airship aerodynamics

7/25/2019 Airship Aerodynamics

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TECHNI CAL MANUAL }No . 1-820

*TM 1-320W R DEP RTMENT

W ASHlNGTON, Pebru m y 11 1941.

AIRSHIP AERODYNAMICS

Prepar ed under direction of

Chief of the Air Corps

SroriON I. Gene ral. ParagraphDefin itio n of aerodynamic s______ ___________ _ 1Purpose and scope_____ ___ _____ __ __ ____ __ __ _ 2Imp ortance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3Gl ossary of terms__ __ _____ ___ __________ __ __ 4Typ es of air ships---- - - - - - - - - - - - - - - - - - - - - - - - 5Aerodynamic forces_ ______________ ____ ______ 6

l l . R esistance .Fluid resi&ance___________ ________ ______ ___ 7Shape coe fficients _______ ___________ _________ 8Coefficient of skin friction_ __________________ 9Re sista nce of streamlined body - - - - - - - - - - - - - - 10Pri smatic coefficient----------- - - - - - - - - - - - - - 11I ndex of form effici ency__ _____ _____ ___ _____ 2l l lust r ative resistance problem______ ___ ______ 13

S ca le effec - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 14Resi stance of completely rigged air ship ______ 15D eceleration test - - - - - - - - - - - - - - - - - - - - - - - 16

III . P ower requirements.Power r equire d to overc ome airship resistance_ 17R esults of vari ous speed t rials____ ___ ____ ____ 18Bur gess form ula for ho rsepower------ - - - - - - - 9Speed developed by given horsepower________ 20

Summary-- - - - - - - - - - - - - - - - - - - - - - '--------- - - 21IV. St ab il ity.Variation of pressure distribution on airs hip

ul l

Specific st ab ili ty and center o f grav ity of ai r -shiP----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 23

Cen ter of buoy ancy_____ ___ ________________ 24D esc rip tion of major ax is of airship__________ 25T ypes of stab il ity_ __ ________ ____ ____ _____ __ 26For ces and moment s acting on airship________ 9 lD ampi ng mom en t - - - - - - - - - - - - - - - - - - - - - - - - - - 28Longi tudina l stabilitY--------- - - - - - - - - - - - - - 29Dir ectiona l stability_________ __ ____ ______ ___ 30La tera l sta bility- - - - - - - - - - - - - - - - - - - - - - - - - - - - 31Sum marY--------- - - - - - - - - - - - - - - - - - - - - - - - - - 32

*Thia m anual supersedes or a ll lG-290 , November 16, 1929.

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SECTION

AIR CORPS

V. Control. Paragraph


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Aff iSHIP AERODYNAMICS

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3 Impor tance . -Ai rships are controlled in two ways, stati


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Se1nirigid. - Airship whose form is maintained by means of arigid or jointed keel in conjun ct ion with internal p ressu re inthe gas containers an d ballone ts (fig. 2).

The term airship is sometimes incorrectly appli ed tohea vier than air aircraft either in full or as ship . Thi s is aslang use of the word and sh ould be avoided .

Air spee d .-Speed of an aircraft relative to the air. I ts symbolis V.

Angle, critical A n gle of attack at wh ich the low about an airfoilchanges ab ruptly with corresponding abrupt changes in lif t anddrag.

Angl e elevator . -Angular di splacemen t of elevator from neutr alpo sit ion. t is positive when t railing edge of the elevator is belowneutra l posit ion.

Angl e of attack.-Acute angle bet v een the . chord of an airfoil andits direction of motion relative to the air. (This defin ition maybe extended to other bodies tha n airfoils.) I t s symbol is a .

Angl e of pitch A cute angle between two planes defined as follows:On e plane includes lat eral axis of the aircraft and direct ion ofthe relat ive wind; the othe r plane includes lat eral axis and longitudinal axis. (In normal li ght the ang le of pitch is the anglebetween longitudinal axis and dir ecti on of relative wind.) Thi sangle is denoted by 0 and is po sit ive when nose of the aircraft hasnsen .

Angle of roll, or angle of bank. - Acute angle through which aircra ftmust be rotated about its longitudinal axis in order t o bring itslateral axi s into a horizontal plane. Thi s angl e is denoted byI> and is positive when t he left wing is higher than the right.

Angle of yaw A cute angle between dire ction of relati ve wi nd andplane of sym metr y of an aircraft . Thi s angle is denoted by IIand is pos itive when the aircraft has turned to the right.

Angl e propeller blad e.-Actual angle b etween chor d of propellersection and plane perpendi cular to axis of rotation of propeller.Usua lly caUed blade ang le.

Angle, rudder.-Ac ute angle between rudder and plane of symmet ryof the aircraft. t is positive when trailing edge has moved to

the lef t with reference to no rm al position of pilot.Angle, zero lift; .-Angle of attack of an airfoil when i ts lift is zero.Aspect rati o of propeller blade.- H alf the ratio of propeller diameter

to maximum blade w idth .Aw es of aircraft.- Thre e fixed line s of re fer ence, usua ll y centroidal

and mutually p erp end icular. The longitudinal axis in the plane


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of symmetry, usually parallel to axis of the propeller, is calledthe longitudinal axis; the axis perpendicular to thi s in the planeof symmet ry is called the normal axis; and the third axis perpendicu lar to the other two is called the lateral axis. In mathematical discussions, the first of these axes, drawn from front torear , is called the X axis; the second, drawn upward, the Z axis;and the third, running from right to left, t he Y axis.

Ballas t . A n y substance, usually sand or water, carried in a balloonor airship and intended to e thrown out, i f necessary, for the purpose of redu cing load carried and thus altering aero static relations.

Ballonet. - Compartment of variable volume const ructed of fabricor partitioned otf within the interior of a balloon or airship. t isusually partially inflated with air under control of va lves from ablower or from an air scoop. By blowing in or letting out air,i t serves to compen sa te for changes of volume in gas contained inthe envelope and to mai nta in gas pre ssure, thus preventing deformati on or structura l failure. By means of two or niore ballonets,often used in nonrigid airships, the trim can also be contro lled.The ballonet should not e confused with gas cell.

Blad e back.-Si


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personne l, car go, or equ ipm ent . t may be s uspended from the buoy-ant portion o r it may be built close up aga inst it. t is not to eapplied to parts of the keel of a rigid or semirigid airship whichhav e been fitted for t he purposes mentioned .

Oeiling, static.-A l tit ude in stand ard atmosphere at wh ich an aerostatis in static equilibrium a.fter removal of all dischargeable weig hts.

Oenter of presswre coetflaient. - Ratio of distance of center of pressurefrom leading edge to chord length.

Oenter of pressure of cd1foil section P oint in chord of airfoil section, pro lon ged i f necessary, which is at the intersection of thechord and the line of action o f the resu l tant air force. Abbreviationi s C P.

Oho rd of airfoi l section) L ine of straightedge brought into contact with lower surface of the section at two points; in the case o fan airfoil having double convex camber, the straight line join ingth e leading and trailing edges . These edges may b e defined for thispur pose as the two point s in the section w ~ i hare farthest apart.)Th e line joining l eadi ng and trailing edges should be used also intho se cases in which lower surface is convex except for a sho r t flatportion. The method used for determining the chord should always

be exp licitly stated fo r those secti ons concerning which ambiguityseems likely to arise.Ohord length . Leng th of pro jection of airfoil sect ion on its chord.

Its symbol is cOont1ols G ene ral term appli ed to means provided to enab le the pilot

to control speed, direction of flig ht, a ltitud e, and power of ai rcraft .D1ag.-C ompo nent parallel to relative wind of tota l air force on

aircraft or airfoil. I t s symbo l is D D ynamic or impact pressure. Product ; p V 2 , where p is density

and V is relative spee d of the ai r. t is th e quantity measured bymost air speed instrum en ts. Its symbo l is q

:Elervator. Movable auxiliary airfoil, function of which is to impr esspi tching moment on th e ai rcra ft. The eleva tor is usually hinged tothe stabilizer .

E nvelope. O uter covering of aerostat, usually of fabric. I t may o rmay not be also the gas container. t ma y be divi ded by diaph ragms into separa te gas compartment s or cells, a nd it may alsocontain internal air cell s or ballonets.

F light path. ath of cente r of gravity of aircraft with reference tthe earth.

H orsepower of engine, ma.:vim-wm.- M aximum horsepower engine candevelop.

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Horsepowe l of engine, rated.-Average horsepower developed by aneng ine of a given type in passing the sta nd ar d 50-hou r endurancetest.u

(airship). M

ain structure of a rigid airship consist ing of acovered elongated framewor k w hi ch incloses gas cells and supportscars and equipment. May also be applied to comp lete buo ya nt un i tof any aerostat. In this latter sense s ometim es called gas bag.

lndraft (i nflow) . -F low 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 ngth to resist hogging and sagging and also serves to distribute effe ct of concent rated .load s along the hull. t may be a simple Gall's chain as in somesemirigids, or a ve ry extensive structure inclo sing the corridor asin mo st rigids.

Leading edge .-Fo remo st edge of airfoil or propeller blade. Alsocalled entering edge.

L if t . -That component of tot al air force on aircraft or airfoil whichis perpendicular to relative wind and in p lan e of symmetry. I tmu st be specified whethe r this applies to comp lete aircra ft or tparts thereof. In the case of an airship this is often calleddynamic lift. I t s sy mbol i s L.

Lift , gross (air ship) . L i f t obtaine d f rom volume of buoyant gasequal to nominal gas capacity of the a;ircraft. Ob tained by multipl ying nominal gas capacity by l if t per unit volume of gas used forinflation.

Lift stat ic (aerostat) . - R e su ltant upward for ce on an aero stat a trest obta ined by multiplying actual volume of the air displaced byden sity of th e air and su btracting weight of contained gas. (The

volume of the air displaced multiplied by the differen ce of densityof 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 radiatorand cooling syste m, all essential instruments and furni shings,fixed electric wiring for lighting, hea ti ng, etc. In the case ofthe aerostat the amount of ballast which must be carried to

assist in making a sa fe landing mu st also be included.Ful l . -W eight empty plus useful load. Also called gross

weight.Pa y Tha t part of useful load from which reven ue is derived.

namely, pa ssengers and freight.


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Useful Crew and pa sseng ers, oil and fuel, ballast other thanemergency, ordnance, and portable equipment .

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

Oscil lation stable. -Oscillation whose amplitude does not increase.O scillation ~ t n s t b l e Os ci l l t i o nwhose amplitude incres. ses con

tinuously until an attitude is reached from which th er e is notendency to return toward the origina l attitude, the motion beco m- .ing a stea dy divergence.

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

Maximum altitude attainable with definite weight relations an dballonet volume if fitted).

Endurance at fu ll and half power .Static cei ling .Dynamic l if t 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 i s pa.

Geo met rical . Dis tan ce which an element of a propeller wo uldadvance in one revolution if i t were moving along a helix o fslope equal to it s blade ang le.

Mean geometrical .- Me an of the geome trical pitche s of the sev-eral elements. I ts symbol is p0

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.- D istance which propeller would have to advance

in one revolutionin

order that theremight

be no thrust. Alsocalled experimental mean pitch. I t s symbo l is pv.Zero torque. D i stance which propeller would have to advance in

one revolution in order that the torque might be zero . I tssymbol is Pa

P itch mtio R a tio of the pitch (geometrical unless otherwi se st ated)to the diam eter pj D.

P i t ch speed.- Product of mean geometrical pitch by number of revolution s of propelle r in unit time, that is, the speed aircraft wouldmake if th ere were no slip.

P ropeller area p r o j e ~ t e d . T o t a larea in the pl ane p erpendicu lar to :propeller shaf t swept by propeller, exce pt portion covered by theboss and that swept by root of the blade. Thi s portion is usuallytaken as extending 0.2 of maximum radius from a xis of the shaft.

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Prope' Ze1t blade area. - Area of the blade face, exclus ive of the bossand the root, that is, of a portion which is usually taken as extend-ing 0.2 of maximum radiu s from axis of the shaft.

Prop eller -caml;er ratio R atio of maximum thickness of proj ellersection to its chord.

Prop eller efficien


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AIRSHIP AERODY N AMICS

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4-5

monly used only of such flo ws as are not eddying, but the dis-tinction should be made clear .by the cont ext.

Streamline flow . -S t e ady flow pa st a solid body, that is, a flow in

which the direction at every p oint is in dependent of time.Strea;mlirw form. Solid body which produ ces appr oximately stream -line flow

Surface control. Mov ab le airfoil de signed to be rota ted or othe rwise moved by the pilot in order t change attit ud e of ai rplaneor air ship.

Tait group (or tail unit).-Stabilizing and control surfaces at rearend of ai rcraft, includin g stabilizer, fin, rudder, and elevator.(Also called empennage. )

Tau heavy (air ship) .-Condition in which in normal flight the afterend of an airship tends to sink and whi ch require s correctio nby m eans o the horizontal controls . In this condition an airshipis said t trim by the stern.'' I t 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 afixed point .

Tracto r propeller P ropeller mount ed on forward end of engine orpropeller shaft. I t is usua lly forward of fu selage or wingnacell e.)

Trailing edge . R earmost edge of airfoil or propeller blade.5. Types of airships. a . Air ship s are div id ed into three genera l

classes in acco rdan ce with their method of construction. Th esethree cla sses are

1) Nonrigid.(2) Semirigid.{3) Ri gid.b The names describe mean s by wh ich shape of the e nv elope is

maintain ed. In the nonrigid, ga s in the en velope is kept und er suffi-cient pre ss ure t keep the hull shape by thi s means alone. In these mirigid a central keel is pro vided which carries th e lo ad ing andis itself swung by suspensions from the top of the envelope. Du eto its ri gid i ty, the keel a ss ists the internal pre ssure in maintaininghape of the envelope . In ri gid const ruction 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 slight superp ressure ismaintained.

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

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0 6 AIR CORPS

1) In sma ll nonri gid s cars are usually open and contain powerplant s as well as altitude and direction controls. Su ch cars a.reusually suspe nded by cables attached to the envelope. In semirigidand rigid constr uction ca rs are in contact w ith the kee l which car r iest heir load. Po wer plant cars are sepn.rat e from the con trol car.

FIGUHE 1 . U . :i. rmy u u u r i gi< l 1 ;-7..

(2) Cont rol surfac es on nearly all air ships consist of fixed v e ~ t ical and horizontal surfa ces , ~ t t t a c h e dto which are elevato rs and

rud der . On nonrigids and some semi ri gids th ese surfaces are at-tached to th e envelope by rigging. O n I talian type semi r igids andon all rigid s con trol surfaces are support ed by metal framework.

d Figur es 1, 2 3, and 4 depict t ypes of airships , showin g genera lstreamlined shape of the hull and arrang ement of cars and su rf aces.

6 Aerodynamic forces. e rod yn ami c forces may be di videdin to two classe s, those parallel and those normal to the path.

a The form er, or drag fo r ces, reta rd the flight of the airs hip and

mu st be overcome by the power plant s acting through the thru st ofthe propell er s. Po wer requirements in their turn affect fuel con-su mp tion and limit p e r f o ~ m a n c eof the air sh ip. He nce a thoroughknowledge of re sistance and power requirements is esse ntial toint elligent op eration of air ship s.

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A I R S H I P AERO D Y N A M I S

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TM 1 320

i::.>

t:l00-

SJ >

t:l0

CIS>

'nD0

0'

-

0

' 'a0

>0

Cl0Cl

>

3:


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TM 1 3206 7 AIR CORPS

b The second class of aerod yna mic :forces sometimes ca lled transverse :forces i s the result of use of control surfaces or of gusts encountered by the airs hip. Calcula tion of the effects of these :forcesis a s mentioned before often a matter of more interest to the designe rtha n to the operator but an und er standing of the pr inciples involved

FIGUIII:l 3.- U S. rmy s m i r i g id S 1

is nece ssary beca use it is through these forces that control andstabi lity are effecte d.

S ECTION

RE SISTANCEParagrap h

Fluid r es istan ce - - - - - - - - 7Shape coeffic ients - - - 8Coeffici ent of skin fricti on__ __ _________ ___ ___ _______ __ _____ ____ ___ ___ __ 9Res istance of s treamlined bod Y - - - 10Pri smatic coefficient - - - - - - - 11Index of fo rm etfi.ciency - - - - 12

Illu st rative r es is tance probl em

-

- - - - - - 13Scal e effect- - - - - 14Res i ; tance of comp letely ri g ged n i r s hiP - - - - - 15D oc eleration tesL - - 16

7 Fluid resistance. . B efor e attempting the study of resistancethe student should be fami liar wjth the composition and nature of

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the atmosphere with den sity and specific gravity calculations andwith the action of gra vitat ional forces. Th ese m at te r s are d iscussedin TM 1-325 .

b Wh eneve r a so lid object mov es through a flu id i t encounters are sist an ce to it s mot ion . This re sista nce may be considere d from twopoin ts of view.

(1) Momentum theory . a By New ton s first law a body at restor in motio n will r emain a t r est or continue to trave l at consta n t

FIGUR 4. . S Nnvy rigid os d t ~ g e l e s

veloci ty unless some force is exer ted to change i ts condit ion. Toenable the solid to maintain it s motio n r elative to the fl uid themo lecu les of the fl uid mu st be deflec ted to ma ke room for t he pa ssageof the sol id. So t o de ect the fl u id or air a force mu st be applied.I n th e case o f the airship this f orce is that furn ish ed by th e propellerthru st.

(b ) t ca n be proved m athematically that i f air were incomp r essibleand nonvi scous tha t is incapable of off er ing r esistance to sh ear be

tween the parti c le s the thru st of ai r partic les oppo sing the motionof t he solid would exact ly equal the th r ust of the air assisting th emotion. H ence there would be no resistance to th e motion. How-ever in th atmo sphere thi s ideal condition doe s not exist and theresist an ce is proportional to th e tota l kinetic energy of the deflectedparticle s of air.

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7 - 8 AIR CORPS

2) Pressure-diff erenoe theory.-Figure 5 shows the motion of thepart icles of an air stream passing a flat plat e held at right anglesto the flow . The air is deflecte d from its cou rse some distance in frontof the plate and ha s a complex eddying motion in rear o.f it. In frontof the plate the air is unde r an increased pr essure, while behind theplate there i s an area of reduced pre ssure. The drag can be considered as due to th e difference between the pr ess ures in front of an dbehind the plat e.

8. Shape coefficients. . The two systems in commo n use for x .pre ssi ng air r esista nce are the engineering and the abso lute.

1) Under the eng inee r ing system the formula is-

R v K A V 2 .where R v=ai r resis tance due to pressur e difference.

A = cro ss section al area norm al to the air strea m insqu ar e feet.

V =ve locity of m otion in m iles per hour.K IJ)=an empirically determine d constant depend ing on the

sha pe of the so lid and the mass densi ty of the air.

In lighter than air practice the lett er K , minu s subscript, is used todenot e K IJ when the ma ss density of the ai r is st anda rd 0.00237pound per cubic foot, which is the va lue whe n the pressure is 29.92inches and the temperature is 60 F.).

2} The absolute syste m, adopted by the National Advisory Committee fo r Aeronauti cs, uses the formula:

. u2

Ro= K DAP 2

wher e p= mass density o f th e ai r.v= velocity of motion in feet per seco nd .

K v an empirical shape coe ffi cient .2

; .is th e dynam ic pr essu re per unit of area or the velocity head ofthe a ir stream. This formula ha s more definite phy sical interpretation than the engineering formula from both the momen tu m andpre ssure-differe nce theorie s. Before stud ying aerodynamic dat a, t hesystem whi ch is being u sed s hould always be de term ine d.

b. Some of the first prac tica l te sts made to determine the effect ofshape upon the re sistance offere d the motion of solids throughthe air were .condu cted by Eiff el. Since th en studies h ave beenconducted by variou s investigators until a t pr esent the store of information on thi s subject is qu it e e laborate . Figure s 5 to 15 givethe action of the air on variou s sha pes together with the values of K

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. 1) Flat plate. Figure 5, as described in paragraph 7b 2), showsa flat plate held normal to the air stream. Eiffel demonstrated thatthe circular di sk gives about 5 percen t less resistance than the squarefla t plate. Rect angle s have slig htly high er value s of than thesquare plate of the same area, the airfl ow around the edges of the

X = 00328

___. . -_... :_. - -

FIOURI l 5 . - A i r st ream fiowing by a fiat plate.

--.

-

- . ~ ..--

.

X = 00328 2 7

-

F IGURFJ 6 . A i r stream tlow ng by an inclined plate.

rectangle being som ewhat more re st ricted t han tha t in th e case othe squ are.

(2) F lat plate, inclined .- Fi gure 6 illustrates the case of the flatplate inclined to the air st ream . E iffel's constants for differentangles of incidenc e are as f ollow s:

Angle of incidenceJ 50

1015 .20

0.000100.00059L).001240.001930.00265

(3) Oon oave h.emisph.ere. - Exp e1 iment s ha ve sh own that the resistan ce of a hemisphere wi th the con cav e s id e facing the -dire ctionof motion is greater than t hat of a flat di sk of the sa me exposed

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cro ss sect ion . for a concave hemisphere is about 0 00389 seefig 7 .

4) onvero hemisphere For a hemi sphere with the convex sidefacing the direction of motion or pointing against the wind the

X = 00389

:

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

= oooea

FIGURE ~ i r stream flowing by a convex hemisp here.

X = 0008

:

:

FIG URE 9. A i r stream flowing by a sphere.

re sistance is much le ss t han for the concave hemi sphere shown infigur e 7 The resistance of the convex hemi sphere is much less thant.hat of a flat plat of the same cro ss section or exposed area. T h ~coefficient of resi stance is found to be about 0 00082 see fig . 8}.

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5) Sphe e. T h e air flow around a sphere (w hich more clo sely approach es a str eamlin e form) . is sho wn diagrammatically in figur e 9.It will be observed that the spr ead in g out of the line s of flow beforereaching the sphere is less marked than for the flat plate in figure 5.The coefficient of resistanc e 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. y l l nders.

but f or ordinary velocities its va lue is about 0.008. Th e s phere is the

simplest geometrical form and is the most efficient shape for maximumvolume per unit weight bu t has a greater resistance than the moreperf ect st reamline form ( see fig. 9).

(6 Oylinder (longitudiMl aa is horizontal .- Th e resistance of suc hcylinders decreases wl.th length until the fineness ratio is approxi -

X = ?0123 fort= 5

,.. ...

li I GOR l 11 . - A l r s t ream flowing by a cylinder (arts normal to a i r t'low).

mately 4 to 1, after which i t increases. The increase is due to the effectof slcin friction which will be discussed la ter . The relative resistanceof cylinders as compared to that of a flat pla te of the same cross section is as shown in figure 10. Where the fineness ratio is 4 to 1,K = 0.00205.

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7) OyUnd rr vertical .-When a cylind er of given cross-sectiona larea is placed wit h it s axis of revolut ion at right ang les t o the directionof motion t he resistance depends upon the finene ss ratio of the cylinder.Wh en the length an d diameter of t he cyli n der are the same the coefficien t of resista nce is on ly slig ht ly greater than for a sphere of the same

LK = 0006 fo r D =

-

FIGURE 1 2 . A i r s t ream flow i ng by a cyli nder hemisph e rical end s) .

cross -sectiona l area. Wh en the length-diameter rat io i s increa sed to4 to 1 the coefficient o f resistance is approximate ly doubled, orK = 0 .0018, and if the length-diamete r ratio is reduced to one-h alf or0 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 . I t is po ssible to r educe

greatly the re sistance of a cylinder by capping th e ends wit h h emi -

WIRJ:S C BLESX . 0026 K : . 00 13 K = 0015 X = 029

FIGURE 13.

spheres . The resista nce is reduced to 20 percent of that of a cylind erw ith fl at ends. Th e va lu e of K for a cylinde r with hemispherica l ends

and a fineness ratio of 4 is approximatel y 0.0006 see fig 12).9) W ires and cables .- W ires and cables m ay be conside red as cylin

d ers of very long length . E xperiments show that the resista nce of wireor st randed cable when placed norma l to direction of motion is verynear ly equa l to the resist ance of a flat plate of the same projected area.Th e gain by the circular form of the wire is counter balanced by its very

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Affi SH I P AERODYNAMICS

T M 1 320

great length. The resistance of a long, narrow ob ject perpendicular todirection of motion is greater than that of a more symmetrical form.Th e expe r imentally determined va lue of the coefficient of resistance is0 0029 for stranded cables and 0 0026 for smooth wi res. K is almost in

N.PL. I

N.P 12

.Fimnessl t:dto 4j/ . K=.ooo4N.PL 11 ..3

/ inmes.s ~ c r l t o41 K: OOQ38NP.J.. ..-4

~ r : - ~

/ /

~ /

l l n e n ~ s saho 2/1 1


23/68

T 1-3208 AIR CORPS

.10) Struts of strecmWirw form. I t is f o u ~ din practice that the

best fineness ratio for struts is 4 to 1. Inclining the strut to the verticaldoes not have the effect of reducing the resistance for streamline forms,but for blunter shapes shorter than the t rue streamline) inclinationreduces the resistance considerably. A group of strut sections areshown in figure 14 and the value of for each shape is shown. I t canbe seen that the effect of yawing is to increase greatly the resistanoo byplacing the strut sidewise or a t a different ang le to the air stream.

11) AirshVp cars. All cars are built to take advantage of streamline form. This is especially t rue of the inclosed models for which anaverage value of K is 0.001. However, there is a wide variance in theshape of airship cars and a corresponding variance in the value of K.

K= OOl average value)

FIGURE 1 5 . - A i r stream fiowing by i r s h i p ~

For each different shape a new value of must be determined by windtunnel 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 a t r ight angles to direction of motion when moving a t a velocityo f 30 miles per hour in air of standard density?

b) What is resistance a t 60 miles per o u r ~2) Sol ution.a) Rv = K A V 2 =0.00328X 1 X900=2.95 pounds.b) Rv = K A V 2 = 0.00328 X 1 X 3600 = 11.81 pounds.

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

d Based on resistance of a fiat disk, the following shapes have therelative resistance shown below :

PercentSquare plate- 104.5Cylinder horizontal-- 65. 5Sphere 25.4Cylinder capped ends-- - - - - - - - - - - 21.0Airship model - - 3 0

22


24/68


T M 1 320

9 10

9. Coeftioient of skin fr ict ion. a . In the case of a flat plate atright angles to the air stream the resistance is almost entirely due tothe pressure difference in front of and behind the _plate . This is nothowever the case with most solids. In general, resistance may bedivided into two parts:

1) Pres sure difference.2) Skin friction.

b When a solid passes through the air i t carries along with it a verythin layer of air, the exterior surface of which forms a pl ane of aircleavage. The resistance of the air particles to shear on this plane iscalled skin fric t ion.

c The value of the skin fr iction on an airship hull, as determinedempirically by Zahm and others, is given by the formula:

R = 0 0035pS 0 9 8 v u e

where S is the total surface area. A somewhat more convenient formula is

R r= 0 00309pS v u 5

10. Resistance of streamlined body. a . As mentioned before,the total resistance i s 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 slenderform. In fact, the greater the fineness ratio, the less will be the pressure-difference resistance. An increase in fineness ratio, however , leadsto an increase in surface area and so to an increase in skin friction . t

is ne cess ary therefore to compromise on a moderate finene ss ratio, asa very long and slend er form would have so high a skin friction as tomore than counterbalance the gain by reduction of the pre ssuredifference resi stance. A fl_neness ratio of 4 to 1 is very good for a smallnonrigid, but for large rigid s i t has been found advisable to increasethis ratio to 6 or 7 to 1. Recen tly an airship had been designed whosehull has a much smaller finenes s ratio than the conventional designs.This airship has a capacity of 200,000 cubic feet and a fineness ratio of2.82, noticea bly shorter than any ships recently constructed. A modelof this ship was tested in the wind tunnel of the Washington NavyYard and was found to have the lowest resistance coefficient of anymodel ever tested there.

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

3


25/68

T M 1 3 201 0 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 airshiphull s as follows :

R 0 DP volume) s v ~ s e

where O D is called the P randtl shape coefficient afte r the eminent authority Professor P r andt l. V alues of D for various speeds are givenin table I.

c The offsets for di ffer ent types of airships are given in tab le II .A study o the shapes given therein in connection with the Prandtlcoefficients will bring out the relative efficiency of the different streamlin es.

d Certain general rules o design developed by experience and testmay 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 ea r portion of the hull doe s not seriouslyaffe ct the resistance.

3) The introduction of a cylin dr ical midsection causes an additional resistance equal to the skin friction on the increased surface

area of the hull.4) The major diameter should lie between 33 and 4 percent of totallength from the bow.

11 Prismatic coefficient. - Th e ratio of the vo lum e of any hullform to that of the circumscribing cylinde r is call ed the prismaticcoefficient, Q v

VolumeQ v= Maximum cross-sectional area X length

VOl = Q t A L

The prismatic coefficients for different shapes are given in table I . .

24


26/68

~00

-- . -- 1 -- 't....C

Name of modelI x.en t h Dlame

, I ter. /0

I........

l- - -. -- I

}

N a.vy B (Goodrich)--- _. 3. 5Navy 0 - - - - - - - - - - - - - - -2. 9Navy E-------- - - - - - - - 4. 1E. P- _ .. __ _ ___ - - - _ _ _- 3 . 0

I. E ____ ___ - - - - - - - - - - - - 2. 9Goodyear 4 2 _______ __ 3. 1Goodyear - L ________ __ 3. 4Goodyear - 2 ______ - - - - - - 3. 8Goodyear - 3 ____ . .___ _ _ 3. 6Goodyear - 4 _ ___ -- -- __ 3. 1

~ Astra-Torres __ . _ _ _ __ . _ 3. 1O l Parseval P. L ________ __ 3. 9

Pa r seval P. _ ____ ___ _ _ 3. 2P arseval P . I l L _____ __ _ 3. 2P arseva l S. S . T ___ ___ __ 5. 6P ony Blimp AA ______ __ 1. 9U B - F C _ ________ _____ 4. 9UB - 2 ___________ ___ __ 4. 4

C class cylindric midships1 1 diameter __ ________ __ 3. 1,z diameter ____ - - - - - - __ 3. 2

1 diameter _______ ____ __ 3. 52 cliamet3r ___________ __ 4. 23 diamete r ____________ _ 4. 84 diame ter_ ____________ 5. 5

Feet

0. 6967. 6417 6417. 6417

. 6417 6870 6660 6350 6150. 6870. 6914. 6417 641 7 6417

1. 13305 8 V

1. 0591l l . 1638

- 64 17. 64 1 7. 6 4 17. 641 7. 6 4 17. 64 17

T A B L E I. - Airsh ip model characteristics and data

Area Prandtl h a 8 ~coefficient, Fine-Dis- Pris-

maxi ness tan ce Dis- maticmum ratio, maxi- tance coe ffiSurface. Volum e,

s cross- Vol. F R mum CG cie nt,s ec t ional L diam e ter from Q VtJI.ar ea 20 40 60 15 from no seA m.p.h . m . p. h . m.p.h . nose AXL

- - - -- - --- - -Sq ft Sq f t u f t P d L P ct . L

5. 800 0. 381 0. 8304 0. 016 8 o. 0 154 0.0148 5. 060 37. 80 ------ 0. 61764. 750 . 323 . 6259 0 159 . 0144 . 0136 4 . 620 30. 00 46.37 . 656 25. 007 . 323 6690 . 01 68 . 0146 . 01 42 4. 870 36. 25 48 . 64 . 66214. 597 . 323 . 589 0 . 0 166 . 0147 . 0138 4. 820 41. 59 43. 92 . 6891

4. 59 7. 323 5955 . 0175 . 0155 . 01 44 4 . 650 38. 18 44 . 25 . 6 1 69

5. 4 70 . 371 . 7840 0162 . 01 44 . 0134 4. 640 28. 76 - . .. -- - . 6 6245. 60 0 . 348 . 7 360 - - - - -- -- - - -- . 0141 5. 130 3 4. 15 - - - . 61846. 000 . 317 . 7 5 20 ------ - ---- - . 0141 6. 0 3 0 36. 1 4 - --- -- . 61945. 900 . 297 . 7760 ------ ------ . 01 40 5. 970 36. 36 ~ . 71195. 470 . 371 . 7 840 ------ ------ . 01 53 4. 6 40 28. 76 --- --- . 66245. 190 . 309 . 6583 . 01 90 . 0 15 9 . 0 147 4. 5 8 0 33. 80 49. 08 . 6 5905. 465 . 323 . 724 0 . 0185 . 0174 . 0165 6. 140 38. 7 5 43 . 19 . 5679 .4. 5 28 . 323 . 5891 . 0181 . 0170 . 0 164 4. 990 38 . 90 44. 4 6 . 56774. 750 . S23 . 6331 . 0179 . 0169 . 0161 4. 699 47 . 33 4 5. 85 . 6095

14.720 1. 008 3. 4550 . 0174 . 0173 . 0170 4. 9 6 0 4 5. 00 45 . 88 . 60902. 7 60 . 267 . 3196 . 0205 . 0254 . 0277 3. 4 10 42 . 50 46 . 00 . 6003

12. 958 4 . 8810 2. 8 60 3 . 0321 . 0223 . 0219 4. 663 - - - - - - - - ... . 65 U 612 . 224 C 1. 0 63::: 2. 92 0 1 . 0205 0 189 . 0 192 3. 823 - - ... - --- .. -- . 611 45

.5. 073 . Z ~ 3 . 677 7 . 0154 . 01 40 . 0 13Z 4. 8 5::: - - . ... - - - 6 7 495. 398 . 323 . 7297 . 0153 . 0 141 . 0135 5. 100

. 6909-- ---- - -- - - -

6.043 . 323 . 8330 . 0164 . 0 14 6 . 0136 5. 570

- - ---- - -----. 71 8 4

7. 337 . 323 1. 0404 . 0175 . 0150 . 0136 6. 600 - -- - -- ------ . 76 118. 62 7 . 323 1. 2471 . 0173 . 0156 . 0148 7. 59 0 ------ ------ . 79259. 922 . 323 1. 45 4 8 . 0175 . 01. >7 . 0146 8. 590 ------ ------ . 81675 diameter _________ ____ 6. 1 . 641711.218 323 1. 6625 0164 0154 0148 9. 602 - - - - - - - - - - - - 8358

Index ofform efficien cy;Q

H r = D

. -- -- - - .20 40 60

m.p.h . m. p. h. m. p. h,

36. 76 40. 10 41. 7 ~41 27 45 . 57 48. 25

- - - - - - - - - -- - ------35. 49 40. 08 42. 7035. 25 39. 80 4 2. 8440. 89 45 . 37 49. 43

- - -- -- --- -- - -- -. ...---- - - ------ - - - -- ------ ------ ----- - - ---- ~ ~ - -- 34. 68 41. 45 44. 8330 . 70 32 . 64 3 4. 4231 . 36 33. 39 34. 6234. 05 36. 06 37 . 8635. 00 35. 23 35 . 8229. 28 23. 63 21 67

- -- -- -- - -- - - - - - - - - - - - '

43 . 82 48. 21 51. 1345. 16 49 . 00 51. 1843. 80 49. 21 52. 8243 . 4 9 50. 74 55 . 9645 . 81 50. 80 53. 5546 . 67 52. 02 55. 9450. 96 54. 27 56. 47

' l:rl~~

>~>


27/68

T L E I . A i r shi p model characteristics and data Continued.

Area Prandtl shape coefficient F in - Di s- . Pris-maxi- ness tanoo Dis- ma ti cmum

D ratio maxi- tan co coom-Lenzth Diame- Sur face, VolumeNa m e of mod el cross - F R mum CG cientter D 8 sectional Vol. L diameter from Q Vol.

area 2 10 60 from noseD A LA m. p. b. m. p. b. m. p. b. nose

- --

- -

EUiptical series British)eet eet Sq. ft . Sq ft. Cu. ft. P.ct . L P.ct. L

E 2. 37 1 0. 3906 ------- 0. 120 0. 1658 0. 0132 0. 0135 -- - 6. 070 33. 19 -- 0 5835E 2 - - 1. 743 . 39 10 --- -- -- . 120 . 126 1 . 0 138 . 0128 ------ 4. 460 33. 86 - . 6024E 3 - 1. 568 3920 ------- . 121 . 1112 . 0147 . 0120 ----- - 4. 000 34. 19 - - . 5876E 4 _____________ ___ ___ 1. 384 3923 - --- . 121 . 09 72 . 0167 . 0139 -- - 3. 500 35. 18 -- . 5810E 5 - 1. 178 3929 ------- . 121 . 0826 . 0184 . 0147 - 3. 000 33. 43 . 5786Parabolic series British)p }____________ ____ ___

1. 594 . 3900 --- ---- . 1 20 . 0970 . 0168 . 0137 --- - 4. 090 49. 39 . 5094P 2 ______________ ____ _ 1. 598 . 3903 - 120 . 1000 . 0169 . 0176 4. 070 32. 06 - - . 5265Pa ________ _______ 1. 173 . 3867 - . 117 . 0729 . 0226 . 0173 ----- - 3. 830 50. 35 ------ . 5293P4 - 1. 217 . 38 70 . 118 0714 . 02-15 . 0193 - 3. 140 35. 05 . 4989

- -

Index of form efficien cyQH D

2 4 om.p.h . m . p.h. m. p. 11

--

44. 20 43. 22 ----- -43. 65 47 . 0640. 00 45. 55 -- - 34. 79 41. 80 - 31. 45 39. 36 -- ----

30. 32 37. 18 ----- -31. 15 30. 00 - --23. 42 30. 60 ------23. 20 25. 85 -- -

-

~. . . I -

... J.

~00

al

t-:


28/68

T A B L E I l - Ojfsets of various streamline forms Un i te State s models

Navy B (Goodrich) NavyO NavyF E. P. Parseval P . I Parse val P. II Parse val P. III- - - - - - - -

D istance Dlam- Distan ce Dlam- Distance Diam- Distance Diam- Di stance Diam - Distance Diam - Dis t ance D am-from ete r from eter from etorfro m eter from etcr from et.c r from eternose nose nose nose noso nose nose

- - - - - -- - - - L P et. 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

2. 36 2 4. 16 2. 81 32. 47 1. 23 23 . 12 0. ];3 24. 88 1. 25 27. 37 1. 25 27. 2 7 1. 25 21. 564. 73 41. 27 5. 62 55. 0 6 2. 45 35 . 06 2. 59 34. 60 2. 50 37. 92 2. 50 37 . 92 2. 50 32. 997. 09 55. 14 8. 43 69. 61 3. 68 43. 90 5. 19 4 8. 44 5. 00 51. 9 5 5. 00 51. 95 5. 00 47. 799. 45 65 . 27 11 24 79 . 22 4. 91 50 . 61 10. 37 66 . 10 10. 00 71. 17 10. 00 71. 17 10. 00 66. 23

11 81 75 . 36 16. 86 91. 17 7. 36 62. 73 15. 56 78. 12 14. 99 83. 3 8 15. 00 8 3. 36 15. 00 78. 70

14.

18 81.

94 22 . 48 97 . 409.

81 72 . 08 20 . 75 86. 66 19. 98 91. 1720.

00 91.

17 20. 00 88. 0518. 90 90 . 31 28. 11 100. 00 12. 26 7 8. 5 7 2 5. 94 92. 7 3 24. 98 96. 10 2 5. 00 96. 10 2 5. ~ 94 . 0323 . 63 9 4; 98 33 . 7 3 100 . 00 14. 71 84. 93 31. 12 96. 75 29 . 98 98. 96 30 . 00 98. 96 30. 0 97 . 402 8. 35 98. 09 42. 16 98. 18 19. 62 9 3. 51 36 . 31 99. 4 0 3 4. 97 100 . 00 35. 00 100. 00 35 . 00 99. 2233 . 09 99 . 6 4 50 . 59 94. 29 24. 54 98 . 05 41. 50 10 0. 00 39 . 96 99. 48 40. 00 99. 48 4 0. 0 0 100. 00

~37 . 82 100 . 00 59. 02 88. 83 29. 45 99 . 61 48. 81 9 8. 44 44 . 96 98. 1 8 45 . 00 98. 18 45. 00 100 . 0047 . 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. 0 656. 70 93. 06 75. 89 7 1. 69 39. 27 99. 74 63. 43 86. 23 54. 96 89. 8 7 55 . 00 89. 8 7 55. 00 95. 8666. 15 83 . 25 84 . 32 59. 48 44 . 17 98. 96 70 . 74 7 5. 32 59. 96 83. 90 60. 0 0 83. 90 60. 00 91. 6970 . 88 7 6. 91 89 . 94 48. 5 7 49. 07 97 . 53 78 . 05 60. 5 2 64. 95 76. 36 65. 00 7 6. 36 65. 00 85. 977 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. 9 680. 33 61. 00 9 5. 56 31. 9 5 58. 78 62. 34 92. 68 23. 90 74 . 94 57. 66 75. 00 57 . 66 75 . 00 70. 918 5. 05 51. 44 9 8. 3 7 18. 96 63. 69 88 . 3 1 100. 0 0 - 0 7 9. 94 4 7. 0 1 80. 00 47. 01 80. 00 59. 7489 . 7 8 39. 35 100. 00 . 0 68. 69 83. 25 - - - 84. 93 35. 84 85. 00 35. 84 85. 00 47. 2792. 1 4 31 . 94 --- ------ 73. 60 77. 27 - - 89. 92 24 . 16 90. 00 24 . 16 90. 00 23. 259 4. 50 23. 44 -- - 7 8. 51 70 . 26 - ------ 9 1. 92 12. 21 95. 00 12. 21 95 . 00 17. 1496 . 86 14. 00 - - - - 83. 4 1 62 . 38 -- - -- - - 100. 00 . 0 100. 00 . 0 100. 00 . 09 8. 14 8. 97 -- -- 88. 32 52. 47 -- - -- - - - - - - -

100. 00 . 0 -- 93. 22 40 . 52 - -- - - - - - - - - -- -

-- ------ - 94. 45 36. 7 5

- - ------ ---- - - ----- ------ --- --- - - - - - - - - - 95 . 68 33. 12 - - - - - - - - - - ------ ------ ---- - - 96 . 91 28. 31 - - - - - - - - - - -- - - -- -- ------ 98. 13 22. 47 - ------ - - - -- - - -

- - 99. 36 12. 26 - -- ---- ------ - --- --- - --- --- 100. 00 . 0

.---- ------ - - - - - -- -- - - -- ----- - ------

a. s. T .

Di st ance Dlam-from ete rnose-

Pet. L Pet. D.1. 24 21. 412. 51 32. 984. 99 47. 839. 99 66 . 07

14 . 98 78. 89

19 . 97 88. 0 724. 97 9 4. 0 429. 96 97. 3234. 97 99. 1139. 98 99 . 8044. 99 100 . 0050. 00 98. 7554. 99 95 . 8759 . 97 91. 7 564. 96 86 . 2469. 9 4 79. 1474. 93 70. 3479 . 91 59. 7684. 8 9 4 7. 3989. 8 7 32. 9994. 86 10 . 83

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

- -- -

- -

- --

Pony blimp A.A.

DistanceDlamfrom ete rnose

Pet. L P et. D.2. 09 20 . 5 84. 19 3 3. 498. 38 54 . 65

12. 57 67. 7116 . 7 5 77. 50

20. 94 84. 6025 . 13 89. 9929. 32 94. 1833. 51 97 . 2337 . 70 99 . 0 141. 88 100 . 0046. 0 7 99. 4350 . 2 6 98. 0854. 45 95 . 8858. 64 9 3. 4762. 83 89. 6467. 02 84. 8171. 20 78. 427 5. 4 0 71. 0 479. 58 63 . 5283. 76 54 . 6587. 9 6 45. 7892. 14 35. 4996. 34 22. 21

100.00 . 0- - --

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

. "d

i:j

~z>

{ / l

I ~


29/68

TM 1-32012-14 AIR CORPS

12. Index of form e:fficiency. - In genera l, in design i t is desiredto get the greatest volume from the . least surface area as this r e d u ~weight and diffusion. Fortunately, good streamlined shapes usuallyhav e high prismatic coefficients, but of course some shapes are r.nore

efficient in this regard than others. In studying relative efficiencyof shapes , both the resistance coefficients a nd the prismatic coefficientsmu st be considered . The ratio of the latt er to the former is calledthe index of form efficiency, t

H= 13. Dlustrat ive resistance problem.-a . Proolem . Given an

airship whose hull has a length of 200 feet and a major diameter o43.5 feet vith the hull offsets those of the C type airship envelope.1) what is total volume of e n v e l o p e ~

(2) What is hull resistance at 60 miles per hour in sta ndard atmosp h r ~

b Solution ., 1) Vol = Q .vA L

From Table I , Qv is 0.6562.

7rd2 3.1416A = = 4 (43.5)2 = 1,485 square feet.

H ence Vol=0.6562X1,485X200=195,000 cubie feet.2 ) R=0Dp vol)2/3vl.86

2260 M P H=60 X15=88 feet per second .

G from T ab le 1 =0.0136 at 60 M P HR=0.0136 X0.00237X (195,000) 213 X881 8

R=455 pounds.

14. Scale effect.- a. One great rea son why so much difficulty isencountered in determining prior to construction the resistance o thecompleted hull lies in the fa ct that the res istance of the model cannotbe multiplied by the ratio of the linear dimensions of the model andthe completed hull to determine the resistance of the latte r. Thediscrepa ncy between the calcu lated resistance and the actual resista nce

of the full- size d airship is attributed to sca le effect. Oft en errorsin calcu lation due to :faul ty data or bad theories are so ex plai ned awayby those re sp onsible :for the mistakes. There are severa l reasons however, why, even with proper data and theory discrepancies will existbetween calculated and actual resi stanc e.

28


30/68

AIRSHIP AERODYNAMICSTM 1-320

1 4 - 1 5

b The theory of dimensions shows that the coefficients of resistance .1 L

vary directly as -; - whe rev=velocity in fe et per second.

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

v kinematic viscosity coefficient of the fluid.a v the kinematic viscosity coe fficient , is defined as the ratio be

tween the absolute viscosity coefficient and the atmospheric massdensity. Hence- -

v = ~ where v s the absolute viscosity coefficient of the air and is a

constant.vLd - ; called the Reynolds number aft er Profes so r Reynolds,

depend s on th ree variable quantities, p v and L : T o predict fullscale performance from the model tests, allowance must be made forthe fact tha t the L in the full-sized airship is very different from th eL in the model, and consequently the co efficient of resistance will bediffer ent.

e To overcome the effect of this difference a wind tunnel has beenbuilt at Langley Field in whi ch p ma y be sufficiently increased tomake the pr oduct pL for the model equal tha t of the full- sized sma llnonrigid airship, thus eliminating scale effect.

15. Resistance of completely r igged airship. . There are very li ttle data avai lable showing the relative resistance of the variousparts combining to produce the total r esistance of a completely riggedair ship due to the difficulty in obtaining dynamic similar i t y betweenthe model tested and the full-scale airship.

b. Total re sistance of air ships may be subdivided approximately asfollows f o r

1) Large nonrigids with closed cars: P ercenta) v l o p 45

b) Surfaces-------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 20c) Rigg ing and suspension cables __ __ _____ ___ ____ ___ 15d) Cars_______________ ___ ___ ___ ________ __ _____ ____ 15

e) Acc essorie s - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5

2) Small nonr igids with open car s :a) ~ n v e l o p e____ - - - - - - - - _- - - - _____ __ - - - - - - - _____ . 35b) Surface s -- - - - - - - - - - - -- - - - - - - - - - - - - - - - - - -- - 25c) Rigging and cable s __ __ __________ ___ ____ __ ____ ___ 20

d) Cars- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _ 15e) Accessories---- - - - - - - - - . . . _ - - - - - - - - - - - - - - - - - - - 5

29


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T M 1 3201 6 1 6 A m CORPS

3 ) Semirigids: Percenta ~ o e ~ 53b) Surfaces _______ _____ ____________ ________ ___ ____ 20

c t i g g j n g ~ 7d Cars __________ ____ _- - - - - - - - - - - - - - - - - __ - - - - - - - - - 13e Accessorie - - - - - - - - - - - - - - - - - - - - - - - -- 74 Large rig ds :a) IIull __________ ________ _______ __ ___ ________ _____ 60b) Surfaces____ ___________ __ ___ ________ _____ ____ __ 15c) Cars and suspe nsio ns - - - - - - - - - - - - - - - - - - - - - - - - - - - - qd Miscellane ous r igging and accessorie s_________ ___ 5

16. Deceler a t ion t e s t a. Te sts are 1nad e frequently on fullsi zed airships to det ermine actual risistance of the airshi p at variousspeeds . In these te sts the airship is brought to a certain velocityand then the motor s are idled, the velocity being recorded againsttime as the airship decelerates.

b. Th e general theory is that the resistance, or force causing deceleration, is given b y the equation :

R = M v a, whereex.= decel eration in f eet per second z.

Mv= the virtual ma ss of Lhe ship .

Th e virtual mass of an ai r ship is the mass of airshi p and contentsplu s the mass of air which is carried along with it. This latter iscomputed by the Mun k formula :

AMo=P1 , wh ere r is the radius of largest cross sec tion.c. Ob serving veloci ty at end of ea ch sec ond gives the ra t e of

ch ange of velocity, or decele ration, for each second and by interpolation for each air speed . A ct ually formu la s a r e employed which in- .volve calculus and are b eyond the scope of this manual.

d. These dec eleration .tests a re quite valuable a s a check againstth e resistance formul as developed in this section. They are howeveroften com plica ted by poor instru ments or faulty observation, rendering i t difficult to pla ce a proper value on re sults so obtained. Forthe present more confidence i s to be placed on the resistance formulas

and the power requiremen t formulas which will be developed in thenext sectio n.

30


32/68


SE CI IO N I I IPOWER REQUIREMENTS

T M 1 3207

ParagraphPower required to overcome airship resistance __ ___ _____________ __ __ ____ __ 17

Result s of various speed t r ials----- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18Burg ess formula for horsep owe r - -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 19Speed e v e l ~ p eby given horsepower______ __ _____ ________ ___ _____ _______ 2Summary - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _______ _______ - - - - - - - - - - - - - - 2 l

17 Power required to overcome airship resis tance.-a . Tomainta in uniform velocity in fli ght, resistance of t he airship must beovercome by thrust of the propellers. The work done by the propellers equals the product of the resistance times the distance throughwhich the airship moves.

b The unit of work in the English system is the foot-pound, or thequantity of work performed by 1-p ou nd force acting through a distance of 1 foot. Hence work done in propelling the airship in footpound s equals resistance in pounds times air distance traveled bythe airship.

a Power is defined as the rate of doing work, 1 horsepower equaling55 foot-pound s per second. Therefore the power utilized to overcome hull re sistance must equal resistance multiplied by velocity in

feet per second divided by 55 .d The resi stance is given by the equation (see sec. I I :

R = CD p (vol) 213 u 86Then the horsepower required to overcome this resis tance is given bythe formula:

Cn (vol) 213 if 86H P. = 550

e. Proble m and solution- 1 Probl em . - W h a t hor sepower w ill berequired to drive an airship of 195,000-cubic-foot capa city at 6 milesper hour (88 feet per second) in atmosphere of standa rd e n s i t y ~The envelope shape coefficient is 0,0136. The propeller efficiency, Eis 6 percent. The envelope resistance, F is 4 percent of the totalres istan ce of the airship.

(2) Solution . T h e horsepower necessary to overcome hull resistance is given b y -

Cn (vol) 213 if 86H. P = 550

_ (0.0136 X 0.00237 X 3376.4 X 359000)55

=71.1 horsepower.

31


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T.M 1 32017-18 A m CORPS

Since hull resistance is but 40 percent of tota l, the horsepower to overcome tota l resistance

Since propeller effici ency is 60 _percent-

Total horsepower required= 7 1 . 1 o . 4 0 ~ o . =296 hor sepower .

f As illustrated in the problem in d abov e, the following is a convenient formula for the hor sepower requ ired when the percentage ofresistance due to the hull and the propeller efficiency are known.

g A commoner method of determining the horsepowe r requirementsis to d ete rmine a shape coe ffi cient by wind tunnel te st of the completelyrigg ed model. In thi s case the body in question is not as perfe cta streamlined shape as the hull i tself so the res ist ance varies more

nearl y as the square of the velocity. Thenthe

horsepowe r re quiredbecomess - D p vol) 213 v8

H P.= 5 5 0 E

where 0 D is the shape coefficient of the model.1) P rob lem. - What horsepower w l ~be required to drive an air

ship of 195,000- cubic- foot capacity at 60 miles per hour 88 feet persecond) when the atmosphe r ic density is standa rd the coe ffi cient ofre sistance 0 D of the completely rigged ship is 0.0165, and the propellerin stallation efficiency is 60 perce n d

2) Sol1JJtion

H P =0 D p vo l) 213 v8

. . 550 E

0.0165 X0 .00237 X 195000 213 8885 s = o ~ x ~ o ~ = 6 o ~

= 275 horsepower, nppro:-dmately.

18. Resul ts of va r i ous speed tr ials. a . The following datawere obtained by pr og ress ive speed trials ma d e on the United S tatesNavy C class nonrigid airship of 180,000-cubic-foot capac i ty:

22


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R- poundsV infoot- R . P M . B. H. P . E sec-onds Total H ull

66. 6 1, 100 109 60 540 33473. 3 1,200 143 60 643 39480. 1 1, 300 183 60 754 45787. 7 1,400 231 60 875 517

Ap-pend-ages

206249297358

T M 1 320

18-19

C D

0.02 0. 019. 019. 018

Th e val ue 0 D is the corrected coe fficient of r esistance , but its accura cy is some what unc erta in , also the proportions o hull re sistanceapp ear high . The value o 0 D obtained from the win d t unnel testwa s o.027. Th e proportional va l ue of the appendages or para siwresi stance was computed fr om the wind t unnel data.

b. Th e follo wing data we re obtained from deceleration tests ofGerma n r igid airshi ps :

Num- M axi- Pr o-ber of mum por-Name Cu b ic feet D L B. H. P. tional C Dveloc-n- effi-gmes ity cten cy

FootFeet Feet seconds

J Z 10 706,000 45. 9 460 3 62. 4 450 67 0. 107L 33 2,1 40,00 0 78. 3 645 6 92. 5 1, 440 49 . 039L 36 2,140,000 78. 3 645 6 92. 5 1, 440 62 . 045L 43 2,140,000 78. 3 645 5 88. 9 1, 200 56 . 047L 44 2,140 , 000 78. 3 645 5 94. 0 1, 200 56 . 031L 46 2, 140,000 78. 3 645 5 95. 5 1, 200 58 . 031L 57 2, 640,000 78. 3 745 5 94. 8 1, 200 69 . 034L59 2, 640,000 78. 3 745 5 94. 6 1 200 66 . 038L 70 2 400 0 00 78. 3 694 7 113. 5 2,000 65 . 031

19. Burgess formula for horsepower. a . A very h and y formula for determining the horsepowe r r equi red to dri ve an ai rs hipof any given volume an d speed is furni shed by t he N atio na l Ad viso ryCommittee for Ae1onauti cs Report No . 194, as follows:

v3p_ vol )2 3H. P . = Op

~


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TM 1-32019 -20 AIR CORPS

whe re Op is a constant which can be take n from the compilationbelow:

N O nrigid a irs h ips .

50,000 to 200,000 cubic feet - - Op=20,000200,000 to 300, 000 cub ic feet_ ________ .. . -- - - - - - - - - - - - Op=21, 000300,000 to 400,0J :> cuui


36/68

..


c Problem UJrU solution

T M 1 320

2Q 21

1) Problem. An airship of 195,000 -cubic-foot capacity is to beequipped with two .engines developing a total of 300 horsepower.What speed can be expected using the following d t ~

a) Standard atmospheric density.b) Shape coefficient, 0 n is 0.0136.e) Propeller efficiency, E, is 60 pe rcent.d) Envelope resistance is 40 percent of total resistance of com

pletely rigged airship.2) Solution. Using Pr andtl coefficient.

300X550X0.60X0.40 ) 086V 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 asdetermined by the Burgess formula. .

21. S u m m a r y. - a. From study of the formulas i t appears tha tthe speed of an airship is proportional to the cube root of the horsepower, or vice versa the hor sepower varies directly as the cube ofthe speed. Since power plant weights vary directly as the horsepower, the weight of the power plant varies also as the cube of thespeed. A point is rea di ly reached therefore beyond which i t is noteconomical to increase the speed due to the excessive weight s involved.

b In still ai r the higher the speed the less economical the fuelconsumption and the shorte r the radius of action. Th is is not truewhen the airship is traveling against adverse winds. The study ofjust which ai r speed is the most economical will not be discussed inthis manual as it properly belongs to the subject of navigation.

8 E a r i O N IV

STABILITYParagraph

Variation of pressur e di stri buti on on airship bull __ _______________ __ _____ 22Specific stability and center of gravity of air shiP 23Center of bu oyanCY 24Descr iption of major a xis of airshiP 25Types of s t a b i l i t y 26Force s a nd mom ents acting on air sh i P 27Damping moment 28Longitudinal stabi ty - - - - - - - 29D ir ectional s t a b i l i t 30Lateral st a b i l i t y 3S 1 J m J u a r r . . -fl -----

35


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TM 1-32022

.

AIR ORPS

.

22 Variation of pressure distribution on airship hull.--a.In section resistance of an airship was shown to be parfly causedby increased n


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AffiSHIP AERODYNAMICS

T M 1 320

22-24

{3) Areas of redu ced press ur e are not symmetrical. Th eir maximum values occur beneath the ste rn an d abo ve the bow.

23. Specific stabi l i ty and center of grav i ty of ai rship . -a .By specific stability is meant the property of the airship itself tomaintain the relative positio n of it s various parts unaltered in anycontingency.

b Con diti ons necessa ry f or specific st ab i lity are the invariahilityo

(1) Shap e of env elope whethe r airs h ip is in motion or not .(2) R ela tive po sitions of envelope and cars and surfa ces .c Meth ods used to maint ain e nve lope shape are di scussed in sec

t ion I. In var iabili ty of sus pen sion of the ca r from the enve lop e is insured by a rectangular system of suspe nsi on s bra ced by diagonal cables

-

.

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

leng thw ise and cro sswi se. Th ese cab les pr event a ny very app reciablemotion of the car in regard to the envelope in case of oscill a ti ons ofthe airship in vertical longitudinal plane or in tran sve r se plane . As

. will be shown later speci fi c stability is a b so lu tely essen t ial to staticsta bil ity of airships .

d W hen invariability of sus p ensions has b een assured, the po sition of the cente r of gravity of the airsh ip may be determined. Th e ce nter

o gr avi ty is the point at which may be aE:3umed to b e applied th e totalresultant of the various weights which oppo se the lifting power ofthe gas. Th e position of th e center of grav ity is natura ll y not invariabl e since the li ve load of the air ship is varia bl e. U sua lly fo r non

rigid a ir ships the cente r of g rayity, M falls above the car and ei thersligh tly abov e or sligh tl y below th e bottom of t he e nvelop e (s eefig . 18).

24. Center of buoyancy. - The cen ter of gravity of th e as censional force of the ga s contained in the envelope is ca ll ed the centerof buoyancy. For an envelope which is not moving thi s point should


39/68

T M 1 3202 4 2 6 AIR CORPS

obviously be located on the vert ica l line passing through the centerof gravity, M and for an envelope whi ch has the form of a symmetrical solid of rotation and whi ch is full of gas, i t should be locatedon the axis of the envelope itself.

a However, when one or t he other of the conditions mentioned is notfulfilled, that is, when the envelope is not a solid of rotation as isthe case with the Italian semirigid) , or when it is not full .of gas, orwhen with the airship partially filled with gas the axis is deviated inthe vertical plane from the position of rest, the center of gravity, Gis not located on the axis in question, since this is supposed to be astraight line connecting the extreme end of the prow with the extremeend 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 enve lope is symmet ricalthe point G will be located above the axis. La stly, if in add ition t

not being full the envelope is incli ned longitudina ll y, movement of the gas toward thehigh end will cause the point G to move in thesame dir ection .

l c Without entering into a minute descrip-FiouRE 18. - Posltlons of h d b

cente rs of gravity andtlon 0 t e vanous arrangements resorte to ybuoyancy 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 w i t h -

1) Horiz ontal axis, the point G is on the axis when the envelope isfull, and move s along a line through M perpendicular to the axisas the amount of gas in the envelope decreases.

2) Oblique axis, the point G moves a moderate distance away fromthe above vertical, or at least i t moves in such a way that the distanceis a definite function of the angle of inclination of the envelope onthe horizon.

25. Description of major axis of ai rship . -a . The airship hull,as previously s tated is a solid of rotation and hence symmetrica l aboutthe axis of rota tion, X X in figure 19 Actually, due to the loadingof a nonrigid, the shape of a cross sectio n of the hull is more nearlyelliptical with the major axis of the ellipse vertical, but the distortionis slight enough to be disregarded.

b To conform to the system of nomenclature used by the NationalAdvi sory Committee for Aeronautics, the system of r:otation outlinedin figur e 19 will be unif orm througho ut this manual.

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

38


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T M 1-32 025-26

motions. With this fact in mind the types of stability now will beconsidered.

26. Types of s tab i l i ty. -a . Stability is defined as the tendencyto return to a position of equi l ibrium after a small deviation from thatposition.

b In airships stabi li ty is accomp lished by two means, static anddynamic.

(1) Strictl y speaking, the only real statical stability is that whichexists when the engines are stopped . Under this condition an air-

o r m t ~ lo r verlh;;a/ Axis

//

\\

o si f i v eO e cf itms o F 1 9 xe.s a n d l n f J (Fo r c es on d .moment 5 ~ w nhit drrow.s )

'

Axis 3 Moment about axis Angle.~

I0

I 0........... ......9l..8 Q-;s s l ~ t:lDesigna tion '" ' 0 0a UJ .... . ...- B ~ ..... Q)0 g 0 >a ~ .0 .... bOs ..... a .... ....... rJl ~ tl.l Q >. Q00 ~

LongitudinaL __ ___ X X Rolling _ __ L1 Y- z RolL __

LateraL __ _______ _ y y Pitching __ M z X Pitch __IormaL _________ z I zYawing __ N x Y Yaw ___

'

Velocities

I ,.-...

8 ~s ~O b i

~ ~....... 0

~.......a a l a~

Q ~Q .

bO. . . . . Q

0 H ~

> u pe v q1 w r

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

39-


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T M 1 320~ 7 AIR CORPS

ship is statically stable if i t tends to return toward initial conditionof steady motion wheneve r slightly disturbed from that motion. Thisrequir eme nt is not dependent upon the plane in which deviation fromsteady motion occurs, and, as will be shown later, an airship is

statically unstable in yaw.2) Dynamic sta bi lity is the stabil ity effected by action of the air~ t r e mupon controlled surfaces . W ere i t not for these surfaces airships would become unmanageable at very slow speeds .

c Stability may b e classified fur ther . An airship in steady flightha s three types of stability, pitch or longitudinal, yaw or directional,and roll about the longi tudina l axis. While these sta b ilities are allcorr 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 ' r t l l ' ~ h / 1 ~h D r i ' z o n l " t ~ l yin l t ~ f l c~ 9 u i l i i J r i 1 1 m .L o n ~ i f u d i n t Jt ~ x i scoinicidenrwith dire t ion o mot ion

FIGURE 20. - Forces on ai rship in hor izonta l flight .

d Th e followi ng discussion will be based upon the assumptionsfor each situation t h t

1) Ascensional force remains cons tant.2) Tota l weight remain s constant.3) Speed remain s the same.4) Form of airship remains unchanged.5) Center of gravity and center of bu oyancy remain fixed .6) Controls remain in neutral.

27 . Forces and moments act ing on a i r sh ip . - a. Suppose anairship flies along a horizontal right-line traje cto ry .while its longitudinal axis makes an angle of with th e flight path, then theair ship will be acted on by the following forces and moments seefig. 20).

1) Fo rces:a) L 0 =Lif t of inflating gas acting through center of buoyancy, G

40


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AIRSHIP AEROD YN AMICSI M 1 3 2 0

7

b) = Total weight of dead and live loading, acting throug hcenter of gravity, M.

c) R = R esistance of enve lop e and append ages, acting through center of pr essure, P.

d) T= P r opeller thrust, act ing parallel to axis of envelope atdi stan ce o below M.

2 ) Mo ments about M:a ) Mo ment L 0 = L 0 X0 =0 .b) Moment W = W X 0= 0.o) Mom ent thru st -r esis tan ce cou pl e = T o+d) .

Obviou sly, for stati c e quilibrium and const an t ve.loc i t y

L u= WR= THowever, if the airship is ridin g on an even keel, the m om ent ofthrust and re sista nce is un ba lanced and will tend to no se t h e s h ip up .F or thi s r eason airs hip s are customa rily trimmed a few degrees noseheavy when full of gas .

b Suppose that some force such as a gu st of air should give thelongitudinal axis a sl ight tilt to the horizontal. D epend ing on

s tatic condition of air sh ip and dire ct ion of inclinatio n , six cases whichar1se .are e - 1) Case N o. i A i r ship in static equili br iu m , no se t ilt ed up. I n

this case, if the angl e between the longit udin al axis and the direct ionof motion is denoted b y }and th e ang le between the direction of motionand the horizonta l by a, since the airship climbs at the angle of tilt ,}=0 and the air shi p will clim b a t the angle, a .

2) Case N o. ~ . s p in static equi l ibriu m, no se tilted down.A s before, = 0 and the ai r ship will descend a t the angle, a .

3) Cas e No. 3. A i r ship statically heavy, nose tilted up. In t hi seven t the ai r ship will climb a t a lesse r angle th an the amount of tilt,an d t he longitudinal axis will make the angle a+ } with th e horizontal.

4) Case No . 4.-Airsh ip statically heavy, nose tilted down. Beca use of the heavines s, the airship will descend a t a greater angle thanthe incl inatio n, the longitu din al axis ma king an a ngle of a - with thehorizontal.

5) Case No. 5 . - A i r ship statically light, nos e tilted up . Th is caseis s imilar to case No . 4. The longitudina l axi s makes the ang le a - 0with the h orizon t al.

6) Oase No. 6 Air shi p statica l l y ligh t, nose tilted down. H erethe airship will descend at a lesser a n gl e t han the in clin ation and theangle between the horizontal and the longitudinal axis will equa l a D

4


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T M 1 320

27 AIR CORPS

c. Figur e 21 shows case No. 3. Figures showing the other caseswould be quite similar. Re ferring to figur e 21, the following forces,lever arms, and moment s, all general to cases Nos. 1 to 6, inclusive, arenot ed:

1) For ces:a L 9 = 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 component of dynamic force on hull./ ) F a= Res ul tant force on tail sur f aces.g) L 8 = L it of tai l su rfaces.h.) R a= Dra g of tail surfaces.i) T = T hru st of propellers.j) t = Hori zontal componen t of propeller thrust .k) Lt=Vertical com ponent of propeller thrust.2) Lever mms about G.-Lever arm o fa) W = k sin a8 ) .b) L 9 = o.c ) T = c+h).

d) F 8 = a assuming F , perpendicular to the surfaces).e) L 8 = a cos a 8 ) .

{f) Rs = a sin a 8).g) F e va ries with the position of P, whic h in turn depends on

th e ang le 8.h) L e=b OS a8).3) Moments about G Moment o a) W eight. D efined as static righting moment. I t is prese nt

irr espective of speed and a t all times equal s W h sin a 8).b) P ropeller thrust, T c + h ).c F 6 D ue t o increased pre ssu re below the hull, F e tends to rotate

en tire airship in a po sit ive direction about M. This is ass iste d byreduced pressure beneath the tail see fig . 17 ). T he force belo w noseand tai l are opp osite in direction . T hei r differ ence , since the no seforc e is slight ly t h e greater , is calle d dynamic lift of hull. How ever ,both forces cause rotation in the same dire ct ion , and their moment

is refer r

edto

as dynamic upsetting moment , Me.

I twill be

evalu

atedlate r .NOTE.-Tbe force beneath the tail has been o m itted from the figure in ord er

to avoid con fu sion in the dra wing, the entire upsetting moment being treateda s though i t were ca used by the increased pressure under the nose.

42


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T l t l 1-32027-29

d) Tail surfaces, Ms Thi s opposes the dynamic u t t i n gmoment. Ms = Ls a cos aO+ R s a sin aO).

28. Damping moment . -a . There is one moment which has not

been discussed.f

he airship, oscillating as i t travels along its path,is considered as having two motions, one of translation as a wholeand one of rotation about the center of gravity, supe rposed on eachother, i t is clear that during that portion of the angular oscillationn which the nose is rising, every part of the airship forward of the

center of gravity is ~ : > V i n gupward, whi le all parts to the rear of thatpoint, including the tail surfaces, are moving downward.

b Ther e will then be an upward pressure o the air again st therear 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 e l e v t ~ t w / L; F e Le

FlGUU 21. - Forces on airsb1p in inclined fligbt case No. 3) .

so far as translational motion is conce rned , but they act together togive a moment tending to depr ess the nose and so to resist the motionexisting. f the rotation were such that the nose was descend ing, amoment tending to raise the nose would appear. This s called thedamping mom ent as i t is entirely independent o position and attitude, but act s always in such a manner as to oppose existing motio nand bring the airshi p to steady f l i ~ h t Oscillations of the airshipare damped exactly as oscillations of a pendulum are damped i thebob is light and has a large vane attached to it . Damping momentsmay be determined experimentally in a wind tunne l, but the mathematical theory when these moments are quantitatively taken into

account is extremely complex and will not be discussed here.29. Longitudinal stability. - a For l ongitudinal stability, the

sum of the restoring moments must exceed the upsetting mom ents.n the case illustrated-

M. + Wh s n a+O) >Me+ T c + h ).

43


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l M 1-3209 AIR CORPS

However, thi s r ela t ion does not hold in each case . For instance, thestatic couple, W h si n ex 0), works against the thrust couple when _the airship is in a climbing attitude and with i t when the airship is ina de scending one . The dynamic moment of he hull on the otherhand , assists the righ ting momen t in case No s. 4 and 5, bu t oppo ses itin case Nos. 3 a nd 6 Ca se Nos. 1 and 2 ar e unimportant as will beshown later. Ob viously case Nos . 3 and 6 are the ones which mu s t becon sidered wh en designing for sta b ili ty .

b. Th e static righting mom en t is nearly a right-line function ofthe angle, 0. So for pra ct ica l purposes is the upsetting moment.But wherea s the righting moment is ind epen dent of the ve locity, the .up setting moment varies as the square of the speed. Obv iously as

th e speed inc reases a velocity will be reached where the upsettingmomen t ju st equal s the r ight ing moment. Thi s is ca lled the critica l .speed.

c. For an airship without cont rol su r fa ces, neg lecting for the momentpropeller thrust and resistance, t he critical speed would e reachedw h e n -

M e= Wh sin a B .

By the formul a of Doctor M:unk:

M .= V o l ~v k 2 - k tsin 28

where k2 and k1 are constants to correct for t he fact that ma sses ofair are carried along with the hull in both transverse and longitudinalmotion. Tabl es of values of k2 and k1 are given in National Advi sor yCommitte e for Aeronauti cs Report No. 184 From the M:unk equa-tion it appears that c varie s directly as si n 20 and as the square of thespeed. Combining the constant factors in the formula into oneco nstan t , M e :

M t= Me sin 28v2.

H ence the relation for critica l speed without fin s becomes

Me sin 28Ve Wh sin a8)Wh sin a 8

Vc= = M e sin 28where Vc=c ritic al speed.

This would give a very low .critica l spe ed. For an Italian militaryairship of the M type the critical speed without fins is 29 milesper hou r.

d. I ntroducing the tail surfa ces gives a much higher valu e of thecri tical speed. From the relations given in a above for case No.3 the

44


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T M 1 3 2 0

29

equation o stability at the criti cal speed omitting the thrust-resistancecouple iss--

F a+ Wh sin a 8) = M e.

S ince th e force on an inclined plate is approxim ately a right-linefunction of the ang le of inclination

F s= 0 J vc2

wher e 01 is a con stant com b ining the surf ace coefficient and the ina rea. As before-e -

H enceM e sin '28v/ = 0 18ve2 a + W h sin a+ B

v _ / W h sin (a + O .e - y M e sin 8 18a

e. For a condition of static equi librium as sta t ed in paragraph 27bthe fl ig ht path theore tica lly coincides with the lo ngit udinal axis.H ence 8 becom es zero and Vo becomes infinite . T hi s agrees with theth eore tic al fa cts s ince with no angle o attack to the air st r eam t het r ansve rse dynami c for ces become zero for all speeds and th e sta ticrighting moment would re sto re qu ickly the airship to the h or izontalposition . A ctua lly ho weve r this can never be pr act ica ll y true s in ceinertia of the air shi p ret ar ds chang e in dir ectio n o m otion from thehor izontal pa th and pr events t he airship immediately adopting a lineo fligh t coincident with its lon gitud inal axis.

f In the preceding dis cussion the cont rol s h ave bee n considered tobe held in neutral. Actua ll y by varying his elevator ang le the pilotmay in cr ease materiall y the effect o the control surfaces. Thi s fu r-th er in creases the speed which th e airs hip m ay t r ave l without lo ss ofcontrol. f the air ship is not longitudinally stab le o r if in ot herword s i t is be ing op erated above its critica l speed the pilot mu st correct devia tions fr om the cho sen path as soon as th ey appear whileon a sta ble airshi p these deviatio ns wou ld be capable of self-correctioni f left manually uncorrec ted .

g: The statical righting moment varies as the fourth powe r of alinear dime nsio n of the air sh ip th e ascensional forc e F being proportion al to th e vo lume and so to the cube of a l inear dim ension. A l l

aerodynami c m oments on the other hand bo th on the hull proper andon the tail surfaces vary as the cube of a linear dimen sion. The crit ical speed is therefore prop ortional for geometrically sim ilar airships to

~ f or to the square root o a linear dimen sion. A lar ge airship can

therefore be stabilized with tail surfaces propor t ionally smaller than

o


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TM 1 : :3202 9 S l AIR CORPS

those necessary on a small one traveling at the same speed. An unstable airship requires closer attention from the pilot than does onewhich is stable but it is not necessarily either difficult or dangerous

to operate and has the advantage of being more easily maneuverablethan the more stable types.

30. Directional s tabi l i ty. a . Directional stability is maintainedin part by use of vertical fixed fins and rudder. When the rudderis set in neutral i t acts as additional in surface but the total in surface is never large . enough to provide complete directional stabilitySince there is no statical restoring moment to overcome a horizontaldeviation from the flight path maintenance of directional stabilitydevolves upon the pilot who must correct any deviations as soon as

they appear. Otherwise a deviation once started will t end t in.crease until the airship is traveling in a circle of so small a radiusthat the ~ m p i n gmoment balances the turning moment due to pressure on the nose. This is quite different from the cond ition of longitudinal stability where the elevator can e left locked in any particularposition and the airship will return to its original attitude if atmospheric 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 tending to turn the airship farth er from its original course. This momentcorresponds exactly to the upsetting moment M e which opposes longitudinal stability. There is then an unbalanced moment which tendsto give the airship an angular acceleration and so to turn her moreand more rapidly. At the same time the lateral force on the envelopewhich corresponds to the dynamic lift is increasing and .furnishes thenecessary centripetal force to keep the airship traveling in a circular

path.t

is quite true that a force resisting this circling is exerted bythe vertical surfaces but as mentione.d above the vertical fin surfacesare never large enough to pro vide full stability and the rudder mustbe used to assist them. Use of the rudder will be more fully discussedin sec6on V.

31. Lateral s tabi l i ty. a . Stability in roll which is a very i i-cult problem in airplanes is taken care o almost automatically in airships; since the same statical restoring moment acts with regard to rollas with regard to pitch and there is no dynamic upsetting moment tooppose it. The only rolling motions are those due to side gusts againstthe car and bag and those due to centrifugal force when turning. The moments of these forces are overcome immediately by the large restoring moment due to the low position of the center of gravity. Roll-

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AffiSHlP AERQ.DYN AM I CST M 1 320

3 1 3 3

ing may be very uncomf ortabl e because of the short and sna pp y period,but there is never any dang er of its r eachin g an excessive value .

b The static stability o f an airshi p w t ~r egard to both roll and

pitch may be increased by loweringthe

car,but thi

s gives equilibriumonly at the sacrifice of ease of contro l and efficiency, since lowering thethru st line increases the thrus t momen t and lowering the ca r incr easeslength of suspens ions and hence parasite resistance.

32. S u m m a r y. a . Air ship stabil ity may be summarized asfollows :

(1) Airship s are very stable about their lateral axis. In this n rgard the designer has no trouble whatsoever .

(2) Air ships mu st be designed carefully to give longitu di nal stability. T his problem i s however of more intere st to the design er tha nto the pilot.

(3) Airships are statically unstable in yaw, nece ssita ting the closestattention on the part of th e direction pilot to counteract circling bymean s of the rudder.

b No con crete problem s have been given in thi s sect ion as the application of fundam en tal s covered therein will be shown in section V.

SECTION vCON T ROL

Paragraph

General types- - - -- - - - - - - - - - - - D ir ectional ... 34AJtitude 35Reverse -- -- - - - - - - - - - - - - 36Ap p li c ation of dynamic cont r ol t o o peration of air shiPS- - - - - - 7

33. General types. a . Control of airship s may be sub dividedinto two classes, directional an d altitude. On nearly all airplanasthese two types of control are so inter r elated as to necessitate t heirboth being performed by one pilot . In airships this is not t he case,and on a ll bu t the smallest air ships tw o pilot s are utilized, one fordir ection , one for altitude. .

b For efficient performance the two pil ots sho uld be familiar wit heach other s style of flying and constant ly alert to render each other

ass ista nce. For instance, to obtain the proper additional supe rheatto effect a landing (see TM 1- 325), the altitude pilot may desire alon ger approach than usual. Th e direction pilot shou ld so arrangethe course as to meet needs of the situatio n. In st an ces of the value ofcoordination are too num ero us to ment ion, but fortunately capablepilo ts have little difficulty in achi evi ng desired r esults.

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T M 1 3 2 03 4 AIR COR P S

34 . Dire ct i onal. a . As st ated in paragraph 33 the dir ec tion pilotis charged with control of the course of the air ship in a horizontalplane. On cross-coun t ry .flights his prob lem resolves itself into t hatof holding the course required by the mis sion of the air ship. Onceth e course is set th e airship will hold its own co ur se unless acted onby some exterior force s such as gusts. These must be overco me bypr ompt applica ti on of the rudder in the oppo sing directio n. Whenfl ying in very gu sty air i t is impossible t prevent yawing but a goodpil ot can keep the m agnitude of t he oscillations from exceeding a f ewdegrees. Th en since the g usts strik e about equall y from both sidesth e mean cour se of the air ship will be the one desired .

b t is essential that the pil ot have a clear conce ption of the react i on to rudd er control of the airship in a turn . W hen it is desired totur n to the r ight for example the rudd er is put ove r to the right .T he instantaneous effec t of t h is rotation is to produce a force to theleft act in g on the right side of the rudd er . Thi s force to the left hasa du al effe ct. I n the fi rst place i t gi ves the moment about the ce nterof gravity tending to turn the nose to the right. I n the sec ond placeit mo ves t he entire airship to the left . As the airship moves to theleft and as its nose t urn s to the right both motions co mbine to cause

the air to strike on the lef t of t he envelope and so to t urn the nosestill farthe r to the ri ght . After this ha s pr oceeded for an in terval th e pr ess ure on the left-hand side of the no s? bec omes equal to that onthe right -hand side of th e rudder and the total re sultan t pressure isth erefore zero but since one force is applied to the fron t and the otherto t he r ear ther e is a r esultant tu r ning mom ent te nding to continu ethe twistin g to the right . As t he mo t ion proceeds still farther theforce o n the left-hand side of the enve lope become s greate r than the

force on the righ t-h and side of the rudder and there is a cent rip etalforce to t he right so th at the ai rshi p starts to move to the r ig ht. fth e rudder is left n hard or even i f i t is turned to neutra l this t urnin g to the right will cont inue and in order to check the circl ing it isnecessa ry t o put the rudd er over to the left of t he envelope .

o The t ur ning radi us is governed by the d ampin g moment on theen velope and is greater for an ai rship of lar ge fi neness ratio th an forone where this ratio is small. t shoul d be one of the fi rst concerns of

the pil ot whene ver he assumes co

ntro l of a new type of air ship tofamiliarize him se lf with its tu rning rad ius. Othe rwi se he m ig htvery conceivably endea vor to execute a turning maneu ver where thespa ce l i m i t t i o ~was insu ffi cien t.

d Refer

airship aerodynamics

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