. When condition and the relative slip apparent at this the tire is rolling along the runway without point consists primarily of elastic shearing the use of brakes, the friction force resulting is simple rolling resistance. The coefficient of deflection of the tire structure.

NAVWEPS DD-BOl-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING When the runway surface is dry, brush- film between the tire and the runway. In this finished concrete, the maximum value for the case, the peak coefficient of friction rarely coefficient of friction for most aircraft tires is exceeds 0.3. In some extreme conditions, the on the order of 0.6 to 0.8. tire may simply plane along the water without Many factors can determine small differences in this peak value contact of the runway and the coefficient of of friction coefhcient for dry surface conditions. friction is much lower than 0.3. Smooth, clear ice on the runway will cause extremely For example, a soft gum rubber composition can develop a very high value of coefficient of low values for the coefficient of friction. In such a condition, the peak value for the co- friction but only for low values of surface efhcient of friction may be on the order of 0.2 shearing stress. At high values of surface or 0.15.

shearing stress, the soft gum rubber will shear Note that immediately past the incipient or scrub off before high values of friction co- efficient are developed. The higher strength skidding condition the coefficient of friction compounds used in the production of aircraft decreases with increased slip speed, especially tires produce greater resistance to surface shear for the wet or icy runway conditions. Thus, and scrubbing but the harder rubber has lower once skid begins, a reduction in friction force intrinsic friction coeflicient. Since the high and rolling torque must be met with a reduc- performance airplane cannot afford the luxury tion in braking torque, otherwise the wheel of excessive tire weight or size, the majority will decelerate and lock. This is an important of airplane tires will be of relatively hard factor to consider in braking technique because rubber and will operate at or near the rated the skidding tire surface on the locked wheel load capacities. As a result, there will be produces considerably less retarding force than when at the incipient skid condition which little difference between the peak values of friction coefficient for the dry, hard surface causes the peak coeflicient of friction. If the runway for the majority of aircraft tires. wheel locks from excessive braking, the sliding If high traction on dry surfaces were the tire surface produces less than the maximum only consideration in the design of tires, the retarding force and the tires become relatively result would be a soft rubber tire of extreme incapable of developing any significant side width to create a large footprint and reduce force. Stop distance will increase and it may surface shearing stresses, e.g., driving tires on be difficult-if not impossible-to control the a drag racer. However, such a tire has many airplane when full slip is developed. In addi- other characteristics which are undesirable tion, at high rolling vel,ocities on the dry sur- such as high rolling friction, large size, poor face runway, the immediate problem of a skid- side force characteristics, etc.

ding tire is not necessarily the loss of retard- When the runway has water or ice on the ing force but the imminence of tire failure. The surface, the maximum value for the coefficient pilot must insure that the application of brakes of friction is reduced greatly below the value does not produce some excessive braking torque obtained for the dry runway condition.

When which is greater than the maximum rolling water is on the surface, the tread design be- torque and particular care must be taken when comes of greater importance to maintain con- the runway conditions produce low values of tact between the rubber and the runway and friction coefficient and when the normal force prevent a film of water from lubricating the on the braking surfaces is small. When it is surfaces. When the rainfall is light, the peak difficult to perceive or distinguish a skidding value for friction coefficient is on the order of condition, the value of an antiskid or auto- 0.5. With heavy rainfall it is more likely that sufficient water will stand to form a liquid matic braking system will be appreciated.

NAVWEPS OD4OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PRO&EMS OF FLYING I NORMAL

FORCE

DRY CONCRETE COEFFICIENT OF 0.6 FRICTION \- --CONCRETE \ \ LIGHT RAIN \ 0.4 \ F/N HEAVY RAIN 0.2 - ROLLING LOCKED i- WHEEL \ WHEEL

I

IO 20 30 40 50 60 70 80 90 100 PER CENT SLIP I Figure 6.7 1. Braking Perhnance NAVWEPS DD-BOT-BO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING the airplane lift may be considerable immedi- BRAKING TECHNIQUE. It must be clearly distinguished that the techniques for ately after landing, retraction of flaps or ex- tension of spoilers immediately after touch- minimum stop distance may differ greatly from the techniques required to minimize wear and down will reduce the wing lift and increase the normal force on the landing gear. With tear on the tires and brakes. For the majority the retraction of flaps, the reduced drag is more of airplane configurations, brakes will provide than compensated for by the increased braking the most important source of deceleration for all but the most severe of icy runway condi- friction force afforded by the increased normal tions. Of course, aerodynamic drag is very force on the braking surfaces.

durable and should be utilized to decelerate the A second possible factor to control braking airplane if the runway is long enough and the effectiveness is the distribution of normal force Aerodynamic drag will be drag high enough. to the landing gear surfaces. The nose wheel of importance only for the initial 20 to 30 per- of the tricycle landing gear configuration usu- cent of speed reduction from the point of touch- ally has no brakes and any normal force dis- down. At speeds less than 60 to 70 percent of tributed to this wheel is useful only for pro- the landing speed, aerodynamic drag is of little ducing side force for control of the airplane.

consequence and brakes will be the principal Under conditions of deceleration, the nose- source of deceleration regardless of the runway down pitching moment created by the friction surface. For the conditions of minimum land- force and the inertia force tends to transfer ing distance, aerodynamic drag will be a prin- a significant amount of normal force to nose cipal source of deceleration only for the initial wheel where it is unavailable to assist in portion of landing roll for very high drag con- creating friction force. For the instant after figurations on very poor runway conditions. landing touchdown, the pilot may control These cases are quite limited so considerable this condition to some extent and regain or importance must be assigned to proper use of increase the normal force on the main wheels.

the brakes to produce maximum effectiveness. After touchdown, the nose is lowered until the In order to provide the maximum possible nose wheel contacts the runway then brakes retarding force, effort must be directed to pro- are applied while the stick is eased back with- duce the maximum normal force on the braking out lifting the nose wheel back off the runway.

surfaces. (See figure 6.11.) The pilot will be The effect is to minimize the normal force on able to influence the normal force on the brak- the nose wheel and increase the normal force ing surfaces during the initial part of the land- on braking surfaces. While the principal ing roll when dynamic pressure is large and effect is to transfer normal force to the main aerodynamic forces and moments are of conse- wheels, there may be a significant increase in quence.

During this portion of the landing normal force due to a reduction in net lift, i.e., roll the pilot can control the airplane lift and tail download is noticeable. This reduction the distribution of normal force to the landing in net lift tends to be particular to tailless or gears.

short coupled airplane configurations.

First to consider is that any positive lift will The combined effect of flap retraction and support a part of the airplane weight and reduce aft stickis a significant increase in braking the normal force on the landing gear. Of friction force. Of course, the flaps should not course, for the purposes of braking friction, it be retracted while still airborne and aft stick would be to advantage to create negative lift should be used just enough without lifting but this is not the usual capability of the air- the nosewheel off the runway. These tech- plane with the tricycle landing gear. niques are to no avail if proper use of the Since NAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING One of the important factors affecting the brakes does not produce the maximum coefi- landing roll distance is landing touchdown cient of friction. The incipient skid condi- tion will produce the maximum coefficient of speed. Any excess velocity at landing causes a large increase in the minimum stop distance friction but this peak is difficult to recognize and maintain without an antiskid system. and it is necessary that the pilot control the Judicious use of the brakes is necessary to landing precisely so to land at the appropriate obtain the peak coefficient of friction but not speed. When landing on the dry, hard surface runway of adequate length, a tendency is to develop a skid or locked wheel which could take advantage of any excess runway and cause tire failure, loss of control, or consider- allow the airplane to touchdown with excess able reduction in the friction coefficient.

speed. Of course, such- errors in technique The capacity of the brakes must be sufficient cannot be tolerated and the pilot must strive to create adequate braking torque and produce for precision in all landings. Immediately the high coefficient of friction. In addition, after touchdown, the airp1ar.e lift may be the brakes must be capable of withstanding considerable and the normal force on the the heat generated without fading or losing braking surfaces quite low. Thus, if excessive effectiveness. The most critical requirements braking torque is applied, the wheel may lock of the brakes occur during landing at the easily at high speeds and tire failure may take maximum allowable landing weight.

place suddenly.

TYPICAL ERRORS OF BRAKING TECH- Landing on a wet or icy runway requires NIQUE. Errors in braking technique are usu- judicious use of the brakes because of the re- ally coincident with errors of other sorts. For duction in the maximum coefficient of friction.

example, if the pilot lands an airplane with excessive airspeed, poor braking technique Because of reduction in the maximum attain- could accompany the original error to produce able value of the coefficient of friction, the an unsafe situation. One common error of pilot must anticipate an increase in the mini- of braking technique is the application of mum landing distance above that applicable braking torque in excess of the maximum for the dry runway conditions. When there possible rolling torque. The result will be is considerable water or ice on rhe runway, an that the wheel decelerates and locks and the increase in landing distance on the order of 40 skid reduces the coefficient of friction, lowers to 100 percent must be expected for similar the capability for side force, and enhances the conditions of gross weight, density altitude, possibility of tire failure. If maximum brak- Unfortunately, the conditions wind, etc.

ing is necessary, caution must be used to likely to produce poor braking action also modulate the braking torque to prevent lock- will cause high idle thrust of the turbojet ing the wheel and causing a skid. On the engine and the extreme case (smooth, glazed other hand, maximum coefficient of friction is ice or heavy rain) may dictate shutting down obtained at the incipient skidding condition the engine to effect a reasonable stopping so sufficient brake torque must be applied to produce maximum friction force. Intermittent distance.

braking serves no useful purpose when the REFUSAL SPEEDS, LINE SPEEDS, AND objective is maximum deceleration because the periods between brake application produce CRITICAL FIELD LENGTH only slight or negligible cooling.

Brake During takeoff, it is necessary to monitor should be applied smoothly and braking the performance of the airplane and evaluate torque modulated at or near the peak value the acceleration to insure that the airplane will to insure that skid does not develop.

NAVWEPS 00401-80 APPLICATION OF AERODYNAlvllCS TO SPECIFIC PROBLEMS OF FLYING achieve the takeoff speed in the specified dis- at the refusal speed as the power is reduced tance. If it is apparent that the airplane is and braking action is initiated.

not accelerating normally or that the airplane During takeoff, the airplane could be accel- or powerplant is not functioning properly, erated to any speed up to the refusal speed, a decision must be made to refuse or continue then decelerated to a stop on- the runway takeoff. If the decision to refuse takeoff is remaining. Once past the refusal speed, the made early in the takeoff roll, no problem airplane cannot be brought to a stop on the runway remaining and the airplane is com- exists because the airplane has not gained much speed and a large portion of runway mitted to an unsafe stop. If takeoff is refused distance is unused. However, at speeds near when above the refusal speed, the only hope the takeoff speed, the airplane has used a large is for assistance from the arresting gear, run- portion of the takeoff distance and the distance way barrier, or an extensive overrun at the required to stop is appreciable. The problem end of the runway. This fact points to the which exists is to define the highest speed need for planning of the takeoff and the require- attained during takeoff acceleration from which ment to monitor the takeoff acceleration.

the airplane may be decelerated to a stop on If the refusal speed data are not available, the runway length remaining, i.e., the “refusal the following equations may be used to ap- proximate the refusal speed and distance: speed. ’’ The refusal speed will be a function of take- off performance, stopping performance, and the length of available runway. The ideal situation would be to have a runway length which exceeds the total distance required to accelerate to the takeoff speed then decelerate from the takeoff speed. In this case, the where refusal speed would exceed the takeoff speed V,= refusal speed and there would be little concern for the case S,= refusal distance of refused takeoff. While this may be the case for some instances, the usual case is that and for the appropriate takeoff configuration, the runway length is less than the “accelerate- V,*= takeoff speed stop” distance and the refusal speed is less than S,,= takeoff distance the takeoff speed. A graphical representation V,= landing speed of the refused takeoff condition is illustrated in figure 6.12 by a plot of velocity versus dis- J,=landing distance tance. At the beginning of the runway, the R. = runway length available airplane starts accelerating and the variation These approximate relationships do not ac- of velocity and distance is defined by the takeoff acceleration profile. The deceleration count for the time spent at the refusal point and profile describes the variation of velocity with must not be used in lieu of accurate handbook distance where the airplane is brought to a data.

stop at the end of the runway. The inter- In the case of the single-engine airplane, the section of the acceleration and deceleration pilot must monitor the takeoff performance to profiles then defines the refusal speed and the recognize malfunctions or lack of adequate ac- refusal distance along the runway. celeration prior to reaching the refusal speed.

Of course, an allowance must be made for the time spent Obviously, it is to advantage to recognize rhe 3’ 92 NAVWEPS OO-EOT-80 APP,LlCATlON OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING TAKEOFF SPEED TAKEOFF SPEED

REF”z

.DECELERATloN PROFlLE ACCELERATION PROFILE / F REFUSAL DISTANCE I P P c c TAKEOFF DISTANCE TAKEOFF DISTANCE RUNWAY AVAILABLE I VARIATION OF SPEED WITH DISTANCE FOR UNIFORMLY ACCELERATED MOTION DURING TAKEOFF ROLL O~mi-rrmLurauLurauupuLnUFFFPI.vm 10 20 30 40 60 i-o 60 90 PER CENT OF TAKEOFF DISTANCE Figure 6.12. Refused Take& and Takeof\ Velocity Variafion NAVWEPS DD4OT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYI’ NG possibility of a refused takeoff before exceed- points along the runway will allow the pilot ing the refusal speed. To this end, the pilot to monitor the takeoff performance and recog- Of course, must carefully evaluate airplane and power- nize a deficiency of acceleration.

plant performance and judge the acceleration a deficiency of acceleration must be recognized of the airplane by the use of “line speeds.” prior to reaching some point along the runway where takeoff cannot be safely achieved or The accelerated motion of the airplane during takeoff roll will define certain relationships be- refused tween velocity and distance when the acceler- The fundamental principles of refusal speeds ation of the airplane is normal. By comparison and line speeds are applicable equally well to of predicted and actual speeds at various points single-engine and multiengine airplanes. How- along the runway, the pilot can evaluate the ever, in the case of the multiengine airplane acceleration and assess the takeoff perfotm- additional consideration must be given to the axe. decision to continue or refuse takeoff when An example of an acceleration profile is engine failure occurs during the takeoff roll.

shown by the second illustration of figure 6.12, IF failure of one engine occurs prior to reaching where the variation of velocity and distance is the-refusal speed, takeoff should be discon- defined for the case of uniformly accelerated tinued and the airplane brought to a stop on motion, i.e., constant acceleration. While the the remaining runway. If failure of one engine case of uniformly accelerated motion doesnot c~curs after exceeding the refusal speed, the correspond exactly to the takeoff performance airplane is committed to continue takeoff with of all airplanes, it is sufficiently applicable to the remaining engines operative or an unsafe illustrate the principle of line speeds and ac- refused take&. Sn some cases, the remaining celeration checks. If the takeoff acceleration runway may not be sufficient to allow acceler- of the airplane were constant, the airplane ation to the takeoff speed and the airplane can would develop specific percentages of the take- neither takeoff or stop on the runway rcmain- off speed at specific percentages of the takeoff ibg. To facilitate consideration of this prob- distance. Representative values from figure lem, several specific defmitions are necessary.

6.12 are as follows: (1) Takeoff and initial climb speed: A speed, usually a fixed percentage above the stall speed, Pmmr 0,‘ &Ofl Pmmr of r‘ iko~ PInmr 0, &off diJh?%Z "docit~ rim at which the airplane will become airborne and 0 0 best clear obstacles immediately after takeoff.

25 so. 0 50.0 For a particular airplane in the takeoff con- SO 70.7 70.7 figuration, this speed (in EAS or CM) is a 75 86. 5 86.5 function of gross weight but in no circumstances 100 100 should it he less than the minimum directional As an example of this uniformly accelerated control speed for the critical asymmetrical motion, the airplane upon reaching the half- power condition. Generally, the takeoff and way point of takeoff roll would have spent initial climb speed is referred to as the “V,” 70.7 percent of the total takeoff time and ac- speed.

celerated to 70.7 percent of the takeoff speed.

(2) Critical engine jaih~~ speed: A speed If the airplane has not reached a specific speed achieved during the takeoff roll at which fail- at a specific distance, it is obvious that the ac- ure of one engine will require the same distance celeration is below the predicted value and the to continue accelerating with the operative en- airplane surely will not achieve the takeoff gines to accomplish safe takeoff or refuse speed in the specified takeoff distance. There- takeoff and decelerate to a stop utilizing the fore, properly computed line speeds at various airplane brakes. At critical engine failure NAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING RUNWAY LENGTH EQUAL TO CRITICAL FIELD LENGTH TAKEOFF d:;‘ , CLIMB SP LACCELERATION WITH 1 CRITICAL ENGINE q ENGINE INOPERATIVE FAILURE SPEED ACCELERATION \ WITH ALL ENGINES PROFILE OPERATIVE \ RUNWAY LENGTH RUNWAY LENGTH LESS THAN CRITICAL FIELD LENGTH MINIMUM SPEED NECESSAR TO CONTINUE TAKEOFF WITH ONE ENGINE IN LERATION WITH REFUSAL SPEE ONE ENGINE INOPERATIVE DECELERATION ACCELERATION TH ALL ENGINES OPERATIVE Figure 6.13. Critical Field Len& NAVWEPS OD-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING speed, the distance necessary to continue take- inadequate distance and the refusal speed is off with one engine inoperative is equal to the less than the minimum speed necessary to stopping distance. The critical engine failure continue a safe takeoff with one engine inoper- ative. If engine failure occurs below refusal speed is generally referred to as the “I’ ,” speed and it is a function of the same factors speed, the takeoff must be refused and adequate which determine the takeoff performance, e.g., distance remains to effect a stop on the runway.

density altitude, gross weight, temperature, If engine failure occurs above refusal speed humidity, etc. but below the minimum speed necessary to (3) &t&l jield kngrh: The runway length continue takeoff with one engine inoperative, necessary to accelerate with all engines opera- an accident is inevitable. Within this range tive to the critical engine failure speed (VJ of speeds, the airplane cannot effect a safe then continue accelerating to the takeoff and takeoff at L’ s with one engine inoperative or initial climb speed (VJ with one engine a safe stop on the remaining runway. For this inoperative and achieve safe takeoff or refuse reason, the pilot must properly plan the takeoff. By this definition, critical field takeoff and insure that the runway available length describes the minimum length of run- is equal to or greater than the critical field way necessary for safe operation of the multi- length. If the runway available is less than engine airplane. Obviously, the critical field the critical field length, there must be sufficient length is a function of the same factors affect- justification for the particular operation be- ing the takeoff distance of the airplane. cause of the hazardous consequences of engine The conditions of Vi, V,, and critical field failure between the refusal speed and the length are illustrated by figure 6.13. The minimum speed necessary to continue takeoff first illustration of figure 6.13 depicts the with one engine inoperative. Otherwise, the case where the runway length is equal to the gross weight of the airplane should be reduced rritical jield kngth. In this case, the airplane in attempt to decrease the critical field length could accelerate to Vi with all engines opera- to equal the available runway.

tive then either continue takeoff safely with SONIC “BOOMS’ one engine inoperative or refuse takeoff and From the standpoint of public relations decelerate to a stop on the remaining runway.

and the maintaining of friendly public support For this condition, an engine failure occurring for Naval Aviation, great care must be taken at lefs than I’ , speed dictates that takeoff must to prevent sonic booms in populated areas.

be refused because inadequate distance remains While the ordinary sonic boom does not carry to effect a safe takeoff at V, speed. However, any potential of physical damage, the disturb- at or below V, speed, adequate distance re- ance must be avoided because of the undesirable mains to bring the airplane to a stop. If annoyance and apprehension. As supersonic engine failure occurs at some speed greater flight becomes more commonplace and an than Vi speed, takeoff should be continued ordinary consequence of flying operations, the because adequate distance remains to accelerate prevention of sonic booms in populated areas to V, speed and effect a safe takeoff with one becomes a difficult and perplexing job.

engine inoperative. If engine failure occurs When the airplane is in supersonic flight, beyond Vi speed, inadequate distance remains the local pressure and velocity changes on the to brake the airplane to a stop on the runway, airplane surfaces are coincident with the The second illustration of figure 6.13 depicts the case where the ranway length is 1~s than formation of shock waves. The pressure jump through the shock waves in the immediate the titical field length. In this case, the term of “V,” speed is not applicable because of vicinity of the airplane surfaces is determined NAVWEPS OD-8OT-RO APP,LICATlON OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING by the local flow changes at these surfaces. be reflected and attenuated to some extent Of course, the strength of the shock waves depending on the character of the reflecting surface. Of course, if this attached wave form and the pressure jump through the wave is carried,across a populated area at the surface, decreases rapidly with distance away from the th.- population will experience the pressure airplane. While the pressure jump through the shock wave decreases with distance away waves as a sonic boom.

The intensity of the boom will depend on from the surface, it does not disappear com- many different factors. The characteristics of pletely and a measurable-but very small- the airplane generating the shock waves will pressure will exist at a considerable distance be of some importance since a large, high drag, from the airplane.

high gross weight airplane in flight at high Sound is transmitted through the air as a In the Mach number will be transferring a greater series of very weak pressure waves.

energy to the air mass. Flight altitude will ordinary range of audible frequencies, the have an important bearing on boom intensity threshold of audibility for intensity of sound since at high altitude the pressure jump across is for pressure waves with an approximate a given wave form is much less. In addition, R.M.S. value of pressure as low as 0.0000002 at high altitude a greater distance exists be- psf. Within this same range of frequencies, tween the generating source of the pressure the threshold of feeling for intensity of sound disturbance and the ground level and the is for pressure values with an approximate strength of the wave will have a greater dis- R.M.S. value of pressure of 0.2 to 0.5 psf.

tance in which to decay. The ordinary vari- Continuous sound at the threshold of feeling ation of temperature and density plus the is of the intensity to cause painful hearing.

natural turbulence of atmosphere will tend to Thus, the shock waves generated by an air- reflect or dissipate the shock wave generated plane in supersonic flight are capable of creat- at high altitude. However, in a stable, quies- ing audible sound and, in the extreme case, can cent atmosphere, the pressure wave from the be of a magnitude to cause considerable dis- airplane in high supersonic flight at high alti- turbance. Pressure jumps of 0.02 to 0.3 psf tude may be of an audible magnitude at lateral have been recorded during the passage of an distances as great as 10 to 30 miles. Thus, airplane in supersonic flight. As a result, supersonic flight over or adjacent to populated the sonic “booms” are the pressure waves areas will produce a sonic boom.

generated by the shock waves formed on the Actually, it is not necessary for any airplane airplane in supersonic flight.

to fly supersonic over or adjacent to a popu- The source of sonic booms is illustrated by lated area to create a sonic boom. This figure 6.14. When the airplane is in level supersonic flight, a pattern of shock waves is possibility is shown by the second illustration developed which is much dependent on the of figure 6.14 where an airplane decelerates to configuration and flight Mach number of the subsonic from a supersonic dive.

As the air- airplane. At a considerable distance from the plane slows to subsonic from supersonic speed, airplane, these shock waves tend to combine the airplane will release the leading bow and along two common fronts and extend away tail waves which formed as the airplane accel- from the airplane in a sort of conical surface.

erated from subsonic to supersonic speed. The The waves decrease in strength with distance release of these shock waves is analogous to away from the airplane but the pressure jump the case where a surface ship slows to below remains of an audible intensity for a consider- the wave propagation speed and releases the able distance from the airplane. If the wave extends to the ground or water surface, it will bow wave which then travels out ahead of NAVWEPS oo-8OT-80 APPUCATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYllNG AIRPLANE IN SUPERSONIC FLIGHT ‘ AIL WAVE FLIGHT Figure 6.14. Sonic Booms Revised JonuaV 1965 NAVWEPS OD-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING the ship. When the airplane slows to sub- are quite prone to sharp dynamic stresses and, sonic, the shock wave travels out ahead of the when .superimposed on the high residual airplane in a form which is somewhat spheri- stresses common to the products and building cal. Because there are density variations construction, slight but insignificant damage through the shock wave, the shock wave may result. Actually, the most objectionable feature of the sonic boom is the audibility and moving ahead of the airplane can cause aber- the anxiety or apprehension caused by the rations in light waves and it may appear.to sharp, loud noise which resembles a blast.

the pilot as if a large sheet of clear cellulose The pressure jump through the shock waves or plastic were in front of the airplane. In addition, the density variation and initial in the immediate vicinity of the airplane is much greater than those common to the shape of the wave leaving the airplane may audible “booms” at ground level. Thus, cause reflection of sunlight which would appear as a sudden, brilliant “flash” to the airplanes in close formation at supersonic speeds may encounter considerable interference pilot.

Of course, the wave released by decelerating between airplanes. In addition, to eliminate to subsonic speed can travel out ahead of the even the most remote possibility of structural airplane and traverse a populated area to cause damage, a high speed airplane should not a sonic boom. The initial direction of the make a supersonic pass close to a large air- released wave will be the flight path of the plane which may have low limit load factor airplane at the instant it decelerates to sub- and be prone to be easily disturbed or damaged sonic speed. To be sure, the released wave by a strong pressure wave.

should not be aimed in the direction of a popu- HELICOPTER PROBLEMS lated area, even if a considerable distance away. There are instances where a released The main difference between helicopter and an airplane is the main source of lift. The wave has been of an audible magnitude as far airplane derives its lift from a fixed airfoil as 30 to 40 miles ahead of the point of release.

surface while the helicopter derives lift from The released pressure wave will be of greatest intensity when created by a large, high drag a rotating airfoil called the rotor. Hence, the aircraft will be classified as either “fixed- configuration at low altitude. Since the wave wing” or “rotating wing.” The word “heli- intensity decreases rapidly with distance away copter” from the source, the boom will be of strongest is derived from the Greek words meaning “helical wing” or “rotating wing. ” audibility near the point of release.

Lift generation, by a “rotating wing” enables It should become apparent that sonic booms the helicopter to accomplish its unique mission are a byproduct of supersonic aviation and, with supersonic flight becoming more common- of hovering motionless in the air, taking off place, the problem is more perplexing. The and landing in a confined or restricted area, and autorotating to a safe landing following potential of sonic booms is mostly of the audible nature and nuisance of the disturbance. a power failure. Lift generation by “rotating wing’ ’ is The damage potential of the ordinary sonic also responsible for some of the boom is quite small and the principal effects unusual problems the helicopter can encounter.

are confined to structures which are extremely Since the helicopter problems are due to par- brittle, low strength, and have characteristic ticular nature of .the rotor aerodynamics, the high residual stresses. In other words, only basic flow conditions within the rotor must be the extremes of pressure waves generated by considered in detail. For simplicity, the airplanes in flight could possibly cause cracked initial discussion will consider only the hover- plaster and window glass. Such materials ing rotor. Although the term hovering NAVWEPS DO-ROT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING usually means remaining over a particular Thus, the velocity due to rotation varies line- spot on the ground, it shall be considered arly from zero at the hub to a maximum at here as flight at zero airspeed. This is necessary the tip. A typical blade section with the because the aerodynamic characteristics of the forces acting on it is shown in figure 6.15.

rotor depend on its motion with respect to A summation of the forces acting perpen- dicular to the plane of rotation (tip path plane) the air and not the ground. Hovering in a 20 will determine the rotor thrust (or lift) char- knot wind is aerodynamically equivalent to flying at an airspeed of 20 knots in a no-wind acteristics while summation of the moments and the characteristics will be resulting from forces acting in the plane of condition, identical in the two conditions. rotation will determine the rotor torque char- The first point to realize is that the rotor is acteristics. As a result of this analysis, the subject to the same physical laws of aero- rotor thrust (or lift) is found to be propoc- dynamics and motion that govern flight of tional to the air density, a nondimensional the fixed-wing airplane. thrust coefficient, and the square of the tip The manner in which speed, or linear speed of the tip of the blade.

the rotor is subject to these laws is much more complicated due to the complex flow con- The thrust coefficient is a function of the aver- ditions. age blade section lift coefficient and the rotor Rotor lift can be explained by either of two solidity, which is the proportion of blade area methods. The first method, utilizing simple to disc area. The lift coefficient is identical to momentum theory based on Newton’ s Laws, that used in airplane aerodynamics while the merely states that lift results from the rotor solidity is analagous to the aspect ratio in air- accelerating a mass of air downward in the plane aerodynamics. The rotor torque is same way that the jet engine develops thrust found to be proportional to a nondimensional by accelerating a mass of air out the tailpipe. torque coefficient, the air density, the disc The second method of viewing rotor lift area, the square of the tip speed, and the blade concerns the pressure forces acting on the radius. The torque coefficient is dependent various sections of the blade from root to tip.

upon the average profile drag coefficient of the The simple momentum theory is useful in blades, the blade pitch angle, and the average determining only lift characteristics while lift coefficient of the blades. The torque can the “blade element” theory gives drag as be thought to result from components of profile well as lift characteristics and is useful in and induced drag forces acting on the blades, giving a picture of the forces at work on the similar to those on an airplane.

rotor. In the “blade element” theory, the As in the airplane, there is one angle of blade is divided up into “blade elements” as attack or blade pitch condition that will result Unfortu- shown in figure 6.15. The forces acting on in the most efficient operation.

each blade element are analyzed. Then the nately, the typical helicopter rotor operates forces on all elements are summed up to give at a near constant RPM and thus a constant the characteristics of the whole rotor. The true airspeed and cannot operate at this most relative wind acting on each segment is the eficient condition over a wide range of altitude resultant of two velocity components: (1) the and gross weight as the fixed-wing airplane.

velocity due CO the rotation of the blades The airplane is able to maintain an efficient about the hub and (2) the induced velocity, angle of attack at various altitudes, and gross or downwash velocity caused by the rotor.

weights by flying at various airspeeds but the the velocity due to rotation at a particular helicopter will operate with a near constant element is proportional to the rotor speed and rotor velocity and vary blade angle to contend the distance of the element from the rotor hub. with variations in altitude and gross weight.

MAVWEPS 00-BOT-80 APPLICATION OF AEBODYNAMICS TO SPECIFIC PBOBLEMS OF FLYING ROTOR BLADE ELEMENT RELATIVE - WIND COMPONENT ROTATION DUE TO ROTATION LOCAL FLOW AT BLADE ELEMENT VELOCITY DUE RESULTANT RELATIVE VELOCITY --_ TIP PATH PLANE Figure 6.75. Rotor Blade Flemenf Aerodynamics NAVWEPS oo-80~-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYl,NG said about rotor aerodynamics is equally valid If the rotor could operate within a wide for all types of rotor systems.

range of rotor speed, the efficiency and per- By analyzing the velocity components acting formance could be improved.

on the rotor blade sections from the blade With the previous relationships established root to the tip on both advancing and retreat- for the rotor in hovering flight, the effect of ing blades, a large variation of blade section forward flight br rotor translation can be con- angle of attack is found. Figure 6.16 illus- sidered. With forward flight, a third velocity trates a typical variation of the local blade component, that tif the forward velocity of the angle of attack for various spanwise positions helicopter, must be considered in determining along the advancing and retreating blades of the relative wind acting on each rotor blade a rotor at high forward speed. There is a element. Since the entire rotor moves with the region of positive angles of attack resulting helicopter, the velocity of air passing over in positive lift over the entire advancing blade.

each of the elements on the advancfng blade is increased by the forward speed of the heli- Immediately next to the hub of the retreating blade there is an area of reversed flow where copter and the velocity of the air passing over the velocity due to the forward motion of the each element of the retreating blade is de- helicopter is greater than the rearward velocity creased by the same amount. This is shown in due to the blade rotation. The next area is a figure 6.16.

negative stall region where, although the If the blade angles of attack on both advanc- flow is in the proper direction relative the ing and retreating blades remained the same blade, the angle of attack exceeds that for as in hovering flight, the higher velocity on negative stall.

the advancing blade would cause a dissym- Progressing out the retreating blade, the blade angle of attack becomes less metry of lift and the helicopter would tend to negative, resulting in an area of negative lift.

roll to the left. It was this effect that created Then the blade angle becomes positive again, great difficu!ty during many early helicopter resulting in a positive lift region. The blade and autogiro projects. Juan De La Cierva was angle continues to increase, until near the tip the first to realize what caused this effect and of the retreating blade the positive stall angle he solved the problem by mounting his auto- of attack is exceeded, resulting in stalling of giro blades individually on flapping hinges, the tip section. This wide variation in blade thus allowing a flapping action to automati- section angles of attack results in a large cally correct the dissymmetry of lift that re- sulted from forward flight. This is the method variation in blade section lift and drag coefK- cients. The overall lift force on the left and still used in an articulated rotor system today.

right sides of the rotor disc are equalized by The see-saw, or semi-rigid, rotor corrects the cyclically varying the blade pitch as explained lift dissymmetry by rocking the entire hub and previously, but the drag variation is not blades about a gimbal joint, By rocking the eliminated. This drag variation causes a entire rotor system forward, the angle of at- shaking force on the rotor system and con- tack on the advancing blade is reduced and tributes to the vibration of the helicopter.

the angle of attack on the retreating blade is RETREATING BLADE STALL. Retreat- increased. The rigid rotor must produce cyclic ing blade stall results whenever the angle of variation of the blade pitch mechanically as attack of the blade exceeds the stall angle of the blade rotates to eliminate the lift dissym- attack of the blade section. This condition metry.

Irrespective of the method used to occurs in high speed flight at the tip of the correct the dissymmetry of lift, identical aero- retreating blade since, in order to develop the dynamic characteristics result. Thus, what is same lift as the advancing blade, the retreating NAVWEPS OO-ROT-RO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING VELOCITY DUE TO FORWARD FLIGHT RETREATING GLADE VELOCITY DUE TO ROTATION REVERSED FLOW NEGATIVE STALL NEGATIVE LIFT VELOCITY DUE

I

- POSITIVE STALL ANGLE -ADVANCING I/ BLADE LOCAL BLADE , nrc7 ANGLE OD- I OF HUB ATTACK ETRiATING BLADE -lop I _- - - NEGATIVE STALL ANGLE Figure 6.16. Rotor Flow Conditions in Forward f/i& NAVWEPS OD-80140 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING blade must operate at a greater angle of attack. following items depending on severity of the stall: If the blade pitch is increased or the forward speed increased the stalled portion of the rotor 1. Decrease collective pitch disc becomes larger with the stall progressing 2. Decrease airspeed 3. Increase rotor RPM in toward the hub from the tip of the retreating blade. When approximately 15 percent of 4. Decrease severity of accelerated ma- the rotor disc is stalled, control of the heli- newer or control deflection copter will be impossible. Flight tests have If the stall is severe enough to result in pitch-up, determined that control becomes marginal and forward cyclic to attempt to control pitch-up the stall is considered severe when the outer is ineffective and may aggravate the stall since one-quarter of the retreating blade is stalled. forward cyclic results in an increase in blade Retreating blade stall can be recognized by The angle of attack on the retreating blade.

rotor toughness, erratic stick forces, a vibration helicopter will automatically recover from and stick shake with a frequency determined a severe stall since the airspeed is decreased in by the number of blades and the rotor speed.

the nose high attitude but recovery can be Each of the blades of a three-bladed rotor will assisted by gradual reduction in collective stall as it passes through the stall region and pitch, increasing RPM, and leveling the heli- create a vibration with three beats pet rotor copter with pedal and cyclic stick.

revolution. Other evidence of retreating blade From the previous discussion, it is apparent stall is partial or complete loss of control or a that there is some degree of retreating blade pitch-up tendency which can be uncontrollable However, stall even at moderate airspeeds.

if the stall is severe.

the helicopter is able to perform satisfactorily Conditions favorable for the occurrence of until a sufficiently large area of the rotor disc retreating blade stall are those conditions that is stalled. Adequate warning of the impend- result in high retreating blade angles of attack. ing stall is present when the stall condition Each of the following conditions results in a is approached slowly. There is inadequate higher angle of attack on the retreating blade warni,ng of the stall only when the blade pitch and may contribute to retreating blade stall: or blade angle of attack is increased rapidly.

1. High airspeed Therefore, unintentional severe stall is most 2. Low totor RPM-operation at low likely to occur during abrupt control motions rotor RPM necessitates the use of or rapid accelerated maneuvers.

higher blade pitch to get a given COMPRESSIBILITY EFFECTS. The highest thrust from the rotor, thus a higher relative velocities occur at the tip of the ad- angle of attack vancing blade since the speed of the helicopter 3. High gross weight is added to the speed due to rotation at this 4. High density altitude point. When the Mach number of the tip 5. Accelerated flight, high load factor section of the advancing blade exceeds the 6. Flight through turbulent air or gusts- critical Mach number for the rotor blade sec- sharp updrafts result in temporary tion, compressibility effects result. The criti- increase in blade angle of attack cal Mach number is reduced by thick, highly 7. Excessive ot abrupt control deflections cambered airfoils and critical Mach number during maneuvers decreases with increased lift coefficient. Most Recovery from a stalled condition can be helicopter blades have symmetrical sections effected only by decreasing the blade angle of and therefore have relatively high critical attack below the stall angle. This can be Mach numbers at low lift coefhcients. Since accomplished by one or a combination of the the principal effects of compressibility are the NAVWEPS CID-ROT-R0 APP,LlCATlON OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYmING large increase in drag and rearward shift of the is upward through the rotor disc and there is airfoil aerodynamic center, compressibility ef- a vertical velocity component equal to the fects on the helicopter increase the power te- rate of descent of the helicopter. In addition, quired to maintain rotor RPM and cause rotor there is a velocity component due to rotation roughness, vibration, stick shake, and an un- of the rotor. The vector sum of these two desirable structural twisting of the blade. velocities is the relative wind for the blade Since compressibility effects become more element. The forces resulting from the relative severe at higher lift coefficients (higher blade wind on each particular blade section will angles of attack) and higher Mach numbers, provide the reason why the rotor will continue the following operating conditions represent to operate without power. First, consider, a the most adverse conditions from the stand- blade element near the tip of the blade as illus- point of compressibility: trated in figure 6.17. At this point there is 1. High airspeed a lift force acting perpendicular to the relative 2. High rotor RPM wind and a drag force acting parallel to the 3. High gross weight relative wind through the aerodynamic center.

4. High density altitude Since the rotation of the rotor is affected only 5. Low temperature-the speed of sound by forces acting in the plane of rotation, the is proportional to the square root of important forces are components of the lift the absolute temperature. Therefore, and drag force in the plane of rotation. In sonic velocity will be more easily this low angle of attack high speed tip section, obtained at low temperatures when the net in-plane force is a drag force which the sonic speed is lower.

would tend to retard the rotor. Next, con- 6. Turbulent air-sharp gusts momen- sider a blade section at about the half-span tarily increase the blade angle of position as illustrated in figure 6.17. In this attack and thus lower the critical case, the same forces are present, but the iti- Mach number to the point where plane component of lift force is greater than compressibility effects may be en- the drag force and this results in a net thrust countered on the blade.

or forward force in the plane of rotation which Compressibility effects will vanish by de- tends to drive the rotor.

creasing the blade pitch. The similarities in During a steady autorotation, there is a the critical conditions for retreating blade balance of torque from the forces along the stall and compressibility should be noticed blade so that the RPM is maintained in equi- but one basic difference must be appreciated- librium at some particular value. The region compressibility occurs at HIGH RPM while of the rotor disc where there is a net drag force retreating blade stall occurs at LOW RPM.

on the blade is called the “propeller region” Recovery technique is identical for both with and the region of the rotor disc where there the exception of RPM control.

is a net in-plane thrust force is called the AUTOROTATION CHARACTERISTICS.

“autorotation region.” These regions are One of the unique characteristics of helicopters shown for vertical autorotation and forward is their ability to take part of the energy of speed (or normal) autorotation in figure 6.17.

the airstream to keep the rotor turning and Forces acting on the rotor blades in forward glide down to a landing with no power.

flight autorotation are similar to those in Consideration of the rotor during a vertical vertical autorotation but the difference will autorotation will provide an understanding of consist mainly of shifts of the autorotation why the rotor continues to rotate without region to the left and the addition of reverse power. During autorotation, the flow of air NAVWEPS 004oT-80 APPLICATION 0~ AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING LIFT FORCES IN THE AUTOROTATION REGION FORCES IN THE LIFT PROPELLER REGION I I t

’ \ DRAG

RESULTANT VELOCITi DUE TO ROTe;TION FLIGHT 1 DIRECTION

I

UTOROTATION FORWARD FLIGHT VERTICAL AUTOROTATION AUTQRQTa-i\QN Figure 6.17. Rotor Autorotation Flaw Conditions NAVWEPS OO-BOT-BO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYl,NG flow and negative stall regions similar to the during autorotation descent would be obtained powered flight condition. at the flight condition which produces the Autorotation is essentially a stable flight greatest proportion between airspeed and rate condition. If external disturbances cause the of descent. Thus, a straight line from the rotor to slow down, the autorotation region of origin tangent to the curve will define the the disc automatically expands to restore the point for maximum autorotative glide dis- rotor speed to the original equilibrium condi- tance. This corresponds to Point B of figure tion. On the other hand, if an external 6.18. If the helicopter is being glided at the disturbance causes the rotor to speed up, the speed for maximum glide distance, a decrease propeller region automatically expands and in airspeed would reduce the rate of descent tends to accelerate the rotor to the original but the glide distance would decrease. If the equilibrium condition. Actually the stable helicopter is being glided at the speed for autorotation condition will exist only when minimum rate of descent, the rate of descent the autorotational speed is within certain (steady state) can not be reduced but the glide limits. If the rotor speed is allowed to slow distance can be increased by increasing the some excessive amount, then the rotor becomes glide speed to that for maximum distance.

unstable and the RPM will decrease even Weight and wind affect the glide character- further unless the pilot immediately corrects istics of a helicopter the same way an airplane the condition by proper control action. is affected. Ideally, the helicopter autorotates In case of engine failure, the fixed-wing at a higher equivalent airspeed at higher gross airplane will be glided at maximum lift-drag weight or when autorotating into a headwind.

ratio to produce maximum glide distance. If In addition to aerodynamic forces which act minimum rate of descent is desired in power-off on the rotor during autorotation, inertia forces flight rather than maximum glide distance, the are also important. These effects are usually fixed-wing airplane will be flown at some associated with the pilot’ s response time be- lower airspeed. Actually, the minimum rate cause the rate a pilot reacts to a power failure of descent will occur at minimum power is quite critical. The time necessary to reduce required. The helicopter exhibits similar char- collective pitch and enter autorotation be- acteristics but ordinarily the best autorota~tion comes critical if the rotor inertia characteristics speed may be considered that speed that results are such as to allow the rotor to slow down to in the minimum rate of descent rather than a dangerous level before the pilot can react.

maximum glide distance. The aerodynamic With power on, the blade pitch is relatively condition of the rotor which produces mini- high and the engine supplies enough torque to mum rate of descent is: overcome the drag of the blades. At the instant of power failure the blades are at a high Maximum ratio of pitch with high drag. If there is no engine (Mean blade lift coetIicient)3” torque to maintain the RPM, the rotor will Mean blade drag coefficient decelerate depending on the rotor torque and rotor inertia. If the rotor has high rotational It is this ratio which determines the auto- energy the rotor will lose RPM less rapidly, rotation rate of descent. Figure 6.18 illus- giving the pilot more time to reduce collective trates the variation of autorotation rate of pitch and enter autorotation. If the rotor has descent with equivalent airspeed for a typical low rotational energy, the rotor will lose RPM helicopter. Point A on this curve defines the rapidly and the pilot may not be able to react point which produces autorotation with mini- quickly enough to prevent a serious loss of rotor RPM. Once the collective pitch is at mum rate of descent. Maximum glide distance PdAVWEPS OD-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING when the landing surface is smooth. In ad- the low pitch limit, the rotor RPM can be in- dition, various stability and control character- creased only by a sacrifice in altitude or air- istics of a helicopter may produce critical con- speed. If insufficient altitude is available to ditions in this area. The critical areas of the exchange for rotor speed, a hard landing is “dead man’ s curve” should be avoided unless inevitable. SufIicient rotor rotational energy such operation is a specific mission require- must be available to permit adding collective pitch to reduce the helicopter’ s rate of descent ment.

POWER SETTLING. The term “power before final ground contact.

settling” has been used to describe a variety of In the case of most small helicopters, at True flight conditions of the helicopter.

least 300 feet of altitude is necessary for an average pilot to set up a steady autorotation “power settling” occurs only when the heli- and land the helicopter safely without damage. copter rotor is operating in a rotary flow This minimum becomes 500 to 600 feet for the condition called the “vortex ring state.” larger helicopters, and will be even greater for The flow through the rotor in the “vortex ring state” is upward near the center of the helicopters with increased disc loading. These characteristics are usually presented in the disc and downward in the outer portion, flight handbook in the form of a “dead man’ s resulting in a condition of zero net thrust on curve” which shows the combinations of air- the rotor. If the rotor thrust is zero, the speed and altitude above the terrain where a helicopter is effectively free-falling and ex- successful autorotative landing would be dish- tremely high rates of descent can result.

cult, if not impossible. The downwash distribution within the A typical “dead man’ s curve” is shown in rotor is shown in figure 6.19 for the conditions figure 6.18. The most critical combinations of normal hovering and power settling. Part are due to low altitude and low airspeed illus- A of figure 6.19 illustrates the typical down- trated by area A of figure 6.18. Less critical wash distribution for hovering flight. If conditions exist at higher airspeeds because of sufficient power were not available to hover the greater energy available to set up a steady at this condition, the helicopter would begin autorotation. The lower limit of area A is a to settle at some rate of descent depending on finite altitude because the helicopter can be the deficiency of power. This rate of descent landed successfully if collective pitch is held would effectively decrease the downwash rather than reduced. In this specific case there throughout the rotor and result in a redistri- is not sufficient energy to reach a steady state bution of downwash similar to Part B of autorotation. The maximum altitude at which figure 6.19. At the outer portion of the this is possible is approximately ten feet on rotor disc, the local induced downwash veloc- most helicopters.

ity is greater than the rate of descent and Area B on the “dead man’ s curve” of figure downflow exists. At the center of the rotor 6.18 is critical because of ground contact flight disc, the rate of descent is greater than the speed or rate of descent, which is based on the local induced downwash velocity and the strength of the landing gear.

The average resultant flow is upward. This flow condition pilot may have difhculty in successfully flaring results in the rotary “vortex ring” state. By the helicopter from a high speed flight con- reference to the basic momentum theory it is dition without allowing the tail rotor to strike apparent that the rotor will produce no thrust the ground or contacting the ground at an ex- in this condition if the net mass flow of air cessive airspeed. A less critical zone is some- through the rotor is zero. It is important to times shown on this curve to indicate that note that the main lifting part of the rotor is higher ground contact speeds can be permitted not stalled. The rotor roughness and loss of NAVWEPS OO-BOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING RATE OF DESCENT, FPM POWER OFF MINIMUM RATE OF / DESCENT

I VELOCITY, KNOTS

DEAD MAN’ S CURVE SAFE ALTITUDE ~ ABOVE TERRAIN F T.

VELOCITY, KNOTS Figure 6.1%. Autorotation Characteristics NAVWEPS DO-BOT-BO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING VARIATION OF INDUCED VELOCITY ALONG THE BLADE SPAN DURING HOVERING FLIGHT VARIATION OF INDUCED VELOCITY ALONG THE BLADE SPAN DURING VORTEX RING STATE VORTEX RING STATE Figure 6.79. Rotor Downwash Distribution NAVWEPS OD-EOT-80 APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYING control experienced during “power settling” When normal autorotation has been estab- results from the turbulent rotational flow on lished, a normal power recovery from the auto- rotation can be made. While such a recovery the blades and the unsteady shifting of the flow in and out spanwise along the blade. technique is effective, considerable altitude There is an area of positive thrust in the outer may be lost. Hence, diving out of the power portion of the rotor as a result of the mass of settling condition provides the most favorable air accelerated downward and an area of means of recovery.

negative thrust at the center of the rotor as a Actually, real instances of true “power result of the mass of air flowing upward. The settling” are quite rare. A condition often rotor is stalled only near the hub but no described incorrectly as “power settling” is important effect is contributed because of the merely a high sink rate as a result of insufficient low local velocities. power to terminate an approach to landing.

This situation frequently occurs during high Operation in the “vortex ring” state is a transient condition and the helicopter will gross weight or high density altitude operation.

seek equilibrium by descending. As the heli- The flow conditions within the rotor are quite normal and there is merely insufficient power copter descends, a greater upflow through the disc results until eventually the flow is entirely to reduce rate of descent and terminate an up through the rotor and the rotor enters auto- approach. Such a situation becomes more rotation where lower rates of descent can be critical with a steep approach since the more achieved. Unfortunately, considerable alti- rapid descent will require more power to tude will be lost before the autorotative type terminate the approach.

of flow is achieved and a positive recovery THE FLIGHT HANDBOOK technique must be applied to minimize the loss of altitude. “Power settling” can be recog- For the professional aviator, there are few nized by rotor roughness, loss of control due documents which are as important as the air- to the turbulent rotational flow, and a very plane flight handbook. The information and high rate of descent (as high as 3,000 fpm).

data contained in the various sections of the It is most likely to be encountered inadvert- flight handbook provide the basis for safe and ently when attempting to hover when suf- effective operation of the airplane.

ficient power is not available because of high Various sections of the flight handbook are gross weight or high density altitude.

devoted to the following subjects: Recovery from “power settling” can be ac- complished by getting the rotor out of the (1) Equipment and Systems. With the me- “vortex ring state.” If the condition is en- chanical complexity of the modern airplane, countered with low power, rapid application it is imperative that the pilot be familiar with of full power may increase the downwash suf- every item of the aircraft. Only through exact ficiently to get .the rotor out of the condition.

knowledge of the equipment can the pilot If the condition is encountered at high or properly operate the airplane and contend maximum power or, if maximum power does with malfunctions.

not effect a recovery, increasing airspeed by (2) Operating Procedures. Good procedures diving will result in recovery with minimum are mandatory to effect safe operation of the loss of altitude. This type of recovery is most airplane and its equipment. The complexity effective but adequate cyclic control must be of modern equipment dictates the use of special available. If cyclic control has been lost, re- and exact procedures of operation and any covery must be effected by reducing power and collective pitch and entering autorotation. haphazard or non-standard procedure is an NAVWEPS O&ROT-SO APPLICATION OF AERODYNAMICS TO SPECIFIC PROBLEMS OF FLYl.NG invitation for trouble of many sorts. The (5) Operating Data. The performance of normal and emergency procedures applicable each specific airplane defines its application to to each specific airplane will insure the various uses and missions. The handbook proper operation of the equipment. operating data must be available at all times (3) Operating Limitatiom. The operation of to properly plan and elnccate the flight of an the airplane and powerplant must be conducted aircraft. Constant reference to the operating within the established limitations. Failure data will insure safe and effective operation to do so will invite failure or malfunction of of the airplane.

the equipment and increase the operating cost Great time and effort are expended in the 1 or possibly cause an accident. preparation of the flight handbook to provide (4) Flight Characteristics. While all aircraft the most exact information, data, and pro- will have certain minimum requirements for cedures. Diligent study and continuous UC flying qualities, the actual peculiarities and of the flight handbook will ensure that the special features of specific airplanes will differ. greatest effectiveness is achieved from the These particular flight characteristics must be airplane while still operating within the well known and understood by the pilot. inherent capabilities of the design.

NAVWEPS 00-802-30 SELECTED REFERENCES

SELECTED REFERENCES

1. Dommasch, Sherby, and Connolly “Airplane Aerodynamics” Pitman Publishing Co.

2d Edition, 1957 2. Perkins and Hage “Airplane Performance, Stability, and Control” John Wiley and Sons 3. E. A. Bonney “Engineering Supersonic Aerodynamics” McGraw-Hill Book Co.

4. Hurt, Vernon, and Martin “Aeronautical Engineering, Section I, Manual of Instruction, Avi- ation Safety Officer Course” University of Southern California 5. Fairchild, Magill, and Brye “Principles of Helicopter Engineering” University of Southern California Revised January 1965

NAVWEPS 00-8OT-80 INDEX

INDEX

P.W *IL*e accelerated motion. .......................... 182 brake horsepower, BHP. ......................

adverseyaw ................................. 291 braking performance. .................. .....

aerodynamic center. .......................... braking technique. ......... .... ..... .....

Aerodynamics, High Speed, Chapter III. ........ 201 center of gravity limitations. ........... 259,275 aileron reversal. .............................. 339 climb angle. .................................

airfoil climb performance. ...... ..... ...... ....

drag characteristics. ........................ climb rate. .. ........................ ......

lift characteristics. ......................... 27 components of the gas turbine. ................

pitching moments. 47 terminology. 20 airspeed compressor stall or surge. .. .... ...... ....

calibrated. 10 indicated .................................. 10 control, Stability and Control, Chapter IV. ......

mcasurcmcnt ...............................

fT”C ....................................... 14 critical altitude. .......... ..................

altitude density altitude. 4 pressure altitude. ........................... 4 cumulative damage. ... ..... ...... .....

primary control of altitude. ............... 154,352 cycle of operation angle of attack. 22 angle of attack indicator. .....................

angleofbank ............................... 37,176 Application of Aerodynamics to Specific Prob- lems of Flying, Chapter VI. ............... 349 detonation .. .:. ....................... 140, 194 aspect ratio. 61 asymmetrical Power, multi-engine airplane, atmosphere divergence ................................ 245, 342 autorotation characteristics. ................... 405 drag boundarylayer ............................... 52 dynamic pressure. .... ... .... ............ : 9 NAVWEPS 00-8OT-80 INDEX Psge endurance Pwe !a”ding gear configuration stability. ...........

landing performance. ...... ... .... ... 192 specific ................................. 158, 170 lateral co”trol, ...............................

engine failure effect on multiengine airplane. ............ 294, 376 lift power off glide performance. ................

equilibrium conditions. .......................

equivalent airspeed, EAT.

equation ...................................

generation .. ............ ............ ... 16, 63 lift-drag ratio. ...............................

expansionwave ..............................

factorofsafcty ...............................

linespeeds ...................................

load factor ................................ 37, 331 feathering and governing of propellers.

flap longitudinal aerodynamic effects. .......................

37, 43 control ....................................

typCS......................................

flutter .......................................

static stability. ...........................

force divergence. .............................

Mach number friction braking, .............................

critical Mach “umber. ......................

2!5 cocfficicnt. ................................

maneuvering load factor .....................

frost ........................................

fuel qualities. ................................

glide performance. ...........................

governing apparatus, turbine engines.

governing and feathering of propellers. .........

gusts and wind shear. .................... ...

operating limitations gust load factor. ...........................

propellers, groundeffect .................................

heating, aerodynamic. ........................

helicopter, problems. .........................

helicopter stability and control. .............

high lift devices .. ...... ............

... ., ., 39 parasite area, equivalent. .... ..............

parasitedrag performance, Airplane Performance, Chapter II.

pilot induced oscillarion.

ice ..........................................

373 pitching moment indicated airspeed, IAS. .........

airfoil.

induced longitudinal. .................. ........ 249, 251 angle of attack. ...........................

pitch-up .....................................

drag. ....................................

pitot-static system. ...........

drag coefficient. ...........................

planform effects. .............................

power effects on stability. .....................

inertia coupling. ................... .......

power off stability ... ........................

315 259 inlets, supersonic powerplant.

interference between airplanes in flight.

........ 383 power settling. ................... ........ 4c3 items of airplane performance. ................. preignition, 140 ........... .... ....

landing and ground loads. .................... pressure altitude. .... ... ... ..

landing flare and touchdown, ............. pressure distribution. .....

NAVWEPS OO-EOT-80 INDEX Page proprllcrs lmd seal pattern.

................................

14s stall rec”very.

efficiency ..................................

standard atmosphere.

.........................

static strength.

...............................

propulsion streamline pattern.

etlicicncy ..................................

supercharging.

...............................

supersonic airfoil sections.

....................

sweepback ...................................

range performance. $ .................... .....

advantages ..................................

off-optimum conditions. ....................

disadvantages.

.............................

propeller airplanes. 231 takeoff ......................................

turbojet airplanes ...........................

164 365 takeoff performance. ..........................

rate of climb. ................................

factors affecting performance.

................

reciprocating engines taper, taper ratio.

operating characteristics .....................

13s thrust augmentation. .........................

operating limitations. .......................

thrust required.

refusal speed, ....... .+: .................... :, .... ..............................

time limitations, powcrplants.

............... 128, 144 tetreating blade stall. 402 .........................

reversed command region. .....................

tip vortex.

Reynolds number. ............. :. ............. 54 ..................................

torque.

............................... ,;, ........

scale effect. 59 transition of boundary layer. 52 separation, airflow. ............................ 56 ..................

..

transon1c aIrfoIl scctlo”s.

......................

shock induced separation. .....................

turbojetengines ..............................

operating characteristics.

...................

operating limitations. ......................

sonic booms. ................................. turboprop, gas turbine-propeller combination. ...

396 132 spanwise lift distribution. ..................... 74 turbulence.................................332, 339 specificendurance ............................. turning performance.

.........................

170 178 specific fuel consumption turn rate, turn radius. ........................

reciprocating engine. ....................... unsymmetrical power, see asymmetrical power.

turbojet cngi.ne. ......................... viscosity. ...................................

specificrange ................................. V-n or V-g diagram.

.........................

158 334 speed, maximum and minimum. ............... vortex system. ...............................

spin,spinrecovery..........................291, 307 line or bound vortex.

Srability and Control, Chapter IV. ............. tip or trailing vortex. 64 ......................

stability w&r injection directional. ................................

reciprocating engine.

dynamic ...................................

turbojetengine .............................

helicopter ..................................

319 wavedrag................................. , 215 lateral .....................................

294 wind, effect on range.

longitudinal. ... : ..........................

250 windshear .................................

miscellaneous problems. .....................

yaw,adverse ................................

305 291 static ............................

.........

243 yawangle ...................................

stallspeeds .................................

35 YPWm”me”t ................................

t?evised Jcmuarv 1965