Some factors affecting the static longitudinal and directional stability characteristics of supersonic aircraft configurations

I RESEARCH MEMORANDUM

SOME FACTORS AFFECTING THE STATIC LONGITUDINAL AND

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DIRECTIONAL STABILITY CHARACTERETICS O F

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SUPERSONIC AIRCRAFT CONFIGURATIONS

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By M. Leroy Spearman

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Langley Aeronautical Lab oratory Langley Field, Va.

CLASSIFIED DOCUMENT This material contains information affecting the National Defense of the United States within the meaning of the espionage laws, Title 18, U.S.C., Secs. 793 and 794, the transmission or revelatioo of which Fo any manner to an unauthorhed person is prohibited by law.

NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

WASHINGTON July 12, 1957

&)NCl,tASSIFIE13

NACA RM L37E24a II

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESEARCH MEMORANDUM SOME FACTORS AFFECTING THE STATIC LONGITUDINAL AND DIRECTIONAL STABILITY CHARACTERISTICS OF SUPERSONIC AIRCRAFT CONFIGURATIONS By M . Leroy Spearman S U M M A R Y A survey is made of the problems introduced by the increased longi- tudinal stability and the reduced directional stability of aircraft operating in the low supersonic speed range. The longitudinal stability increases markedly at supersonic speeds and results in high drags due t trimming and in limited control for maneuvering. The large untrimmed pitching moments can be reduced and the control requirements alleviated to some extent through the use of fuselage camber. The use of canard configurations offers some promise of reducing the drag due to trimming and increasing the controllability.

The directional stability generally deteriorates rapidly at super- sonic speeds because of the reduction in vertical-tail lift-curve slope coupled with the large unstable yawing moment of the fuselage. The vertical-tail contribution is shown to be affected by many factors including the wing position, the fuselage shape, and the horizontal-tail position. The directional stability can be increased, particularly at high angles of attack, by such devices as ventral fins and forebody strakes. In addition, indications are that the directional stability might be improved through modifications to the fuselage afterbody.

INTRODUCTION Aircraft advancing from subsonic to low supersonic speeds frequently encounter performance and control problems as a result of significant changes in static stability characteristics. These changes, which are usually evident as increased longitudinal stability and reduced direc- tional stability, are a result of various changesin the aerodynamic characteristics of the lifting surfaces and of changes in the aerodynamic interference effects between various components that occur with increasing Mach number. Changes in the aerodynamic characteristics of lifting NACA. RM L57E24a

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surfaces with Mach number might be reduced through the - use of thin sec- tions and low-aspect-ratio plan forms. "he chiages in interference effects, and to some extent the effects of the lifting-surface aerody changes, might be offset through changes in the aircraft design.

Some effects of aircraft configuration on the stability character- 1 . This istics at supersonic speeds have been presented in reference paper provides a summary of some current thoughts and studies on the causes of, and possible corrections for, the static longitudinal and directional stability and control problems of supersonic aircraft conf urations. The discussion is based primarily on results obtained in the Langley 4- by 4-foot supersonic pressure tunnel for Mach numbers from 1.41 to 2.01, although some limited results are given for high subsonic spe and the supersonic Mach number range for one configuration extends from 1.41 to 4.65.

The longitudinal stability characteristics are referred to the win axis system whereas the lateral stability characteristics are referred to the body-axis system. The symbols are defined as follows: vertical-tail span bV CD drag coefficient CL lift coefficient Cm pitching-moment coefficient yawing-moment coefficient Cn P - P , pressure coefficient, cP s, C vertical-tail chord at any station V mean vertical-tail chord EV C section lateral-force coefficient Y pitching-moment coefficient at zero lift Cm, 0 lift-curve slope

cLa

. . . 3 effective dihedral parameter d i r e c t i o n a l s t a b i l i t y parameter lateral-forceparameter increment of provided by v e r t i c a l t a i l cyP fuselagediameter l i f t - d r a g r a t i o Machnumber l o c a l s t a t i c p r e s s u r e free-stream static pressure free-stream dynamic pressure longitudinal distance along vertical t a i l v e r t i c a l d i s t a n c e a l o n g v e r t i c a l t a i l wing height angle of attack angle of s i d e s l i p h o r i z o n t a l - t a i l d e f l e c t i o n , p o s i t i v e w i t h t r a i l i n g edge down canard deflection, positive with trailing edge down elevon deflection, positive with trailing edge down fuselage-forebody deflection (cyP)wBv - ( " ' P ) . .

v e r t i c a l - t a i l f a c t o r ,

(CYp)BV - ("P)B

l o n g i t u d i n a l s t a b i l i t y parameter 4 NACA RM L57E24a Components and Subscripts B fuselage (body) H horizontal t a i l W wing

v v e r t i c a l t a i l

mBx m a x i m u m min minimum DISCUSSION Longitudinal Stability The primaryproblemof l o n g i t u d i n a l s t a b i l i t y f o r s u p e r s o n i c a i r c r a f t configurations i s the increased stability which occwsthroughthetran- sonicrange and t h e r e s u l t a n t l a r g e s t a t i c margins at lower supersonic speeds. This increasedstability,aspointedoutinreference 1, usually r e s u l t s from the combined e f f e c t s of a rearward shift i n t h e c e n t e r of pressure of the wing, the loss of wing downwash a t t h e tail, and the stabilizing influence of the wing l i f t carried over to the fuselage after- body. Although this i n c r e a s e ds t a b i l i t y i s not a dangerouscondition, it can r e s u l t i n s e r i o u s l i m i t a t i o n s t o t h e a i r c r a f t performance. These l i m i t a t i o n s a r i s e from t h e f a c t t h a t t h e e x c e s s i v e s t a t i c margins occurring a t low supersonic speeds result in large pitching moments that must be trimmed throughlargedeflections of the pitch control and t h i s e f f e c t , of course,resultsinincreased t r i m drag. Moreover, fortail-rearwarddesigns (designs with controls behind the center of gravity), the control deflec- tions required for trimmingproduce substantial negative increments of l i f t . Thus, i n orderto t r i m a t a given l i f t , a higherangle of a t t a c k w i t h an attendant drag increase i s required and t h e r e s u l t i s generally a marked r e d u c t i o ni n L/D due t o trimming. Inaddition, i f largedeflec- t i o n s of the control are required for trimming, the amount of control deflection available for maneuvering w i l l be small.

The primary f a c t o r s t h a t govern the magnitude of the pitching moment t o be trimmed a t a given l i f t arethe pitching-moment c o e f f i c i e n t a t z e r o

l i f t cm, and the slope of the pitching-moment curve aC&lC,. Desirable

d e s i g n c h a r a c t e r i s t i c s a t low supersonicspeeds would be those that increase thepositivevalue of C,,o or decreasethenegativeslope of a&/aCL, inasmuch as these characteristics would tend t o reduce the control deflec- tionsrequiredfor trimming. Some of thefactors that a f f e c t Cm,, and aCm/aC, arediscussedinthesubsequent'sections.

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NACA RM L57E2b.a - 5

Effects of fuselage camber.- One means of varying Cm,o f o r a basic configuration i s throughtheuse of fuselage camber. Such a planhasbeen discussed i n reference 1, and t h e e f f e c t s of fuselage camber f o r a 6 0 ’ delta-wing-fuselage Combination a t M = 1.61 arepresentedinreference 2.

These r e s u l t s , which a r e reproduced i n f i g u r e 1, i n d i c a t e t h a t t h e cambered fuselageproduces a constant pitching-momentincrementthroughout t h e l i f t rangewith no significant increase in drag and henceshouldbeuseful i n alleviating the pitch-control requirements and the attendant drag due t o trimming.Resultsobtained i n t h e Langley8-foottransonictunnel a t high subsonic and transonicspeedsfortheconfigurations shown i n f i g u r e 1 i n d i c a t ee s s e n t i a l l yt h e same increment of Cm,o as thatobtained at M = 1.61 althoughthestatic margin i s lower. This factshouldbe con- sidered in assessing the merits of fixed fuselage camber.

Anotherform of t h e cambered fuselage effect canbe realized through the use of a deflected forebody which hastheadvantage of being adjustable i n f l i g h t . The e f f e c t s of deflectingtheforebody of a 4 5 O swept-wing- fuselage Combination at M = 2.01 a r e shown i nf i g u r e 2. Deflections of t h e forebodyprovideprogressiveshifts i n Cm similar t o t h a t provided by conventionalpitchcontrolsbutwithout any increaseindrag. Although the deflections shown a r e o p p o s i t e t o t h o s e r e q u i r e d f o r trimming at positive l i f t s , upward deflections of the nose would beexpected t o pro- vide positive increments of C,,,.

Effect of v e r t i c a l l o c a t i o n of horizontal t a i l . - The v e r t i c a l l o c a t i o n of the horizontal t a i l has a s i g n i f i c a n t e f f e c t on the longitudinal sta- b i l i t y and c o n t r o lc h a r a c t e r i s t i c s . A primaryconsideration a t subsonic speeds i s the location of t h e t a i l with respect to the wing downwash f i e l d .

Generally it i s advantageous,particularlyfor swept-wing configurations, t o place the t a i l on or below t h e extendedchordplane of t h e wing i n order t o avoid the regions of high downwash variation with angle of attack thatleadtopitch-up.Unfortunately,theselow-tailpositionsusually aggravatethe problemof excessive longitudinal stability at supersonic speeds, inasmuch as t h e t a i l may encounter a f i e l d of upwash from t h e fuselage.(Seerefs. 3 t o 5 , f o r example. ) High horizontal tails, on theother hand, have some b e n e f i c i a l e f f e c t s at supersonicspeeds. A s shown inreference 3, f o r example, s u b s t a n t i a l i n c r e a s e s i n trim l i f t were obtainedthroughthepositiveshiftsin Cm,o provided by a relativelyhigh-tailconfiguration at M = 2.01. However, such t a i l positions would probably cause undesirable pitch-up tendencies a t subsonic and law supersonicspeeds.

Some e f f e c t s of Mach number on Cm,o and hC,/aCL for a 45’ sweptback-wing and t a i l configurationare shown i n f i g u r e 3. These r e s u l t s i n d i c a t e r a t h e r l a r g e changes for the high horizontal t a i l s and r e l a t i v e l y ”.

small changes f o r t h e low h o r i z o n t a l t a i l s . With t h e h i g h e s t t a i l , f o r Cm,o and aCm/aC, decrease with increasing example, values of both Mach number ( a s i m i l a r e f f e c t was noted i n r e f . 6 for a high-tail config- uration). For t h e second highest tail, however, Cm,o increases and &&/aCL decreaseswith Mach number ( f i g . 3). Similarresults were obtainedwith a high wing and with the wing removed. Although c e r t a i n combinations of C and aCm/aC, may r e s u l t i n improved performance m, 0 a t a given Mach number, the large variation in these quantities with Mach number may l e a d t o some undesirablecharacteristics.Inparticular,the variation of control deflection for t r i m with Mach number may be undesir- ably nonlinear.

The v a r i a t i o ni n Cm withhorizontal-tailpositionatsupersonic speedsappears t o b e r e l a t e d t o t h e v e r t i c a l - t a i l induced flow-field e f f e c t s on t h eh o r i z o n t a lt a i l . Notice, f o r example, thedifferencein theincrement of Cm,o providedbythe t a i l s j u s t above and j u s t below the body even though these tails are located symmetrically with respect t o t h e body ( f i g . 3). The f l o w - f i e l de f f e c t sa r es e n s i t i v et ot h el o c a - t i o n of t h e h o r i z o n t a l t a i l w i t h r e s p e c t t o t h e v e r t i c a l t a i l and would beexpected t o change w i t h Mach number as well as with vertical-tail plan form and section.

Some e f f e c t s of the modifications of t h e v e r t i c a l - t a i l p l a n form on the pitching-moment characteristics for the high-tail configuration ( f i g . 3 ) are shown i n f i g u r e 4 w i t h the wing removed. These modifications, whichwere designed to relocate the leading edge of t h e v e r t i c a l t a i l , had a pronounced e f f e c t on Cm and on thevariation of Cm,o with p.

Effects of auxiliary canard surfaces.- Perhaps the most frequently suggested means for reducing the stability level at supersonicspeeds i s the use of auxiliary canard surfaces in conjunction with a conventional horizontal-tailpitchcontrol. Such surfaces,ofcourse,provide a destabilizing moment which reducesthepitch-controlrequirements.In addition, the canard surface may be deflected to provide additional pitch control.Resultsfor a 4 0 ’ sweptback-wing a i r p l a n ea t M = 1.89 w i t h an auxiliary canard surface are reported in reference 7 and some r e s u l t s a r e shown i n f i g u r e 5. The addition of thecanard at zerodeflectionprovides a s u b s t a n t i a lr e d u c t i o ni ns t a b i l i t y and a ni n c r e a s ei n t r i m CL. With thecanarddeflected loo, an additionalincreasein t r i m CL was obtained.

The use of auxiliary canard surfaces would a l s o reduce the stability a t subsonicspeeds so t h a t a t t h e s e speeds it may benecessary t o r e t r a c t thecanardsurface,allow it t o f l o a t f r e e l y , o r becontrolled by a servo- control systemsuch t h a t it acts as a free-floating surface.

NACA RM L57E24a Characteristics of basiccanard-typeconfiguration.- Anotherapproach t o t h e l o n g i t u d i n a l s t a b i l i t y problem i s throughtheuse of a basic canard- type configuration rather than auxiliary canard surfaces added t o a con- ventionalconfiguration. The s t a b i l i t y and controlcharacteristics of two suchbasiccanardconfigurations a t M = 1.41 and 2.01 arepresentedin reference 8. The purpose of thebasiccanardconfiguration would benot only t o r e d u c e t h e s t a b i l i t y l e v e l a t supersonicspeedsbutalso t o reduce the longitudinal stability increase that occurs in going fromsubsonic speeds t o supersonicspeeds.Thisreduction i n s t a b i l i t y throughthe transonic range i s p a r t i a l l y accomplishedthroughtheelimination of t h e afterbody and the conventional rearward horizontal t a i l s o t h a t t h e lift carry-overeffects of t h e wing on theafterbody and the do-mwash changes a t t h e t a i l areavoided. Thus, inasmuch as t h e s t a t i c margin may bekept small because it i s essentially invariant with Mach number, t h e c o n t r o l deflectionsrequiredfor trimming may bekept small. The controleffec- tiveness of canard surfaces may benefit through the use of a long moment arm with only small deflections and Lifts required s o t h a t t h e wake e f f e c t s and dragfromthecanardsurfaces would beminimized. The use of a long moment a r m i s compatiblewiththecurrenttrendtowardlargebodies of highfinenessratio.Inaddition,other problems thatareassociatedwith the wing downwash effects or jet-exhaust effects on rearward t a i l s might beavoidedthroughtheuse of canardconfigurations.

A comparisonof the variation of t h e s t a t i c l o n g i t u d i n a l s t a b i l i t y parameter aCm/aCL with Mach number f o r a sweptback-wing tail-rearward configuration and a 60° delta-wingcanardconfiguration (ref. 8) i s shown i n f i g u r e 6. Because of theelimination of theconventionalafterbody and t a i l , t h e change i n t h e l e v e l of s t a b i l i t y from subsonic t o supersonic speeds i s considerablylessforthedelta-wingcanardconfigurationthan f o rt h e sweptback-wing tail-rearwardconfiguration. Thus, t h es t a b i l i t y parameter for the canard eonfiguration could be safely reduced t o a low level in order to reduce the pitch-control requirements, whereas the s t a b i l i t y parameter for the tail-rearward arrangementcouldonlybe reducedabout 0.05 b e f o r e n e u t r a l s t a b i l i t y would beencountered a t sub- sonicspeeds.

The use of canardconfigurations a t low speeds may provide some problemssuch as t h a t oftrimming t o maximum l i f t . However, t h e r e s u l t s oflow-speed studies(such as thosereported i n r e f s . 9 and 10) indicate t h a t t h e s e problems arenotinsurmountable.

Comparison ofcanard and tailless configurations.- The s t a b i l i t y change with Mach number can a l s o b e minimized through the use of delta- wing tailless configurations. However, taillessconfigurations may s t i l l experience t r i m and control deficiencies because of the inherently short moment a r m for the control surfaces.

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A comparisonof thelongitudinal t r i m c h a r a c t e r i s t i c s f o r a tailless ' configuration and a canarddelta-wingConfiguration (ref. 8) at a Mach number of 2.01 i s shown i n f i g u r e 7. The value of aCm/&L f o rb o t h configurations w a s -0.15. The resulrtsindicate a considerablyhigher maximum t r i m l i f t f o r t h e canard configuration that could be reflected i n s i g n i f i c a n t performancegains. For example, with an assumed wing loading of 100 pounds per square foot, the maximum t r i m l i f t s obtained would p e r m i t l e v e l f l i g h t at 70,000 feet for the canard configuration, as compared w i t h l e v e l f l i g h t a t 48,000 f e e t f o r t h e t a i l l e s s a i r c r a f t .

I n ad.dition, the higher maximum t r i m l i f t available would r e s u l t i n greater maneuverability for the canard configuration than for t h e t a i l l e s s configuration.

The canardconfigurationindicateshigher trimmed values of L/D than those obtained for the tailless configuration although the compar- ison of L/D f o r t h e two configurations i s affected by thedifference i n minimum drag. However, w i t h t h e d r a g f o r t h e t a i l l e s s a i r c r a f t a d j u s t e d t o t h e same minimum value as for the canard aircraft, the m a x i - mum trimmed value of L/D f o r t h e t a i l l e s s a i r c r a f t wouldbeabout 4.3 compared t o 5.6 f o r t h e canardconfiguration.

A comparison of the trimmed and untrimmed (Sc or 8, = 0) r e s u l t s f o r t h e t a i l l e s s and canardconfigurations i s shown i n f i g u r e 8. The primary e f f e c t of trimming i s apparent i nt h el i f t - c u r v es l o p e s . The canard control has essentially no e f f e c t on t h e l i f t curve inasmuch as the positive l i f t incrementsfromthecanardareoffset by slight losses i n wing lift. O n theother hand, deflection of thetrailing-edgeflap control for the tailless configuration causes a r e d u c t i o n i n l i f t - c u r v e slope. Thus, inordertomaintain a constant l i f t i n t r i m , t h e t a i l l e s s configuration must o p e r a t e a t a higherangle of a t t a c k and,hence, a t a higherdrag.

Longitudinal-stability characteristics of canardconfigurationover wide Mach number range.- The longitudinal-stability characteristics throughout a large Mach number range f o r a canard airplane with an unswept-tapered wing a r e shown i n f i g u r e 9. These r e s u l t s were obtained from t e s t s ofone model i n t h e Langley high-speed 7- by10-foottunnel, the Langley 4- by4-footsupersonicpressuretunnel(ref. 8), and the Langley UnitaryPlan wind tunnel. The r e s u l t s i n d i c a t e amoderate i n c r e a s e i n l o n g i t u d i n a l s t a b i l i t y from subsonic t o supersonicspeeds t h a t i s somewhat greater than that indicated by thedelta-wingcanard airplane(fig. 6) but is s t i l l lessthantheincreasegenerallyexperi- enced by tail-rearward aircraft.

A transonic drag-rise factor of approximately 2 i s indicated and r e l a t i v e l y low minimum drag values were obtained in the supersonic range.

The naximwn trimmed values of L/D varyfromabout .4.5 a t M = 1 . 4 1 t o 5.8 a t M = 4.65. R e l a t i v e l yl i t t l e loss i n L/D due t o trimming i s NACA RM L57E24a indicated, particularly a t thehigher Mach numbers where t h e s t a b i l i t y l e v e l i s lowest. The s t a b i l i t y parameter aCm/aCL f o rt h i sc o n f i g u r a - t i o n couldbesafelyreduced by a t l e a s t 0.10 s o t h a t t h e trimmed values of L/D would approach the untrimmed values.

Directional' Stability The d i r e c t i o n a l s t a b i l i t y parameter Cnp, as pointedout i n r e f e r - ence 1, i s characterizedby a rapiddecreasewithincreasingsupersonic speed. The primary a e r o d y n d ce f f e c ti n v o l v e d i s thelift-curveslope of t h e v e r t i c a l t a i l which begins t o decrease with increasing supersonic Mach number, whereas the forces and moments on thefuselageremainessen- t i a l l y c o n s t a n t . The fundamentalproblem i n maintainingadequate s t a t i c d i r e c t i o n a l s t a b i l i t y f o r many currentdesigns i s i n t h e l a r g e u n s t a b l e yawing moment of thefuselagethat must be overcome by t h e t a i l . These large unstable moments generally result from theuse of large fuselages

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with high-fineness ratio and far rearward center-of-gravity positions.

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Such fuselageshapes are usually required to provide the volume necessary

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t o s t o r e t h e equipment and f u e l and s t i l l provide a low-drag p r o f i l e .

The far rearwardcenter-of-gravitypositionsoccurbecause it i s neces- sarytolocatelargejetengines i n t h e r e a r of thefuselage. The trend in fuselage design i s i l l u s t r a t e d i n f i g u r e 10 wherein three single- place, single-engine fighter airplanes ranging from the World War I1 I period t o t h e time of thepublication of t h i sr e p o r t are compared. These \ designsare drawn t o t h e same scale and are alined with their centers of g r a v i t yi nt h e same plane. The largeincreaseinfuselagelengthforward of thecenter of gravity i s apparent. The t a i l lengthhasnot changed greatly although the size of t h e v e r t i c a l t a i l has increased considerably.

Becauseof these changes i n fuselageshape, a considerableportion of t h e v e r t i c a l - t a i l c o n t r i b u t i o n t o d i r e c t i o n a l s t a b i l i t y i s required t o overcome the fuselage instability, while a proportionatelysmaller amountof the t a i l contribution i s available to provide a positive margin of s t a b i l i t y . Hence, any l o s s i n t a i l contributionarising fromsuch f a c t o r s as decreasing t a i l lift-curveslope,aeroelasticity,wing-fuselage wake, interference flow fields, or forebody vorticity would subtract d i r e c t l y from t h e s t a b i l i t y margin.

Thus, w i t h a n i n i t i a l l y low l e v e l of d i r e c t i o n a l s t a b i l i t y a t low angles of attack, many currentsupersonicdesigns become p a r t i c u l a r l y sensitive to angle-of-attack changes sincewithincreasingangleof attack the induced wake and v o r t i c i t y e f f e c t s appear i n t h e wingand fuselageflowfields. (See, f o r example, refs. 1 1 t o 13.)

Estimated vertical-tail contribution at CL = 0'. - The accurate pre-

diction of t h e v e r t i c a l - t a i l c o n t r i b u t i o n t o d i r e c t i o n a l s t a b i l i t y i s

10 c NACA R M L5p24a

t difficult because of the many f a c t o r s that a f f e c t the flow at the tail.

A c o r r e l a t i o n of estimated and experimental values of the v e r t i c a l - t a i l lateral force c o n t r i b u t i o n t o at a = Oo i s sham i nf i g u r e 11.

P P ) v .

These r e s u l t s were obtained for a number of models tested i n t h e .Langley 4- by &-foot supersonic pressure tunnel i n t h e Mach number rangefrom

1.4 t o 2. The estimated values were obtained by, first, determining the -

l i f t - c u r v e s l o p e f o r t h e exposed portion of the v e r t i c a l t a i l i n a uniform free-stream flow field w i t h the assumption t h a t t h e bodyforms a perfect end p l a t e . Then a f a c t o r was a p p l i e d t o this slope-by the methodof reference 14 t o account for the l i f t carry over between the t a i l and the body.Although this method of e s t i m a t i n g t h e t a i l c o n t r i b u t i o n i s arbi- t r a r y , t h e r e s u l t s i n d i c a t e a f a i r l y even scatter about the l h e of per- f e c t agreement. The s c a t t e r i s quitelarge, however, and indicates dif- ferences between the estimated and experimental values thus far obtained as largeas 20 t o 25percent. These differencesare a r e s u l t of changes , i n t h e flow f i e l d that a r e inducedbysuch things as t h e body, wing, and horizontal t a i l and are notaccountedforin the estimatedvalues. Some of these factors that affect the flow field are discussed in the following sections. - , .

Effect ofwing position.- Some e f f e c t s of t h e body and wing on the v e r t i c a l - t a i l c o n t r i b u t i o n t o and C a r e sham i n f i g u r e l2 f o r cyP a 45' sweptback-wingmodel a t M = 1.41.and 2.01. With the wing off,the v e r t i c a l - t a i l c o n t r i b u t i o n t o CyP and CnP (difference between t a i l - o n and tail-off curves) decreases w i t h increasing angle of attack because of the sidewashinducedby body v o r t i c i t y . As pointedoutinreference 1, the addition of a high wing t o a circular body causes an additional side- wash d i s t r i b u t i o n i n t h e wing wake t h a t i s adverse above the center of t h e wing wake and favorable below. The addition ofa low wing, on the other hand, causes additional sidewash distribution that i s favorable above and adversebelowthecenter of the wing wake. Thus, a t a = Oo,

the contribution of t h ev e r t i c a lt a i lt o Cy and CnP is decreased by -

P the addition of the high wingand increased by the addition of the low

wing ( f i g . 12) . A s theangle of attackisincreased,theafterbody and

v e r t i c a l t a i l must move down through the wing-inducedsidewash f i e l d s w i t h t h e r e s u l t ( s e e f i g . 12) t h a t , f o r t h e high-wing arrangement, the tail contribution decreases while the wing-bodybecomes less unstable, whereas f o r t h e low-wing arrangement, t h e t a i l c o n t r i b u t i o n i s e s s e n t i a l l y constantbutthe wing-body configuration becomes more unstable. The d i r e c t i o n a l s t a b i l i t y f o r t h e complete model decreases w i t h increasing angle of attack in both cases, however, because of thedecreased t a i l contribution for the high-wing configuration and because of an increase i n t h e i n s t a b i l i t y of t h e wing-body model f o r t h e low-wing configuration.

In addition to the expected difference in the level Of and C y P between M = 1.41 and 2.01 ( f i g . 12), theeffects of wing positionappear

NACA RM L57E24a I 1 1

t o be l e s s at thehigher Mach number. Thereareseveralfactorsthat may c o n t r i b u t e t o t h i s l e s s e n i n g of t h e e f f e c t s ofwing position. For one thing,because of thedecreased wing lift-curve slope at the higher \ Mach number, t h e s t r e n g t h of the wing-body inducedvortexflow and t h e resultantsidewashangle at t h e t a i l may bereduced. A decrease in wing- I p o s i t i o n e f f e c t s might a l s o r e s u l t from the decreased t a i l l i f t - c u r v e slope which, even f o r a constantsidewashangle at t h e t a i l , would result i n a smaller incremental change i n v e r t i c a l - t a i l c o n t r i b u t i o n .

A n a d d i t i o n a l e f f e c t t o c o n s i d e r , p a r t i c u l a r l y at Mach numbersabove about 2, i s t h e change withangle of a t t a c k of t h e dynamic p r e s s u r e i n the wingflow field. Thischange.involvesanincreasein dynamic pres- s u r e i n t h e compression f i e l d below the wingand a decrease i n dynamic i pressureintheexpansionfield above t h e wing. Above M = 2 t h e s e pressurechanges become l a r g e and, when coupled with the fact that the wing Mach l i n e s become directed more nearly. over the afterbody and t a i l , may outweigh t h e e f f e c t s offorebcdyand wing-body v o r t i c i t y . Under , these conditions the high-wing configuration may have more favorable d i r e c t i o n a l c h a r a c t e r i s t i c s t h a n t h e low-wing configuration since, with increasing angle of attack, the afterbody and t a i l would tend t o move down i n t o a high dynamic p r e s s u r e f i e l d f o r t h e high-wingconfiguration whereas f o r t h e low-wing configuration the afterbody and t a i l would be l \ subjected more t ot h e low p r e s s u r ef i e l d above t h e wing.

- V e r t i c a l - t a i l p r e s s u r e d i s t r i b u t i o n . - The changes i n t a i l contribu- t i o n w i t h wing position and withangle of a t t a c k f o r M = 1 . 4 1 and M = 2.01 ( f i g . - 1 2 ) a r e t h e r e s u l t of inducedsidewash a t t h e v e r t i c a l t a i l . Some pressure measurementshave been made on a v e r t i c a l t a i l t o determinethemagnitude of these effects for various wing locations.

Some of t h e s e r e s u l t s f o r M = 1 . 4 1 are shown i n f i g u r e s 13 and 14 f o r t h e same model used i n o b t a i n i n g t h e f o r c e r e s u l t s shown i n f i g u r e 12.

\ For a chordwise s t a t i o nn e a rt h er o o t of t h ev e r t i c a l t a i l at a = Oo and p = -5' ( f i g . l3), t h ee f f e c t of t h e wing-induced sidewash i s t o increase the local angle of s i d e s l i p and the corresponding section loading for the low-wing configuration and t o decrease the local angle of s i d e s l i p and corresponding section loading for the high-wing config- uration. The complete span loading cy cv of t h ev e r t i c a l t a i l f o r CTT p = - 5 O at a = 0 ' and l5O i s shown i nf i g u r e 14. A t a = Oo, t h e span loading i s uniformly increased for the low winganduniformly decreasedforthehigh wing. A t a = l 5 ' , t h e same generalchangesoccur although the wing e f f e c t s a r e combined with body e f f e c t s so t h a t t h e changes i n spanloading are less uniform. The influenceofthe body flow at a = 15' i s apparentneartheroot of t h e t a i l where t h e s e c t i o n loading i s less f o r t h e wing o f f t h a n f o r t h e wing on i n e i t h e r the high or low positions.

.. .

12 NACA RM L57E24a The changes i n t a i l contribution with angle of attack could also r e s u l t from dynamic pressure changes rather than fromsidewashangle changes. This i s notlikely, however, since some d i r e c t i o n a lc o n t r o l i n v e s t i g a t i o n ( f o r example, r e f s . ll and 12) indicate that the effective- ness of a rudder or all-moving v e r t i c a l t a i l is maintained even though t h e t a i l c o n t r i b u t i o n t o C and C diminishes. This character- YP i s t i c i s indicative of a flowangle change at t h e t a i l rather than a dynamic pressure change.

Comparisonof supersonic and subsonicsidewasheffects.- The super- sonic effects of t h e wing-inducedsidewash a t t h e v e r t i c a l t a i l up t o M = 2 a r e similar t ot h o s e determined at low speeds.Infigure 15, a comparison i s made of the wing-position effects on the experimentally determined t a i l f a c t o r qv f o r 4-5' sweptback-wing models a t subsonic and supersonicspeed ( M = 2.01). The subsonicresults(ref. 15) and thesupersonicresults(ref. 16) indicateessentiallythesaneeffects ofwing height and angle of attack.

Effects of fuselageforebody on t a i l contribution.- The t a i l con- t r i b u t i o n t o d i r e c t i o n a l s t a b i l i t y may be affected bya numberof other thingssuch as body cross-sectional shape, inlets,canopies, and hori- z o n t a l t a i l s . Some e f f e c t s of fuselageforebodyshape on t h e l a t e r a l and d i r e c t i o n a l s t a b i l i t y c h a r a c t e r i s t i c s of a fuselage and fuselage- v e r t i c a l - t a i lc o n f i g u r a t i o na t M = 1.41 a r e shown i nf i g u r e 16. These fuselages have the sane volumeand cross-sectional-area distribution but d i f f e r i n forebodycross-sectional shape - one having a circular shape, one having a v e r t i c a l l y e l l i p t i c a l shape,and one having a horizontally e l l i p t i c a l shape. The r e s u l t si n d i c a t e a s l i g h t i n c r e a s e i n t a i l c o n t r i - bution with increasing angle of a t t a c k f o r t h e h o r i z o n t a l l y e l l i p t i c a l forebody when compared t o t h a t f o r t h e c i r c u l a r forebody. With t h e v e r t i c a l l y e l l i p t i c a l forebody, however, there i s a considerabledecrease i n t a i l contribution w i t h increasing angle of a t t a c k and the indications a r e t h a t t h e t a i l c o n t r i b u t i o n r e v e r s e s above a = 1 2 ' .

The e f f e c t ofawing on t h e d i r e c t i o n a l c h a r a c t e r i s t i c s of a model with a forebodywithprotuberancessimulating side i n l e t s i s shown i n figure 17 f o r a 3 5 ' sweptback-wing configurationat M = 1.61. With the wing off,theinducedflows around the body r e s u l t i n a rapid decrease i n t a i l contribution and, i n f a c t , i n d i c a t e a r e v e r s a l i n t a i l c o n t r i b u - t i o n above a = 14O. With the wing i n s t a l l e d i n a semihighposition,the t a i l contribution i s reduced s l i g h t l y a t low angles of attack, but w i t h increasing angle of attack, the wing apparently shields the t a i l from some of the body flow f i e l d a r i s i n g from the side protuberances and the decrease i n t a i l c o n t r i b u t i o n i s much less than for the wing-offcase.

Effects of horizontal tail.- The e f f e c t s of a h o r i z o n t a l t a i l on the d i r e c t i o n a l s t a b i l i t y of two 4 5 O sweptback-wing airplane models are sham

NACA RM L57E24a - 13

i n f i g u r e 18 f o r a high-and low-tailposition a t M = 1.41. The addi- t i o n of thehorizontal t a i l a t CL = 0 ' i n e i t h e r a high o r low position causesanincrease i n d i r e c t i o n a l s t a b i l i t y . With increasingangle of attack, the increase provided by the low t a i l becomes smaller whereas the increaseprovided by thehigh t a i l becomes l a r g e r . The r e s u l t s shown i n figure 18 a r e f o r t h e t a i l fixed a t zerodeflection, whereas i n f i g u r e 19 deflections of the horizontal t a i l i n a direction to provide longitudinal t r i m (trailing-edge up) at highangles of a t t a c k a r e shown t o r e s u l t i n an i n c r e a s e i n d i r e c t i o n a l s t a b i l i t y w i t h t h e low t a i l and a decrease i n d i r e c t i o n a l s t a b i l i t y w i t h t h e h i g h t a i l .

Effects of v e n t r a l f i n s . - A r e l a t i v e l y simple way t o augment t h e d i r e c t i o n a l s t a b i l i t y i s throughtheuse of v e n t r a l f i n s . The e f f e c t s of v e n t r a l f i n s on t h e d i r e c t i o n a l s t a b i l i t y of two configurations at M = 2.01 a r e shown i n f i g u r e 20. The s i n g l e v e n t r a l f i n mounted on t h e bottomcenterline of the fuselage adds an essentiallyconstantincrement t o Cn through the angle-of-attack range for both configurations. The P addition of four small c r u c i f o r m f i n s t o one of the configurations has l i t t l e e f f e c t at a, = Oo butprovides a s u b s t a n t i a li n c r e a s ei n CnP withincreasingangle of attack. A furtherdescription of t h i s t y p e of f i n arrangement may befound i n r e f e r e n c e 17.

I Effects of afterbody modification.- Inasmuch as the fundamental , problem i n maintaining adequate directional stability for current high- speed a i r c r a f t stemsfrom the large unstable moments of the fuselage, I some consideration should be given to reducing this source of i n s t a b i l i t y .

I This planmightinvolvereshaping of the fuselage o r t h e use of multiple- body arrangements.

Some preliminary directional characteristics obtained for a body- i alone configuration and a combination of body and v e r t i c a l t a i l with two afterbodyshapes a t M = 2.01 a r e shown i nf i g u r e 21. The basic body ! had a circular cross section and a length-diameter r a t i o of 11. The rearward 20 percent of the body was modified t o have e l l i p t i c a l c r o s s - sectionswiththe major a x i s v e r t i c a l . The maximum r a t i o of t h e major I a x i s t o t h e minor axis w a s 2.25 a t thebase of the body. Both bodies maintainedthe same cross-sectional-areadistribution. The v e r t i c a l t a i l for both bodies had the same t o t a l a r e a t o t h e body center line. Thus, the exposed area of t h e t a i l was l e s s f o r t h e e l l i p t i c a l body t h a n f o r the basic body.

The e f f e c t of t h e modifiedafterbody was substantially to reduce the i n s t a b i l i t y of t h e body throughout theangle-of-attackrange. With t h e v e r t i c a l t a i l added, t h e g a i n i n s t a b i l i t y p r o v i d e d by t h e e l l i p t i c a l afterbody was about half that indicated for the body alone. However, w i t h t h e e l l i p t i c a l a f t e r b o d y , t h e exposed t a i l area i s reducedabout 25 percent and t h e a s p e c t r a t i o of the t a i l i s reduced.

14 . NACA RM L5p24a The e f f e c t s of the addition of a 45' sweptback wing i n b o t h a high and low p o s i t i o n f o r the body w i t h t h e v e r t i c a l l y e l l i p t i c a l a f t e r b o d y both w i t h and without a v e r t i c a l t a i l a r e s h a m i n f i g u r e 22 f o r M = 2.01.

The e f f e c t s of wing p o s i t i o n f o r t h e model w i t h t h e e l l i p t i c a l a f t e r b o d y a r eq u a l i t a t i v e l yt h e same a sf o r a conventionalafterbody. (See f i g . 12, f o r example. ) That is, withincreasingangle of attack,theaddition of the high wing reduced the instability of the wing-body combinationbut a l s o reduced t h e t a i l contribution; whereas, the addition of the lowwing i n c r e a s e d t h e i n s t a b i l i t y of the wing-body combination but had l i t t l e e f f e c t on t h e t a i l contribution.Quantitatively, however, i n comparison to results for the conventional afterbody, the effects of wing position w i t h t h e e l l i p t i c a l a f t e r b o d y were more pronounced f o r t h e t a i l - o f f configurations and l e s s pronounced forthetail-oncontribution. There- fore, unlike the model w i t h a conventionalafterbody(fig.12),the model w i t h t h e v e r t i c a l l y e l l i p t i c a l a f t e r b o d y ( f i g . 22) has higher directional s t a b i l i t y and lower t a i l loads w i t h the high wing than with the low wing.

Effects ofsmall-spanforebodyfins.- Some preliminary results have beenobtained a t M = 2.01 t o determinetheeffects of small-span fore- body fins, calledstrakes,extendingovertheforward 30 percent of t h e body, on t h e d i r e c t i o n a l s t a b i l i t y c h a r a c t e r i s t i c s of a model w i t h a 60° d e l t a wing (fig.23). The strakes, whichwere mounted on thehorizontal centerline, had a spanof 0.1 of the body diameter. The e f f e c t s of the strakes were t o r e d u c e t h e d i r e c t i o n a l i n s t a b i l i t y of the wing-body com- bination at higher angles of attack as well as t o i n c r e a s e t h e t a i l con- t r i b u t i o n s l i g h t l y so t h a t a s u b s t a n t i a l i n c r e a s e i n d i r e c t i o n a l s t a b i l i t y was realized. These r e s u l t s a r e i n general-agreement with resultsobtained f o r a 45' sweptback-wing configurationat high subsonicspeeds ( r e f . 18) and at M = 1.41 (unpublished).

Characteristics of multiple-bodyconfigurations.- Low-speed t e s t s of a multiple-bodyconfiguration(ref. 19) i n d i c a t e t h a t t h e d i r e c t i o n a l s t a b i l i t y improved considerably over that for a conventionalconfigura- tion, primarily because ofa decrease i n t h e i n s t a b i l i t y of the wing-body combination with increasingangle of attack. This decreaseresultsin p a r t from the elimination of the center afterbody that is generally adversely affected by the vorticity induced by the forebody and t h e wing- body juncture.Inaddition,the two outerbodiesprovide a s t a b i l i z i n g w i t h increasing angle of attack because of theforward increment i n CnP location of the center of gravity w i t h respect to the outer bodies.

Similar characteristics mightbeexpected at supersonicspeeds.

Inaddition,multiple-bodyconfigurations(such as t h a t shown i n f i g . 24) may o f f e r some r e l i e f t o t h e i n e r t i a c o u p l i n g problemand may also provide horizontal-tail locations suitable from the standpoint of p i t ch-up .

CONCLUDING R F W S A survey w a s made of the problems introduced by the increased longi- t u d i n a l s t a b i l i t y and reduced directional stability of a i r c r a f t o p e r a t i n g i n t h e low supersonicspeedrange. The increasedlongitudinalstability results in high drags due t o trimming and i n l i m i t e d c o n t r o l f o r maneuvering.

The untrimmed pitching moments canbereduced and hence t h e c o n t r o l requirementscanbealleviated t o some extent through the use of fuselage camber. The use of canardconfigurationsofferspromise of reducingthe drag due t o trimmingand i n c r e a s i n g t h e c o n t r o l l a b i l i t y .

The primaryproblem of concern i n t h e c a s e of d i r e c t i o n a l s t a b i l i t y at supersonicspeeds i s the reduction in lift-curve slope of t h e v e r t i c a l t a i l coupledwiththelargeunstable yawing moment of thefuselage. The v e r t i c a l - t a i l c o n t r i b u t i o n i s shown t o be affected by many f a c t o r s including the wing position, the fuselage shape, and t h e h o r i z o n t a l - t a i l position. The d i r e c t i o n a l s t a b i l i t y canbeincreased,particularly a t highangles of attack,bysuchdevices as v e n t r a l f i n s and forebody strakes.Inaddition,indications are t h a tt h ed i r e c t i o n a ls t a b i l i t y mightbeimprovedthroughmodifications t o the fuselage afterbody.

Langley Aeronautical Laboratory, NationalAdvisory Committee for Aeronautics, Langley Field, Va., M a y 3 , 1957.

....

t- 16 NACA RM L5p24a REFERENCES 1. Spearman, M. Leroy, and Henderson, Arthur, Jr. : Some Effects of Aircraft Configuration on Static Longitudinal and Directional S t a b i l i t y C h a r a c t e r i s t i c s at Supersonic Mach Numbers Below 3.

NACA RM L571115a, 1936.

2. Sevier, John R., Jr.: Investigation of the Effects of Body Camber and Body Indentation on the Longitudinal Characteristics of a 60' Delta-Wing-Body Combination at a Mach Number of 1.61. NACA RM L56A03, 1956.

3. Spearman, M. Leroy, and Driver,Cornelius:Investigation of Aero- dynamic C h a r a c t e r i s t i c s i n P i t c h and S i d e s l i p of a 4 5 O Sweptback- Wing Airplane Model With Various Vertical Locations of Wing and Horizontal T a i l - Static Longitudinal Stability and Control, M = 2.01. NACA RM ~ 5 5 ~ 0 6 , 1936.

4. Palazzo, Edward B., and Spearman, M. Leroy: StaticLongitudinal and L a t e r a l S t a b i l i t y and Control Characteristics of a Model of a 35' Swept-Wing Airplane a t a Mach Number of 1.41.

NACA RM L54G08, 1955.

5. Spearman, M. Leroy, Driver, Cornelius, and Robinson, Ross B.: Aero- dynamic Characteristics of VariousConfigurationsof a Model of a 45' Swept-Wing Airplane at a k c h Number of 2.01. NACA RM L54J08, 1.955.

6. Smith, Willard G.: Wind-Tunnel Investigation a t ' Subsonic and Super- sonic Speedsof a Fighter Model Employing a Low-Aspect-Ratio Unswept

Wing and a Horizontal T a i l Mounted Well Above t h e Wing Plane -

LongitudinalStability andControl. NACA RM A54D05, 1954.

7. Spearman, M. Leroy, and Palazzo, Edward B.: A n Investigation of a Supersonic Aircraft configuration Having a Tapered Wing With Circular-

Arc Sections and 40' Sweepback - Aerodynamic Characteristics of the

Configuration EquippedWith a Canard Control Surface at a Mach Number of 1.89. NACA- RM L54H19, 19%.

8. Driver,Cornelius:Longitudinal and L a t e r a lS t a b i l i t y and Control Characteristics of Two Canard AirplaneConfigurations at Mwh Numbers of 1 . 4 1 and 2.01. NACA RM ~ 5 6 ~ 9 , 1957.

9. Bates, William R.: Low-Speed StaticLongitudinalStabilityCharacter- i s t i c s of a Canard Model Having a 60° Triangular Wing and Horizontal Tail. NACA RM LgH17, 1949.

10. Johnson, Joseph L., Jr.: A Study of t h e Use of Various H i g h - x f t Devices on the Horizontal Tail of aCanard Airplane Model as a Means of Increasingthe AllowableCenter-of-GravityTravel. NACA RM ~ 5 2 ~ 1 8 a , 1953.

11. Spearman, M. Leroy, and Robinson, Ross B. : S t a t i cL a t e r a lS t a b i l i t y and Control Characteristics of a Model of a 45' Swept-Wing Fighter Airplane With VariousVertical Tails at Mach Numbers of 1.41, 1.61, and 2.01. NACA RM L56DO5, 1956.

12. Spearman, M. Leroy: S t a t i cL a t e r a l and D i r e c t i o n a lS t a b i l i t y and Effective Sidewash Characteristics of a Model of a 35' Swept-Wing Airplane*at a Mach Number of 1.61. NACA RM L56E23, 1956.

13. Spearman, M. Leroy, and Driver, Cornelius: Longitudinal and Lateral S t a b i l i t y C h a r a c t e r i s t i c s of a Low-Aspect-Ratio Unswept-Wing Airplane Model at Mach Numbers of 1.82and 2.01. NACA RM ~ 5 6 ~ 0 6 , 14. Nielsen,Jack N., Kaattari, George E., and Anastasio,RobertF.: A Method for Calculating the L i f t and Center of Pressure of Wing- Body-TailCombinations a t Subsonic,Transonic,andSupersonic Speeds. NACA RM A53G08, 1953.

15. Goodman, Alex: Effects of Wing Position and Horizontal-TailPosition on t h e S t a t i c S t a b i l i t y C h a r a c t e r i s t i c s of Models With Unswept and 4 5 O Sweptback Surfaces With Some Reference t o Mutual Interference.

NACA TN 2504, 1951.

16. Spearman, M. Leroy, Driver,Cornelius, and Hughes, W i l l i a m C . : Investigation of Aerodynamic C h a r a c t e r i s t i c s i n P i t c h and S i d e s l i p of a 45' Sweptback-Wing Airplane Model With Various Vertical Locations of Wing and Horizontal T a i l - Basic-DataPresentation, M = 2.01. NACA RM ~ 5 4 ~ 0 6 , 1955.

17. Spearman, M. Leroy, Robinson, Ross B., and Driver, Cornelius: The of Small Fuselage-Mounted Fins on t h e Effects of the Addition S t a t i c D i r e c t i o n a l S t a b i l i t y C h a r a c t e r i s t i c s ofa Model of a 45' Swept-Wing Airplane at Anglesof Attack Up t o 15.3' a t a bhch Number of 2.01. NACA RM L56Dl6a, 1956.

18. Sleeman, W i l l i a m C., Jr.: Investigation a t High SubsonicSpeedsof the Effects of VariousFuselage Forebody Fins on the Directional and Longitudinal Stability of a Complete Model'Having a 45' Sweptback Wing. NACA RM L56J25, 1957.

19. Fournier,Paul G.: Low-Speed Investigation of StaticLongitudinal and Lateral S t a b i l i t y c h a r a c t e r i s t i c s of anAirplaneConfiguration With a HighlyTapered Wing andWith Several Body and T a i l Arrangements. NACA RM ~ 5 7 ~ 0 8 , 1957.

'L

NACA RM L5m24a

ctn

-04

-.08

”

.08

CD .04

.4

-.I 0 .I .2 . 3

Figure 1.- Effect of fuselage camber on l o n g i t u d i n a l s t a b i l i t y c h a r a c t e r i s t i c s at M = 1.61.

.04

-04

0 1 . 7

o 3.0

-.08

- . I 2

cD 04

. 3 .4

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- . 2 -.I

Figure 2.- Effect of fuselage-forebody deflectionon longitudinal stability characteristicsat M = 2.01.

NACA RM L57EZ%a

i ?

-. 2

.08

Cm,o . 04

I . 6 1 . 8 2.0

I .4

M

Figure 3 . - Effect of horizontal-tail positionon variation of C , , o and ~ C & C L with Mach number.

.04 -04

- .08

Figure 4.- Effect of vertical-tail plan form on pitching-moment I characteristics of BVH configuration at M = 1 . 4 1 .

C L

I ?

Figure 5.- Effects of auxiliary canard on l o n g i t u d i n a ls t a b i l i t y and controlcharacteristics of 2

40' sweptback-wing airplane at M = 1.89. P

P ,

/-I

-. I

I

L

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-.2

-.3

I

-.4

.4 .8

I 2 I . 6

2D

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Figure 6.- Variation of longitudinal-stability parameter with Mach

number for canard and tail-rearward configurations.

NACA RM L57E2h L 2 D -2 a , k g CL Figure 7.- Trimmed l o n g i t u d i n a l s t a b i l i t y c h a r a c t e r i s t i c s f o r canard and t a i l l e s s delta-wingconfigurations at M = 2.01.

I

NACA RM L57E24a 25 I -.I 0 .I .2 .3 0 .I .2 .3 .4 CL CL Figure 8.- Comparison of trimmed and untrimmed l o n g i t u d i n a l s t a b i l i t y c h a r a c t e r i s t i c s f o r canard and t a i l l e s s delta-wing configurations a t M = 2.01.

NACA R M L57E24a I Canard

.08 I

Untrimmed ( 8 2 0)

L

' 0 .4 .8 1 : 2 1:6 2.0 2.4 2:8 32 3.6 4:O 4:4 48 M Figure 9.- Variation of longitudinal-stability characteristics with Mach number for canard configurat,ion.

"

t I

Figure 10.- Design trends of single-engine, single-place fighter airplanes.

NACA RM Lf57E2k.a IO O / O I -.020 I 0 O/O - .016 - .012 Estimated 1 I I I 0 -.004 -.008 7 0 1 2 -.016 -.020 Experimental (%)V Figure 11.- Correlation of estimated and experimental values of vertical- tail contribution to Cy M = 1.4 to 2.0; a = 0’.

P ‘ ( a ) M = 1.41. (b) M = 2.01.

Figure 12.- Effect of wing position on directional stability characteristics of a 45' sweptback- wing model.

NACA RM L57E24a

- :4

-. 2

CP

-2

Wing

.4

V High A Low 0 O f f

. 6

0 -2 .4 . 6 -8 I "0

X/C" Figure 13.- Effect of wing position on v e r t i c a l - t a i l s e c t i o n p r e s s u r e d i s t r i b u t i o n of a 4 5 O sweptback-wing model. a = 0'; p = -5'; M = 1.41.

Wing v H i g h n L o w 0 O f f

1.2 t

" :I

a= 15"

J-J , a = o o ,

-0 .2 .4 0 .2 .4

". L".

Figure 14.- Effects of wing position on v e r t i c a l - t a i l span-load distribution of a 4 5 O sweptback- w wing model. p = - 5 O ; M = 1 . 4 1 .

t - I

" Subsonic (ref. 15)

0 Supersonic (ref. 16) 1.2

.8

rlv

.4

a =Oo

0 - . 6 i -4 -.2 0

.4

.2

I .2

c

I

-8

I

rlv

.4 a 1 deg Figure 15.- Effect of wing position on v e r t i c a l - t a i l e f f i c i e n c y ofa 45' swept-wingmodel a t subsonic and supersonicspeeds.

Figure 16.- Effect of forebodyshape on v e r t i c a l - t a i l c o n t r i b u t i o n at M = 1.41.

.. - __ . . . .- NACA RM L57E24a -.002

- 004

- .01

- -02

-.O 3

-

4 0 4 a I2 1 6 20

a , deg Figure 17.- Effect of wing on v e r t i c a l - t a i l c o n t r i b u t i o n of a 3 3 ' sweptback-wing configuration at M = 1.61.

-

.012

ooa

r u l - 3

C

e

"

"B

P

.004

- .Ol

C

YB

- .02

.02

c, 01

(a) a = 5.2'. (b) a = 4.2'.

Figure 19.- Effects of horizontal-tail deflection on directional-stability characteristics for high and l o w horizontal tailsat M = 2.01.

/ AJ -"-------- .004

.-"\-

I.

'4

- Y

.002

\ A r

Cn 0 - " "~""" "

- ~ """"""~"" -0

""

-DO2

"--.

-.rO

-.004

0 4 a 12 1 6 20 0 4 8 12 16

01, deg 01, deg

Figure 20.- Effects of ventral fins on directional-stability parameter at M = 2.01.

.004 .002

cnP

-.002

-.OM

"- Figure 21.- Effect of afterbody shape on directional-stability characteristics at M = 2.01.

NACA RM L5P24a - 39

Wing n

" High - Low -.Ol C -.02 0 4 0 12 1 6 20 24 28 Figure 22.- Effect of wing position ondirectional characteristics of configuration with vertically elliptical afterbody at M = 2.01.

' A

Strokes 0 On 0 Off Figure 23.- Effect of forebody strakeson the directional stability characteristics of a 60° delta-wing configuration at M = 2.01.

F 09, Y Q /