PILOT'S HANDBOOK of Aeronautical Knowledge

Basic Calculations 174 Effect of Wind I 7 4 Calculating Time, Speed, Distance, and Fuel Consumption 176 Converting Minutes to Equivalent Hours 176 Converting Knots to Miles per Hour 176 Fuel Consumption 177 The Wind Triangle 1 7 1 Data for Return Trip 179 Radio Navigation 183 VHF Omnidirectional Range (VOR) 183 Using the V O R 1 8 4 Tracking with Omni 185 Tips on Using the VOR 186 Automatic Direction Finder (ADF) 186 Flight Planning 1 8 8 Assembling Necessary Materials 189 Weather Check 1 8 9 In-Flight Visibility and the VFR Pilot l f i 9 Visibility vs. Time 1 9 0 How to Get a Briefing 1 9 2 Using the Aeronautical Chart 193 Use of the Airport/Facility Directory 194 Aircraft Flight Manual or Pilot's Operating Handbook 194 Using the Plotter, Computer, or Electronic Calculator, etc 194 VFR Flight Plan 195 C h a p t e r V I I I — F L I G H T I N F O R M A T I O N P U B L I C A T I O N S Flight Information Publication Policy 197 Low-Level Wind Shear 113 Wind and Pressure Representation on Surface Weather Maps 116 Moisture and Temperature 117 Relative Humidity 117 Temperature-Dewpoint Relationship 118 Methods by W h i c h Air Reaches the Saturation Point 118 Effect of Temperature on Air Density 118 Effect of Temperature on Flight 119 Effect of High Humidity on Air Density 119 Effect of High Humidity on Flight U 9 Dew and Frost 119 Fog 119 Clouds 119 Ceiling 123 Visibility 125 Precipitation 125 Air Masses and Fronts 125 Warm Front 125 Cold Front 126 Occluded Front 129 Aviation Weather Forecasts, Reports, and Weather Charts 134 Aviation Forecasts 135 Aviation Weather Reports 142 Surface Aviation Weather Reports 143 Pilot Weather Reports (PIREPS) 148 Radar Weather Reports (RAREPS) 148 Weather Charts 149 C h a p t e r V I — B A S I C C A L C U L A T I O N S U S I N G N A V I G A T I O N A L C O M P U T E R S O R E L E C T R O N I C C A L C U L A T O R S Determining En Route Time for a Flight 161 Determining Groundspeed During Flight 161 Determining Total Flight Time Available 162 Determining Total Fuel to be Used on a Flight 162 Determining True Airspeed 162 Converting Knots to Miles Per Hour 162 Solution of a W i n d Triangle Problem 162 Page viii Page Other Airspace Areas 212 Air Traffic Control 213 Services Available to Pilots 213 Airport Advisory Practices at Nontower Airports 214 Automatic Terminal Information Service (ATIS) 216 Radar Traffic Information Service 217 Terminal Control Area Operation 221 Radar Service for VFR Aircraft in Difficulty 222 Transponder Operation 222 Radio Communication 225 Phraseology and Techniques 225 Airport Operations 229 Tower-Controlled Airports 230 Nontower Airports 230 Light Signals 234 Communications 234 Departure Delays 235 Taxiing 235 Special V F R Clearances 236 Preflight 237 Flight Plan—VFR 238 Emergency Procedures 239 Emergency Locator Transmitters 240 Search and Rescue 241 Wake Turbulence 242 Medical Facts for Pilots 246 Good Operating Practices 251 A P P E N D I X I—Obtaining FAA Publications 257 Aeronautical Information and the National Airspace System 198 Air Navigation Radio Aids 198 General 198 Nondirectional Radio Beacon (NDB) 198 VHF Omnidirectional Range (VOR) 199 VOR Receiver Check 199 Tactical Air Navigation (TACAN) 200 VHF Omnidirectional Range/Tactical Air Navigation ( V 0 R T A C ) . . 200 Distance Measuring Equipment (DME) 201 Class of NAVAIDS 201 Maintenance of FAA NAVAIDS 202 Navaids with Voice 202 VHF/UHF Direction Finder 202 Radar 202 Air Traffic Control Radar Beacon System (ATCRBS) 203 Airport, Air Navigation Lighting and Marking Aids 204 Aeronautical (Light) Beacons 204 Rotating Beacon 204 Auxiliary Lights 204 Obstructions 205 Airway Beacons 205 Control of Lighting Systems 205 Visual Approach Slope Indicator (VASI) 206 Tri-Color Visual Approach Slope Indicator 207 Markings 208 Airspace 209 Uncontrolled Airspace 209 Controlled Airspace 210 Special Use Airspace 211 Illustrations Page Parts of the airplane xiv Figure 1-1. Forces acting on the airplane in flight 1 Figure 1-2. Typical airfoil sections . 2 Figure 1-3. Angle of attack and flightpath 3 Figure 1-4. Cross sectional view of an airfoil 4 Figure 1-5. Nomenclature of airfoil section 4 Figure 1-6. Component forces 4 Figure 1-7. Relationship between flightpath and relative wind 5 Figure 1-8. Vectors 5 Figure 1-9. Wing planforms 5 Figure 1-10. Bernoulli's Principle applied to airfoils 6 Figure 1-11. Wing deflecting the air downward 6 Figure 1-12. Relationship between relative wind, lift, and drag 7 Figure 1-13. Airplane suspended from the center of gravity 7 Figure 1-14. Drag acts parallel to and in the same direction as the relative wind 7 Figure 1-15. Form drag and skin friction drag 8 Figure 1-16. Typical airplane drag curves 8 Figure 1-17. Flow of air around a wing at various angles of attack . . . 9 Figure 1-18. Use of flaps increases lift and drag 10 Figure 1-19. View of wingtip twist 11 Figure 1-20. Slotted and plain wing II Figure 1-21. Stall strip 12 Figure 1-22. Effect of altitude, temperature, and humidity on takeoff run and rate of climb 13 Figure 1-23. Factors which cause left-turning tendency 14 Figure 1-24. Static stability 15 Figure 1-25. Relationship of oscillation and stability 16 Figure 1-26. Axes of rotation 17 Figure 1-27. Neutral stability 17 Figure 1-28. Negative stability 17 Figure 1-29. Positive stability 18 Figure 1-30. Effect of elevators 19 Figure 1-31. Effect of trim tabs 20 Figure 1-32. Effect of dihedral 20 Page Figure 1-33. Effect of sweepback 21 Figure 1-34. Keel effect 21 Figure 1-35. Effect of ailerons 22 Figure 1-36. Effect of rudder 22 Figure 1-37. Forces acting on an airplane in a bank 24 Figure 1-38. Load factors in turns 25 Figure 1-39. Load factor chart 26 Figure 1-40. Stall speed chart 26 Figure 1-41. Flight at airspeeds slower than cruise 28 Figure 1-42. Forces acting on an airplane in a climb 29 Figure 1-43. Power available vs. power required 29 Figure 1-44. Forces acting on an airplane in a glide 30 Figure 1-45. Forces acting on an airplane in a turn 31 F i g u r e 2 - 1 . Wingflaps 34 Figure 2 - 2 . Electrical system schematic 36 Figure 2 - 3 . Circuit breaker panel 36 Figure 2 - 4 . Ammeter 37 Figure 2-5. Basic parts of a reciprocating engine 38 Figure 2-6, Four strokes of the piston 39 Figure 2-7. A float-type carburetor 41 Figure 2-8. Formation of ice in the fuel intake system 42 Figure 2 - 9 . Normal combustion and explosive combustion 44 Figure 2-10. Factors affecting propellers 46 Figure 2 - 1 1 . Changes in propeller blade angle from hub to tip 46 Figure 2-12. Relationship of travel distance and speed of propeller blade 47 Figure 2-13. Effective and geometric propeller pitch 47 Figure 2-14. Certificate of aircraft registration 52 Figure 2-15. Standard airworthiness certificate 53 Figure 2-16. Preflight inspection chart 55 Figure 3 - 1 . Pitot-static system with instruments 59 Page Figure 3-2. Sensitive altimeter 60 Figure 3-3. Vertical speed indicator 62 Figure 3-4. Airspeed indicator 63 Figure 3-5. Airspeed indicator showing color-coded marking system. 64 Figure 3-6. Typical pump-driven vacuum system 66 Figure 3-7. Precession of a gyroscope 66 Figure 3-8. Turn and slip indicator 67 Figure 3-9. Indications of the ball in various types of turns 68 Figure 3-10. Turn coordinator , . 68 Figure 3-11. Heading indicator 69 Figure 3-12. Heading indicator 69 Figure 3-13. Attitude indicator 70 Figure 3-14. Various indications on the attitude indicator 70 Figure 3-15. Earth's magnetic field 71 Figure 3-16. Magnetic compass 71 Figure 4 - 1 . Lateral or longitudinal unbalance 74 Figure 4-2. Weight and balance illustrated 77 Figure 4-3. Determining moments 77 Figure 4-4. Establishing a balance 78 Figure 4 - 5 . Airplane weight and balance 79 Figure 4-6. Weight and balance data 80 Figure 4-7. Loading schedule placard 80 Figure 4-8. Airplane weight and balance diagram 82 Figure 4-9. Loading graph 82 Figure 4-10..C.G. moment envelope 82 Figure 4-11. Weight shifting diagram 83 Figure 4-12. Solution to proportion problem 84 Figure 4-13. Pressure altitude and density altitude chart 89 Figure 4-14. Determining density altitude 90 Figure 4-15. Takeoff performance data chart 91 Figure 4-16. A cruise performance chart 92 Figure 4-17. Cruise and range performance chart 93 Figure 4-18. Power setting table 94 Figure 4-19. Cruise performance chart 94 Figure 4-20. Climb data chart 95 Figure 4-21. Climb data chart 95 Page Figure 4-22. Maximum glide distance chart 95 Figure 4 - 2 3 . Crosswind and headwind component chart 96 Figure 4-24. Stall speed chart 96 Figure 4-25. Stall speed chart 96 Figure 4-26. A landing performance data chart 97 Figure 4-27. Determining speed for best rate and best angle of climb. 97 Figure 5 - 1 . Data flow in the Aviation Weather Service 100 Figure 5-2. The realm of flight 103 Figure 5-3. Barometric pressure at a weather station 104 Figure 5-4. Effect of atmospheric density at sea level 105 Figure 5-5. Takeoff distance increases with increase in field eleva tion 106 Figure 5-6. Effect of heat at the equator on atmospheric circulation. 107 Figure 5-7. Principal air currents in the Northern Hemisphere . . . . 108 Figure 5-8. Circulation of wind within a " l o w " 109 Figure 5-9. Use of favorable winds in flight 109 Figure 5-10. On-shore winds 110 Figure 5-11. Off-shore winds I l l Figure 5-12. Avoiding turbulence caused by convection currents . . . . 112 Figure 5-13. Varying surfaces affect the normal glidepath 113 Figure 5-14. Effect of descending currents on landings 114 Figure 5-15. Turbulence caused by obstructions 115 Figure 5-16. Effect of hills or mountains on air currents 116 Figure 5-17. Wind as shown on weather map 116 Figure 5-18. Flow of air around a " h i g h " 117 Figure 5-19. Temperature conversion chart 118 Figure 5-20. Cumulus clouds 120 Figure 5-21. Stratus-type clouds 121 Figure 5-22. Various types of bad weather clouds 122 Figure 5-23. Cross section of a cumulonimbus cloud (thunderhead) . . 124 Figure 5-24. A warm front 127 Figure 5-25. A cold front 128 Figure 5-26. Weather map wind shift line 129 Figure 5-27. An occluded front 130 Figure 5-28. Stages in the development of an occlusion 131 Figure 5-29. Development of an occlusion 132 x Page Page xi Figure 5-30. Clouds and precipitation accompanying a typical occlu sion 133 Figure 5-31. Section of typical weather map 134 Figure 5-32. Example of an area forecast . 135 Figure 5-33. Synopsis 136 Figure 5-34. Clouds and weather 137 Figure 5-35. Icing and freezing level 137 Figure 5-36. Terminal forecasts 138 Figure 5-37. Portions of hourly sequence report 139 Figure 5-38. Summary of sky cover designators 144 Figure 5-39. Ceiling designators 144 Figure 5-40. Weather symbols and meanings 145 Figure 5-41. Obstructions to vision—symbols and meanings 145 Figure 5-42. Precipitation intensity and intensity trend 148 Figure 5-43. Radar weather report 149 Figure 5-44. Contractions reporting operational status of radar 149 Figure 5-45. Symbols used on the weather map 150 Figure 5-46. Frontal symbols 151 Figure 5-47. Numerical classification of fronts 152 Figure 5-48. Section of a surface weather map as transmitted on fac simile 153 Figure 5-49. Weather depiction chart 154 Figure 5-50. Notations used on weather depiction charts 155 Figure 5-51. Radar summary chart 156 Figure 5-52. Symbols used for echo intensity and trend 157 Figure 5-53. Echo coverage symbols on the radar summary chart. . . . 157 Figure 5-54. Weather symbols 158 Figure 5-55. U.S. low-level significant weather prog (SFC-400MB). . . 159 Figure S-56. Some standard weather symbols 160 Figure 7-1. Index of sectional and V F R terminal area charts 166 Figure 7-2. Altitude, form, and slope o f terrain indicated on chart . . 167 Figure 7-3. Meridians and parallels 168 Figure 7-4. Time zones 169 Figure 7-5. The compass rose 169 Figure 7-6. Course determination by reference to meridians 170 Figure 7-7. Variation, the angle between a magnetic and geographic meridian 170 Figure 7-8. A typical isogonic chart 171 Figure 7-9. Areas of variation 172 Figure 7-10. Relationship between true heading, magnetic heading, and variation 172 Figure 7-11. Cause of deviation 173 Figure 7-12. Compass deviation card 173 Figure 7-13. Relationship between true, magnetic, and compass headings 174 Figure 7-14. Relationship between ground speed and airspeed 174 Figure 7-15. Effect of wind on flightpath 175 Figure 7-16. Effects of wind drift on maintaining desired course . . . . 176 Figure 7-17. Establishing a wind correction angle 176 Figure 7-18. Principle of the wind triangle 177 Figure 7-19. The wind triangle as it is drawn 177 Figure 7-20. Steps in drawing the wind triangle 178 Figure 7-21. Finding true heading by direct measurement 179 Figure 7-22. Finding true heading by the wind correction angle 179 Figure 7-23. Pilot's planning sheet and visual flight log 180 Figure 7-24. Computations for a round-trip flight 181 Figure 7-25. Steps in constructing the wind triangle 182 Figure 7-26. VHF transmission follows a line-of-sight course 184 Figure 7-27. Omnihead 184 Figure 7-28. Tracking a radial in a crosswind 185 Figure 7-29. ADF with fixed azimuth 187 Figure 7-30. ADF terms 187 Figure 7-31. ADF tracking 188 Figure 7-32. Rule of thumb 191 Figure 7-33. Cockpit cut-off angle 192 Figure 7-34. Flight plan form 195 Figure 7-35. Reverse side of flight plan form 196 Figure 8-1. VASI ^07 Figure 8-2. Basic runway Figure 8-3. Nonprecision instrument runway Figure 8-4. Precision instrument runway Figure 8-5. Threshold/displaced threshold markings 208 Figure 8-6. Overrun/stopway and blast pad area Figure 8-7. Closed runway or taxiway ^ Page Figure 8-8. STOL runway 209 Figure 8-9. Minimum visibility and distance from clouds—VFR . . . 209 Figure 8-10. Altitudes and flight levels 210 Figure 8-11. General dimensions of control zones, airport traffic areas, and vertical extent of airspace segments 211 Figure 8-12. Radar traffic information 218 Figure 8-13. Radar traffic information 218 Figure 8-14. Phonetic alphabet and Morse code 229 Figure 8-15. Traffic pattern 230 Page Figure 8-16. Recommended traffic patterns at nontower airports. . . . 232 Figure 8-17. Light signals 234 Figure 8-18. Vortex generation 242 Figure 8-19. Vortex roll 243 Figure 8-20. Vortices 243 Figure 8-21. Vortex sink 244 Figure 8-22. VorLex—no wind 244 Figure 8-23. Vortex movement in wind 244 xii VERTICAL Parts of the Airplane CHAPTER 1— There are certain laws of nature or physics that apply to any object that is lifted from the earth and moved through the air. T o analyze and predict airplane performance under various operating conditions, it is important that pilots gain as much knowledge as possible concerning the laws and principles that apply to flight. The principles of flight discussed in this chapter are intended primarily for beginning pilots, and are not intended as a detailed and complete explana tion of the complexities of aerodynamics. However, this information should encourage interested individuals to further their study. Forces Acting on the Airplane in Flight When in flight, there are certain favorable forces and other unfavorable forces acting on the airplane. It is the primary task of a pilot to control these forces so as to direct the airplane's speed and flightpath in a safe and efficient manner. T o do this the pilot must understand these forces and their effects. Among the aerodynamic forces acting on an airplane during flight, four are considered to be basic because they act upon the airplane during all maneuvers. These basic forces are lift, the upward acting force; weight (or gravity), the downward acting force; thrust, the forward acting force; and drag, the rearward acting, or retarding, force (Fig. 1-1). While in steady state flight the attitude, direction, and speed of the airplane will remain constant until one or more of the basic forces changes in magnitude. In unaccelerated flight (steady flight) the opposing forces are in equilibrium. Lift and thrust are considered as positive forces ( + ) , while weight and drag are considered as negative forces (—), and the sum of the op posing forces is zero. In other words, lift equals weight and thrust equals drag. When pressure is applied to the airplane controls, one or more of the basic forces change in magnitude and become greater than the opposing force, causing the airplane to accelerate or move in the direction of the ap plied force. For example, if power is applied (increasing thrust) and altitude is maintained, the airplane will accelerate. As speed increases, drag increases, until a point is reached where drag again equals thrust, and the airplane will continue in steady flight at a higher speed. As another example, if power is ap plied while in level flight, and a climb attitude is established, the force of lift would increase during the time back elevator pressure is applied, but after a OF FLIGHT steady state climb is established, the force of lift would be approximately equal to the force of weight. The airplane does not climb because lift is greater than in level flight, but because thrust is greater than drag, and because a component of thrust is developed which acts upward, perpendicular to the flightpath. Airplane designers make an effort to increase the performance of the airplane by increasing the efficiency of the desirable forces of lift and thrust while reducing, as much as possible, the undesirable forces of weight and drag. Nonetheless, compromise must be made to satisfy the function and desired performance of the airplane. Before discussing the four forces further, it will be helpful to define some of the terms used extensively in this section. a. Acceleration—the force involved in overcoming inertia, and which is defined as a change o f velocity per unit of time. It means changing speed and/or changing direction, including starting from rest (positive acceleration) and stopping (deceleration or negative acceleration). b . Airfoil—any surface, such as an airplane wing, designed to obtain reaction such as lift from the air through which it moves. Typical airfoil sec tions are shown in Fig. 1-2. Thrust I Weight Figure 1-1. Forces acting on the airplane inflight. I Sub-sonic Airfoil Later Airfoil Super-sonic AirfoM Clark "Y" Airfoil Super-sonic Airfoil Figure 1-2. Typical airfoil sections. c. Angle of Attack—the acute angle between the chord line o f the wing and the direction of the relative wind (Fig. 1-3). d. Angle of Incidence—the acute angle formed by the chord line of the wing and the longitudinal axis of the airplane (Fig. 1-4). It is determined dur ing the design o f the airplane and is the angle at which the wing is attached to the fuselage. Therefore, it is a fixed angle and cannot be changed by the pilot. Angle of incidence should not be confused with angle of attack. e. Camber—the curvature of the airfoil from the leading edge to the trail ing edge. "Upper camber" refers to the curvature of the upper surface; "lower camber" refers to the curvature of the lower surface; and "mean camber" refers to the mean line which is equidistant at all points between the upper and lower surfaces (Fig. 1 -5). f. Chord—an imaginary straight line drawn from the leading edge to the trailing edge o f a cross section of an airfoil (Fig. 1-4). g. Component—one of the various forces or parts o f a combination of forces. See Figure 1-6, which illustrates the component o f lift vertically and the component of drag horizontally. h. Relative Wind—the direction of the airflow produced by an object moving through the air (Fig. 1-7). The relative wind for an airplane in flight flows in a direction parallel with and opposite to the direction of flight 2 Figure 1-3. (Above) The angle of attack is the angle between the wing chord and the flightpath. (Below) The angle of attack is always based on the flightpath, not the ground. Therefore, the actual flightpath of the airplane determines the direction of the relative wind. i. Speed—the distance traveled in a certain time. j . Vectors—the graphic representation of a force drawn in a straight line which indicates direction by an arrow and magnitude by its length. When an object is being acted upon by two or more forces, the combined effect of these forces may be represented by a resultant vector. After the vectors have been resolved, the resultant may be measured to determine the direction and magnitude of the combined forces (Fig. 1-8). k. Velocity—the speed or rate of movement in a certain direction. !. Wing Area—the plan surface of the wing* which includes control sur faces and may include wing area covered by the fuselage (main body o f the airplane), and engine nacelles. m. Wing Planform—the shape or form of a wing as viewed from above. It 3 Figure 1-4. Cross sectional view of an airfoil may be long and tapered, short and rectangular, or various other shapes (Fig. 1-9). n. Wing Span—the maximum distance from wingtip to wingtip. Lift Lift is the upward force created by an airfoil when it is moved through the air. Although lift may be exerted to some extent by many external parts of the airplane, there are three principal airfoils on an airplane—the wing, pro peller, and horizontal tail surfaces. P o s i t i v e C a m b e r L e a d i n g E d g e -i " ^ 1 ( U p p e r ) L i n e M e a n — ' C a i r b e r L i n e - T r a i l i n g E d g e N e g a t i v e C a m b e r ( L o w e r ) Figure 1-5. Nomenclature of airfoil section. 4 Figure 1-6. Component forces. T o understand how an airplane wing produces lift, Bernoulli's Principle and one of Newton's Laws should be reviewed. Bernoulli's Principle states in part that "the internal pressure of a fluid (liquid or gas) decreases at points where the speed of the fluid increases." In other words, high speed flow is associated with low pressure, and low speed flow with high pressure. This principle is made apparent by changes in pressure of fluid flowing within a pipe where the inside diameter o f the pipe decreases, similar to a venturi tube (Fig. 1-10). In the wide section o f the gradually narrowing pipe the fluid flows at a lower speed, producing a higher pressure. As the pipe narrows it still contains the same amount o f fluid, but because the passageway is constricted the fluid flows at a higher speed pro ducing a lower pressure. This principle is also applicable to an airplane wing, since it is designed and constructed with a curve or camber (Fig. 1-10). When air flows along the upper wing surface it travels a greater distance in the same period o f time than the airflow along the lower wing surface. Therefore, as established by Bernoulli's Principle, the pressure above the wing is less than it is below the wing, generating a lift force over the upper curved surface of the wing in the direction of the low pressure. Since for every action there is an equal and opposite reaction (Newton's third law of motion), an additional upward force is generated as the lower sur face of the wing deflects the air downward (Fig. 1-11). Thus both the develop ment of low pressure above the wing and reaction to the force and direction CLIMB LEVEL FLIGHT Figure 1-7. Relationship between flightpath and relative wind. of air as it is deflected from the wing's lower surface contribute to the total lift generated. The amount of lift generated by the wing depends upon several factors: (1) speed of the wing through the air, (2) angle of attack, (3) planform of the wing, (4) wing area, and (5) the density of the air. Lift acts upward and perpendicular to the relative wind and to the wing LIFT VECTOR RESULTANT VECTOR span (Fig. 1-12). Although lift is generated over the entire wing, an imaginary point is established which represents the resultant of all lift forces. This single point is the center of lift, sometimes referred to as the center of pressure (CP). Tapered leading edge, straight trailing edge Swept back wingi Tapered leading and trailing edges Straight leading and trailing edges Delta w i n g Straight leading edge, tapered trailing edge Figure 1-8. Vectors. Figure 1-9. Wing planforms. 5 BERNOULLI'S PRINCIPLE, which explains how liff is created by an airplane's w i n g , is d e p i c t e d in these three diagrams. A fluid traveling through a constriction in a pipe (above) speeds u p , and at the same time the pressure it exerts on the pipe decreases. THE CONSTRICTED AIRFLOW shown here, formed by two opposed airplane wings, is analogous to the p i n c h e d - p i p e situation a t l e f t : air moving between the wings accelerates, and this increase in speed results in lower pressure between the curved surfaces. Figure 1-10. Bernoulli's Principle applied to airfoils. THE SAME PRINCIPLE applies when the air is distrubed b y a single w i n g . The a c c e l e r ating airflow over the top surface exerts less pressure than the airflow across the b o t t o m . It is this continuing difference in pressure that creates and sustains lift. Air Deflected downward The location o f the center of pressure relative to the center o f gravity (weight) is very important from the standpoint of airplane stability. Stability will be covered in more detail later. Gravity (Weight) Gravity is the downward force which tends to draw all bodies vertically toward the center of the earth. The airplane's center of gravi ty (CG) is the point on the airplane at which all weight is considered to be concentrated. It is the point of balance. For example, if an airplane were sus pended from a rope attached to the center of gravity, the airplane would balance (Fig. 1-13). The center of gravity is located along the longitudinal centerline of the airplane (imaginary line from the nose to the tail) and somewhere near the center o f lift of the wing. The location of the center of gravity depends upon the location and weight of the load placed in the airplane. This is controlled through weight and balance calculations made by the pilot prior to flight. The exact location of the center of gravity is important during flight, because of its effect on airplane stability and performance. Thrust The propeller, acting as an airfoil, produces the thrust, or forward force that drives the airplane through the air. It receives its power directly 6 LIFT Figure 1-12. Relationship between relative wind, lift, and drag. from the engine, and is designed to displace a large mass of air to the rear. It is this rearward displacement that develops the forward thrust that carries the airplane through the air. This thrust must be strong enough to counteract the forces of drag and to give the airplane the desired forward motion. The direc tion of this thrust force is referred to as the thrust line. Figure 1-13. Airplane suspended from the center of gravity. Drag Drag is the rearward acting force which resists the forward movement of the airplane through the air. Drag acts parallel to and in the same direction as the relative wind (Fig. 1-14). Every part of the airplane which is exposed to the air while the airplane is in motion produces some resistance and contributes to the total drag. Total drag may be classified into two main types: induced drag and parasite drag. Induced drag is the undesirable but unavoidable by-product of lift, and increases in direct proportion to increases in angle of attack. The greater the angle of attack up to the critical angle, the greater the amount of lift developed, and the greater the induced drag. The airflow around the wing is deflected downward, producing a rearward component to the lift vector which LIFT Figure 1-14. Drag acts parallel to and in the same direction as the relative wind. 7 is induced drag. The amount of air deflected downward increases greatly at higher angles of attack; therefore, the higher the angle of attack or the slower the airplane is flown, the greater the induced drag. Parasite drag is the resistance of the air produced by any part of the airplane that does not produce lift. Several factors affect parasite drag. When each factor is considered in dependently it must be assumed that other factors remain constant. These fac tors are (1) the more streamlined an object is, the less the parasite drag; (2) the more dense the air moving past the airplane, the greater the parasite drag; (3) the Larger the size of the object in the airstream, the greater the parasite drag; and (4) as speed increases, the amount of parasite drag increases. If the speed is doubled, four times as much drag is produced. Parasite drag can be further classified into form drag, skin friction, and interference drag. Form drag is caused by the frontal area of the airplane components being exposed to the airstream. A similar reaction is illustrated by Figure 1-15, where the side of flat plate is exposed to the airstream. This drag is caused by the form of the plate, and is the reason streamlining is Example of form drag. Example of skin friction drag. Figure 1-15. Form drag and skin friction drag. 8 necessary to increase airplane efficiency and speed. Figure 1-15 also il lustrates that when the face of the plate is parallel to the airstream the largest part of the drag is skin friction. Skin friction drag is caused by air passing over the airplane's surfaces, and increases considerably if the airplane surfaces are rough and dirty. Interference drag is caused by interference of the airflow between adja cent parts of the airplane such as the intersection of wings and tail sections with the fuselage. Fairings are used to streamline these intersections and decrease interference drag. It is the airplane total drag that determines the amount of thrust re quired at a given airspeed. Figure 1-16 illustrates the variation in parasite, in duced, and total drag with speed for a typical airplane in steady level flight. AIRSPEED (MPH) Figure 1-16. Typical airplane drag curves. Thrust mu6t equal drag in steady flight; therefore the curve for the total drag also represents the thrust required. Also note in Figure 1-16, that the airspeed at which minimum drag occurs is the same airspeed at which the maximum lift/drag ratio (L/D) takes place. At this point least power is required for both maximum lift and minimum total drag. This is important for determining maximum endurance and range for the airplane. The force of drag can be controlled to a certain extent by the pilot. Loading the airplane properly, retracting the landing gear and flaps when not used, and keeping the surface of the airplane clean, all help to reduce the total drag. Relationship Between Angle of Attack and Lift As stated previously, the angle of attack is the acute angle between the relative wind and the chord line of the wing. At small angles of attack most of the wing lift is a result of the difference in pressure between the upper and lower surfaces of the wing (Ber noulli's Principle). Additional lift is generated by the equal and opposite reac tion of the airstream being deflected downward from the wing (Newton's Law). As the angle of attack is increased, the airstream is forced to travel faster because of the greater distance over the upper surface o f the wing, creating a greater pressure differential between the upper and lower surfaces. At the same time the airstream is deflected downward at a greater angle, causing an increased opposite reaction. Both the increased pressure differential and in creased opposite reaction increase lift and also drag. Therefore as angle of at tack is increased, lift is increased up to the critical angle of attack (Figure 1-17). When the angle of attack is increased to approximately 18° to 2 0 ° (critical angle of attack) on most airfoils, the airstream can no longer follow the upper curvature of the wing because of the excessive change in direction. As the critical angle of attack is approached, the airstream begins separating from the rear of the upper wing surface. As the angle of attack is further in creased, the airstream is forced to flow straight back, away from the top sur face of the wing and from the area of highest camber. This causes a swirling or burbling of the air as it attempts to follow the upper surface of the wing. Figure 1-17. Flow of air around a wing at various angles of attack. 9 When the critical angle of attack is reached, the turbulent airflow, which ap peared near the trailing edge o f the wing at lower angles of attack, quickly spreads forward over the entire upper wing surface (Figure 1-17). This results in a sudden increase in pressure on the upper wing surface and a considerable loss of lift. Due to the loss of lift and increase in form drag, the remaining lift is insufficient to support the airplane, and the wing stalls. T o recover from a stall, the angle of attack must be decreased so that the airstream can once again flow smoothly over the wing surface. Remember that the angle of attack is the angle between the chord fine and the relative wind, not the chord line and the horizon. Therefore, an airplane can be stalled in any attitude of flight with respect to the horizon, if the angle of attack is in creased up to and beyond the critical angle of attack. Relationship of Thrust and Drag in Straight-and-Level Flight Dur ing straight-and-level flight, thrust and drag are equal in magnitude if a constant airspeed is being maintained. When the thrust of the propeller is in creased, thrust momentarily exceeds drag and the airspeed will increase, provided straight-and-level flight is maintained. As stated previously, with an increase in airspeed drag increases very rapidly. At some new and higher airspeed, thrust and drag forces again become equalized and speed again becomes constant. If all the available power is used, thrust will reach its maximum, airspeed will increase until drag equals thrust, and once again the airspeed will become constant This will be the top speed for that airplane in that configuration and attitude. When thrust becomes less than drag, the airplane will decelerate to a slower airspeed, provided straight-and-level flight is maintained, and thrust and drag again become equal Of course if the airspeed becomes too slow, or more precisely, if the angle of attack is too great, the airplane will stall. Relationship Between Lift and Weight in Straight-and-Level Flight A component of lift, the upward force on the wing, always acts perpendicular to the direction of the relative wind. In straight-and-level flight (constant altitude) lift counterbalances the airplane weight. When lift and weight are in equilibrium, the airplane neither gains nor loses altitude. If lift becomes less than weight, the airplane will enter a descent; if lift becomes greater than weight, the airplane will enter a climb. Once a steady-state climb or descent is established, the relationship of the four forces will no longer be the same as in straight-and-level flight. However, for all practical purposes lift still equals weight for small angles of climb or descent. 10 Factors Affecting Lift and Drag A number of the factors that influence lift and drag include: wing area, shape of the airfoil, angle of attack, speed of the air passing over the wing (airspeed), and density of the air moving over the wing. A change in any of these factors affects the relationship between lift and drag. When lift is in creased, drag ts increased, or when lift is decreased, drag is decreased. Effect of Wing Area on Lift and Drag The lift and drag acting on a wing are proportional to the wing area. This means that if the wing area is doubled, other variables remaining the same, the lift and drag created by the wing will be doubled. Effect of Airfoil Shape on Lift and Drag Generally, the more curvature there is to the upper surface of an airfoil, the more lift is produced (up to a point). High-lift wings have a large convex curvature on the upper surface and a concave lower surface. Most airplanes have wing flaps which, when lowered, cause an ordinary wing to approximate this condition by increasing the cur vature of the upper surface and creating a concave lower surface, thus increas ing lift on the wing (Figure 1-18). A lowered aileron also accomplishes this by Figure 1-18. Use of flaps increases lift and drag. increasing the curvature of a portion of the wing and thereby increasing the angle of attack, which in turn increases lift and also drag. A raised aileron reduces lift on the wing by decreasing the curvature of a portion of the wing and decreasing the angle of attack. The elevators can change the curvature and angle of attack o f the horizontal tail surfaces, changing the amount and direction of lift. The rudder accomplishes the same thing for the vertical tail surfaces. Many people believe that the only hazard of in-flight icing is the weight of the ice which forms on the wings. It is true that ice formation will increase weight, but equally important is that ice formation will alter the shape of the airfoil and adversely affect all aspects of airplane performance and control. As the ice forms on the airfoil, especially the leading edge, the flow of air over the wing is disrupted. This disruption of the smooth airflow causes the wing to lose part or all of its lifting efficiency. Also, drag is increased substan tially. Even a slight coating o f frost on the wings can prevent an airplane from becoming airborne because the smooth flow of air over the wing surface is disrupted and the lift capability of the wing is destroyed. Even more hazard ous is becoming airborne with frost on the wing because again performance and control could be adversely affected. This is why it is extremely important that all frost, snow, and ice be removed from the airplane before takeoff. Effect of Wing Design on Stall The type of wing design for a particular airplane depends almost entirety on the purpose for which that airplane is to be used. If speed is the prime consideration, a tapered wing is more desirable than a rectangular wing, but a tapered wing with no twist has undesirable stall characteristics. Assuming equal wing area, the tapered wing produces less drag than the Tectangular wing because there is less area at the Up of the tapered wing. The elliptical wing is more efficient (greater lift for the amount of drag), but does not have as good stall characteristics as the rectangular wing. T o achieve good stall characteristics, the root of the wing should stall first, with the stall pattern progressing outward to the tip. This type of stall pattern decreases undesirable rolling tendencies and increases lateral control when approaching a stall. It is undesirable that the wingtip stalls first, par ticularly if the tip of one wing stalls before the tip of the other wing, which usually happens. A desirable stall pattern can be accomplished by: (1) designing the wing Figure 1-19. View of wingtip twist. Ailerons are still effective even though wing root is in the stalled condition. with a twist so that the tip has a lower angle of incidence and therefore a lower angle of attack when the root of the wing approaches the critical angle of at tack (Fig. 1-19); (2) designing slots near the leading edge of the wingtip to allow air to flow smoothly over that part of the wing at higher angles of attack, therefore stalling the root of the wing first (Fig. 1-20); and (3) attaching stall or spoiler strips on the leading edge near the wing root. This strip breaks up the airflow at higher angles of attack and produces the desired effect of the root area of the wing stalling first (Fig. 1-21). Effect of Airspeed on Lift and Drag An increase in the velocity of the air passing over the wing (airspeed) increases lift and drag. Lift is increased Slotted wiog P , o I n w ! f > 9 Figure 1-20. Slotted and plain wings at equal angles of attack. 11 Figure 1-21. The stall strip ensures that the root section stalls first. because (1) the increased impact of the relative wind on the wing's lower sur face creates a greater amount of air being deflected downward; (2) the in creased speed of the relative wind over the upper surface creates a lower pressure on lop of the wing (Bernoulli's Principle); and (3) a greater pressure differential between the upper and lower wing surface is created. Drag is also increased, since any change that increases lift also increases drag. Tests show that lift and drag vary as the square of the velocity. The velocity of the air passing over the wing in flight is determined by the airspeed of the airplane. This means that if an airplane doubles its speed, it quadruples the lift and drag (assuming that the angle of attack remains the same). Effect of Air Density on Lift and Drag Lift and drag vary directly with the density of the air—as air density increases, lift and drag increase; as air density decreases, lift and drag decrease. Air density is affected by pressure, temperature, and humidity. At an altitude of 18,000 feet the density of the air is half the air density at sea level. Therefore, if an airplane is to maintain the same lift at high altitudes, the amount of air flowing over the wing must be the same as at lower altitudes. T o do this the speed of the air over the wings (airspeed) must be increased. This is why an airplane requires a longer takeoff distance to become airborne at higher altitudes than with similar conditions at lower altitudes (Fig. 1-22). Because air expands when heated, warm air is less dense than cool air. When other conditions remain the same, an airplane will require a longer takeoff run on a hoi day than on a cool day (Fig. 1-22). Because water vapor weighs less than an equal amount of dry air, moist air (high relative humidity) is less dense than dry air (low relative humidity). Therefore, when other conditions remain the same, the airplane will require a longer takeoff run on a humid day than on a dry day (Fig. 1-22). This is especially true on a hot, humid day because the air can hold much more water 12 vapor than on a cool day. The more moisture in the air, the less dense the air. Less dense air also produces other performance losses beside the loss of lift. Engine horsepower falls off and propeller efficiency decreases because of power loss and propeller blades—being airfoils—are less effective when air is less dense. Since the propeller is not pulling with the force and efficiency it would were the air dense, it takes longer to obtain the necessary forward speed to produce the required lift for takeoff—thus the airplane requires a longer takeoff run. The rate of climb will also be less for the same reasons. From the above discussion it is obvious that a pilot should beware of high, hot, and humid conditions—high altitudes, hot temperatures, and high moisture content (high relative humidity). A combination of these three condi tions could be disastrous, especially when combined with a short runway, a heavily loaded airplane, or other takeoff-limiting conditions. Turning Tendency (Torque Effect) By definition, "torque" is a force, or combination of forces, that produces or tends to produce a twisting or rotating motion of an airplane. An airplane propeller spinning clockwise, as seen from the rear, produces forces that tend to twist or rotate the airplane in the opposite direction, thus turning the airplane to the left Airplanes are designed in such a manner that the torque effect is not noticeable to the pilot when the airplane is in straight- and-levet flight with a cruise power setting. The effect of torque increases in direct proportion to engine power, airspeed, and airplane attitude. If the power setting is high, the airspeed slow, and the angle of attack high, the effect of torque is greater. During takeoffs and climbs, when the effect of torque is most pronounced, the pilot must apply sufficient right rudder pressure to counteract the left-turning tendency and maintain a straight takeoff path. Several forces are involved in the insistent tendency of an airplane of standard configuration to turn to the left. All of these forces are created by the rotating propeller. How they are actually created varies greatly from one ex planation to the next. Individual explanation of these forces is perhaps the best approach to understanding the reason for the left turning tendency. The four forces are: reactive force, spiraling slipstream, gyroscopic precession, and " P " factor. Reactive Force This is based on Newton's Law of action and reaction. Ap plying this law to an airplane with a propeller rotating in a clockwise direc- Figure 1-22. Effect of altitude, temperature, and humidity on takeoff run and rate of climb. 13 lion, as seen from the rear, a force is produced which tends to roll the entire airplane about its longitudinal axis in a counterclockwise direction. T o better understand this concept, consider the air through which the propeller rotates as a restraining force. This restraining force acts opposite to the direction the propeller rotates, creating a tendency for the airplane to roll to the left (Fig. 1-23). Spiraling Slipstream This theory is based on the reaction of the air to a rotating propeller blade. As the airplane propeller rotates through the air in a clockwise direction, as viewed from the rear, the propeller blade forces the air rearward in a spiraling clockwise direction o f flow around the fuselage. A por tion of this spiraling slipstream strikes the left side of the vertical stabilizer forcing the airplane's tail to the right and the nose to the left, causing the airplane to rotate around the vertical axis (Fig. 1-23). The portion of the spi raling slipstream traveling under the fuselage is not obstructed; therefore, creating a different resistance between the obstructed and the unobstructed flow which causes the left turning tendency. T O R Q U E R E A C T I O N PRECESSION ASCENDING DESCENDING LEFT BLADE RIGHT BLADE N O S E H I G H A • A T T I T U D E P - F A C T O R Figure 1-23. Factors which cause left-turning tendency. SLIPSTREAM 14 Gyroscopic Precession This theory is based on one of the gyroscopic properties which apply to any object spinning in space, even a rotating air plane propeller. As tbe nose of the airplane is raised or lowered, or moved left or right, a deflective force is applied to the spinning propeller which results in a reactive force known as precession. Precession is the resultant action or deflection of a spinning wheel (propeller in this case) when a force is applied to its rim. This resultant force occurs 9 0 ° ahead in the direction of rotation, and in the direction of the applied force (Fig. 1-23.). "P"Factor or Asymmetric Propeller Loading The effects of " P " fac tor or asymmetric propeller loading usually occur when the airplane is flown at a high angle of attack. The downward moving blade, which is on the right side of the propeller arc, as seen from the rear, has a higher angle of attack, greater action and reaction, and therefore higher thrust than the upward-moving blade on the left (Fig. 1-23). This results in a tendency for the airplane to yaw around the vertical axis to the left. Again this is most pronounced when the engine is operating at a high power setting and the airplane is flown at a high angle of attack. Corrections for Turning Tendency or Torque During Flight Since the airplane is flown in cruising flight most of the time, airplane manufac turers design the airplane with certain built-in corrections that counteract the left-turning tendency or torque effect during straight-and-level cruising flight only. This correction eliminates the necessity of applying constant rudder pressure. Because the effect of torque varies to such an extent during climbs and changes in angle of attack, it is impractical for airplane designers to cor rect for the effect of torque except during straight-and-level flight. Conse quently the pilot is provided other means such as rudder and trim controls to counteract the turning effect during conditions other than straight-and-level flight. Many manufacturers " c a n t " the airplane engine slightly so that the thrust line of the propeller points slightly to the right. This counteracts much of the left turning tendency of the airplane during various conditions of flight. Other manufacturers, when designing the airplane, increase the angle of in cidence of the left wing slightly, which increases the angle of attack and therefore increases the lift on this wing. The increased lift counteracts left- turning tendency in cruising flight. The increase in lift will, however, increase drag on the left wing and, to compensate for this, the vertical stabilizer is off set slightly to the left Torque corrections in flight conditions other than cruising flight must be accomplished by the pilot. This is done by applying sufficient rudder to over come the left-turning tendency. For example, in a straight climb, right rudder pressure is necessary to keep the airplane climbing straight. When thinking of "torque" such things as reactive force, spiraling slipstream, gyroscopic precession, and asymmetric propeller loading ( " P " factor) must be included, as well as any other power-induced forces that tend to turn the airplane. Airplane Stability Stability is the inherent ability of a body, after its equilibrium is dis turbed, to develop forces or moments that tend to return the body to its original position. In other words, a stable airplane will tend to return to the original condition of flight if disturbed by a force such as turbulent air. This means that a stable airplane is easy to fly; however, this does not meaii that a pilot can depend entirely on stability to return the airplane to the original condition. Even in the most stable airplanes, there are conditions that will re quire the use o f airplane controls to return the airplane to the desired at titude. However, a pilot will find that a well designed airplane requires less effort to control the airplane because of the inherent stability. Stability is classified into three types: (1) positive, (2) neutral, and (3) negative. Positive stability can be illustrated by a ball inside of a bowl (Fig. 1-24). If the ball is displaced from its normal resting place at the bottom of the bowl, it will eventually return to its original position at the bottom of the bowl. Neutral stability can be illustrated by a ball on a flat plane (Fig. 1-24). If the ball is displaced, it will come to rest at some new, neutral position and show no tendency to return to its original position. Negative stability is in fact instability and can be illustrated by a ball on the top of an inverted bowl (Fig. 1-24). Even the slightest displacement o f the ball will activate greater forces which will cause the ball to continue to move in the direction of the applied force. It should be obvious that airplanes should display positive stability, or perhaps neutral stability, but never negative stability. Stability may be further classified as static and/or dynamic. Static stabili ty means that if the airplane's equilibrium is disturbed, forces will be ac tivated which will initially tend to return the airplane to its original position. However, these restoring forces may be so great that they will force the TENOENCY TO RETURN TO EQUILIBRIUM EQUILIBRIUM POSITIVE STATIC STABILITY EQUILIBRIUM ENCOUNTERED AT ANY POINT OF DISPLACEMENT NEUTRAL STATIC STABILITY TENDENCY TO CONTINUE IN DISPLACEMENT DIRECTION O EQUILIBRIUM NEGATIVE STATIC STABILITY Figure 1-24. Static stability. IS airplane beyond the original position and continue in that direction (Fig. 1-25). On the other hand, dynamic stability is a property which dampens the oscillations set up by a statically stable airplane, enabling the oscillations to become smaller and smaller in magnitude until the airplane eventually settles down to its original condition of flight (Fig. 1-25). Therefore an airplane should possess positive stability which is both static and dynamic in nature. Before further discussion on stability, the axes of rotation will be re viewed because that is where stability has its effect. The airplane has three axes of rotation around which movement takes place. These are (1) lateral axis—an imaginary line from wingtip to wingtip, (2) longitudinal axis—an imaginary line from the nose to the tail, and (3) ver tical axis—an imaginary line extending vertically through the intersection of the lateral and longitudinal axes. The airplane can rotate around all three axes simultaneously or it can rotate around just one axis (Fig. 1-26). Think of these axes as imaginary axles around which the airplane turns, much as a wheel would turn around axles positioned in these same three planes. The three axes intersect at the center of gravity and each one is perpendicular to the other two. Rotation about the lateral axis is called pitch, and is controlled by the elevators. This rotation is referred to as longitudinal control or longitudinal stability. Rotation about the longitudinal axis is called roll, and is controlled by the ailerons. This rotation is referred to as lateral control or lateral stability. Rotation about the vertical axis is called yaw and is controlled by the rud der. This rotation is referred to as directional control or directional stability. Stability of the airplane then, is the combination of forces that act around these three axes to keep the pitch attitude of the airplane in a normal level flight attitude with respect to the horizon, the wings level, and the nose of the airplane directionally straight along the desired path of flight. Longitudinal Stability About the Lateral Axis Longitudinal stability is important to the pilot because it determines to a great extent the pitch char acteristics of the airplane, particularly as this relates to the stall characteris tics. It would be unsafe and uncomfortable for the pilot if an airplane con tinually displayed a tendency to either stall or dive when the pilot's attention was diverted for some reason. If properly designed, the airplane will not display these unstable tendencies when the airplane is loaded according to the manufacturer's recommendations. 16 (POSITIVE STATIC) (POSITIVE DYNAMIC} © UNDAMPED OSCILLATION Z U l £ < (POSITIVE STATIC) (NEUTRAL DYNAMIC) (POSITIVE STATIC) (NEGATIVE DYNAMIC) Figure 1-25. Relationship of oscillation and stability. Figure 1-26. Axes of rotation. The location of the center of gravity with respect to the center of lift determines to a great extent the longitudinal stability of the airplane. Fig. 1-27 illustrates neutral longitudinal stability. Note that the center of lift is directly over the center of gravity or weight. An airplane with neutral stability will produce no inherent pitch moments around the center of gravity. Fig. 1-28 illustrates the center of lift in front of the center of gravity. This airplane would display negative stability and an undesirable pitchup moment during flight. If disturbed, the up and down pitching moment will tend to in crease in magnitude. This condition can occur, especially if the airplane is Figure 1-27. Neutral stability. Figure 1-28. Negative stability. loaded so that the center of gravity is rearward of the airplane's aft loading limits. Fig. 1-29 shows an airplane with the center of lift behind the center of gravity. Again, this produces negative stability. Some force must balance the down force of the weight. This is accomplished by designing the airplane, in such a manner that the air flowing downward behind the trailing edge of the wing strikes the upper surface of the horizontal stabilizer (except on T-tails). This creates a downward tail force to counteract the tendency to pitch down and provides positive stability. 17 Figure 1-29. Positive stability. T o further explain, if the nose is pitched down and the control released, the airspeed will increase. This in turn, will increase the downwash on the tail's horizontal stabilizer forcing the nose up (except on T-tails). Conversely, if the nose is pitched up and the control released, the airspeed will diminish, thus decreasing the downwash on the horizontal stabilizer. This permits the nose to pitch downward. There is one speed only for each degree of angle of attack and eventually, after several pitch oscillations, the airplane tends to stabilize at the airspeed (angle of attack) for which it is trimmed. The above concept is of prime importance to the pilot. A common misconception about longitudinal stability is that an airplane is stable in respect to the horizon. This would be an .undesirable characteristic of an airplane. Keep in mind that longitudinal stability is with respect only to airspeed (angle of attack). The foregoing explanation of longitudinal stability needs some qualifica tion because during certain flight maneuvers the airplane is not entirely "speed seeking," but "angle of attack seeking." This can be demonstrated by placing the airplane in a power-off glide and trimming the airplane for a specific speed. Then if the throttle is opened suddenly, the airplane will nose up and finally assume an attitude that results in a speed considerably less than that of the power-off glide. This is because of additional forces developed by the propeller blast over the horizontal stabilizer (except T-tails), and the fact that the airplane is stable only with relation to airflow, or the relative wind. In other words, the stable airplane is not concerned with its own attitude relative to the earth or horizon, but with the relative wind. It will always tend to maintain an alignment with the relative wind. 18 Longitudinal Control fPitch) About the Lateral Axis In the previous discussion, the one speed or angle of attack concept was used to explain how longitudinal stability was attained. It is important for the pilot to know that the airplane is stable at various speeds or angles of attack, not just one. The controls which allow the pilot to depart from the one speed or angle of attack concept or the controls used to give the pilot longitudinal control around the lateral axis, are the elevators (Fig. 1-30) and the elevator trim tab (Fig. 1-31). The function of the elevator control is to provide a means by which the wing's angle o f attack may be changed. On most airplanes the elevators are movable control surfaces hinged to the horizontal stabilizer, and attached to the control column in the cockpit by mechanical linkage! This allows the pilot to change the angle of attack of the entire horizontal stabilizer. The horizontal stabilizer normally has a negative angle of attack to provide a downward force rather than a lifting force. If the pilot applies back elevator pressure the elevator is raised, increasing the horizontal stabilizer's negative angle of attack and consequently increasing the downward tail force. This forces the tail down, increasing the angle of at tack of the wings. Conversely, if forward pressure is applied to the elevator control, the elevators are lowered, decreasing the horizontal stabilizer's negative angle of attack and consequently decreasing the downward force on the tail. This decreases the angle of attack of the wings (Fig. 1-30). The elevator trim tab is a small auxiliary control surface hinged at the trailing edge o f the elevators. The elevator trim tab acts on the elevators, which in turn acts upon the entire airplane. This trim tab is a part of the elevator but may be moved upward or downward independently of the elevator itself. It is controlled from the cockpit by a control which is separate from the elevator control. The elevator trim tab allows the pilot to adjust the angle of attack for a constant setting and therefore eliminates the need to ex ert continuous pressure on the elevator control to maintain a constant angle of attack. An upward deflection of the trim tab will force the elevator downward with the same result as moving the elevator downward with the elevator con trol, and conversely a downward deflection of the trim tab will force the elevator upward. The direction the trim tab is deflected will always cause the entire elevator to be deflected in the opposite direction (Fig. 1-31). Lateral Stability About the Longitudinal Axis Lateral stability is the stability displayed around the longitudinal axis of the airplane. An airplane that tends to return to a wings-level attitude after being displaced from a level attitude by some force such as turbulent air, is considered to be laterally stable. Figure 1-30. Effect of elevators. Three factors affect lateral stability; (1) dihedral, (2) sweepback, and (3) keel effect Dihedral is the angle at which the wings are slanted upward from the root to the tip (Fig. 1-32). The stabilizing effect of dihedral occurs when the airplane sideslips slightly as one wing is forced down in turbulent air. This sideslip results in a difference in the angle of attack between the higher and lower wing with the greatest angle of attack on the lower wing. The increased angle of attack produces increased lift on the tower wing with a tendency to return the airplane to wings-level flight Note the direction of the relative wind during a slip by the arrows in Fig. 1-32. Sweepback is the angle at which the wings are slanted rearward from the root to the tip (Fig. 1-33). The effect of sweepback in producing lateral stabili ty is similar to that of dihedral, but not as pronounced. If one wing lowers in a slip, the angle of attack on the low wing increases, producing greater lift. This results in a tendency for the lower wing to rise, and return the airplane to level flight. Sweepback augments dihedral to achieve lateral stability. Another reason for sweepback is to place the center of lift farther rearward, which af fects longitudinal stability more than it does lateral stability. Keel effect depends upon the action o f the relative wind on the side area of the airplane fuselage. In a slight slip the fuselage provides a broad area upon which the relative wind will strike, forcing the fuselage to parallel the relative wind. This aids in producing lateral stability (Fig. 1-34). Lateral Control (Roll) About the Longitudinal Axis Lateral control is obtained through the use of ailerons, and on some airplanes the aileron trim tabs. The ailerons are movable surfaces hinged to the outer trailing edge of the wings, and attached to the cockpit control column by mechanical linkage. Moving the control wheel or stick to the right raises the aileron on the right wing and lowers the aileron on the left wing. Moving the control wheel or stick to the left reverses this and raises the aileron on the left wing and lowers the aileron on the right wing. When an aileron is lowered, the angle of attack on that wing will increase, which increases the lift This permits rolling the airplane laterally around the longitudinal axis (Fig. 1-35). 19 Elevators in the neutral position U p position of the elevators is required to hold the nose in the level Misfit attitude Trim tab must b e adjusted downward to hold ele vators in this position to relieve the pressure on the control wheel DIHEDRAL ANGLE LOWER ANCLE OF ATTACK Figure 1-32. Effect of dihedral Many airplanes are equipped with an aileron trim tab which is a small movable part of the aileron hinged to the trailing edge of the main aileron. These trim tabs can be moved independently of the ailerons. Aileron trim tabs function similar to the elevator trim tabs. Moving the trim tabs produces an effect on the aileron which in turn affects the entire airplane. If the trim tab is deflected upward the aileron is deflected downward, increasing the angle of attack on that wing, resulting in greater lift on that wing. The reverse is true if the trim tab is deflected downward. Lateral Stability or Instability in Turns Because of lateral stability, most airplanes will tend to recover from shallow banks automatically. How ever, as the bank ts increased, the wing on the outside of the turn travels faster than the wing on the inside of the turn. The increased speed increases the lift on the outside wing, causing a destabilizing rolling moment or an overbank- ing tendency. The angle of bank will continue to increase into a steeper and steeper bank unless the pilot applies a slight amount of control pressure to counteract this tendency. The overbanking tendency becomes increasingly significant when the angle of bank reaches more than 30 °. During a medium banked turn (a bank angle between the shallow bank and steep bank), an airplane tends to hold its bank constant and requires less SWEEPBACK SWEEPS ACK Figure 1-33. Effect ofsweepback. control input on the part of the pilot. This is because the stabilizing moments of lateral stability and the destabilizing moments of overbanking very nearly cancel each other out. A pilot can discover these various areas of bank through experimentation. Directional Stability About the Vertical Axis fYaw) Directional stability is displayed around the vertical axis and depends to a great extent on the quality of lateral stability. If the longitudinal axis of an airplane tends to follow and parallel the flightpath of the airplane through the air, whether in straight flight or curved flight, that airplane is considered to be directionally stable. Directional stability is accomplished by placing a vertical stabilizer or fin to the rear of the center of gravity on the upper portion of the tail section. The surface of this fin acts similar to a weathervane and causes the airplane to weathercock into the relative wind. If the airplane is yawed out of its flightpath, either by pilot action or turbulence, during straight flight or turn, the relative wind would exert a force on one side of the vertical stabilizer and return the airplane to its original direction of flight. Wing sweepback aids in directional stability. If the airplane is rotated Figure 1-34. Keel effect. about the vertical axis, the airplane will be forced sideways into the relative wind. Because of sweepback this causes the leading wing to present more fron tal area to the relative wind than the trailing wing. This increased frontal area creates more drag, which tends to force the airplane to return to its original direction o f flight (Fig. 1-33). The combined effects of the vertical stabilizer (Fin) and sweepback can be compared with feathers of an arrow. It would be difficult to imagine an arrow traveling through the air sideways at any appreciable rate of speed. Directional Control About the Vertical Axis (Yawf Directional con- 21 NORMAL LIFT RAISING AILERON DECREASES LIFT A N D LOWERS W I N G ACTION O F AILERONS MOVES THE PLANE O N ITS LONG I TUDINAL AXIS AILERONS, trol o f the airplane is obtained through the use of the rudder. The rudder is a movable surface hinged to the trailing edge of the vertical stabilizer (fin) and attached by mechanical linkage to the rudder pedals located in the cockpit. By pressing the right rudder pedal, the rudder is deflected to the right, which causes the relative wind to deflect the tail to the left and the nose to the right. If left rudder pressure is applied the reverse action occurs and the nose is deflected to the left (Fig. 1-36). It should be understood that the purpose of the rudder during flight is to control yaw and not to turn the airplane. Some airplanes are equipped with a rudder trim tab, which reacts in a similar manner on the rudder as does the aileron trim tab on the aileron and the elevator trim tab on the elevator. The amount of control which the pilot has over the airplane is dependent upon the speed of the airflow striking the control surfaces. Effective airplane stability also depends upon speed of the airplane through the air. The greater the airspeed the greater the effect of stability as a restoring force. Loads and Load Factors An airplane is designed and certificated for a certain maximum weight during flight This weight is referred to as the maximum certificated gross Figure 1-36. Effect of rudder. weight. It is important that the airplane be loaded within the specified weight limits before flight, because certain flight maneuvers will impose an extra load on the airplane structure which may, particularly if the airplane is overloaded, impose stresses which will exceed the design capabilities o f the airplane. Overstressing the airplane can also occur if the pilot engages in maneuvers creating high loads, regardless of how the airplane is loaded. These maneu vers not only increase the load that the airplane structure must support, but also increase the airplane's stalling speed. The following will explain how extra load is imposed upon the airplane during flight. During flight the wings of an airplane will support the maximum allow able gross weight of the airplane. So long as the airplane is moving at a steady rate of speed and in a straight line the load imposed upon the wings will re main constant A change in speed during straight flight will not produce any appreciable change in load, but when a change is made in the airplane's flightpath, an ad ditional load is imposed upon the airplane structure. This is particularly true if a change in direction is made at high speeds with rapid forceful control movements. According to certain laws of physics a mass (airplane in this case) will con tinue to move in a straight line unless some force intervenes, causing the mass (airplane) to assume a curved path. During the time the airplane is in a curved flightpath, it still attempts, because of inertia, to force itself to follow straight flight This tendency to follow straight flight, rather than curved flight, generates a force known as centrifugal force which acts toward the outside of the curve. Any time the airplane is flying in a curved flightpath with a positive load, the load the wings must support will be equal to the weight of the airplane plus the load imposed by centrifugal force. A positive load occurs when back pressure is applied to the elevator, causing centrifugal force to act in the same direction as the force of weight. A negative load occurs when forward pressure is applied to the elevator control, causing centrifugal force to act in a direc tion opposite to that of the force of weight. Curved flight producing a positive load is a result o f increasing the angle of attack and consequently the lift. Increased lift always increases the positive load imposed upon the wings. However, the load is increased only at the time the angle of attack is being increased. Once the angle of attack is established, the load remains constant The loads imposed on the wings in flight are stated in terms of loadfactor. Load factor is the ratio of the total load supported by the airplane's wing to the actual weight of the airplane and its contents; i.e., the actual load sup ported by the wings divided by the total weight of the airplane. For example, if an airplane has a gross weight of2,000 lbs. and during flight is subjected to aerodynamic forces which increase the total load the wing must support to 4,000 lbs., the load factor would be 2.0. (4,000 + 2,000 = 2 . ) In this example the airplane wing is producing "lift" that is equal to twice the gross weight of the airplane. Another way of expressing load factor is the ratio of a given load to the pull of gravity; i.e., to refer to a load factor of three, as "three C ' s , " where " G " refers to the pull of gravity. In this case the weight of the airplane is equal to "one G , " and if a load o f three times the actual weight of the airplane were imposed upon the wing due to curved flight, the load factor would be equal to "three G ' s . " Load Factors and Airplane Design T o be certificated by the Federal Aviation Administration, the structural strength (load factor) of airplanes must conform with prescribed standards set forth by Federal Aviation Regula tions. All airplanes are designed to meet certain strength requirements depend ing upon the intended use of the airplanes. Classification of airplanes as to strength and operational use is known as the category system. The category of each airplane can be readily identified by a placard or document (Airworthiness Certificate) in the cockpit which states the opera tional category or categories in which that airplane is certificated. The category, maneuvers that are permitted, and the maximum safe load factors {limit load factors) specified for these airplanes are as follows: Permissible Limit Load Category Maneuvers Factor* Normal I—Any maneuver incident to 3.8 normal flying. 2—Stalls (except whip stalls). 3—Lazy eights, chandelles, and steep turns in which the angle of bank does not exceed 6 0 ° . * T o the limit loads given, a safety factor of 5 0 % is added. Continued 23 Category Permissible Maneuvers Limit Load Factor* Utility 1—All operations in the normal 4.4 category. 2—Spins (if approved for that airplane). 3—Lazy eights, chandelles, and steep turns in which the angle of bank is more than 6 0 ° . Acrobatic No restrictions except those shown 6.0 to be necessary as a result of required flight tests. * T o the limit loads given, a safety factor of 5 0 % is added. It should be noted that there is an increase in limit load factor with an in creasing severity of maneuvers permitted. Small airplanes may be certificated in more than one category if the requirements for each category are met. This system provides a means for the pilot to determine what operations can be performed in a given airplane without exceeding the load limit. Pilots are cautioned to operate the airplane within the load limit for which the airplane is designed so as to enhance safety and still benefit from the intended utilization of the airplane. Effect of Turns on Load Factor A turn is made by banking the airplane so that lift from the wings pulls the airplane from its straight flightpath. In a un 4& -4F WEIGHT M O B I Z O N T A L C O M P O N E N T VERTICAL C O M P O N E N T LEVEL FLIGHT MEDIUM BANKED TURN STEEP BANKED TURN Figure 1-37. Forces acting on an airplane in a bank. 24 constant altitude coordinated turn the load factor (resultant load) is the result of two forces: (1) pull of gravity, and (2) centrifugal force (Fig. 1-37). It is not within the scope of this handbook to discuss the mathematics of the turn. However, in any airplane at any airspeed, if a constant altitude is maintained during the turn, the load factor for a given degree of bank is the same, which is the resultant of gravity and centrifugal force. For any given angle of bank the rate of turn varies with the airspeed. In other words, if the angle of bank is held constant and the airspeed is increased, the rate o f turn will decrease; or if the airspeed is decreased, the rate of turn will increase. Because of this, there is no change in centrifugal force for any given bank. Therefore, the load factor remains the same. Fig. 1-38 and Fig. 1-39 reveal an important fact about load factor in turns. The load factor increases at a rapid rate after the angle of bank reaches 50°. The wing must produce lift equal to this load factor if altitude is to be maintained. It should also be noted how rapidly load factor increases as the angle of bank approaches 90°. The 9 0 ° banked, constant altitude turn is not mathematically possible. An airplane can be banked to 9 0 ° , but a continued coordinated turn is impossible at this bank angle without losing altitude. At an angle of bank of slightly more than 8 0 ° the load factor exceeds 6, which is the limit load factor of an acrobatic airplane. The approximate maximum bank for conventional light airplanes ts 6 0 ° which produces a load factor of 2. This bank reaches the limit of a normal category airplane. An additional 10° of bank will increase the load factor by approximately 1 G (Fig. 1-39), bringing it dangerously close to the point at which structural damage or complete failure may occur in these airplanes. Effect of Load Factor on Stalling Speed Any airplane, within the limits of its structure and the strength of the pilot can be stalled at any airspeed. At a given airspeed the load factor increases as angle of attack increases, and the wing stalb because the angle of attack has been increased to a certain angle. Therefore, there is a direct relationship between the load factor imposed upon the wing and its stalling characteristics. When a sufficiently high angle of attack is reached, the smooth flow of air over an airfoil breaks up and tears away, producing the abrupt change of characteristics and loss of lift which is defined as a stall. A rule for determining the speed at which a wing will stall is that the stall ing speed increases in proportion to the square root of the load factor. T o fur ther explain, the load factor produced in a 7 5 ° banked turn is 4 (Fig. 1-39). Applying the rule the square root of 4 is 2. This means that an airplane with a Figure 1 -38. The load supported by the wings increases as the angle of bank increases. The increase is shown by the relative lengths of the white arrows. Figures below the arrows indicate the increase in load factor. For example, the load factor during a 60-degree bank is 2.00, and the load supported by the wings is twice the weight of the airplane in level flight normal unaccelerated stalling speed of 50 knots can be stalled at twice that speed or 100 knots, by inducing a load factor of 4. If the airplane were capable of withstanding a load factor of 9, this airplane could be stalled at a speed of 150 knots. Since the load factor squares as the stalling speed doubles, tremendous loads may be imposed on structures by stalling an airplane at relatively high airspeeds. An airplane which has a normal unaccelerated stalling speed of 50 knots will be subjected to a load factor of 4 G's when forced into an ac celerated stall at 100 knots. As seen from this example, it is easy to impose a load beyond the design strength of the conventional airplane. Reference to the chart in Fig. 1-40 will show that banking an airplane just over 75° in a steep turn increases the stalling speed by 100%. If the nor mal unaccelerated stalling speed is 45 knots, the pilot must keep the airspeed above 90 knots in a 75° bank to prevent sudden entry into a violent power stall. This same effect will take place in a quick pullup from a dive or a maneuver producing load factors above 1G. Accidents have resulted from sudden, unex pected loss of control, particularly in a steep turn near the ground. The maximum speed at which an airplane can be safely stalled is the design maneuvering speed. The design maneuvering speed is a valuable refer ence point for the pilot. When operating below this speed a damaging positive flight load should not be produced because the airplane should stall before the load becomes excessive. Any combination o f flight control usage, in cluding full deflection of the controls, or gust loads created by turbulence should not create an excessive air load if the airplane is operated below maneuvering speed. (Pilots should be cautioned that certain adverse wind shear or gusts may cause excessive loads even at speeds below maneuvering speed.) Design maneuvering speed can be found in the Pilot's Operating Hand book or on a placard within the cockpit. It can also be determined by multiply ing the normal unaccelerated stall speed by the square root of the limit load factor. A rule of thumb that can be used to determine the maneuvering speed is approximately 1.7 times the normal stalling speed. Thus, an airplane which normally stalls at 35 knots should never be stalled when the airspeed is above 60 knots (35 knots x 1.7 = 59.5 knots). A knowledge of this must be applied from two points of view by the com petent pilot: the danger of inadvertently stalling the airplane by increasing 25 0 10 10 10 40 SO M 70 00 M SANK AIIOII - IN D H I I I I Figure 1-39. Load factor chart. the load factor such as in a steep turn or spiral; and that intentionally stalling an airplane above its design maneuvering speed imposes a tremendous load factor on the structure. Effect of Speed on Load Factor The amount o f excess load that can be imposed on the wing depends on how fast the airplane is flying. At slow speeds, the maximum available lifting force of the wing is only slightly greater than the amount necessary to support the weight of the airplane. Consequent ly, the load factor should not become excessive even if the controls are moved abruptly or the airplane encounters severe gusts, as previously stated. The reason for this is that the airplane will stall before the load can become ex cessive. However, at high speeds, the lifting capacity of the wing is so great that a sudden movement of the elevator controls or a strong gust may increase the load factor beyond safe limits. Because of this relationship between speed and safety, certain ''maximum" speeds have been established. Each airplane is restricted in the speed at which it can safely execute maneuvers, withstand abrupt application of the controls, or fly in rough air. This speed is referred to as the design maneuvering speed, which was discussed prevously. Summarizing, at speeds below design maneuvering speed, the airplane 26 0 10 20 30 40 50 60 70 80 90 SANK A N G L E - I N DEGREES Figure 1-40. Stall speed chart. should stall before the load factor can become excessive. At speeds above ma neuvering speed, the limit load factor for which an airplane is stressed can be exceeded by abrupt or excessive application of the controls or by strong turbulence. Effect of Flight Maneuvers on Load Factor Load factors apply to ail flight maneuvers. In straight-and-level, unaccelerated flight a load factor of 1G is always present, but certain maneuvers are known to involve relatively high load factors. Turns. As previously discussed, increased load factors are a characteristic of all banked turns. Load factors become significant both to flight per- formance and to the load on wing structure as the bank increases beyond ap proximately 4 5 ° . Stalls. The normal stall entered from straight-and-level flight, or an unac- celerated straight climb, should not produce added load factors beyond the 1 G of straight-and-level flight. As the stall occurs, however, this load factor may be reduced toward zero, the factor at which nothing seems to have weight, and the pilot has the feeling o f "floating free in space." In the event recovery is made by abruptly moving the elevator control forward, a negative load is created which raises the pilot from the seat This is a negative wing load and usually is so small that there is little effect on the airplane structure. The pilot should be cautioned, however, to avoid sudden and forceful control move ments because o f the possibility o f exceeding the structural load limits. During the pullup following stall recovery, however, significant load fac tors are often encountered. These may be increased by excessively steep div ing, high airspeed, and abrupt pullups to level flight One usually leads to the other, thus increasing the resultant load factor. The abrupt pullup at a high diving speed may easily produce critical loads on structures, and may pro duce recurrent or secondary stalls by building up the load factor to the point that the speed of the airplane reaches the stalling airspeed during the pullup. Advanced Maneuvers. Spins, chandelles, lazy eights, and snap maneuvers will not be covered in this handbook. However, before attempting these ma neuvers, pilots should be familiar with the airplane being flown, and know whether or not these maneuvers can be safely performed. Effect of Turbulence on Load Factor Turbulence in the form of ver tical air currents can, under certain conditions, cause severe load stress on an airplane wing. When an airplane is flying at a high speed with a low angle of attack, and suddenly encounters a vertical current of air moving upward, the relative wind changes to an upward direction as it meets the airfoil. This increases the angle of attack of the wing. If the air current is well defined and travels at a significant rate of speed upward (15 to 30 feet per second), a sharp vertical gust is produced which will have the same effect on the wing as applying sudden sharp back pressure on the elevator control. All certificated airplanes are designed to withstand loads imposed by tur bulence of considerable intensity. Nevertheless, gust load factors increase with increasing airspeed. Therefore it is wise, in extremely rough air, as in thunderstorm or frontal conditions, to reduce the speed to the design maneu vering speed. As a general rule, when severe turbulence is encountered, the airplane should be flown at the maneuvering speed shown in the FAA- approved Airplane Flight Manual, Pilot's Operating Handbook, or placard in the airplane. This is the speed least likely to result in structural damage to the airplane, even if full control travel is used, and yet allows a sufficient margin of safety above stalling speed in turbulent air. Placarded "never exceed speeds" are determined for smooth air only. High dive speeds or abrupt maneuvering in gusty air at airspeeds above the maneuvering speed may place damaging stress on the whole structure of an airplane. Stress on the structure means stress on any vital part of the airplane. The most common failures due to load factors involve rib structure within the lead ing and trailing edges of wings. The cumulative effect of such loads over a long period of time may tend to loosen and weaken vital parts so that actual failure may occur later when the airplane is being operated in a normal manner. Determining Load Factors in Flight The leverage in the control sys tems of different airplanes varies; some types are balanced control surfaces while others are not. (A balanced control surface is an aileron, rudder, or elevator designed in such a manner as to put each side of its hinged axis in balance with the other side.) Therefore the pressure exerted by the pilot on the controls cannot be used as a means to determine the load factor produced in different airplanes. Load factors are best judged by feel through ex perience. They can be measured by an instrument called an accelerometer, but since this instrument is not commonly used in general aviation-type airplanes, developing the ability to judge load factors from the feel of their ef fect on the body is important One indication the pilot will have of increased load factor is the feeling of increased body weight In a 6 0 ° bank the body weight would double. A knowledge of the principles outlined above is essential to estimate load factors. In view of the foregoing discussion on load factors, a few suggestions can be made to avoid overstressing the structure of the airplane: 1. Operate the airplane in conformance with the Pilot's Operating Hand book. 2. Avoid abrupt control usage at high speeds. 3. Reduce speed if turbulence of any great intensity is encountered in flight or abrupt maneuvers are to be performed. 4. Reduce weight of airplane before flight if intensive turbulence or abrupt maneuvering is anticipated. 5. Avoid turns using an angle of bank in excess of 60°. 27 Forces Acting on the Airplane When at Airspeeds Slower than Cruise At a constant cruise airspeed, maintaining straight-and-level flight, the force of thrust and drag acts opposite to each other and parallel to the flightpath. These opposing forces are equal in magnitude. Also, the force of lift is equal in magnitude to the force of weight. While maintaining straight-and-level flight at constant airspeeds slower than cruise, the opposing forces must still be equal in magnitude, but some of these forces are separated into components. In this flight condition the actual thrust no longer acts parallel and opposite to the flightpath and drag. Actual thrust is inclined upward as illustrated in Fig. 1-41. Note that now thrust has two components; one acting perpendicular to the flightpath in the direction of lift, while the other acts along the flightpath. Because the actual thrust is in clined, its magnitude must be greater than drag if its component of thrust along the flightpath is to equal drag. Also note that a component of thrust acts 9 0 ° to the flightpath, and thus acts in the same direction as wing lift. Fig. 1-41 also illustrates that the forces acting upward (wing lift and the compo nent of thrust) equals the forces acting downward (weight and tail down force). Wing loading (wing lift) is actually less at slow speeds than at cruise speeds because the vertical component of thrust helps support the airplane. T o summarize, in straight-and-level flight at slow speeds, the actual thrust is greater than drag and wing lift is less than at cruise speed. Forces in a Climb The forces acting on an airplane during a climb are il lustrated in Fig. 1-42. When the airplane is in equilibrium, the weight can be resolved into two components: one opposing the lift, and the other acting in the same direction as the drag along the line of the relative wind. The re quirements for equilibrium are: the thrust must equal the sum of the drag and the opposing component of the weight; and the lift must equal its opposing component of the weight. The steeper the angle of climb the shorter becomes the length of the component o f lift, and simultaneously the component of drag becomes longer. Therefore, the lift requirement decreases steadily as the angle of climb steepens until, in a true vertical climb, if this were possible, the wings would supply no lift and the thrust would be the only force opposing both the drag and the weight, which would be acting downward in opposition. At a constant power setting, a given rate of climb can be obtained either by climbing steeply at a low airspeed or by climbing on a shallow path at high airspeed. At one extreme, if the airspeed is too low the induced drag rises to a figure at which all thrust available is required to overcome the drag and none is available for climbing. At the other extreme, if the speed is the maximum 28 Component of Thrust acting perpendicular to flight path LIFT A Component of Thrust acting along flight path V WEIGHT Tail - down Force Figure 1-41. The forces on the airplane in straight-and-level flight at air speeds slower than cruise. obtainable in level flight, again all the power is being used to overcome the drag and there is no rate of climb. Between these two extremes lies a speed, or a small band o f speeds, which will achieve the best rate of climb. The best rate of climb is achieved not at the steepest angle, but at some combination of moderate angle and optimum airspeed at which the greatest amount o f excess power is available to climb the airplane after the drag has been balanced. Fig. 1-43 shows that the speed for minimum drag or the lowest point on the power-required curve, although low, is not the lowest possible that can be * fc^CouportKit of Drag Wrtjltt Figure 1-42. Forces acting on an airplane in a climb. flown without stalling. The increase in power required at the lowest speeds (to the left of the minimum power-required point) is caused by the rapidly rising effects of induced drag at the lower speeds. The propeller driven airplane, under the same set of circumstances and for a given rated horsepower, suffers a gradual loss of propeller efficiency and, therefore, a gradual loss of thrust at both ends of its speed range. The vertical distance between the power-available and power-required curves (Fig. 1-43) represents the power available for climbing at the particular speed. The best climbing airspeed is that at which excess power is at a max imum so that after expending some power in overcoming drag the maximum amount of power remains available for climbing the airplane. At the intersec tion of the curves all the available power is being used to overcome drag, leav ing none available for climbing. Of course, at the lower range, excess power for climb soon becomes available if the angle o f attack is reduced to allow an increase in speed. The thrust horsepower of piston engines decreases with altitude. Even if it is possible to prolong sea-level power to some greater altitude by super charging, or some other method ot power boosting, the power will inevitably decline when the boosting method employed reaches an altitude at which it can no longer maintain a set power. At higher altitudes the power available curves are lowered. Since power required increases with true airspeed (veloci- AIRSPEED MPH Figure 1-43. Power available vs. power required. ty), the thrust horsepower required to fly at any desired indicated airspeed in creases with altitude. In summarizing, it Is a fallacy to think that an airplane climbs because of "excess lift." It does not; the airplane climbs because of power available over power required. Forces in a Glide The forces acting on an airplane in a glide are il lustrated in Fig. 1-44. For a steady glide with the engine providing no thrust, the lift, drag and weight forces must be in equilibrium. The illustration shows that weight is balanced by the resultant of lift and drag. The lift vector, acting as it does at right angles to the path of flight, will now be tilted forward, while the drag vector will be til