Airship Aerodynamics Technical Manual

*TM 1-320 WAR DEPARTMENT , TECHNI C AL MANUAL } W ASHlNGTON, Pebr·um ·y 11, 1941.

No . 1-820 AIRSHIP AERODYNAMICS Prepar ed under direction of Chief of the Air Corps SroriON I. General. Paragraph Definition of aerodynamic s______ ___________ _ 1 Purpose and scope_____ ___ _____ __ __ ____ ____ _ 2 Imp ortance --- - -- ---- - --------------------- 3 Glossary of terms__ __ _____ ___ __________ ____ 4 Typ es of a ir ships---- ------ - -------- -- ------ 5 Aerodynamic forces__ _____________ ____ ______ 6 ll. Resistance.

Fluid resi&ance___________ _ _______ ______ ___ 7 Shape coe ffi cients _______ ___________ _ ________ 8 Coefficient of skin friction_ _ _________________ 9 Resistance of streamlined body -- ---- --- ----- 10 Pri smatic coefficient----------- - --- -- ------- 11 I ndex of form e ffi ciency__ _____ _____ ___ _ ____ 12 ll lust r ative resistance problem______ ___ ______ 13 S ca le effec t- - ------ ----- - ------ --- - -- - - -- - - 14 Resistance of completely r igged air ship ______ 15 Deceleration test --- ----- - --- -- - -- - ---- - ---- 16 III. P ower requirements.

Power r equired to overcome airship resistance_ 17 Results of vari ous speed t rials____ ___ _ ___ _ ___ 18 Bur gess form ula for ho rsepower------ --- ---- 19 Speed developed by given horsepower________ 20 Summary---------------------- -""'---------- - 21 IV. St ability.

Variation of pressure distribution on airs hip hull--------- - --------- - - ---------------- 22 Specific st abili ty and center of grav i ty of ai r - s hiP----- -- ---------------- ---- -- ---- - --- 23 Cen ter of buoyancy______ __ ________________ 24 D esc rip tion of major axis of airship__________ 25 T ypes of stab ility_ __ ________ _ ___ ____ _____ __ 26 For ces and moments acting on airship________ 9/l Dampi ng mom ent----- --- ------------------ 28 Longi tudina l stabilitY--------- -- ----- ------ 29 Dir ectional stability_________ __ ____ _ _____ ___ 30 La tera l sta bility- - ------ --------- ------ -- - -- 31 Sum marY--------- -- ---- - ------ ------------ 32 *Thia m anual supersedes or:a ll'lG-290 , November 16, 1929.

285746°--41 1

TM: 1-320 1-2 AIR CORPS SECTION V. Control. Paragraph <Jenera! types______________________________ 33 Directional__ _______ _____ __________________ 34 Altitude-------- -------------------- - ------ 35 verse_____________________ _____ __ __ _____ _

Re 36

Applica tion of dynamic control to operation of airs Ips _____ _______________________ ___ __ _ . h' VI. Aerodynam ic stress.

Assumption as to con di tior1 of maximum st ress_ Transverse forces acting on airship flying at constant angle of pitch ________ __ ________ _ Transverse forces acting on airship in steady turn____________________ ___________ ______ 40 Force s ca us ed by gusts______________________ 41 Empirical formulas for max imum aerodynamic bending moment on hull and for forces on tail surfaces----- · ------------------------ 42 Method of calculating shear and ben _ ding mo- ment on hulL __ _._________________ ;________ 43 Conclusion______ __ _ ___ _____________________ 44 SE<:mON I <JENERAL Paragraph Definition of aerodynamics -- - ~ ------ --- --- --- -- - ---- -- --- ----------- -- -- 1 Purpose and scope---- - ------ - -- - ------- - ---·-- --- ------ -- ---------- ---- -- 2 Importance-- --------------~--------------- -- ----- - ---- - ---- - ------ ----- 3 Glossary of terms -- ------ ----- --- -- -- - ----- --- - ------ -- ------ ----- - - ---- 4 Types of airships_· ----- ---- -- ---------- - ------------ - ----- -- --- ------- -- 5 A erod ynamic forces --- --- --------- --- -------- ----- - ---- - ------ -- ------ - - 6 .

1. Definition of aerodynamics.-Aer o dy namics is tha t branch of dynamics which treats of the motion of air and other gaseous fluids, and of the forces on solids in motion relative to such fluids.

2. Purpose and scope. - Thi s manual is designed as a text for the · instru ct ion of airship student pilots and as a reference text for th~ rated pilot. A cco rdingly the subject h as been so approached as to · give th e knowledge of aerodynamics essential to the operation of air- ships . Intricate formulas involving higher mathematics, although valuable to the designer, are of secondary importance to the pilot.

Such formulas therefore have been omitted and the en tire subject so treated as to bring . out basic principles and their application to lighter than air aircraft operation.

TM 1-320 3-4 AffiSHIP AERODYNAMICS 3. Importance.-Ai rships are controlled in two ways, stati<-ally a.nd dynamically. Th e former method is discussed in TM 1-3 25 and will be mentioned but incidentally in this manual. Because of the existence of stat ic means of control, the st udy of aerodynamics may" appear of minor importance to the operation of airships. This is un true . Stabili ty and control are constantly effected by a combina- tion of static and dynamic forces. To insure safety of the airship and to pr eclude possibil ity of exposing it to dang erous conditiOJ:!.S, the pilot must be aware of existing dynamic forces and their e ff ects on the airship itself and on its fl ight path. F requently airships, due tJ unavoidable causes such as leakage of gas or accumulation of mois- ture, have become statically uncontrollable but have been sayed by the intelligent application of dynamic means of control.

4. Glossary of t er m s.-During recent years many t er ms have been i nt roduced into the English language covering vari ous aspects of aeronautical science. R eport No. 240, National Advisory Commit- tee for Aeronautics, defines the meaning of the most common of these expressions, from which most of the following definitions have been abstracted : .A. erodynamics. -Br anch of dynamics which treats of the motion of a ir and other gaseous fluids and of the forces acting on solids in motion re la tive to such fluids .

.A.e ronautics.-Science and art pertaining to the fl igh t of a ir cr a ft .

.A. ero3 tat.-Ge neric term for aircraft whose support ·is chie fly due to buoyancy derived from . aerostatic forces. The immersed body consists of one or more bags, cells, or other containers filled with a gas which is lighter than air.

A irfoil.- Any surface designed to be projected through the air in ord er to produce a usef ul dynamic rea ction.

Ai rfoil section (or profile) .- Cross section of an airfoil made by a plane parallel to a specified reference plane. A line perpendicul ar to this plane is called the axis of the airfoil.

A ir scoop. -Pr ojecting scoop which uses the wind or slipstream to maintain air pressure in the interior of the ball<:met of an aerostat.

A irship .-Ae rostat provided with a propelling . system and w ith means of controlling the dire ct ion of motion. When its power pla nt is not operating it acts like a fr ee balloon.

No nrigid .-Air ship whose form is maintained by the inte r na l pressure in the gas bags and ballonets ( fi g. 1) .

R igid.-Airsh ip whose form is maintained by a rigid structure (fig. 3 ).

TM 1-320 4 AIR CORPS Se1nirigid.- Airship whose form is maintained by means of a rigid or jointed keel in conjun ct ion with internal pressu re in the gas containers and ballone ts (fig. 2).

The term "airship" is sometimes incorrectly applied to heavier than air aircraft either in full or as "ship." Thi s is a slang use of the word and sh ould be avoided.

Air spee d'.-Speed of an aircraft relative to the air. Its symbol is V.

Angle, critical .-An gle of attack at wh ich the flow about an airfoil changes abr uptly with corresponding abrupt changes in lif t and drag.

Angl e, elevator .-Angular displacement of elevator from neutral position. It is positive when t railing edge of the elevator is below neutral position.

Angl e of attack.-Acute angle bet -.v een the. chord of an airfoil and its direction of motion relative to the air. (This defin ition may be extended to other bodies tha n airfoils.) It s symbol is a .

Angl e of pitch .-A cute angle between two planes defined as follows: One plane includes lat e ral axis of the aircraft and direction of the relative wind; the other plane includes lat e ral axis and longi- tudinal axis. (In normal fli ght the angle of pitch is the angle between longitudinal axis and dir ection of relative wind.) Thi s angle is denoted by 0 and is po sit ive when nose of the aircraft has • nsen .

Angle of roll, or angle of bank.- Acute angle through which aircra ft must be rotated about its longitudinal axis in order t o bring its lateral axis into a horizontal plane. Thi s angle is denoted by <I> and is positive when the left wing is higher than the right.

A ngle of yaw .-A cute angle between direction of relative wi nd and plane of sym metr y of an aircraft . Thi s angle is denoted by 'II and is positive when the aircraft has turned to the right.

Angl e, propeller blad'e.-Actual angle between chord of propeller section and plane perpendic ular to axis of rotation of propeller.

Usually caUed "blade angle."

Angle, rudder.-Ac ute angle between rudder and plane of symmet ry of the aircraft. It is positive when trailing edge has moved to the left w ith reference to no rm al position of pilot.

Angle, zero lift;. -Angle of attack of an airfoil when i ts lift is zero.

A spect rati o of propeller blade.- H alf the ratio of propeller diameter to maximum blade w idth .

Aw es of aircraft.- Three fixed lines of re ference, usua ll y centroidal and mutually pe rp endicular. The longitudinal axis in the plane

TM 1-320 AIRSHIP AERODYNAMICS of symmetry, usually parallel to axis of the propeller, is called the longitudinal axis; the axis perpendicular to thi s in the plane of symmet ry is called the normal axis; and the third axis perpen- dicu lar to the other two is called the lateral axis. In mathe- matical discussions, the first of these axes, drawn from front to rear , is called the X axis; the second, drawn upward, the Z axis; and the third, running from right to left, the Y axis.

Ballast .-Any substance, usually sand or water, carried in a balloon or airship and intended to be thrown out, if necessary, for the pur- pose of reducing load carried and thus altering aeros tatic rela- tions.

Ballonet.- Compartment of variable volume constructed of fabric or partitioned otf within the interior of a balloon or airship. It is usually partially inflated with air under control of valves from a blower or from an air scoop. By blowing in or letting out air, it serves to compensa te for changes of volume in gas contained in the envelope and to mai nta in gas pre ssure, thus preventing defor- mation or structura l failure. By means of two or niore ballonets, often used in nonrigid airships, the trim can also be controlled.

The ballonet should not be confused with gas cell.

Blad e back.-Si<le of propeller blade which corresponds to upper surface of an airfoil.

Blade face. -Surface of propeller blade which corresponds to lower surface of an airfoil. Sometimes called " thrust face" or "driving face."

Blade width ratio.-Ratio of developed width of propeller blade at any point to circumferen ce of ·a circle whose radius is the distance of that point from the propeller axis.

B ow stiffener.- Rigid member attached to bow of nonrigid or semi- rigid envelope to reinforce it against pressure caused by motion of the airship. Sometimes called "nose stiffener" or "no se batten."

Buoyancy .-Upw ard air force on aerostat which is d er ived from aerostatic conditions. It is equal to weight of air displaced.

Buoyancy, center of (aero stat).-Center of gravity of volume of contained gas.

Oamber.-Rise in curve of an airfoil section from it s cho rd , usually expressed as ratio of departure of the curve from the chord to the length of the chord. "Upper camber" refers to the upper surface of an airfoil and "lower camber" to the lower surface; "mean camber" is the mean of these two.

Capacity.- Volume of the gas-containing portion of an aerostat.

Oar. - That portion of an airship intended to carry power unit or units,

TM 1-320 4 AIR CORPS personnel, car go, or equ ipm ent. It may be suspended from the buoy- ant portion or it may be built close up again st it. It is not to be applied to parts of the keel of a rigid or semirigid airship which have been fi tted for the purposes mentioned.

Oeiling, static.-A l tit ude in stand ard atmosphere at which an aerostat is in static equilibrium a.fter removal of all dischargeable weights.

Oenter of presswre coetflaient.- Ratio of distance of center of pressure from leading edge to c hord length.

Oenter of pressure of cd1•foil section .-P oint in chord of airfoil sec- tion, prolonged if necessary, which is at the intersection of the chord and the line of action of the resul tant air force. Abbreviation is C. P.

Oho rd (of airfoil section) .- L ine of straightedge brought into con- tact with lower surface of the section at two points; in the case of an airfoil having double convex camber, the straight line join ing th e leading and trailing edges. (These edges may be defined for this pur pose as the two points in the section w~ich are farthest apart.)

Th e line joining leadi ng and trailing edges should be used also in tho se cases in which lower surface is convex exc ept for a sho rt fl at portion. The method used for determining the chord should always be explicitly stated for those sections concerning which ambiguity seems likely to arise.

Ohord length. -Length of projection of airfoil section on its chord.

Its symbol is c.

O ont1•ols .-G eneral term applied to means provided to enable the pilot to control speed, direction of flig ht, a ltitud e, and power of air craft .

D1•ag.-Compo nent parallel to relative wind of tota l air force on aircraft or airfoil. It s symbol is D .

Dynamic (or impact) pressure. -Product 1;2p V , where p is density and V is relative speed of the air. It is the quantity measured by most a ir speed instrum en ts. Its symbol is q.

:El ervator .-Movable auxiliary airfoil, function of which is to impr ess pi tching moment on th e ai rcraft. The eleva tor is usually hinged to the stabilizer.

E nvelope. -O uter covering of aerostat, usually of fabric. It may or may not be also the gas co ntainer. It ma y be divided by dia- ph ragms into separate gas compartments or cells, and it may also contain internal air ce ll s or ballonets.

F light path. -P ath of center of gravity of aircraft with reference to the earth.

H orsepower of engine, ma.:vim-wm.-Maximum horsepower engine can develop.

TM 1-320 AIRSHIP AERODYNAMICS I Horsepowe'l' of engine, rated.-Average horsepower developed by an e ng ine of a given type in passing the sta nd ar d 50-hour endurance test.

H ull (airship) .-M ain structure of a rigid airship consist ing of a covered elongated framework w hi ch incloses gas cells and supports cars and equipment. May also be applied to co mp lete buo ya nt un it of any aerostat. In this la tter sense sometimes called "gas bag."

lndraft (i nflow) .-Flow of air from in front of propeJler into blades.

K eel (airship) .-Assembly of members at bottom of hull of semi- rigid or rig id airship which provides special st re n gth to resist hog- ging and sagging and also serves to distribute e ffe ct of concent rated .

loads along the hull. It may be a simple Gall's chain as in some semirigids, or a ve ry extensive structure inclo sing the corridor as in mo st rigids.

Leading edge. -Foremo st edge of airfoil or propeller blade. Also called "entering edge."

L ift .-That component of tot al air force on aircraft or airfoil which is perpendicular to relative wind and in p lan e of symmetry. It mu st be specified whether this applies to complete aircra ft or to parts thereof. In the case of an airship this is often called "dynamic lift." It s symbol is L.

Lift , gross (air s hip) .-Lift obtained from volume of buoyant gas equal to nominal gas capacity of the a;ircraft. Obtained by multi- pl ying nominal gas capacity by lift per unit volume of gas used for inflation.

L ift, static ( aerostat) .-Re su ltant upward for ce on an aeros tat at rest obtained by multiplying actual volume of the air displaced by density of th e air and su btracting weight of contained gas. (The volume of the air displaced multiplied by the differen ce of density of the air u.nd the contained gas.)

Load: Dead.-Structure, power plant, and fixed equipment of an air· craft. Included in this fixed equipment are water in radiator and cooling system, all essential instruments and furni shings, fixed electric wiring for lighting, hea ti ng, etc. In the case of the aerostat the amount of ballast which must be carried to assist in making a sa fe landing mu st al so be included.

Full.-W eig ht e mpty plus useful load. Also called "gross weight."

Pa y.- Tha .t part of useful load from which revenue is derived.

namely, pa ssengers and freight.

TM 1-3 20 4 AIR CORPS Useful .- Crew and pa ssengers, oil and fuel, ballast other than emergency, ordnance, and portable equipment.

Nose heavy.-Condition of an airship which when at rest in still air trims with its axis inclined down by the bow. T he term "bow heavy" is pref er red to "nose heavy" in describing ai rships.

Oscillation, stable. -Oscillation whose amplitude does not increase.

Oscillation, ~tnstable .-O sc illation whose amplitude incres.ses con- tinuously until an attitude is reached from which th er e is no tendency to return toward the original attitude, the motion becom- .

ing a stea dy divergence.

P erform anc e CM'I'CUJteristics (air ship) . -I n general: Maximum speed at various altitudes.

Maximum altitude attainable with definite weight relations and ballonet volume (if fitted).

Endurance at fu ll and half power.

Static cei ling .

Dynamic li ft under specified conditions.

Pi tch of propeller: Etf ect iv e. -Distance which aircraft advances along its flight path for one revolution of propeller. Its symbol is pa.

Geo met , rical. -Distan ce which an element of a propeller wo u ld advance in one revolution if it were moving along a helix of slope equal to it s blade ang l e.

Mean geometrical.- Me an of the geometrical pitches of the se v- eral elements. I ts symbol is p • Standa r d.-Geometrical pitch taken at two-thirds of thE' radius.

Al so called "nominal pitch." Its symbol is Ps· Z e1'0 th?'U8t.-Distance which propeller would have to advance in one revolution in order that there might be no thrust. Also called "experimental mean pitch." It s symbol is pv.

Zero torque. -Di stance which propeller would have to advance in one revolution in order that the torque might be zero. I ts symbol is Pa· P itch mtio .-Ra tio of the pitch (geometrical unless otherwise st ated) to the diameter pj D.

P it ch speed.- Product of mean geometrical pitch by number of revo- lutions of propeller in unit time, that is, the speed aircraft would make if th ere were no slip.

Propeller area, proje~ted.-Total area in the plane perpendicul ar to: propeller shaft swept by propeller, exce pt portion covered by the boss and that swept by root of the blade. Thi s portion is usually taken as extending 0.2 of maximum radius from axis of the shaft.

'rM 1-320 AIRSHIP AERODYNAMICS 4 Prope'!Ze1t blade area.- Area of the blade face, exclusive of the boss and the root, that is, of a portion which is usually taken as extend- ing 0.2 of maximum radius from axis of the shaft. · Propeller-caml;er ratio .-R atio of maximum thickness of proj)eller section to its chord.

Propeller efficien<n.J.-Ratio of thrust power to power input of pro- peller. It s symbol is 'YJ · Propeller, pusher.-Propeller mounted to rear of engine or propeller shaft. (It is usually behind the wing cell or nacelle.)

Pr9peller rak e .-Mean angle which the line joining the centroids of the sections of propeller blade makes with a plane perp endic ular tO the axis.

Propeller section.-Cross section of propeller blade made at any point by a plane parallel to axis of rotation of propeller and tangent at · the centroid of the section to an arc drawn with th e axis of rotation as its center.

Pr opeller th1'U8t. --Component parallel to propeller axis of the tota l air force on the propeller. I ts sym boli sT .

Propeller torque.- Moment applied to propeller by engine shaft. Its .

symbol is Q.

Race rotation. -R otation produced by action of propeller of stream of air passing through or influenced by propeller.

Vl

Rey nold~ number.-N ame given the fraction P-;lli which-

p= density of the air.

V =relative velocity of the air.

l= linear dimension of the body.

,u.=coefficient of viscosity of the fluid.

R evolutions, ma.a:imum. -Nu mber of revolutions per minute cone.

sponding to maximum horsepower.

Revolution.s, normal.- Hi ghest number of revolutions per minute that may be maintained for long periods.

Righting rM11& ent (or restoring moment).-Moment which tends to restore aircraft to its previous attitude after any small rotational displacement.

Rudde 1'.- Movable auxiliary airfoil function of which is to impress a yawing moment on aircraft in normal flight. I t is usually located at rear of aircraft.

Skiln frictiO'n.~Tangential compone nt of flu id force at point on surface.

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TM 1-320 AIR CORPS . . .

Slip . -Diiference between mean geometrical pitch and effective pitch.

Slip maY' be expressed as a percentage of the mean geometrical pitch' or as a linear di mension. · SliiJ junction.- Ratio of speed of advance through undisturbed a:ir to the product of propeller diameter by number of revolutions in

unit time, _ that is, Jv· Slip function is the primary factor con-

trolli ng propeller performance. It is 1r times ratio of forwa rd speed to tip speed of propeller.

Sli pstream.- Stream of air driven astern by propeller. (The indraft ~- is sometimes included also.) · Speed, grouou.l .-Hor~zontal c•mponent of velocity of aircraft rela- tive to the earth.

S tability .-That property of a body which causes it, when disturbed · from a condition of equilibrium or steady motion, to develop .forces or moments which tend to re store the body to its original condi- tion.

.Automatic.-Stability dependent upon movable control surfaces automatically operated by mechanical means.

Directional .-S tability w ith ref erence to rotations about the nor- mal axis, th at is, an airship possesses directional sta bility in it s simple st form if a resto rin g moment comes into action when it is given a small angle of yaw. Owing to symmetry, directional stab ilit y is closely associated with lateral stability.

I nherent. -S tabil ity of an aircraft due solely to di sposition and arra ngement of its fixed parts, that is, that property which causes it when disturbed to return to its normal attitude of flight w ithout use of controls or interposition of any mechani- cal devices.

La teral. -St ab ility with reference to disturbances involving rolling, yawing, or side slip ping , that is, disturbances in which position of the plane o£ symme try of the aircraft is affected.

Lo ngitudinal.- Stability with reference to disturbances in the plane of symmetry, that is, disturbances involving pitching .and variation of longitudinal an d normal velocities.

Static.-Stability of such a cha- racter th at, if the airship is dis- pl aced slightly £rom its normal a ttitud e by rot ati on about an axis through its center of gravity (as may be done in wind tunn el experiments), moments come into play which tend to return the airship toward its original attitude.

Str eamline .-Path of a small portion of a fl uid relative to a solid body with respect to which the fluid is moving. The term is coin-

TM 1-320 · AIRSHIP AERODYN AMICS 4-5 monly used only of such flows as are n ot eddying, but the dis- tinction should be made clear .by the context.

Streamline flow .-Ste ady flow pa st a solid body, that is, a flow in which the direction at every po int is in dependent of time.

Strea;mlirw form.-Solid body which produces appr oximately stream- line flow.

Surface, control.- Mov ab le airfoil designed to be rota ted or othe r- wise moved by the pilot in order to change attit ud e of airplane or air ship.

Tait group (or tail unit).-Stabilizing and control surfaces at rear end of ai rc raft, including stabilizer, fin, rudder, and elevator.

(Also called "empennage.") Tau heavy (air ship) .-Condition in which in normal flight the after end of an airship tends to s ink a nd which requires correction

by means of the horizontal controls. In this condition an airship

is said to "trim by the stern.'' It may be due to either aerody- namic or static conditions, or to both.

Thrust, static .-Thru st developed hy propeller when ro tatin g at a fixed point.

Tractor propeller .-P ropeller mounted on forward end of engine or propeller shaft. (It is usually forward of fu selage or wing nacelle.)

Trailing edge .-R earmost edge of airfoil or propeller blade.

5. Types of airships. -a. Air s hip s are div id ed into three general classes in acco rdan ce with their method of construction. Th ese three classes are (1) Nonrigid.

(2) Semirigid.

{3) Rigid.

b. The names describe means by which shape of the e nv elope is maintained. In the nonrigid, gas in the en velope is kept under s uffi- cient pre ss ure to keep the hull shape by thi s means alone. In the se mirigid a central keel is provided which carries th e load ing and is itself swung by suspensions from the top of the envelope. Du e to its ri gid it y, the keel assists the internal pre ss ure in maintaining f; hape of the envelope. In ri gid construction a met al structu re is provided to maintain sha pe of the hull. Usually the ga s is at at- mospheric pr essure, although in so me cases a s light superpressure is maintained.

c. All types .have control and power plant cars and control sur- faces.

TM 1-320 0-6 AIR CO RPS (1) In sma ll nonrigids cars are usually open and contain power plant s as well as altitude and direction controls. Su ch cars a.re usually suspended by cables attached to the envelope. In se mirigid and rigid construction cars are in contact w ith the keel which car r ies their load. Po wer plant cars are sepn. rat e from the control car.

FIGUHE 1.-U. !:i. Army u u uri gi<.l 1' (;-7.

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(2) Co nt rol surfaces on nearly all air ships consist of fixed ve~ti- cal and horizontal s urfa ces, ~tttached to which are elevators and rud der . On nonrigids and some semi ri gids th ese surfaces are at- tached to th e envelope by rigging. On I talian type semirigids and on all rigid s con trol surfaces are s upport ed by m etal framework.

d. Figur es 1, 2, 3, and 4 depict types of airships, showing general streamlined shape of the hull and arrang ement of cars and su rf aces.

6. Aerodynamic forces. -Ae rodynamic forces may be di vided in to two classes, those parallel and those normal to the path.

a. The former, or drag for ces, r eta rd the flight of the airs hip and mu st be overcome by the power plant s acting through the thru st of the propeller s. Po wer requirements in their turn a ff ect fuel con- su mp tion and limit perfo~·mance of the airship. He nce a thorough knowledge of resistance and power requirements ·is esse ntial to i nt elligent operation of air s hip s.

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TM 1-320 6-7 AIR CORPS b. The second class of aerod yna mic :forces, sometimes called trans- verse :forces, is the result of use of control surfaces or of gusts en- countered by the airship. Calculation of the effects of these :forces is, as mentioned before, often a matter of more interest to the designer tha n to the operator, but an understanding of the pr inciples involved ' • FIGUIII:l 3.- U. S. Army ;sem iri g id R S - 1.

' is necessary be ca use it is through these forces that control and stability are effected.

S ECTION II RE S ISTANCE Paragrap h Fluid resistance --- - - -- - --- ----- - - -- -- ------ -- -- ----- - --- - ------ - --- ---- 7 S hape coeffic i ents- - ---- ------ -- ------ -- ----- - ---------------- -------- - -- 8 Coefficie nt of skin fricti o n__ __ _ ________ _ __ _ __ _ ______ __ _ ____ ____ ___ _ __ __ 9 Resi stance of streamlined bodY --- - - ----- ---------- -- -------- ---- ------ -- - 10 Pri smatic coefficient --- - -- - ---- ---- --- -- - ------- - - --- --- ------- ----- -- - - 11 I ndex of fo rm etfi.ciency - ---- --- --------- - - ----- ---- -------- - -- --- ------ 12 Illu st rative resis tance problem ------- - ---- - - ---- --- ---- - - - --- ---- - -- ----- 13 Scale effect-- -- -- ---- - --- ---- ---- -- ----- --- -- --- -- - ---- ----- ---- - --- --- 14 Res i!;) tance of completely rig ged n i rs hiP ------ ---- - - - -- - -- -- --------- - -- 15 D oc eleration tesL- ------ -- ----- ----------- ---- ------ ---- ------ ---- - --- - 16 7. Fluid resistance. -a . Before attempting the study of resistance the student should be famil iar wjth the composition and nature of

TM 1-320 AIRSHIP AERODYNAMICS 7 the atmosphere, with dens ity and specific gravity calculations, and with the action of gra vitat ional forces. Th ese mat te rs are discussed in TM 1-325.

b. Wh enever a so lid object moves through a flu id it encounters a re si st an ce to it s mot ion. This re sista nce may be considered from two poin ts of view.

(1) Momentum theory. -( a) By N ew ton' s first law, a b ody at rest or in motion will remain at r est or c ontinue to trave l at consta nt • • ' FIGURE 4. -U . S. Nnvy rigid Los .d.t~geles.

veloci ty unless some force is exer ted to change i ts condit ion. To enable the so lid to maintain it s motion relative to the fl uid , the molecules of the fl uid mu st be deflect ed to ma ke room for t he pa ssage of the solid. So to de fl ect the fl u id or air a force mu st be applied.

I n th e case of the airship this f orce is that furn is h ed by th e propeller thru st.

(b) It can be proved mathematically that if air were incompr essible and nonviscous, tha t is, incapable of o ff er ing r esistance to sh ear be- tween the parti c le s, the thru st of air partic les oppo s ing the motion of the solid would exactly equal the th r ust of the air assisting th e motion. H ence there would be no resistance to th e motion. How- ever, in th& atmosphere thi s ideal condition does not exist and the resi st ance is proportional to th e tota l kinetic energy of the deflected particles of air.

TM 1-320 7-8 AIR CORPS (2) Pressure-differenoe theory.-Figure 5 shows the motion of the part icles of an air stream passing a flat plat e held at right angles to the flow . The air is de fl ected from its course some distance in front of the plate and ha s a complex eddying motion in rear o.f it. In front of the plate the air is under an increased pr essure, while behind the plate there is an area of reduced pre ssure. The drag can be con- sidered as due to th e difference between the pr ess ures in front of and behind the plat e.

8. Shape coefficients. -a . The two systems in co mmon use for ex- .

pre ssi ng air resis ta nce are the engineering and the absolute.

(1) Under the engineer i ng system the formula is- R v= K a: AV 2 .

where R v=ai r resistance due to pressure difference.

A = cross sectional area norm al to the air stream in square feet.

V =ve locity of motion in miles per hour.

K IJ)=an empirically determined constant dependi ng on the s ha pe of the so lid and the mass density of the air.

In lighter than air practice the l ett er "K ," minus subscript, is used to denote K IJ) when the ma ss density of the air is st a nda rd (0 .0 0237 pound per cubic foot, which is the ·value when the pressure is 29.92 inches and the temperature is 60 ° F.).

(2} The absolute system, adopted by the National Advisory Com- mittee for Aeronauti cs, uses the formula: . u2 Ro = K DAP 2 where p= mass density of th e ai r.

v= velocity of motion in feet per seco nd .

K v=an empirical shape coe ffi cient.

';' .is th e dynamic pr essure per unit of area or the velocity head of the air stream. This formula ha s more definite phy sical interpreta- tion than the engineering formula from both the momentum and pre ssure-difference theorie s. Before s tud y ing aerodynamic dat a, the system which is being used should always be determined.

b. Some of the first prac tical te sts made to determine the effect of shape upon the re sistance offered the motion of solids through the air were .conducted by Eiffel. Since th en studies have been conducted by various investigators until at pr es ent the store of in- formation on thi s subject is qu ite elaborate. Figure s 5 to 15 give the action of the air on various sha pes together with the values of K.

TM 1-320 AIRSHIP AERODYNAMICS 8 . (1) Flat plate.-Figure 5, as described in paragraph 7b (2), shows a flat plate held normal to the a ir stream. Eiffel demonstrated that the c ircular di sk gives about 5 percent less resistance than the s quare fla t plate. Rectangles have slig htly high er values of K than the square plate · of the same area, the airflow around the edges of the X= .00328 ___ . ...

. -_ . ... ·-: _ .. .

-· · -

' -

FIOURI!l 5.-Air stream fiowing by a fiat plate.

cc X= .00328 27

-

-- . -

- .. .. .. ·-~ - - -~ .. --

·-

...... _~ .. -· .

-· ..

F IGU R FJ 6.-Air stream tlow!ng by an inclined plate.

rectangle being s om ewhat more re st ricted t han tha t in th e case of the square.

(2) Flat plate, inclined.- Fi gure 6 illustrates the case of the flat plate inclined to the air st ream. E iffel's constants for different angles of incidence are as follow s: Angle of incidence K J • 0.00010 0.00059 L).00124 10° 15° .

0.00193 0.00265 20° (3) Oonoave h.emisph.ere.- Exp e1'iments ha ve sh own that the re- sistance of a hemisphere wi th the co nc av e s id e facing the - dire c tion of motion is greater than t hat of a flat di sk of the sa me exposed 28 5746 "-- 41 8

TM 1-320 AIR CORPS cross section. K for a concave hemisphere is about 0.00389 (see fig. 7).

(4) Oonvero hemisphere.- For a hemisphere with the convex side facing the direction of motion or pointing against the wind the X= . 00389 :

-

Jl'louam 7 .- Air stream tlowing by a concave hemisphere.

x = .oooea

FIGURE ~.- Ai r stream flowing by a convex hemisp here.

X= .0008 : : FIG URE 9. -Air stream flowing by a sphere.

re sistance is much less t han for the concave hemisphere shown in figure 7. The resistance of the convex hemisphere is much less than t.hat of a flat plat of the same cross section or exposed area. Th~ coefficient of resistance is found to be about 0.00082 (see fig. 8}.

TM 1-320 AIRSHIP AERODYNAMICS 8 (5) Sphe-1-e . -The air fl ow around a sphere (w hich more closely ap- proaches a str eamline form) . is shown diagrammatically in figure 9.

It will be observed that the s pr ead in g out of the lines of flow before reaching the sphere is less marked than for the flat plate in figure 5.

The coefficient of resistance of a sphere va.ries somewhat with the speed, R. = 1.00 fat- flat -pla.te R .= .83 where L:o. = t R= . 77 where L: 0=3:1 FIGOREl 10. -Cyll nders.

but f or ordinary velocities its va lue is about 0.008. Th e sphere is the simplest geometrical form a nd is the most efficient shape for maximum volume per unit weight but has a greater resistance than the more perf ec t st reamline form ( see fig. 9).

( 6) Oylinder ( longitudiMl aaJis horizontal) .- Th e resistance of such cylinders decreases wl.th length until the fineness ratio is approxi-

X= ·?0123 fort= .5

,.

,. , ...

li'I GOR!l 11.-Alr stream flowing by a cylinder (arts normal to air t'low).

mately 4 to 1, after which it increases. The increase is due to the effect of slcin friction which will be discussed la ter . The relative resistance of cylinders as compared to that of a flat pla te of the same cross sec- tion is as shown in figure 10. Where the fineness ratio is 4 to 1, K = 0.00205.

TM 1-320 8 AIR CORPS (7) OyUnd err ( vertical).-When a cylinder of given cross-sectional area is placed wit h it s axis of revolution at right ang les to the direction of motion the resistance depends upon the fineness ratio of the cylinder.

Wh en the length an d diameter of the cylinder are the same the coe ffi - cient of res ista nce is only slightly greater than for a sphere of the same L

K = . 0006 for D = 4

-

-

FIGURE 12.-Air stream flowi ng by a cyli nder (hemisph e rical e nd s) .

.

cross-sectional area. Wh en the length-diameter rat io is increased to 4 to 1 the coefficient of resistance is approximate ly doubled, or K =0 .0018, and if the length-diameter ratio is reduced to one -h a lf (or 0.5 / 1) t he coefficient of r esistance is increased 27 p erce nt, or K =0.00123 (see fi g. 11). .

(8 ) Cylinder with hemispherical ends .-It is possible to r educe greatly the resistance of a cylinder by capping th e ends wit h hemi- WIRJ:S CABLES X: . 0026 K: . 00 13

K =. 0015 X = • 0029

- ~ • ·~ FIGURE 13.

spheres. The resistance is reduced to 20 percent of that of a cylinder w it h fl at ends. Th e va lu e of K for a cylinder with hemispherical ends ·and a fineness ratio of 4 is approximately 0.0006 (see fig 12).

( 9) W ires and cables.- W ires and cables may be considered as cylin- ders of very lo ng length. E xperiments show that the resistance of wire or st randed cable when placed norma l to direction of motion is very n ear ly equal to the resistance of a flat plate of the same projected area.

Th e gain by the circular form of the wire is counterbalanced by its very

TM 1-320 Affi SH IP AERODYNAMICS great length. The resistance of a long, narrow object perpendicular to direction of motion is greater than that of a more symmetrical form.

Th e experimentally determined va lue of the coefficient of resistance is 0.0029 for stranded cables and 0 .0026 for smooth wires. K is almost in- dependent of the diameter for a ll sizes of N.PL. "I wire and cable. Stranded wire or cable ha~ a resistance about 14 perce nt greater than solid wire.

(a) Th e above discussion relates only to N.P! .. 2 wires and cables perpendicular to the wind direction or direction of motion. . When a wire or cable is inclined to the perpendicular . Fimnessl!t:dto 4j/!. K=.ooo4 its resistance is very much decreased as the N.PL 11'..3 air flo ws around it in more uniform stream- lin es or in a more gradual curved path. An ' inclination of about 30° from the vertical /'inmes.s ~crlto 41% K:.OOQ38 reduces the resistance 20 per c ent and an in- NP.J.. ..-4 ~-r-:- ·- ·- · ~ clination of · 45° reduces the resistance 50 / ' "/ percent.

-~ / (b) When two wires or cables are close together and placed one just behind. the other there is a reduction in resistance due to shielding of the second wire by the firs t. If they are placed very clo se together their combined resistance is considerably less than the resistance of one wire .alone, as the two wires have the effect of an increased fineness ratio. If they are spaced more than 3ljz di - ameters th eir combined resistance becomes greater than a single wire bu t is still less than the resistance of the two wires tested l'lnen~ss Raho 2/1 1<Q.ooo8:J FIGURE 14.-Struts .

separately. This shows that if two wires or cables are close together (within 5 diameters of each other) it is very advisable to put a filler block in between them, thus preventing the air from flowing in between them an d .

giving them the advantage of a single member of high fineness-ratio.

If the two wires are streamlined in thi s way their combined resistance can be kept down to about 50 percent of the resistance of a single wire until their fineness ratio becomes greater than seven. The hig h value of the resistance caused by wi re s and cables immediately sug- gests reduction of wires and cables to the minimum by means of refinements in design and arrangement.

- .

TM 1-320 AIR CORPS .

(10) Struts of strecmWirw form.-It is fou~d in practice that the best fineness ratio for struts is 4 to 1. Inclining the strut to the vertical does not have the effect of reducing the resistance for streamline forms, but for blunter shapes (shorter than the true streamline) inclination reduces the resistance considerably. A group of strut sections are shown in figure 14 and the value of K for each shape is shown. It can be seen that the effect of yawing is to increase greatly the resistanoo by placing the strut sidewise or at a different ang le to the air stream.

(11) AirshVp cars.-All cars are built to take advantage of stream- line form. This is especially true of the inclosed models for which an average value of K is 0.001. However, there is a wide variance in the shape of airship cars and a corresponding variance in the value of K.

K=.OOl (average value) FIGURE 15.-Air stream fiowing by airship~ For each different shape a new value of K must be determined by wind tunnel test.

c. The following problem illustrates use of the resistance formula: ( 1) Problem.- (a) What is resistance of a fiat . plate 1 foot square placed at right angles to direction of motion when moving at a velocity of 30 miles per hour in air of standard density?

(b) What is resistance at 60 miles per hour~ (2) Sol!ution.

(a) Rv= KAV =0.00328X 1 X900=2.95 pounds.

(b) Rv = KA V = 0.00328 X 1 X 3600= 11.81 pounds.

Thi s problem illustrates rapidity with which resistance increases with increasing velocity.

d. Based on resistance of a fiat disk, the following shapes have the relative resistance shown below : Percent Square plate- ----- ------ -- --- - -- - - - -- --- - - --- - ----------- - 104.5 Cylinder, horizontal-- - ------- - ---- -- ------ ------------ - - 65. 5 Sphere-- -------------------------- - ----- - --------------- - 25.4 Cylinder, capped ends------------ - -- - - - - - ----------------- 21.0 Airship model -------- - - - ·- -·- -- - --- ---- ------- ----- 3. 0

TM 1-320 AIRSHIP AERODYNAMICS 9-10 9. Coeftioient of skin friction.-a. In the case of a flat plate at right angles to the air stream the resistance is almost entirely due to the pressure difference in front of and behind the _ plate . This is not however the case with most solids. In general, resistance may be divided into two parts: ( 1) Pres sure difference.

(2) Skin friction.

b. When a solid passes through the air it carries along with it a very thin layer of air, the exterior surface of which forms a pl ane of air cleavage. The resistance of the air particles to shear on this plane is called skin friction.

c. The value of the skin fr iction on an airship hull, as determined empirically by Zahm and others, is given by the formula: 0 98 R ,= 0.0035pS • vue where S is the total surface area. A somewhat more convenient for- mula is-- R r= 0.00309pS vu 10. Resistance of streamlined body.-a. As mentioned before, the total resistance is composed of resistanc:A-e- (1) Caused by pressure difference.

(2) Due to skin friction.

The pressure-difference resistance is least for a very long and slender form. In fact, the greater the fineness ratio, the less will be the pres- sure-difference resistance. An increase in fineness ratio, however, leads to an increase in surface area and so to an increase in skin friction. It is ne cess ary therefore to compromise on a moderate fineness ratio, as a very long and slender form would have so high a skin friction as to more than counterbalance the gain by reduction of the pre ssure- difference resistance. A fl_neness ratio of 4 to 1 is very good for a small nonrigid, but for large rigid s it has been found advisable to increase this ratio to 6 or 7 to 1. Recen tly an airship had been designed whose hull has a much smaller fineness ratio than the conventional designs.

This airship has a capacity of 200,000 cubic feet and a fineness ratio of 2.82, noticeably shorter than any ships recently constructed. A model of this ship was tested in the wind tunnel of the Washington Navy Yard and was found to have the lowest resistance coefficient -of any model ever tested there.

b. Since the volume varies as the cube of a linear dimension, while the cross-sectional area and surface area both vary only as the square,

TM 1-3 ' 20 10-11 AIR COR PS the resistance is proportional to the two-thirds power of the volume.

TMs leads to a more convenient expression for th e resistance of airship hulls as follows : R = 0 DP (volume) •;s v~.se where OD is called the P randtl s hape coefficient afte r the eminent au- thority, Professor Pr andt l. Values of 0 D for various speeds are given in table I.

c. The offsets for di ffer ent types of airships are given in tab le II.

A study of the shapes given therein in connection with the Prandtl coefficients will bring out the relative efficiency of the different stream- lin es.

d. Certain general rules of design developed by experience and test may be summarized as follows: ( 1) The best form is one of continuous curvature with radius of cu r- va ture constantly increasing toward rear portion.

(2) T he shape of extreme r ear portion of the hull does not seriously affe ct the resistance.

( 3) The introduction of a cylin dr ical midsection causes an addi- tional resistance equal to the skin friction on the increased surface area of the hull.

(4) The major diameter should lie between 33 and 40 percent of total len gth from the bow.

11. Prismatic coefficient. - Th e ratio of the vo lume of any hull form to that of the circumscribing cylinder is called the prismatic coefficient, Qv.

Volume Qv= Maximum cross-sectional area X length VOl = Q.t.A.L The prismatic coefficients for different shapes are given in table I . .

TABLE I.- Airsh ip model characteristics and data

--

-- -. - -· - -1

Index ofform efficien cy; Dis- Pris- Area Fine- ~ Prandtl sha8~ coefficient, Q tan ce Dis- matic maxi· ness Hr=- · maxi- tance CD mum co e ffi · ratio, Volume, -t I x. en Surface.

~ th. Dlame· .

mum CG

"'

cient, cross- -- -- - ·- .

FR .... Name of model Vol.

s

, I ter. /) C) diameter from sectional L Q=- VtJI.

20 40 60 from nose 40 60 ar ea A XL m.p.h. m. p. h. m. p. h, I m. p.h . m.p.h. nose m.p.h.

A ....

....

--

- -- · ·· ·· - - -

--

- ·- -. -- I

-·

P.d. L P.ct . L } Sq.ft. Sq.ft. Ou.f t .

Feet 40. 10 36. 76 41. 7~ 0. 6176 0.0148 37. 80

0. 0168 o. 0 154 5. 060

0. 8304 0. 6967 5. 800 0. 381

l

N a.vy B (Goodrich)--- ·_. 3. 5 ------

41 27 45. 57 48. 25 . 656 2 46.37 . 0144 . 0136 4. 620 30. 00 . 6259 • 0159 4. 750 . 323 . 6417 Navy 0 --- ------- ---- -2. 9 . 6621 . 0142 36. 25 48. 64 . 01 68 . 0146 4. 870 - - - ---

--- ---

5. 007 . 323 6690

• 6417 -- ----

Navy E-------- - - - - - - - 4. 1 40. 08 42. 70 35. 49 . 6891 . 0138 4. 820 41. 59 43. 92 . 0 166 . 0147 . 5890 E. P- _ .. __ __ __ -- - __- _- 3. 0 . 6417 4. 597 . 323 39. 80 4 2. 84 35. 25 44. 25 . 61 69 . 0144 4. 650 38. 18 . 0175 . 0155 . 323 • 5955 . 6417 4. 59 7 I. E _____ __ -- -- - - - - ---- 2. 9

'!

40. 89 45. 37 49. 43 . 66 24 28. 76 Goodyear 4 2 _______ __ 3. 1 . 01 44 . 0134 4. 640

. 7840 • 0162 - . .. -- -

5. 4 70 . 371 • 6870 . 6184

Goodyear - L _ _____ __ __ 3. 4 . 0141 34. 15 -- - . . .. l:rl

5. 130

. 7 360 - - -- -- --- ---

5. 600 . 348 -- ·· - - - • 6660

- - - - -- --- - --

. 6194 . 0141 6. 030 36. 14 . 317 . 7520 ---- --

Goodyear - 2 _ __ ___ - - --- - 3. 8 6. 000 - --- -- --- -- ··

• 6350

- ---- - ------

------

. 7119 . 01 40 5. 970 36. 36 Goodyear - 3 ____ .. ___ _ . _ 3. 6

5. 900 . 297 . 7760 ------ ----- · ~

• 6150 --~ ·---

------

------

------

. 6624 28. 76 . 01 53 4. 640 -- --- ·~ . 7840

5. 470 . 371 - - ---- --~- - -

Goodyear - 4 __ __ -·- ·· -- __ 3. 1 . 6870

------ - -- - --

------

~

- 34. 68 41. 45 44. 83 . 65 90 4. 580 33. 80 49. 08 . 0147 ~ Astra- Torres __ . . _____.. _ 3. 1 . 6583 . 01 90 . 0 15 9 . 6914 5. 190 . 309 . 5679 . 3 4. 42 30 . 70 32 . 64 Ol Parseval P. L __ __ ____ __ 3. 9 6. 140 38. 75 43 . 19 . 0185 . 0174 . 0165 . 724 0 . 6417 5. 465 . 323 33. 39 34. 62

31. 36 ~

44. 46 . 5677 Par seval P. !!_ ____ ___ _ _ 3. 2 . 0 164 4. 990 38 . 90 . 0181 . 0170 . 323 . 5891 • 6417 4. 5 28

>

34. 05 36. 06 37 . 86 . 6095 47. 33 45. 85 P arseval P . IlL _____ __ _ 3. 2 . 0161 4. 699 . 6331 . 0179 . 0169 4. 750 . S23 • 6417 ~ 35. 23 35 . 82 . 6090 35. 00 4. 960 45. 00 45. 88 P arseva l S. S. T _ __ ___ __ 5. 6 . 0170 3. 4550 . 0174 . 0173 14.720 1. 008 1. 1330 >-<1 21 67 29. 28 23. 63 46. 00 . 6003 P ony Blimp AA ______ __ 1. 9 . 0277 3. 4 10 42 . 50 . 0205 . 0254 . 267 . 3196 58" " • ~ ) V 2. 7 60

Q

UB-FC ____ _____ _ ____ 4. 9 . 65U 6 . 0219 4. 663 . 0321 . 0223 - ~~- - - -· ·- ---

12. 958 4 . 8810 2. 8 60 3 - -- ---

~ 1. 0591 - -· - ~ -- -- ·- ·- ...

UB - 2 ___________ _ __ __ 4. 4 . 61145 . 0192 3. 823

2. 92 01 . 0205 • 0 189 - - .... ... - · -----""'

12 . 224C 1. 0 63::: --- · --

ll. 1638 --- .. · -- - - ·· ·-- -

C class cylindric midships .

48. 21 51. 13 1-1 diameter __ ________ __ 3. 1, 6749 43. 82 . 013Z 4. 8 5::: . 6777 . 0154 . 01 40 5. 073 . Z~3 - 64 17 -· · -· · .. .. . ··-·- - -- • 49. 00 51. 18 . 6909 45. 16 . 0141 . 0135 5. 100 . 7297 . 0153

Yz diameter ____ ----- - __ 3. 2 . 6417 5. 398 . 323

-- ---- - - ·- - --

1 diameter _____ __ ____ __ 3. 5 49. 21 52. 82 . 7184 43. 80 . 0 14 6 . 0136 5. 570 . 323 . 8330 . 0164 . 6417 6. 043

- -----

-- ----

55. 96 2 cliamet3r ___________ __ 4. 2 43. 49 50. 74 . 76 11 6. 600 . 0175 . 0150 . 0136 7. 337 . 323 1. 0404 . 6417

- --- --

------

3 diamete r ____________ _ 4. 8 . 7925 45. 81 50. 80 53. 55 . 0148 7. 59 0 . 0173 . 0156 . 6417 8. 627 . 323 1. 2471

------

------

4 diameter_ ____________ 5. 5 55. 94 . 8167 46. 67 52. 02

~

. 0146 8. 590 . 0175 . 01.'>7 . 64 17 9. 922 . 323 1. 4548

------

------

5 diameter _________ ____ 6. 1 56. 47 50. 96 54. 27 • 323 1. 6625 • 0164 • 0154 • 0148 9. 602 ----- - -- ---- • 8358 . 641711.218 ~-'t-4 ..... ~ t.:l

~

... I-' ... J.,

TABL E I . -Air ship model characteristics and data-Continued

t-:) .

Area Di s- .

F in&- Pris- Index of form efficien cy Prandtl shape coefficient maxi- ness tanoo Dis- matic Q CD

H,- -

mum ratio, maxi- tan co coom- CD Diame- Sur face, Volume, Lenzth· Nam e of model cross- FR mum CG cient, ter, D Vol.

sectional L diameter from Q Vol.

~- · area 20 10 from nose 60 20 40 eo -A-L D m. p. b. m. p. b.

A m. p. b. nose m.p.h. m. p.h.

m. p. 11.

- - -· · ·- .

-

- - -

-

EUiptical series (British) Feet Feet Sq. ft . Sq. ft. Cu. ft. P.ct. L P.ct .L 2. 371 0. 3906 0. 120 0. 1658 0. 0132 0. 0135 6. 070 33. 19 44. 20 43. 22 0 5835

-- --- - ---- --

-------

------

E ~ ---------------- --- - 1. 743 . 3910 . 120 . 1261 . 0128 . 0138 4. 460 33. 86 . 6024 43. 65 47 . 06 E 2- -- - ------------- -- ----- -

--- -- -- --- ---

------

1. 568 • 3920 . 121 . 1112 . 0147 . 0120 4. 000 . 5876 40. 00 34. 19 45. 55 E 3 ---- -------------- - ---- - -

-- - ---

-------

------

E4 _____________ _ __ _ __ 1. 384 • 3923 . 121 . 0972 . 0167 . 0139 3. 500 35. 18 . 5810 34. 79 41. 80

--- ----

-- - --- ---- -- - --- --

1. 178 . 121 • 3929 . 0826 . 0184 . 0147 3. 000 33. 43 . 57 86 31. 45 39. 36 E 5----- -- ----- -- -- -- -

-- --- - -- ----

-- ----

-------

'

~

~ Parabolic series (British) p } ____________ ____ ___ 1. 594 . 3900 . 120 . 0970 . 0168 . 0137 4. 090 49. 39 . 5094 30. 32 37. 18

~

-- --- - -- ----

--- - --- P2 ______________ ____ _

------

al 1. 598 . 3903 . 1000 - 120 . 0169 . 0176 4. 070 32. 06 . 5265 31. 15 30. 00

------- -- ---- - - -- -- - --- --

Pa ________ __ _______ __

1. 173 . 3867 . 117 . 0729 . 0226 . 0173 3. 830 . 5293 23. 42 30. 60 50. 35

---- -- -

----- - ------

------

1. 217 . 38 70 • 0714 . 118 . 02-15 . 0193 3. 140 35. 05 . 4989 23. 20 25. 85 -- --- -

-------

P4- ------- --- ------- - ------ -- - ---

- --···- -------------------------- -··- - ---- --------------- ···---------- ------ --- --- - ..

T ABLE Il. - Ojfsets of various streamline forms, Un it ed States models

Navy B (Goodrich) Parse val P. III a. s. T. Pony blimp A.A.

NavyO NavyF E. P. Parseval P . I Parse val P. II

- - .... -

-

- - - - - ---

--

Distance Di stance Distance Dis tance Di st ance Distance D istance Distance Distance Dlam- Diam- Diam- Diam - Diam- D!am- Dlam- Dlam- Dlam· from fro m from from from from from from from eter etcr et .c r eter eter eter etor eter eter nose nose nose noso nose nose nose nose nose

-- - -- -

- - - -

- - -- -- ·-

- --

Pet. L.

Pa . L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. L. Pet. D. Pet. D. Pet. L. Pet. D.

0. ];3 24. 16 2. 81 32. 47 1. 23 23 . 12 24. 88 1. 25 27. 37 1. 25 27. 27 1. 25 21. 56 1. 24 21. 41 2. 09 2. 36 20 . 58 4. 73 41. 27 5. 62 55. 06 2. 45 35 . 06 2. 59 34. 60 2. 50 37. 92 2. 50 37 . 92 2. 50 32. 99 2. 51 32. 98 4. 19 3 3. 49 47. 79 7. 09 5 5. 14 8. 43 69. 61 3. 68 43. 90 5. 19 4 8. 44 5. 00 51. 95 5. 00 51. 95 5. 00 4. 99 47. 83 8. 38 54 . 65 9. 45 65 . 27 79 . 22 4. 91 50 . 61 10. 37 66 . 10 10. 00 71. 17 10. 00 71. 17 10. 00 66. 23 66 . 07 12. 57 11. 24 9. 99 67. 71 11. 81 75 . 36 16. 86 91. 17 7. 36 62. 73 1 5. 56 78. 12 14. 99 83. 38 1 5. 00 8 3. 36 15. 00 7 8. 70 14 . 98 78. 89 16 . 75 77. 50 91. 17 20. 00 20. 00 1 4. 18 8 1. 94 22 . 48 97 . 40 9. 81 72 . 08 20. 75 86. 66 19. 98 9 1. 17 88. 05 19 . 97 88. 07 20. 94 84. 60

~

2 8. 11 100. 00 12. 26 7 8. 57 25. 94 92. 73 24. 98 96. 10 2 5. 00 96. 10 94 . 03 9 4. 04 25. 13 1 8. 90 90 . 31 24. 97 89. 99 H 2 5. ~8 .!"d 23 . 63 94; 98 33 . 73 100 . 00 1 4. 71 84. 93 31. 12 96. 75 29 . 98 9 8. 96 30 . 00 98. 96 30. 0 97 . 40 29. 96 97. 32 29. 32 94. 18 42. 16 2 8. 35 98. 09 98. 18 19. 62 9 3. 51 36 . 31 99. 40 34. 97 1 00 . 00 35. 00 100. 00 35 . 00 99. 22 34. 97 99. 11 33. 51 97 . 23 99 . 64 94. 29 24. 54 39 . 96 99. 48 40. 00 99. 48 40. 00 100. 00 33 . 09 50 . 59 98 . 05 41. 50 10 0. 00 39. 98 99 . 80 37 . 70 99 . 01 37 . 82 100 . 00 59. 02 88. 83 29. 45 99 . 61 48. 81 9 8. 44 44 . 96 98. 18 45 . 00 98. 18 45. 00 100. 00 4 4. 99 100 . 00 41. 88 100. 00

i

t:j ~ 47 . 25 98. 44 fr7 . 45 81. 56 34. 35 100 . 00 56 . 12 93 . 77 49. 96 94. 81 50. 00 94. 81 50. 00 98. 06 50. 00 98. 75 46. 07 99. 43 ~ 39. 27 56. 70 93. 06 7 5. 89 7 1. 69 99. 74 63. 43 86. 23 54. 96 89. 87 55 . 00 89. 87 55. 00 95. 86 54. 99 95 . 87 50 . 26 98. 08

z

83 . 25 84 . 32 59. 48 44 . 17 70 . 74 7 5. 32 83. 90 60. 00 66. 15 98. 96 59. 96 60. 00 83. 90 91. 69 59 . 97 91. 75 54. 45 95. 88

>

70 . 88 7 6. 91 89 . 94 48. 57 49. 07 97 . 53 78 . 05 60. 52 64. 95 76. 36 65. 00 7 6. 36 65. 00 85. 97 86 . 24 64. 96 58. 64 9 3. 47 ~ 7 5. 60 69 . 38 92 . 75 4 1. 56 53. 98 9 5. 15 85 . 36 4 4. 16 69. 95 67. 53 70. 00 67. 53 70. 00 7 8. 9 6 69. 94 7 9. 14 62. 83 89. 64 ~ 58. 78 23. 90 80. 33 61. 00 9 5. 56 31. 95 62. 34 9 2. 68 74 . 94 57. 66 7 5. 00 57 . 66 75 . 00 70. 91 74. 93 7 0. 34 67. 02 84. 81 {/l 9 8. 37 18. 96 63. 69 88 . 3 1 100. 00 7 9. 94 47. 01 80. 00 80. 00 59. 74 8 5. 05 51. 44 47. 01 79 . 91 59. 76 71. 20 78. 42 - 0 89 . 7 8 39. 35 100. 00 .0 68. 69 83. 25 84. 93 35. 84 85. 00 85. 00 47. 27 7 5. 40 35. 84 84. 89 47. 39 71. 04 -- - --- - --- - -- 77. 27 92. 14 31. 94 73. 60 89. 92 24 . 16 90. 00 24 . 16 90. 00 23. 25 89. 87 32. 99 79. 58 63. 52

-- - --- - ------

--- ---- ------

7 8. 51 70 . 26 9 1. 92 1 2. 21 9 4. 50 23. 44 95. 00 12. 21 95 . 00 17. 14 9 4. 86 10 . 83 83. 76 54 . 65 ------

---- -- -

------ -

------

1 4. 00 83. 41 62 . 38 100. 00 . 0 100. 00 100. 00 96 . 86 .0 .0 100. 00 . 0 87. 96 45. 78 -- - --- - -- - -- -

-- - -- --

---- -- ·

9 8. 14 8. 97 88. 32 52. 47 92. 14 35. 49 -- ---- ---- ---- --- - -- ---

---- --- -- -- -- -- --- - - - · -- - - ---- - --- --

------

------ ------

100. 00 . 0 93. 22 40 . 52 96. 34 22. 21 - - -- -- -- - ---

-- - -- -- - ------ -- ---- -- - - -- - - -- --- ------ --- ---

-- ~ ---- ---- --

-- --- -

94. 45 36. 75 100. 00 . 0

------

------ ------ -- -- -- --- -- - ------

-- - ---- - -- --- - ---- - -- ------ --- ---

-- -- -- ------ --- -- --

95 . 68 33. 12 - - - - - - - - - - -- - - ---- -

- ----- -- -- --- ---- - - ------ - -- ----- - - ----

-- ----

------ --- --- ------ -- ----

-- -- -- ---- --

96 . 91 28. 31 --- -- - - - - ---- ----

--- - -- ---- --- ----- - -- - - -- - -- -- --- - --- -- -- -- ----

---- -- ------

-- ---- --- - -- ----- -

--- ---

~

22. 47 98. 13 - - - ---

-- ---- ------ -- -- --- ------ -- - --- - --- --- ---- -- - -- ---

------ -- - ---- ------ ---- - -- ------

------

---- --

99. 36 12. 26 ... I-£ -- -- --

----- -- - ----- --- ---- ---- --- ------ --- --- ----- -

------ --- --- ---- --

-- --- - ---- -- -- - ---- -- ----

------

.

100. 00 .0 -- --- - --- -- - -

------ - - -- --- - ---- -

--- - -- ----- .. ----- - -- ---- ... ~

-- -- - -- -- -- --- -- - ---

-- ---- ------ ------

---- --

~

TM 1-320 12-14 AIR CORPS 12. Index of form e:fficiency.- In general, in design it is desired to get the greatest volume from the. least surface area as this reduc~ weight and diffusion. Fortunately, good streamlined shapes usually hav e high prismatic c oeffic ients, but of course some shapes are r.nore efficient in this regard than others. In studying relative efficiency of shapes, both the resistance coefficients and the prismatic coefficients mu st be considered. The ratio of the latt er to the former is called the index of form efficiency, H t· ·

H ,= &

13. Dlustrative resistance problem.-a. Proolem .. -Given an airship whose hull has a length of 200 feet and a major diameter of 43.5 feet 'vith the hull offsets those of the C type airship envelope.

( 1) w·hat is total volume of envelope~ (2) "What is hull resistance at 60 miles per hour in sta ndard atmos- ph ere~ b. Solution .

, (1) Vol =Q .v AL From Table I, Qv is 0.6562.

7rd 3.1416 A =4= (43.5) = 1,485 square fe et.

H ence Vol=0.6562X1,485X200=195,000 cubie feet.

(2 ) R=0Dp(vol)2/3vl.86 60 MP H=60 X15=88 feet per second.

GD from T able 1 =0.0136 at 60 M PH 213 86 R=0.0136 X0.00237X (195,000) X881· R=455 pounds.

14. Scale effect.- a. One great rea son why so much difficulty is encountered in determining prior to construction the resistance o£ the completed hull li es in the fa ct that the resistance of the model cannot be multiplied by the ratio of the linear dimensions of the model and the co mpleted hull to determine the resistance of the latter. The discrepancy between the calculated resistance and the actual resistance of t he full-sized airship is attributed to scale effect. Oft en errors in calculation due to :faul ty data or bad theories are so explained away by those re sp onsible :for the mistakes. There are several reasons how- ever, why, even with proper data and theory discrepancies will ·exist between calculated and actual resistance.

TM 1-320 AIRSHIP AERODYNAMICS 14-15 b. The theory of dimensions shows that the coefficients of resistance.

1'L vary directly as -;-· whe re v=velocity in fe et per second.

L=som e convenient linear dimension of the body such as the diameter in the case of a cylinder.

v= kinematic viscosity coefficient of the fluid.

a. v, the kinematic viscosity coefficient, is defined as the ratio be- tween the absolute viscosity coe ffi cient and the atmospheric mass density. Hence- e - v=~' where v 1s the absolute viscosity coefficient of the air and is a constant.

vL d. -;' called the Reynolds number aft er Profes sor Reynolds, depends on th ree variable quantities, p, v, and L : To predict full- scale performance from the model tests, allowance must be made for the fact tha t the L in the full-sized airship is very different from th e L in the model, and consequently the co-efficient of resistance will be different.

e. To overcome the effect of this difference a wind tunnel has been built at Langley Field in w hi ch p ma y be sufficiently increased to make the pr oduct pL for the model equal tha t of the full-sized sma ll nonrigid airship, thus eliminating scale effect.

15. Resistance of completely rigged airship. -a . There are · very li ttle data available showing the relative resistance of the various parts combining to produce the total r esistance of a completely rigged air s hip due to the difficulty in obtaining dynamic similar it y between the model tested and the full-scale airship.

b. Total re sistance of air s hips may be subdivided approximately as follows for- (1) Large nonrigids with closed cars: Percent (a) ~n velope_____ ____ ____ __ ___ ___ _ _ _ ____ _ ______ ___ _ 45 (b) Surfaces-------- - - - --- -- - - -- --- - - ----- - ---- - - -- 20 (c) Rigg ing and suspension cables __ __ _____ ___ __ __ ___ 15 (d) Cars_______________ _ __ ___ _ __ ________ __ _____ ____ 15 (e) Accessories -- - ------ -- ------ -- - ----------------- 5 (2) Small nonr igids with open car s : (a) ~nvelope ____ -------- _ - --- ·· __ ___ __ -· - ------ __ ___ . 35 (b) Surface s---- ---- -- - ---- --- --- - --- - --- - ----- -- - · 25 (c) Rigging and cables __ __ __ ________ ___ ____ __ ____ ___ 20 (d) Cars------------------ -- - ----- --- -- ----- ---- - - _ 15 (e) Accessories---- ------ - - . .. _ - ------ ------------ 5

TM 1-320 16-16 Am CORPS (3) Semirigids: Percent

(a ) ~ve l o p e- ------------ ------------- ------ - --- -- ~ 53

(b) Surfaces _______ _____ ____________________ _ __ _ ___ 20 ( c) Jtiggjng- -- -- -----~-------- ---- -- ---- -------- -- - 7 ( d) Cars __________ ____ _- -- --- ----------- __ - - ------- 13 ( e) Accessorie s------------ -- - ------- ------------- -- 7 ( 4) Large rig ids : (a) IIull _________________________ __ ___ ________ _____ 60 (b) Surfaces____ ___________ __ _ __ ________ _____ _ ___ __ 15

(c) Cars and suspension s------ ---- --- -- -------- ----- 2q

( d) Miscellaneous r igging and accessories_________ ___ 5 16. Deceler ation test.- a. Te sts are 1nade frequently on full- siz ed airships to det ermine actual risistance of the airshi p at various speeds. In these te sts the airship is brought to a certain velocity and then the motor s are idled, the velocity being recorded against time as the airship decelerates.

b. Th e general theory is that the resistance, or force causing de- celeration, is given by the equation : R= Mv a, where ex.= (decele ration in f eet per sec ond) z.

Mv = the virtual ma ss of Lhe ship .

Th e virtual mass of an airs hip is the mass of airshi p and contents plu s the mass of air which is carried along with it. This latter is computed by the Mun k formula : AMo=P1 , wh ere r is the radius of largest cross section.

c. Ob serving veloci ty at end of each sec ond gives the ra te of change of velocity, or decele ration, for each sec ond and by interpola - tion for each air speed. A ct ually formu la s are employed which in- .

volve calculus and are beyond the scope of this manual.

d. These deceleration .tests a re quite valuable as a check against th e resistance formul as developed in this section. They are however often com plica ted by poor instru m ents or faulty observation, render- ing it difficult to pla ce a proper value on re s ults so obtained. For the present more confidence is to be placed on the resistance formulas and the power requirement formulas which will be developed in the next sectio n.

TM 1-320 AIRSHIP AERODYNAMICS SECI'ION III POWER REQUIREMENTS Paragraph Power required to overcome airship resistance __ ___ _____________ ____ _ ___ __ 17 Results of various speed trials----- - - ------------- - --- -'- - --------------- 18 Burg ess' formula for horsepower- --· -- ---- -- --- -- - - -- - -- - -- -- ---- - - - - ---- 19 Speed devel~ped by given horsepower______ __ _ ____ ________ ___ _ ____ _ ______ 20 Summary ------------------------ - - -- ----- - - __ _____ _ ______ -- · -------- --- - 2l 17. Power required to overcome airship resistance.-a. To maintain uniform velocity in fli ght, resistance of the airship must be overcome by thrust of the propellers. The work done by the pro- pellers equals the product of the resistance times the distance through which the airship moves. · b. The unit of work in the English system is the foot-pound, or the quantity of work performed by 1-pound force acting through a dis- tance of 1 foot. Hence work done in propelling the airship in foot- pounds equals resistance in pounds times air distance traveled by the airship.

a. Power is defined as the rate of doing work, 1 horsepower equaling 550 foot-pounds per second. Therefore the power utilized to over- come hull re sistance must equal resistance multiplied by velocity in feet per second divided by 550 .

d. The resistance is given by the equation (see sec. II): 213 86 R = CD p (vol) ut.

Then the horsepower required to overcome this resistance is given by the formula: 213 86 Cn p (vol) if· H. P. = 550 e. Problem and solution-( 1) Problem .-What horsepower will be required to drive an airship of 195,000-cubic-foot ca pa city at 60 miles per hour ( 88 feet per second) in atmosphere of standa rd density~ The envelope shape coefficient is 0,0136. The propeller e ffi ciency, E, is 60 percent. The envelope resistance, F, is 40 percent of the total resistan ce of the airship.

(2) Solution. -The horsepower necessary to overcome hull re- sistance is given by- 213 86 Cn p (vol) if· H. P = 550 _ (0.0136 X 0.00237 X 3376.4 X 359000) =71.1 horsepower.

T.M 1-320 17-18 Am CORPS Since hull resistance is but 40 percent of total, the horsepower to over- come tota l resistance Since propeller e ffici ency is 60 _ percent- Total horsepower required= (71.1)(o.40~o.

60)

=296 hor sepower.

f. As illustrated in t he problem in d above, the following is a con- venient formula for the hor sepower requi red when the percentage of resistance due to the hull and the propeller efficiency are known.

g. A commoner method of determining the horsepower requirements is to determine a shape coe ffi cie nt by wind tunnel te st of the completely rigg ed model. In thi s case the body in question is not as perfe ct a streamlined s hape as the hull itself so the resi st ance varies more nearl y as the square of the velocity. Then the horsepower required b ecomess- - 213 8 0 D p(vol) v H. P.= 550E where 0' D is the shape coefficient of the model.

(1) P roblem.- What horsepower wil~ be required to drive an air - ship of 195,000-cubic-foot capacity at 60 miles per hour (88 feet per second) when the atmospheric density is standa rd, the coe ffi cie nt of resistance 0' D of the completely rigged ship is 0.0165, and the propeller installation efficiency is 60 perce nd (2) Sol1JJtion.

213 8 = 0' D p(vol) v H P . . 550 E 213 8 0.0165 X0 .00237 X 195000 88 ~----~~ 5s=o~x~o~.=6o~----- = 275 horsepower, nppro:-dmately.

18. Results of var i ous speed trials. -a. The following data were obtained by pr ogressive speed trials mad e on the United States Navy C class nonrigid airship of 180,000-cubic-foot capac ity:

TM 1-320 18-19 AIRSHIP AERODYNAMICS R- pounds V in foot- E ' B. H. P .

R . P M. C'D A p- sec- • Total Hull pend- onds ages 206 0.02 0 66. 6 1, 100 109 60 540 334 143 249 . 01 9 73. 3 1,200 60 643 394 . 019 1, 300 183 60 754 457 29 7 80. 1 1,400 231 60 875 5 17 358 . 01 8 87. 7 Th e value 0' D is the corrected coe ffi cient of resistance, but its ac- cura cy is somew hat unc erta in , al so the proportions o£ hull resistance app e ar high . The value o£ 0' D obtained from the win d t unnel test wa s · o.027 . Th e proportional va l ue of the appendages or para siw resistance was computed fr om the wind t unnel data.

b. Th e follow·ing data we re obtained from deceleration tests of German r igid airshi p s: Pr o- Num- Maxi- por- ber of mum Name Cub ic f eet B. H. P. tional D L C' D veloc- en- effi- ity gmes • ctency Foot- .

Feet Feet seconds 62. 4 450 67 0. 10 7 706,000 45. 9 460 3 J -' Z 10 92 . 5 1, 440 49 . 039 L 33 2,140,000 7 8. 3 645 6 92. 5 62 . 045 L 36 2,140,000 78 . 3 64 5 6 1, 440 • 1, 200 . 047 L 43 2,140,000 7 8. 3 645 88. 9 56 94. 0 1, 200 56 . 031 L 44 2,140, 000 7 8. 3 645 5 1, 200 . 031 L 46 2, 140,000 7 8. 3 645 5 9 5. 5 58 1, 200 . 034 L 57 2, 640,000 78 . 3 74 5 94. 8 69 1 ,200 L59 2, 640,000 7 8. 3 7 45 94. 6 66 . 038 113. 5 2,000 65 . 031 L 70 2 ,400 ,0 00 78. 3 694 7 19. Burgess formula for horsepower. -a. A very h a nd y for- m ula for determining the horsepower required to dri ve an ai rs hip of any given volume and speed is furni shed by t he N atio na l Ad viso ry Committee for Ae1·o nauti cs Report No . 194, as follows: 3 2 3 v p_(vo l) ' H. P .= Op ~8

TM 1-320 19 -20 AIR CO RPS where Op is a constant which can be taken from the co mpilation below: N O"nrigid a irs h ips .

50,000 to 200,000 cubic feet -- ----------- - - ----- -------- Op=20,000 200,000 to 300,000 cub ic feet_ ________ .. . -· ---- -- --- - -- Op=21, 000 300,000 to 400,0J :> cuui<: f eeL--- ---- -·-·--- -------- -- ---- Op = 22,000 R igid airsh ips 1,000,000 to 2,000,000 c ubi c feeL ___ ____ ______ ________ __ Op=3 0,000 2,000,000 to 3,000,000 cubic fe eL - -------- ---- ------ -- -- Cp= 32 ,000 3,000,000 to 4,000,000 cubic feeL ________ _ __ ___ _________ Cp=33,000 4,000,000 to 6,000, ()()() cubic f eet_ _ __ __ ____ ____ ________ __ Cp= 34,000 6,000,000 to 10,000,000 cubic f eeL __ ____ __ ____ -- - ----- Cp =3 5,000 b. Solv ing the pr oblem given in pa ragraph 17g (1) by the Burg ess formula gi ves- • P ( vol )213 va H. P .= Cp 3 8 - (0.00237) (1 95 ,000) ' (8 8) 20 ,000 = 273 horsepower .

20 . Speed developed by g i ven hor se power. -a. By transpos- in g the horsepower for mulas th e following f or mul as are ob ta ined for th e s pe ed developed by a given horsepower : 0 36

.s n / H. P. X550XE X F (H. P.X550 XEX F\ '

v= -y CvXPX (vol)2ta = CvXP X (vol)2/3 - ) from paragraph 17}.

/ H. P. X 550 X E = -y , X P X ( vol )2' 3 fr om paragraph 17 g.

3f H.P. X 01)f h 9 = V P ( vol) rom paragrap 1 a.

b. Problem and. solution .-( 1) Problem .- An airship of 195,000- cubic-foot capacity has a power in st all at ion of two motors developing 1 50 horsepower each, or a tot al of 300 horsepower. Th e at mospheric density is standard. W hat speed should be obtained at full po wed (2) S olution.- Using Bu rgess' formula.

/H. P. X 01)

v= -y p(vol )21a

I 300 X 20 000

2 3

- v o.oo 23 7 x (1 95ooo) '

=90.8 feet p er second = 6L9 miles per hour.

..

TM 1-320 AIRSHIP AERODYNAMICS 2Q-21 c. Problem UJrU1 solution.

(1) Problem.-An airship of 195,000-cubic-foot capacity is to be equipped with two .engines developing a total of 300 horsepower.

What speed can be expected using the following data~ (a) Standard atmospheric density.

(b) Shape coefficie nt, 0 n is 0.0136.

(e) Propeller efficiency, E, is 60 percent.

(d) Envelope resistance is 40 percent of total resistance of com- pletely rigged airship.

(2) Solution.-Using Pr andtl coe ffi cient.

0 86 300X550X0.60X0.40 ) · ( V= 0.0136X0.00237X3,376.4 =88.4 feet per second=6 0.3 miles per hour.

d. Experience has shown the lower figure, as determined by Prandtl coefficients, to be more generally correct than the higher figure as determined by the Burgess formula. .

21. Summary.- a. From study of the formulas it appears tha t the speed of an airship is proportional to the cube root of the horse- power, or vice versa the hor sepower varies directly as the cube of the speed. Since power plant weights vary directly as the horse- power, the weight of the power plant varies also as the cube of the speed. A point is readily reached therefore beyond which it is not economical to increase the speed due to the excessive weight"s involved.

b. In still ai r the higher the speed the l ess economical the fuel consumption and the shorter the radius of action. Th is is not true when the airship is traveling against adverse winds. The study of just which air speed is the most economical will not be discussed in this manual as it properly belongs to the subject of navigation.

8EariON IV STABILITY Paragraph Variation of pressur-e di stri buti on on airship bull __ _______________ __ __ ___ 22 Specific stability and center of gravity of air shiP -- ----- ------ - -- ----- - ---- 23 Center of bu oyanCY - ------------------- - - -- - -- --- - -- - --- ---- - ---------- 24 Descr iption of major a xi s of airshiP - ----- - -- --- - ------------- --- - -- - --- 25 Types of stability----------- ---- - ---- ---- - - -- --- ----· -- - -- ---- - ------ 26 Forces a nd moments acting on air s hiP---------- - ---------- ----------- -- - 27 Damping moment------- ------ ---- -- --- -- - ----- - ------------------ ---- 28 Longitudinal stabi I i ty - --- -- - --- -- - -- - -- - --- --- ---- - -- ---- --- ------- -- - -- 29 Dir ectional stabilitY---------------------- - ----------- - - -- ------------ 30 Lateral s tability--------------------- - - - - -- - - --- ------------------- ---- 31 S1JmJuarr-----·-----·--------- -- -- . .... . · ·· ·- ---------------- ... -·fl"'---·-·- ~

TM 1-320 .

AIR CORPS .

22! Variation of pressure distribution on airship hull.--a.

In section II resistance of an airship was shown to be parfly caused by increased n<?Se pressure. Throughout the discussion the airship was considered to be flying on an even keel and in a straight line..

All forces were parallel to the direction of flight. Before entering· the subject of stability proper it will be necessary to show variation in pressure distribution on the hull when the airship is not flying as considered in section II, or, in other words, when transverse aero- .

dynamic forces are present on the hull.

b. Figure 16 shows a typical pressure distribution on an airship hull when the airship is in horizontal flight in a straight line and on an even keel. This pressure distribution will be true whenever the line join~ ing the tip of the nose with the tip of the tail (longitudinal axis) is

-

+ + Direefion o! mofiDfl FIGURE 16.-Pressure distribution on air s hip hull (longitudinal arls pa rat:el to direction · of motion).

pa.rallel with the direction of motion. Because an air s hip can be con~ .

sidered as a symmetrical solid of re v olut ion, the pre s sure distribnt.ion has the following charactertisti cs : · ( 1) Distribution depicted is uniform for any plane passed th rough ~ the longitudinal axis.

(2) Varying reduced pressure exists from a section ju st in rear of the nose to a section just forward of the tail.

{3) Both nose and tail have positive pressure, but that on the tail is too small to be of much assistance to forward motion.

c. Figure 17 shows the distributions in pre ss ure for an 18° angle of attack to the relative air. Other angles of attack have similar dis- tributions. The distribution shown holds equally true whether the deviation of the axis from the direction of motion is in a horizontal or a vertical plane. When, for instance, the inclination is in the verti- cal plane, the following chara_cteristics are observed: (1) Positive pressure on the nose lies almost entirely in a zone be- neath the axis.

(2) Plane of transition, BO, figure 17, is oblique with regard to the .

.

aX;J.S.

TM 1-320 AffiSHIP AERODYNAMICS 22-24 {3) Areas of reduced press ur e are not symmetrical. Th eir maxi- mum values occur beneath the ste rn an d above the bow.

23. Specific stability and center of gravity of airship.-a.

By specific stability is meant the property of the airship itself to maintain the relative position of it s various parts unaltered in any contingency.

b. Conditions necessa ry f or specific st ab i lity are the invariahility of- (1) Shap e of envelope whether airs h ip is in motion or not.

(2) Relative positions of envelope and cars and s urfa ces.

c. Methods used to maint ain envelope shape are di scussed in sec- tion I. In var iabili ty of suspension of the car from the envelope is in- sured by a rectangular system of suspen si ons bra ced by diagonal cables ...

-

------

-

.

FIG URE 17 .- Pressure distribution on nlrsbip hull (longitudin a l axis Inclined to dir ectio n of motion).

le ng thwi se and cross wi se. Th ese cables pr event a ny very app reciable motion of the car in regard to the envelope in case of oscilla ti ons of the airship in vertical longitudinal plane or in tran sver se plane. As . will be shown later speci fi c s tability is ab so lu tely essential to s tatic sta bil ity of airships.

d. W' hen invariability of suspensions has been assured, the position · of the center of gravity of the airsh ip may be determined. Th e ce nter of gr avi ty is the point at which may be aE:3umed to be applied th e total resultant of the various weights which oppo se the lifting power of the gas. Th e position of th e center of grav i ty is natura lly not invari- able since the li ve lo ad of the air s hip is varia bl e. Usually for 'non- rigid a ir s hips the center of grayity, M , falls above the car a nd ei ther sligh tly above or sligh tl y below th e bo ttom of the envelope (see fig. 18).

24. Center of buoyancy. - The cen ter of gravity of th e ascen- sional force of the ga s contained in the envelope is called the c enter of buoyancy. For an envelope which is not moving thi s point should

TM 1-320 AIR CORPS 24-26 obviously be located on the vert ical line passing through the center of gravity, M, and for an envelope w hi ch has the form of a sym- metrical solid of rotation and w hi ch is full of gas, it should be located on the axis of the envelope itself.

a. However, when one or the other of the conditions mentioned is not fulfilled, that is, when the envelope is not a so lid of rotation (as is the case with the Italian semirigid) , or when it is not full . of gas, or when with the airship partially filled with gas the axis is deviated in the vertical plane from the position of rest, the center of gravity, G, is not located on the axis in question, since this is supposed to be a straight line connecting the extreme end of the prow with the extreme end of the stern (see fig. 18) .

b. That dissymmetry may cause this phenomenon is quite obvious.

Moreover, if the airship is not full, even if the envelope is symmetrical the point G will be located above the axis. La stly, if in a dd ition to not being full the envelope is inclined longi- tudina ll y, movement of the gas toward the high end will cause the point G to move in the same dir ection.

l c. Without entering into a minute descrip- FiouRE 18.- Posltlons of · f h · d b cente rs of gravity and tlon 0 t e vanous arrangements resorte to y buoyancy in nonrigid air· different constructors in order to lessen as far ship. as possible movement of the gas in the gas bag, assume, before going any further, that for an envelope with- (1) Horiz ontal axis, the point G is on the axis when the envelope is full, and moves along a line through M perpendicular to the axis as the amount of gas in the envelope decreases.

(2) Oblique axis, the point G mo ves a moderate distance away from the above vertical, or at least it moves in such a way that the distance is a definite function of the angle of inclination of the envelope on the horizon.

25. Description of major axis of airship.-a. The airship hull, as previously s tated, is a so lid of rotation and hence symmetrical about the axis of rota tion, X' X in figure 19. Actually, due to the loading of a nonrigid, the shape of a cross section of the hull is more nearly elliptical with the major axis of the ellipse vertical, but the distortion is slight enough to be disregarded.

b. To conform to the system of nomenclature used by the National Advi sory Committee for Aeronautics, the system of r:otation outlined in figure 19 will be unif orm througho ut this manual.

a. Obviously any angu lar deviation whatsoever of the airship will be found to be either pit.ch, yaw, or roll, or a combination of these

TM 1-32 0 AIRSHIP AERODYNAMICS 25-26 motions. With this fact in mind the types of stability now will be considered.

26. T ypes of stability.-a . Stability is defined as the tendency to return to a position of equil ibrium after a small deviation from that position.

b. In airships stabili ty is accomplished by two means, static and dynamic.

(1) Strictly speaking, the only real statical s tability is that which exists when the engines are stopped. Under this condition an air- Normt~l or verlh;;a/ Axis / /

\

\

~ os ifive O ir e cf"itms oF 1'9 xe.s a nd /l nfJ ~

(Fo rc es o nd . moment- .5 .s ~wn hit drrow.s)

' Axis Angle Moment about axis Velocities 3' .

~ I ~ I ~ . I ,.-...

. ....

...........

~ Q 8.·~ ..9l..8 s~

-;s

s:l t:l Obi) 0 0 '"'» .,...

~ ....

Designa tion a!UJ ~~ Q) B 0 ~ ..... ~ .......

,.. .....

0 > 0 0 ~

-

....

g, ala!

.a bO .a .0 ~ .

..... ..... ~

....

~ Q)~ ,..

rJl tl.l bO

s

a

~ Q .

Q) Q) ..... Q)

>. ~

~ & ~ ~

£ 00 ~ 00 H ~=: ·

LongitudinaL __ ___ Rolling _ __ RolL __ X X L 4> u p

Y- -z

LateraL __ _______ _ y y Pitch __ Pitching __

M z X e v q

I NormaL _________ Yaw ___ Yawing __

z

z N '1' w r

x--Y

I

' FJGtJRE 19.-Cbart showing axes of airship and conventional symbols related thereto.

-

TM 1-320 2~27 AIR CORPS ship is statically stable if it tends to return toward initial condition of steady motion whenever slightly disturbed from that motion. This requir eme nt is not dependent upon the plane in which deviation from steady motion occurs, and, as will be shown later, an airship is statically unstable in yaw.

(2) Dynamic sta bi lity is the stability effected by action of the air ~tream upon controlled surfaces. W e re it not for these surfaces air- ships would become unmanageable at very slow speeds.

c. Stability may be classified fur ther . An airship in steady flight ha s three types of stability, pitch or longitudinal, yaw or directional, and roll about the longi tudina l axis. While these stabilities are all corr elated in the case of an airplane, this is not the case with an air- ship, the three types of stability being independent of each other.

,.

w Airs/lip l'rtll'~h/1~ hDri'zonl"t~l!y in Sl"t~flc ~9uiliiJri11m. Lon~ifudintJ! t~xis coinicidenr with direction o/ mot-ion FIGURE 20.- Forces on airship in horizontal flight .

d. Th e followi ng discussion will be based upon the assumptions for each situation that- (1) Ascensional force remains constant.

(2) Tota l weight remains constant.

(3) Speed remains the same.

(4) Form of airship remains unchanged.

(5) Center of gravity and center of buoyancy remain fixed.

(6) Controls remain in neutral.

27 .. Forces and moments acting on airship.- a. Suppose an airship flies along a horizontal right-line traje cto ry .while its longi-

tudinal axis makes an angle of oo with th e flight path, then the

air ship will be acted on by the following forces and moments (see fig. 20).

(1) Forces: (a) L =Lift of inflating gas acting through center of buoyancy, G.

'I'M 1-320 AIRSHIP AEROD YN AMICS (b) W = Total weight of dead and live loading, acting throug h ce nter of gravity, M.

(c) R = Resistance of enve lop e and append ages, acting through ce n- ter of pr essure, P.

(d) T= Pr o peller thrust, a ct ing parallel to axis of envelope at di s tan ce o below M.

(2) Mo ments about M: (a ) Mo ment L = L X0 =0 .

(b) Moment W = W X 0= 0.

( o) Mome nt thru st -r esis tan ce cou pl e= T ( o +d).

Obviously, for s tati c e quilibrium and constant ve.loc ity- L u= W

R=T

However, if the airship is ridin g on an even keel, the mom ent of thrust and resistance is un ba lanced and will tend to no se the ship up .

F or thi s r eason airs hip s are cu stoma rily trimmed a few degrees nose heavy when full of gas .

b. Suppose that some force such as a gu st of air s hould give the l ongitudinal axis a s light tilt to the horizontal. D epend ing on s tatic condition of air sh ip and dire ct i on of inclinatio n, six cases which • ar1se. are-e - (1) Case N o. i.-Air s hip in static equili br ium, nose t ilt ed up. In this case, if the angl e between the l ongit udin al axis and the direct ion of motion is denoted by (} and th e ang le between the direction of motion and the horizonta l by a, since the airship climbs at the angle of tilt , (}=0° and the air shi p will climb at the angle, a.

(2) Case N o. ~.- A irshi p in static equil ibriu m, no se tilted down.

As before, (} = 0° and the ai r ship will descend at the angle, a .

(3) Case No. 3. -Air s hip statically heavy, nose tilted up. In t hi s event the ai rs hip will c limb at a lesser angle th an the amount of tilt, and t he l ongitudinal axis will make the angle a+(} with th e horizontal.

(4) Case No . 4. -Airship statically heavy, nose tilted down. Be- ca use of the heaviness, the airship will descend at a greater angle than the incl inatio n, the l ongitu din al axis ma king an a ngle of a-& with the horizontal.

(5) Case No. 5.-Air s hip statically light, nose tilted up . Th is case is s imilar to case No. 4. The longitudina l axi s makes the ang le a - 0 with the horizont al.

(6) Oase No. 6.- Air shi p statica ll y ligh t, nose tilted down. H e re the airship will descend at a lesser an gl e t han the in clin ation and the angle between the horizontal and the longitudinal axis will equal a+ D.

TM 1-320 27 AIR COR PS c. Figur e 21 shows case No. 3. Figures showing the other cases would be quite similar. Re ferring to figure 21, the following forces, lever arms, and moments, all general to cases Nos. 1 to 6, inclusive, are not e d: (1) For ces: ( a) L = Lif ting force of gas.

( b) W = Tot al weight.

(c) Fe=Resultant air force on hull.

( d) L e= Vertical component of dynamic for ce on hull.

(e) R e= H orizontal co mponent of dynamic force on hull.

(/ ) F a= R es ul tant force on tail sur faces.

(g) L = Li£t of tai l surfaces.

(h.) R a= Dra g of tail surfaces.

(i) T =T hru st of propellers.

(j) t = Hori zontal component of propeller thrust .

(k) Lt=Vertical component of propeller thrust.

(2) Lever mms about G.-Lever arm of- ( a) W =k sin ( a±8 ).

(b) L = o.

(c) T = (c+h).

( d) F =a (assuming F , perpendicular to the surfaces).

( e) L =a cos (a ±8 ).

{f) Rs =a sin (a± 8).

(g) Fe va ries with the position of P, which in turn depends on th e ang le 8.

(h) L e =b COS ( a±8).

(3) Moments about G.- Moment o f- (a) Weight. Defined as static righting moment. I t is present irr espective of speed and at all times equals W h sin (a ± 8).

(b) P ropeller thrust, T ( c +h ).

( c) F • D ue to increased pre ssure below the hull, Fe tends to rotate en tire airship in a po sit ive direction about M. This is assisted by reduced pressure beneath the tail (see fi g. 17 ). The force below nose and tai l are o pp osite in direction. T heir difference, since the nose force is slight ly the greater, is called dynamic lift of hull. However , both forces cause rotation in the same dire ct ion, and their moment is refe rr ed to as dynamic upsetting momen t, Me. I t will be eva lu ated later.

NOTE.-Tbe force beneath the tail has been om itted from the figure in order to avoid con fu sion in the dra wing, the entire upsetting moment being treated as though it were ca u sed by the increased pressure under the nose.

Tltl 1-320 27-29 AIRSHIP AERODYNAMICS (d) Tail surfaces, Ms. Thi s opposes the dynamic up ~tting moment. Ms = Ls a cos (a±O+ R s a sin (a±O).

28. Damping moment.-a. There is one moment which has not been discussed. If the airship, oscillating as it travels along its path, is considered as having two motions, one of translation as a whole and one of rotation about the center of gravity, superposed on each other, it is clear that during that portion of the angular oscillation in which the nose is rising, every part of the airship forward of the center of gravity is m~ :>Ving upward, whi le all parts to the rear of that point, including the tail surfaces, are moving downward.

b. Ther e will then be an upward pressure of the air against the rear part of the airship and a downward pressure on the forward part.

The upward and downward forces approximately cancel each other Ship lxvlvy-No.se elevt~tw/ F"e Le L; FlGUU 21.- Forces on airsb1p in inclined fligbt (c ase No. 3).

so far as translational motion is concerned, but they act together to give a moment tending to depr ess the nose and so to resist the motion existing. If the rotation were such that the nose was descending, a moment tending to raise the nose would appear. This is called the damping moment as it is entirely independent of position and atti- tude, but acts always in such a manner as to oppose existing motion and bring the airship to steady fli~ht. Oscillations of the airship are damped exactly as oscillations of a pendulum are damped if the bob is light and has a large vane attached to it . Damping moments may be determined experimentally in a wind tunnel, but the mathe- matical theory when these moments are quantitatively taken into account is extremely co mplex and will not be discussed here.

29. Longitudinal stability. - a. For longitudinal stability, the sum of the restoring moments must exceed the upsetting moments.

In the case illustrated- M. + Wh sin (a+O) >Me+ T(c +h ).

'l'M 1-320 29 AIR CORPS However, thi s r e la t ion does not hold in each case . . For instance, the static couple, W· h si n (ex± 0), works against the thrust couple when _ the airship is in a climbing attitude and with it when the airship is in a de scending one. The dynamic moment of £he hull, on the other hand , assists the righ ting moment in case Nos. 4 and 5, bu t o ppo ses it in ca se Nos. 3 a nd 6. Ca se Nos. 1 and 2 ar e unimportant as will be shown later. Ob viously case Nos. 3 and 6 are the ones which mu st be con sidered when designing for sta bi li ty .

b. Th e static righting moment is nearly a right-line function of the angle, 0. So for pra ct ical purposes is the upsetting moment.

But whereas the righting moment is ind epen dent of the velocity, the .

up setting moment varies as the square of the speed. Obviously as th e speed inc reases a velocity will be reached where the upsetting moment ju st equals the right ing moment. Thi s is called the critica l .

speed.

c. For an airship without cont rol su rfa ces, neg lecting for the moment propeller thrust and resistance, t he critical speed would be reached when- M e= Wh sin (a± B).

By the formul a of Doctor M:unk: M .= ( Vol)~ v (k2-kt) sin 28 where k2 and k1 are constants to correct for t he fact that ma sses of air are carried along with the hull in both transverse a nd longitudinal motion. Tabl es of values of k2 and k1 are given in National Advi sory Committe e for Aeronauti cs Report No. 184. From the M:unk equa- tion it appears that 111 c varie s directly as sin 20 and as the square of the speed. Combining the constant factors in the formula into one co n stan t, Me: M t= Me sin 28v2.

H ence the relation for critica l speed without fin s becomes- Me sin 28Ve = Wh sin (a±8) Wh s in (a± 8) Vc=-= M e sin 28 where Vc=c ritic al speed.

This would give a very low . critica l s pe ed. For an Italian military airship of the M type the critical speed without fins is 29 miles per hour.

d. I ntroducing the tail s urfa ces gives a much higher value of t he cri tical speed. From the relations given in a above for case No.3, the

TM 1-320 AIRSHIP AERODYNAMICS equation of stability at the criti cal speed, omitting t he thrust-resistance couple, iss-- F$a+ Wh s in (a- 8) =M e.

S,ince th e force on an inclined plate is approximately a right-line function of the ang le of inclination, F s= 0.(J vc where 01 is a con stant comb ining the s urf ace coefficient and the fin a,rea. As be fore-e - Hence M e sin '28v/= 0 8 ve a+ W h sin (a+ B) v _ / Wh s in (a + O ) .

e - -y M e sin 28- 018a

e. For a condition of static equilibrium, as sta ted in paragraph 27b, the fl ig ht path theoretically coincides with the lo ngit udinal axis.

Hence 8 becomes zero and Vo becomes infinite. T hi s agrees with the th eore tic al fa cts since with no angle of attack to the air st r e am t he tr ansverse dynamic for ces become zero for all speeds and th e sta tic righting moment would restore quickly the airship to the h or izontal position. A ctua lly, however , this can never be pr act ica ll y true , s in ce inertia of the air ship ret ar ds c hang e in dir ection of mo tion from the horizontal pa th and pr events t he airship immediately adopting a line of flight coincident with its lon gitud inal axis.

f. In the preceding discussion the controls h ave b ee n considered to be held in neutral. Actually by varying his elevator ang l e, the pilot m ay in cr ease materially the e ff ect of the control surfaces. Thi s fu r- th er in creases the speed which th e airs hip m ay tr avel without loss of co ntrol. If the air ship is not longitudinally stable, or if in ot her words it is be ing ope rated above its critical speed, the pilot must cor- rect deviations fr om the chosen path as soon as th ey appear, , while on a sta ble airship these deviations wou ld be capable of self-correction if left manually uncorrect ed .

g: The statical righting moment varies as the fourth power of a linear dimension of the air sh ip , th e ascensional force F being propor- tional to th e volume a nd so to the cube of a l inear dimension. A ll aerodynamic moments, on the other hand, both on the hull proper and on the tail surfaces, vary as the cube of a linear dimension. The crit i- cal speed is therefore prop ortional, for geometrically sim ilar airships, to

~fa or to the square root of a linear dimension. A lar ge airship can

therefore be stabilized with tail surfaces propor tionally smaller than 4o

TM 1....:.:320 29-Sl AIR CORPS those necessary on a small one traveling at the same speed. An un- stable airship requires closer attention from the pilot than does one which is stable, but it is not necessarily either difficult or dangerous · to operate and has the advantage of being more easily maneuverable than the more stable types.

30. Directional stability.-a. Directional stability is maintained in part by use of vertical fixed fins and rudder. When the rudder is set in neutral it acts as additional fin surface, but the total fin sur- face is never large. enough to provide complete directional stability Since there is no statical restoring moment to overcome a horizontal deviation from the flight path, maintenance of directional stability devolves upon the pilot who must correct any deviations as soon as they appear. Otherwise a deviation once started will te nd to in- .crease until the airship is traveling in a circle of so small a radius that the d~mping moment balances the turning moment due to pres- sure on the nose. This is quite different from the condition of longitu- dinal stability where the elevator can be left locked in any particular position and the airship will return to its original attitude if atmos- pheric disturbances have momentarily changed that attitude.

b. As soon as there is any deviation from the straight line of flight the a.ir strikes on the side of the envelope and sets up a moment tend- ing to turn the airship farth er from its original course. This moment corresponds exactly to the upsetting moment, Me, which opposes lon- gitudinal stability. There is then an unbalanced moment which tends to give the airship an angular acceleration and so to turn her more and more rapidly. At the same time the lateral force on the envelope, which corresponds to the dynamic lift, is increasing and .furnishes the necessary centripetal force to keep the airship traveling in a circular path. It is quite true that a force resisting this circling is exerted by the vertical surfaces, but, as mentione.d above, the vertical fin surfaces are never large enough to pro vide full stability, and the rudder must be used to ass ist them. Use of the rudder will be more fully discussed in sec6on V.

31. Lateral stability.-a. Stability in roll, which is a very diffi- cult problem in airplanes, is taken care of almost automatically in air - ships; since the same statical restoring moment acts with regard to roll as with regard to pitch and there is no dynamic upsetting moment to oppose it. The only rolling motions are those due to side gusts against the car and bag and those due to centrifugal force when turning. The· moments of these forces are overcome immediately by the large re- storing moment due to the low position of the center of gravity. Roll-

TM 1-320 31-33 AffiSHlP AERQ.DYN AM I CS ing may be very uncomfortable because of the sh ort and sna pp y period, but there is never any danger of its reaching an excessive value.

b. The static stability of an airship wit~ regard to both roll and pitch may be increased by lowering the car, but thi s gives equilibrium only at the sacrifice of ease of co n tro l and efficiency, since lowering the thru st line increases the thrus t moment and lowering the car increases length of suspensions and hence parasite resistance.

32. Summary.- a. Air ship stability may be summarized as follows : (1) Airships are very stable about their lateral axis. In this nr gard the designer has no trouble whatsoever.

(2) Air ships must be de signed carefully to give longitudi nal sta - bility. T his problem is however of more interest to the designer tha n to the pilot.

(3) Airships are statically unstable in yaw, necessita ting the closest attention on the part of th e direction pilot to counteract circling by means of the rudder.

b. No con crete problems have been given in thi s section as the appli- cation of fundamentals covered therein will be shown in section V.

SECTION v

C ON T ROL Paragraph General types --- ----- ---- --- - ------- - ------- --- --- --- -- -- --- -- -- -- --- -- 33 Dir ectional - -- ------- -····--- ---- - ------ - --- · - -- - - - - ------ ---- - - --...---- - - - 34 AJtitude--- ---- - - -- ------ - -- ----------------- - - --------- - ----- - ---- - --- 35 R ever se ---- -- -- --- -- --- ---- -- --------- - ---- - --- -- -- --- ---- - ---- --- -- - -- 36 Ap pli c ation of dynamic contr ol t o o peration of airs hiP S---- ------ ---- - -- - -- 37 33. General types. -a. Control of airships may be subdivided into two cl asses, directional and altitude. On nearly all airplanas these two types of control are so interrelated as to necessitate t heir both being performed by one pilot . In airships this is not the case, and on a ll bu t the smallest air s hips tw o pilots are utilized, one for dir ection, one f or altitude. .

b. For efficie nt performance the two pil ots should be familiar wit h each other's style of fl ying and constantly alert to render each other assis ta nce. For instance, to obtain the proper additional supe rheat to e ff ect a l anding (see TM 1- 325), the altitude pilot may desire a lon ger approach than usual. Th e direction pilot should so arrange the course as to meet needs of the situation. In st an ces of the value of coordination are too numerous to m ent ion, but fortunately capable pilo ts have little difficulty in achievi ng desired r es ults.

TM 1-320 AIR CORP S 34 . Dire ct i o nal. -a. As st ated in paragraph 33, the dir ec tion pilot is charged with control of the course of the air ship in a horizontal plane. On cross-count ry .flights his problem resolves itself into t hat of holding the course required by the mission of the air ship. Once th e course is set, th e airship will hold its own co ur se unless acted on by some exterior forces such as gusts. These must be overcome by pr ompt applica ti on of the rudder in the opposing direction. When fl ying in very gusty air it is impossible tD prevent yawing, but a good pil ot can keep the magnitude of the oscillations from exceeding a f ew degrees. Th en since the g usts strike about equally from both sid es th e mean course of the air ship will be the one desired.

b. It is essential that the pil ot have a clear conception of the reac- ti on to rudd er control of the airship in a turn . When it is desired to tur n to the right, for example, the rudder is put over to the right,.

The instantaneous effec t of this rotation is to produce a force to the l eft acting on the right side of the rudd er . Thi s force to the left has a dual e ffe ct. I n the fi rst place, it gi ves the moment about the ce nter of gravity tending to turn the nose to the right. I n the second place, it moves the entire airship to the left . As the airship moves to the l eft and as its nose t urn s to the right, both motions co mbine to cause the air to strike on the left of t he envelope and so to turn the nose still farther to the ri ght . After this ha s pr oceeded for an interval, th e pr essure on the left-hand side of the nos? bec omes equal to that on the right - hand side of th e rudder and the total re sultant pressure is th erefore zero, but since one force is applied to the front and the other to the rea r, ther e is a resu ltant tu r ning mom ent te nding to continue the twisting to the right . As the mo tion proceeds still farther, the force on the left-hand side of the envelope becomes greater than the for ce on the righ t-h a nd side of the rudder and there is a cent rip etal force to the right so th at the airship starts to move to the r ig ht. If th e rudder is left in hard or even if it is turned to neutral, this turn- ing to the right will continue, and in order to check the circling it is necessa ry t o put the rudder over to the le ft of the envelope.

o. The t ur ning radius is governed by the damping moment on the en velo pe and is greater f or an airs hip of lar ge fi neness ratio th an for one where this ratio is small. It should be one of the fi rst concerns of the pil ot whenever he assum es co ntrol of a new type of air s hip to familiarize him se lf with its tu rning rad ius. Otherwi se he m ig ht very conceivably endeavor to execute a turning maneuver where the spa ce limitatio~ was insu ffi cient.

d. Refe rring ag ain to the turn described in b above, it appears, curious ly enough, tha t the first e ffe ct on pu tting the rudder over to 48 .

TM 1- 320 AIRSHIP AERODYNAMICS 34 .

the right is to s hift the air ship slightly to the left so that if the air- ship were being fl own along close to th e right side of a wall or other obstruction, it would not be safe to put the rudder over s harply to the right in order to turn to the right and get away from the obstruc- tion, as the immediate e ff ect of such an action would be to drive the airship into the wall. The approximate path of the air s hip when the rudder is put o ver to th e right, together with seve ral successive positions of the axis of the a ir s hip , ar e indicated in figure 2 2.

e. It occasionally happ ens, especially when flying through foggy atmosphere, that an obstacle will suddenly loom up in fro nt of t he r; I I I I 1Y e I I I

rrr \

'Yr

(I) '(' Y,.

'( Yr FI GURE 22.- r lction of ai rs hi p In a tu rn . F IGUR E 23. -A c tlo n of alrsbl p in a ,·o id - ing nn obst acle.

air ship. To miss the obstacle t he pil ot mu st fir st put over the rudder to defl ect the nose of th e airship and then completely reverse the rud der. In t hi s case th e action is as shown in figure 23.

f. There is one other situatioll in which the dir ec tion pilot must exercise caution. As the air ship t urn s under a ct ion of th e rudder, centrifugal force act ing on th e ce nter of gra v ity will swing t he car to th e ou ts ide. Thi s action will so t ilt the hu1l tha t the rudder will become in part an elevator. .Air s triki ng on the insi de of t he rud- der will depress the nose of the s hip . This de pr ession can be stopped by prompt a pp lication of the elevator controls by the al tit ude pilot.

H owever in so me cases, especially when near the ground with a he avy airship, the altitude pilot may be unable to . use the elevators without endangering the tail of the airship. H ence the 'direction pilot must .

TJ4 1-320 AIR CORPS 84-86 be very careful to turn a heavy airship slow ly when at low altitudes.

On the other hand, he can very materially assist the altitude pilot in holding a light airship down by making abrupt turns.

35. Altitude.-a. Methods. -(l) Altitude control of airships is effected by two means, static and dynamic. Tha former method is dis cussed in TM 1-325.

{2) Static means of control must always be augmented by dy- namic means. Even though an airship takes off in perfect equi- librium it will not remain so. Changes occur in the static lift due to changes in meteorological conditions and loading is being varied constantly by consumption of fuel. To balance inequalities between loading and lift, dynamic means must be used.

b. Trim of airship .-(1) In the study of stability, to simplify the dis cussion th e subject of trim of the airship wa s omitted. A thor- ough know ledge of trim is however essential to intelligent control of the airship.

(2) Under action of t he stat ic righting moment, the center of gravity of t he airship will li e directly below the center of buoyancy.

If the line joinil!-g these two points is at right angles to the longitu- dinal axis, this axis is horizontal, and the airship is said to be trimmed in neutral. If, on the other hand, due to the manner of loading or to location of the air i.n the ballonets of a pressure airship, the longitudinal axis is inclined to the horizontal when the center of gravity is directly below the center of bu oyancy, the airship is said to be trimmed nose h eavy or tai l heavy, as the case may be. The application of trim to dynamic control of airships is discussed in paragraph 37.

c. Olimbing fJifiA.l descending. -(l) Change in altitude is accom- plished dynamically by use of elevators in co njunction with thrust of propellers. To sim plify the following discussion the airship is assumed to be flying with n eut ral trim and in st atic equilibrium. If it is desired to climb, the altitude pilot raises the elevators which causes an action in the vertical plane similar to that described in paragraph 34 for turning in a horizontal plane. How ever, in thi s case, the ele- vators mu st be he ld in the raised position to prevent the static righting moment bringing t he longi tudin al axis back to the horizontal.

(2) It should be especially noted that when the elevator is raised the tail of the airship actually descends. For this reason extreme caution shou ld be used in use of the elevator when the airship is near the ground.

36 . Reverse. -a. There is one curious paradox in control of air- ships at very low speeds. It the speed falls below a certain definite lSO

TM 1-32 0 .

AIRSHIP AERODYNAMICS 36 value kn own as the "revers ing speed," control becomes r eversed and pull ing up the elevators causes the airship to descend, although it turns the nose upward. The reason for this is that at low speeds (for most types about 15 miles per hour) the air forces are entirely unimportant in comparison with the static restoring moment due to the weight when the airship is inclined. Then if the elevators are pulled up, the momentary effect is to turn the nose upward, but the axis will incline only at a very sma ll angle before the static re storing moment becomes equal to the moment due to the force on the elevators, and the inclina- tion will then cease to increase. If this angle of inclination is held to a small enough value, the dynamic force on the nose will be less than the downward force on the elevators. There will then be an excess of downward force and the air s hip will be thrust downward as a whole.

This reversing speed offers a reason for not making the static stability excessive, since reversi ng speed in creases as the center of gravity is lowered and the resulting difficulty in control becomes more serious where the static stability is l arge .

b. The phenomenon of reverse control is especially apparent if the airship is trimmed quite nose heavy. Then any attempt on the part of the pilot to lift the nose at slow speeds is r esisted by the static moment.

The decrease in the dynamic thrust downward on the nose will be less than the gain in the down ward force on the elevator and the airship as a whole will descend.

c. Th e particular situation just described is one of the most serious into which the airship can be brought. It is of most frequent occur- rence when a nose heavy air s hip is being brought to a landing and due to loss· of superheat becomes s tati cally heavy. The air s hip will descend as a result of this heaviness and, if the speed is below reversing speed, application of the elevators at that speed w ill simply cause more rapid descent.

d. Th e only recourse of the pilot in this situation, unless his airship is equipped with reversing propellers, is to throw ballast or materially increase hi s speed beyond the reversing limit as he raises the elevators.

· wh en the airship is quite near the ground there may no t be sufficient altitude to execute the latter maneuver without striking the ground with the tail. If his ai rship is equipped with r evers ing propellers, the pilot can cause the airship to ascend while the nose is down by merely reversing the direction of propeller rotation.

e. There is one other situation in which reverse control occurs. The maximum dynamic lift on the hull occurs at an angle of attack of 10° or 11 ° for mo st. typ es of airships. If an airship is flying with this angle of attack and the elevators are raised so as to increase the ang le

TM 1-320 36-37 AIR CORPS of attack beyond that giving the ma- ximum lift, the dynamic lift nat ..

ur ally decreases. At the same time the downward thrust on the eleva- tors is increased. The gain in the upward component of the propeller thrust at reversing speed or below will not compensate for the loss in lift just described and the airship will be under the action of a greater resultant downward force than at the s tart.

f. The opposite effect to that described in c above occurs when an airship is trimmed tail heavy and the elevator is depres se d. In this case the whole airship will rise.

g. It might appear that reverse control wou ld be a source of great annoyance to the pilot. This is not the case when the phenomenon is Ls FIG URE 24.-Fl!gbt at constant altitude (airship statica lly heray, t rimm ed tail heavy, ·e levators neutral).

properly understood. I n fact, many maneuvers are executed by in- telligent use of reverse control, for example, heavy take-off. This is described in paragraph 37.

37. Application of dynamic control to operation of air- ships.-a. The three major maneuvers in airship operation which are assisted by dynamic control a re- (1) Flight at consta nt altitude.

(2) Take-off.

(3) L anding~ These operations are fully covered in TM 1 -3 10 and are discussed but briefly here to bring ou t the aerodynamic principles involved therein.

b. As soon as the take-off is completed and the obstacles in the imme- diate foreground cleared, the pilot climbs to the altitude at which he desires to cruise. He then trims the airship so tha t with the controls in neutral the algebraic sum of th e vertical forces is zero. Since the airship is almost never in static equilibrium, one of two situations will prevail, static heaviness or lightness.

TM 1-320 AIRSHIP AERODYNAMICS (1) Figure 24 shows the case in which the airship is sta tica:Jly·heavy and trimmed nose light . In thi s case the equation of vertical forces to give constant altitude flight with neutral controls becomes- W = £ 0+ L e+ L t+ L ~ The pilot may be called upon to fly a heavy air s hip on account of va ri - ous reasons such as-- (a) Collection of moisture if rain is encountered.

(b) Leakage in envelope.

(c) Loss of super heat.

(d) H eavy tak e- off.

Most airships can car ry about 10 percent. of their gross lift dynamically at the su rfa ce of the earth . Since th e dynamic lift va ri es as the air ·density, it decreases with nltitude. Table III shows results of some ex- periments on an Italian M type airship at- full speed : TABLE III. - Lijt of Itali an M type at full speed [In pounds] Altitud e, 3,000 fe et Altitude , 10,000 feet Altitude, 16,500 feet I I I I I Angle of I <I) !XI 1:1 1:1 0 1:1 0 1:1 ~ inclination in

.... Q)Q) .... Q)Q) Q)Q) .... fl)

'"'fl) ....

....

!').~ ~ ~ o. .... ~ 0.~-o ~ ..... o. ..... o.

;..::: ..... o.

radiants :=l .....

.._.a> ._Cil .....

..... ....

oo oo 0 .....

-~ .....

0 0 0~ o- 0~ . . Q) Q)

Q3 -

Q3

- - <IS

.5 .... .... .... ....

s .... 0.

-+"> -+"> -+"> +>o.

<!:0.

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

0 0 0 ......

~ ~

-

-

·- ·- ·- ·-

·- ·-

H H H E-< H E-. H H E-. H H ..:I 1, 224 330 834 I, 012 269 48 218 60 695 839 40 481 0.0 3- - - -- - - - - 0.06 __ ___ ____ 1, 855 612 125 1, 542 1, 118 495 101 946 1, 287 400 82 2, 290 810 200 1, 2801, 914 657 163 1,095 1, 608 530 130 948 0.09 _- ----- -- 0.12 ___ __ __ __ 2,497 913 290 1, 294'2, 101 742 235 1, 124 1, 778 599 189 99 (2) Figure 25 shows the case in which the airship is fl.yin~ s tatically light at constant altitude with contro ls in neutral. In this case ' the equation of the vertical forces becomes-

L0= W + L e + Lt + L8

(3) In the unusual case in which the airship is in perfect static equilibrium, it will be necessary to trim the airship about 2° nose heavy to overc6me the upturning mom ent of the propeller thrust. So trimmed the airship will fly on an even keel at cruising speed. The motorized observation ba1loon, having only one ballonet, cannot be trimmed for an individua l flight. An approximate 2° nose heavy

Tl4 1-320 87 AIR CORPS trim is given this type of airship during initial inflation by proper adju stment of car suspension rigging.

c. It is customary to take o ff la rge se mir igids and rigids sta tically light, but nonrigids ar e taken off as much as 6 or 7 perce nt heavy.

(1) Th e light ta ke. -o ff may be made with the air ship in any trim from tail heavy to a few degrees nose heavy. I n th e la tter case the air s hip sh ou ld be fr ee-ballooned to a safe altitude before the motors are opened. Th e light take-o ff presents little di ffi cul ty .

(2) For the take-o ff when the ai rship is in static equi li brium the trim should be neutral or a few degrees tail heavy, pref era bly the lat- ter. In t hi s case t he c ar party of the maneuvering cr ew gives the air- ship a to ss upward, the men on the nose of the c ar throwing their end up fi rst , then the men to the rear throwing up their end. This gives • FI GURl'l 25.- Fli g ht at constant alt i tude (ai r sb ip statica ll y Hght, tri mm ed nos e heavy, el evators ne\ l tral) .

t.he airsh ip an initial angle of attack to the air s tr eam. When clear of the party the pilot opens his mot c· rs and rai ses his elevators sligh tly .

Th e thru st of the prop ellers assisted by the s light fo rce on the eleva- tor s w ill further rai se the no se of the air ship and it . will climb rapidly.

(3) For the heavy ta ke-off the ajrship must be carefully trimmed tail heavy. The amount of the t rim varies with degree of heaviness, type of airship, and wind velocity. If there is a good wind blowing it gi ves the a irsh ip an initial air speed to assist the ascent. Experience ha s shown that an air ship of the TO type wit h a trim of 9° tail heavy will ta ke o ff 700 pounds heavy in st ill air . F or thi s degree of heavi- n ess the car party should be augmented to at least 20 me n and 4 men should be assigned to lift on the tail s urfa ce. At the proper signal th e c ar is th rown up, nose fi r st as before. The elevators should be de pr essed about 10° and as the pi l ot opens his motors he will find it necessa ry to depress the elevators fully to keep the ta il from striking the ground. Action of the air s hip in ri sing is a pur e case of reverse control. The air from th e slipstream of the pr opellers strikes the

TM 1-320 AIRSHIP AERODYNAMICS 87 elevators and gives the tail a posi tive lift. At the same time the trim of the airship will keep its nose elevated so that there will be the familiar dynamic lift on the hull s urface and the vertical component of the propeller thrust to assist the ascent. In this cas: e-e - L u+ Le+L t+ L s> W d. The mo st diffic•lit maneuver which confronts th e pilot is the landing. Thi s operation may b~ divided into three parts, as· follows: (1) Weigh-off.

(2) Approa ch.

(3) Arri val at the landing party.

e. Weigh-off is made at a sa fe altitude (1, 000 feet for large airships, 250 to 500 feet for sma ller ones). For this maneuver controls are ~~~W<tl9h oil horo _,. • NJ • ......,.-JtOO ~---------- --- 2Mi-- ----------------~ FI GURE 26.-Approa ch of an a.irs hip to a landing.

placed in neutral and air speed reduced to as low a speed as possible.

The airship will quickly assume an attitude determined by the trim, which can be read from the in c lin ometer. At the sa me time the pilot can notice whether the airship is ris ing or descendi ng statically. It is useless to bring t he airship to an even keel to elimi nate dynamic lift caused by una voidable r esidual speed incident to idling prop ellers, as this would, in re a lity create a dynamic thr ust on the tail surfaces.

As a result of the knowledge of condition of the airship derived from weigh-off and after due considera ti on of existing meteorological condi- tions, the pilot is ready to make the approach.

f. The princip al object of the ap proa ch is to determine in advance

of the arrival at t he party the beh av ior of the air s hip at landing s pe ed.

Figure 26 gives a graphic al picture of the approach.

(1) From the altitude of weigh-off the airship is brought qui c kly to the altitude of approach. Thi s varies from 150 feet for a nonrigid to 500 feet for a large rigid, depending in some meas ure on gustiness of the atmosphere. During the descent the pilot arranges the trim he estimates to be necessary to make the landing. On arrival at the

TM 1-320 AIR CO RPS 87-38 approach altitude the speed of the airship is reduced to 15 miles per ho ur plus the wind velocity. This is an excellent approach speed.

(2) Th e pilot now wishes to check behavior of the airship at this speed. Controls are placed in neutral and if the trim is correct the airship will maintain constant altitude in a manner described in b above. If it does not, it is necessary to adjust further the trim to effect that result. The principle is exactly the same whether the air.

ship is stati cally light or heavy. Dur ing remainde~ of the approach ·controls are useu to overcome gusts or changes in static conditions, care being taken to observe principles of reverse control shou ld the speed fa ll below reversing speed or should the ai rship be placed in dang er by loss of static lift.

g. When the airship arri ves within 50 to.200 yards of the landing party it is brought to l anding height. This depends on type of air- ship and length of handling gu ys used. Large nonrigids usually land about 60 feet off the ground, rigids at a much higher altitude, while the motorized observation balloon must be landed at an altitude of 25 feet or less. In this conn. ection it should be borne in mind that the lower a statically h~avy landing can be made the smaller the drop after aerodynamic control ceases. In th at case,· al so , care shou ld be t aken to level the airship by use of elevators as it falls into the hands of the party, as otherwise the ta il would be injured.

h. The landing described above is the usual type of landing. The description is not at all complete since it omits nearly a ll the static pr inciples involved. The other types of landings, such as turn land- ings, will not be discussed, since the dynamic prin ciples involved therein are simil ar to those already explained.

SECTION VI AERODYNAMIC STRESS Paragraph Assumption as to condition of maximum stress -- --- - -------- ---- - -- - -- - 38 Tr an s verse forces acting on airship flying at constant angle of pitch __ ___ _ 39 Transverse forces acting on airship in s teady turn _ __ ___ __ _ __ ___ ____ ___ 40 Forces caused by gusts------- - - -- - - - - --- -- - - - ----- - --------- --- ------- 41 Empirical formulas for maximum aer o dyn a mic bending moment on hull and for forces on ta il surfaces----- - --- - - - -- -- - ---- -- -- - - - -- -- -------- 42 M ethod of calculating shear and bending moment on hnll ___ ___ __ _ __ _ _____ 4g Conclusion____________________________ ______ ____ __ __ __ ________________ 44 38. Assumption as to condition of maximum stress.-a . For airships designed prior to th e World W ar the air speeds were quite slow. The aerodynam ic forces acting on these airships were conse-

TM 1-320 AIRSHIP AERODYNAMICS 38 quently insufficient to give shear or bending moments large enough to endanger an airship designed to care for the static loading. At pres- ent the speed of airships has been so materially increased that aero- dynamic forces, which vary as the square of the speed, must be con- sidered. While it is not the function of this manual to teach design of airships, a general know ledge of results of these forces and moments is sufficiently important to the pilot to warrant inclusion herein a simplified discussion thereof.

b. As previously stated, the longitudinal aerodynamic forces are usually not a source of danger to the airship. The single exception to this statement occurs in the case of the pressure airship flying at maximum or near ly maximum speed. At this time the nose pressure · may attain such magnitude that it 'may very conceivably exceed the pressure for which the airship was designed, in which event the nose will cave in. Since it is the internal pre ssure of the gas which resists such caving action, it should be the duty of the pilot to increase his internal pressure to the maximum allowable pressure when fl ying at velocities approximating maximum design speed.

o. The most important aerodynamic stresses are those caused by transverse forces. I n order to design for such stresses, it becomes necessary to make assumptions concerning conditions which give great- est transverse forces. It was early believed that the worst condition occurred at the instant of si,multaneous application of full rudder and elevator control. This assumption would appear reasonable in view of the fact that momentarily in e rtia of the airship will arrest any tendency toward rotation, but as soon as an angular velocity is at- tained, rotation of the tail reduces the forces on the surfaces. How- ever, this argument omits one important consideration. It frequently occurs that at the moment of application of the controls, the airship may be under the acti~n of forces giving it yaw or pitch in a direction opposite to that desired. In this case while initial yaw or pitch is being overcome, the hull will be subjected to a twisting action caused by two opposing moments. Theoretical treatment of stresses so caused is quite complicated and many designers simply arbitrarily doub le the forces which arise when full rudder and elevator are applied simul- taneously.

d. Du ring the design of the RS-1 airship various conditions of stat ic loading, with a load factor of 4, were investigated. Stresses found in the keel members under static loading conditions were com- bined with st resses found under the following conditions of aero- dynamic loading to determine maxi~um stress in any member: In · arriving at !ow load factors applied to aerodynamic loading condi-

TM 1-320 88-89 AIR CORPS tions, the effect of the envelope in relieving the keel by resisting a portion of the shear and bending was neglected. It was found that this was very conservative as subsequent tests on water-filled models and full-scale tests on the RS-1 a irs hip indicate that the keel resists approximately 50 percent of total bending due to static loads. How- ever, in flight tests it was found that the keel re sists only 10 percent of the bendi ng moment due to external air loads in pitch. · In order to l!>e conservative however in future designs of semirigid airships the design should be ba sed on the assumption that the proportion of the total loads on the ai rship due to external air loads in pitch in flight re sis ted by the keel is half that found in the case of static weights and that a load factor of 2.0 be used.

(1) Horizontal flight at 55 miles per hour with a load factor of 4.0.

(2) Horizontal fl ight at 70 miles per hour with a load factor of 3.0.

(3) Pitch up or down at an angle of 3° 19' at 55 miles per hour with a load factor of 3.0.

( 4) Yaw at 55 miles per hour with load factor of 3 .0 .

(5) Turning, 1,500 feet radius at 55 miles per hour with load factor of 2.0.

(6) Mooring by the nose with pi tch up, pitch down, and yaw of 4° 0', in a gale of 70 miles per hour with a load fa c tor of 2.0.

e. From the foregoing di scussion it is evident that the pilot should be cognizant of maximum angles of pitch and yaw for which his air- craft was designed. Then when atmospheric conditions render it impos si ble to keep the . airship within design limits he should reduce hi s ai r speed to effect a reduction of the aerodynamic for ces.

f. To simplify th e discussion transverse forces will be considered under three classes : (1) Transv erse forces at fixed ang le of pitch.

(2) Tran sverse forces in steady turn .

(3) Forc es caused by ·gusts.

39. Transverse forces acting on airship :flying at constant angle of pitch. -a . 'When an airship is flying at a constant positive angle of pitch it is acted on by the following dynamic transverse forces: (1) Component normal to longitudinal axis of dynamic force on tail surfaces.

(2) Component normal to longitudinal axis of dynamic force on hull.

Since rotation is considered about the center of buoyancy it is neces- sary to divide the latter force into two parts. Thi s is essential because the normal force on the forebody is directed upward, whereas the normal ·foroo on the afterbody is directed downward. It has been

TM 1-320 'AIRSHIP AERODYNAMICS 39=40 . shown by a member of the · National Advisory Committee for Aero- nautics that the algebraic sum of the forces on the fore and after bodies is theoretically zero, which would indicate that the dynamic lift on the hull was zero, and that the total lift obtained dynamic~lly by the airship, exclusive of the vertical component of the propeller thrust, was that furni s!1ed by the surfaces. This is not in strict agree- ment with the actual facts, since the down thrust on the afterbody is -less than the theoretical down thrust. However, the fact remains that, since the pitch remains constant, the sum of the moments about the , center of buoyancy must equal zero.

· b. The turning moment of the aerodynamic forces on the hull theoretically equals the formula : (Vol)iv (k -kl) sin 20 where O=angle of pitch.

k and k =constants correcting for additional masses of air carried 2 1 longitudinally and transversely. Values of k and k are given in National Advisory Committee for Aeronautics Report No. 184.

o. If it is granted that the dynamic force on the tail equals the total resultant static transverse force, its moment must equal the formula given ~n b above. . Hen ce- Fa = (Vol)~v (kz-k ) sin 20 where F = component of force on ta il surface normal to longitu- dinal axis.

a= dis ta nce from center of buoyancy to center of pressure of tail surface.

' The above formula will give an approximation of dynamic l if t of the airship. .

d. Practically, F need not be as large as indicated aboye due to the di screpancy betwen actual and theoretical values of the down thrust on the afterbody. The point of application of F is sl ig htly forward of the center of the area of the tail surfaces.

e. For method of calct1lation of shear bending moments due to dynamic forces see paragraph 43.

40. Transverse forces acting on airship in steady turn.- The theory in this case is quite similar to that described in paragraph 39.

· Assuming, as before, that the algebraic sum of the forces on the for& .. :, and after portions of the airship hull equals zero, the other two forces :>acting on the airship (the force on the fins and centrifugal force) must . · . .. . ~

TM 1-320 4o-42 AIR CORPS be equal to produce motion in a co nstant turn . From this is derived the relation- 2a sin 2 'I! = R(k 2 -k l) where 'I! = angle of yaw.

a=di stance from center of volume to center of pressure of tail surfaces.

R = radius of turning circle.

This relation gives resul ts widely at variance :from the results o:f actual.

tests on full-sized airships, pr esuma bl y due to the assumption that the· resultant of the hull forces is zero. Fortunately, the total bending moment due to a steady angle of turn is only about one-fifth as great as that due to an equal fixe d ang le of pitch where unbalanced weight and cen trifug al force are of equal magnitude.

41. Forces caused by gusts. -a . Very lit tle is kno wn concerning maximum value of forces caused by gusts. The following statement very excellently sums up the s it uation : "The existence of veritable fountains of upward rushing air whose sides at times and places are shar ply se para ted from the surrounding atmosphere mu st be taken into account in the design of airships. The most violent of such currents, the tornado, combines vertical velocity with rotation, but fortunately can be seen from a great distance, and can and must be avoided. The thunder storm with large fully devel- oped cumulus tops is also conspicuous and avoidable. It would appear to be :folly to enter such a cloud and subject the ship to the unknown dangers of wind, rain, hail, and lightning. Barring ·suc h spectacular hazards, there remain convection currents which the ship may run into at full speed. There is ample evidence that upward velocities as high as 10 feet per second may be encountered. This vertical air velocity u, combined with the relative horizontal speed v of the airship, will give -1 the effect of a change of pitch of tan vu., b. It rem ains simply for the pilot, as stated in paragraph 38e, to reduce the speed in bumpy atmosphere, especially if at the same time the airship is developing large dynamic lift, positive or negative, as then the stresses are already large.

42. Empirical formulas for maximum aerodynamic bendi n g moment on hu ll and for forces on tail surfaces.-a. The follow- ing formula has been developed :for the maximum aerodynamic bend- From "Airship Design" by C. P . Burgess by · permiss ion of tbe Ronald Press .

TM 1-320 AIRSHIP AERODYNAMICS 42-48 ing moment to be expected from such bumpy weather as would be en- countered in mountainous co untry: Mb=0.005 ,W (vol) L where Mb = the maximum bending moment in foot-pounds.

L = the length of the airship in feet.

Use of thi s formula enables the pilot to calculate rapidly maximum st resses to which hi s velocity in bumpy air may be subject ing hi s airship.

b. Where surfaces are designed in approximate accordance with the formula A = 0.13 ( vol) 1 , the tota l transverse force on either vertical or horizontal surfaces may be computed quickly by the relatio n: 2 8 2 F = 0.026 (vol) 1 p v • In above formulas A=total area of e ither surface.

F = total force on either surface.

43. Method of calculating shear and bending moment on hull.-a. The designer and also the pilot in determining shear and bending moments on the airship must consider both static and dy- namic loads. Both mu st be computed independently and then added together algebraically. I t often happens that dynamic loads serve to redu ce s tr esses due to static loading, but naturally th e dangerous case occurs when stresses are arithmetically additive.

b. The method to be described applies more particularly to rigid airships, but the principle can be applied to a nonrigid. In the latter case, the load instead of being distributed th rougho ut the length of the hull is sw ung from the envelope by suspension cables which by their tensions control very larg ely distribution of loading on the envelope.

c. For calculation of stresses, the hull is considered as a beam loaded with the weights acting downward, lift of ga s cells acting upward and aerodynamic forces acting in any longitudinal plane whatsoever. All loads . are considered as concentrated at the frames rath er than as uniformly di st ributed. The calculations may be divided into steps, as follows: ( 1) Calculation of static load.

(2) Calculation of shear due to static loading.

(3) Calculation of bendi ng moment due to static loading.

( 4) Calculation of load, shear, and bending moments due to aero- dynamic forces.

( 5) Algebraic summation of effects of static and dynamic loading.

TM 1-320 48 AIR CORPS d. The initial step in the computation is determination of .distribu- tion of weights. This is taken from the detailed weight st~tement, weights therefrom being distributed to the proper frames. Lift of the gas in each cell is computed next and di st ributed as concentrated forces on the frames. Th e static loads on the hull are the differen ces between weight and buoyancy at each frame, lift being considered {Plane conftnl1in? C.G al1d C.8.

po

80 00 &olf4ncr <~ncl 1000 1000 Loadi~ ,., I /() 0 .Jo 20 so LBS .

-

2 000 /. .

000 /0 tq 000 I""'!•,__--- Overall len9rh oF /lir.ship----~ 2000 2000 • t 1 I Loads'" 1.85.

j

~----~------~~-----~.r-----~------~.

1000 /000 /000 1000 1+1000 I I

...__ ____ __,,_,QOQ

I - 1000 fjft1. IN LB. Meter.s F tcu •n: :.!7 . -L oads, shear , a1111 bending moments ca used by static loading.

positive and loads negative. When the airship is in stat ic equilibrium, the algebraic sum of the loads must equal zero. Figur e 27 illustrates the co mputa ti on of loads at each frame of an airship 50 meters long, having four fram es spaced 10 meters apart. The method shown is applied to the large st airships.

e. Commencing at either end of the airship, the shear at any frame equals the algebraic sum of loads up to that frame. This system gives a constant shear between frames, changing at each frame QY

TM 1-320 AmSHIP AERODYNAMICS the amount of load at that frame. The shear in figure 27 was com- puted in this manner.

(1) For instance, the load at station 0 is -1,000 pounds. Then the shear between stations 0 and 10 equals -1,000 pounds. At station 10 the load is + 2,000 pounds. Hence the shear between stations 10 and 20 is -1,000 pounds + 2,000 pounds, or + 1,000 pounds.

(2) For an airship in static equilibrium, when centers of buoyancy and gravity are vertically disposed, areas under the shear curve must add algebraically to zero. This should be checked before proceeding to computation of bending moments.

f. For calculation of bending moments, all loads between ends of the airship and any frame are considered as supported by cantilever action from that frame. In the case illustrated by figure 27 starting at station 0, the bending moment for- (1) Station 0= 0.

(2) Station 10 = - 1 ,000 X 10= -10,000 meter-pounds.

(3) Station 20= ( -l,OOOX20) + (2,000X 10) =0.

g. An easier method of computing bE di ng moments is to sum up the areas under the shear curve. Thus in figure 27, for station 20, the bending moment= 10,000 - 10,000 = 0. For an air s hip in static equilibrium, when the center of gravity is vertically below the center of buoyancy, the bend- ing moment c_ urve returns to zero at both ends of the airship, since the summations of positive and negative areas under the shear curve are numerically equal.

h. Table IV, extracted from "Air s hip De sign," by C. P. Burgess, of the Bureau of Aeronauti cs , United States Navy, shows loads, she ar , and bending moments on the ZR - 1, computed in accordance with the method described therein.

i. In computing aerodynamic loads, shear, and bending moments, a method. somewhat similar to that described above is employed.

(1) Upturning dynamic forces on the hull are computed, using the Munk formula. This formula is omitted here as it involves mathe- matical computation beyond the scope of thi s manual. The forces so determined are distributed to the frames as concentrated loads.

(2) Excess static weight or buoyancy is then distributed to the frames in proportion to the cross-sectional area at the frames, unless known eccentric loading shows this distribution to be greatly in error.

(3) Dynamic force on surfaces is then distributed to proper frames.

This force, as shown in paragraph 39c , is given by the relation- F= (Vol) v [a(kz- k sin 28 1)

TM 1-320 43 AIR CORPS

TABL E IV. -Loads, shear, a nd bend in g moments in U. S. S. ZR-1

when the gross lift is 136, 631,. pounds [This table reproduced from Airship Design, by C. P. Burgess, by permission of the Ro n ald Press] Dispos- Bending Gross Fixed Total Station Load Shear able moment meters lift weight weight weight m.

Po unds Pounds Po unds Pounds Po unds Po unds Pounds

o ___ __ ____

2, 618 2, 618 - 2, 311 307 0 10 ______ ___ - 2, 311 1,453 1,87 7 0 1, 877 - 424 -23, 110 20 _________ - 2, 735 2,812 1, 902 1, 902 910 - 50,460 .

- 1, 825 30 ___ ____ __ 1, 991 2, 276 4, 267 229 4, 496 -68,710 40 _________ - 1, 596 5, 789 2 ,328 2,200 4, 528 1, 261 -84, 670 - 335 50 _________ 7, 128 2,389 5, 182 7, 571 - 44 3 - 88, 020 60 _________ - 778 1, 512 7, 370 8, 218 5,8 58 848 -9 5,800 70 _ ______ __ 8, 985 2, 708 2,378 5, 086 3, 8 99 - 95 , 10 0 3, 969 80 _____ ____ 3, 091 8, 747 9, 402 5, 656 6 55 -55, 410 4, 624 9 ,5 10 9 ,483 6, 100 1 5,58 3 - 6, 073 - 9, 170 90 --------- - 1, 449 100 _____ ____ 3, 224 6, 055 9, 279 261 9 ,54 0 -24 660 - 1, 188 '

uo __ . ______

3,069 5, 704 8, 773 811 9, 584 -36, 540 120 __ _ ____ __ -37 7 9, 560 8, 183 5, 016 13 , 199 - 3, 639 -40 , 310 - 4, 016 130 ___ __ ____ 1, 790 4,886 4, 650 9, 536 3, 096 -80,470 140 _ __ ____ __ 8, 626 791 9,417 3, 064 5, .562 -74 , 130 1,425 150 ___ _____ _ 2, 712 5, 4 06 8, 118 885 9, 003 - 59 , 880 2, 310 }6() _________ 2, 259 10 , 316 8, 16 9 8,057 - ~. 147 -36, 780 160 170 _________ 3, 076 2, 653 . 5, 729 1, 049 6, 778 -35, 150 1 80 ___ __ ____ 1, 212 4, 439 28 4, 467 3, 212 1, 227 -23,030 1, 240 70 2 2, 222 1, 5 20 1, 520 - 13, 110 1 88 - ---- ---- 1, 942 194.75 __ _ ___ 258 1, 100 2, 200 - 1, 942 0 1, 100 136 , 634 74, 558 62. 076 136, 634 0000 .

I I (4) The load on each fram e, s hearing forces, and be nding moments

ar e then computed and tabulated as explained in d, e, f, g, and h

above. A ta ble so prepar ed, extracted from Air s hip Design, is given below.

TM 1-320 AIRSH I P AERODYNAMICS 43 TABLE V .-Aerodynamic forces, shear, and bending moments in U. S.

S. ZR - 1 at 85 foot /se conds and 5° 42' pitch

I

Unbal- Bending

I

Turning ' I anced moment .

Station meters forces ' L Load Shear

I I

' s tati c I on hull

I

weights pounds I

-

Pounds 1 Pounds ,

o_ _______________ _

-820 -5 7 - 877 - ------- ~---- ---- .

10 _____ ____________ - 1,032 - 179 l. 089 - 877 -8, 770 0 2, 3oo 1 20 __ __ ____ ___ ______ -1 , 200 - 334 -6,650 I 2, 300 ! 766 212

ao _ ____ ____________

-1 , 228 -5 00 3. 754 2.026 978 3, 130 I 40 _____ ____ __ __ ____ - 1, 180 - 665 4. 937 30 092 3, 004 33, 170 I 50 _____ ____ ___ __ ___ ' I -985 2, 300 499 6. 096 94, 130 60 _____ ________ ____ I - 933 - 755 - 1. 688 160, 0 80 6, 595 -- ------ I 70 _________ _ ___ _ ___ - 494 - 1, 020 - 1, 514 4, 90 7 209, 1~0 ---- - --- 80 _______ __ ___ ___ __ - 151 - 1,067 -1. 218 243,08 0 3. 393

--------

- 55 - 1, 077 - 1. 132 2, 175 264,830 90- ---- ----- ------ - --- --- - - 100 _____ ____ _ _____ __ - 1, 077 -1.077 0 1, 043 275, 260

--------

110 _____ _____ ____ ___ 0 - 1 ,0 77 - 1, 077 - 34 274, 920 ----- - -- 120 ________________ _ 0 - 1, 077 -1.0 77 - 1. 111 263,810 ---- ---- 130 ____________ _____ 41 - 1, 077 -1. 036 - 2, 188 241, 930

----- ---

140 _____ ___ ___ ____ __ - 1, 067 151 - 916 - 3, 224 209, 0 690 ------- - 150 _____ __ _____ ___ __ 494 -1, 030 -536 - 4, 140 168, 290 -- -- -- -- - L60 _____ _ ______ ___ __ 851 - 933 - 82 - 4, 676 121, 530 -- -- - --- 1 ,346 - 783 563 - 4, 758 73, 950 170- - - - - - - - - - - - - - - . - -- - -- --- 180 _________ ________ 1,891 -5 63 1, 328 - 4, 195 32, 000 ----- - -- 188 ____________ _____ 1, 780 - 250 1, 530 - 2, 867 9,02 0 --------, .

1. 346 - 9 194.75 __ , - - -0 -- ------ 1. 337 -1. 337 0 -- - --- -- , I -15, 591 1 5. 591

I

j. T o determine total shear or bending m<?ment at any frame, it is necessary to add results obtained from static loading to those computed fr om aerodynamic forces.

TM 1-320 43-44 AIR CORPS ( 1) To obtain total shearing force between stations 30 and , 40: Pounds · Shear due to aerodynamic forces from table V = 3, 004 Shear due to static loading from table IV =- 1, 596 Total shearing force = 1, 408 (2) To obtain total shearing force between sta tions 80 to 90: P o unds - 4 624 Shear due to stat ic lo ading ' Shear due to aero dynamic forces 2 ,1 75 6,799 Total shea ri ng force (3) To obtain total bending moment at station 130: Mete r pounds Bendi ng moment due to static loading from table IV = - 80, 470 Bending moment due to aerodynamic forces from table V = 241, 930 Tot al bending moment = · 161, 460 44. Conclusion.- While s tatic means of sustentation and control are available to lighter than air aircraft, the intelligent pilot should constantly bear in rriind the effects of aerodynamic for ces on his air - ship. H e must und e rstand the relation of velocity to resistance, power requirements, and fuel consumption. He must be cognizant of the characteristics of his prop ellers and be able to make utmost use of variable pitch should his propellers be·capable of adjustment in that regard. He shou ld comprehend the theory of air s hip stability and be alert to augment that stabi lity by use of his controls. It is essen-· tial that he at all times appreciate effect of dynamic forces on his flight path in regard to both direction and altitude, and be able to assist his static control by dynamic means whenever necessary. F ina ll y, he · must be aware of the stresses to which his airship is being subjected and, knowing maximum performance for which his airc raft was de- signed, so vary t he velocity as to preclude possibility of exces.S structural s tre sses.

[A. G. 062 .11 (9- 11 -40 ) .]

BY ORDER OF THE SECRETARY OF wAR: G. C. MARSHALL, Ohief of Staff.

OFFICIAL: E. S. ADAMS, Major General, The Adjutant General.

DISTRIB OTION : D 1 ( 3) ; B 1 ( 2) ; IR 1 (5) -; IBn 1 ( 10).

II.!. GOVERNMENT PRINTING OFFICE: 1$41 For sale by the Superintendent of Documents,. W.ashington, D. C. · · - .. . - Price, 15 cents