Document
MEMORANDUM
1 . _.
.. .
<'' .. ',<COMPARISON O F CONTROL-FIXED STABILITY DENVATIVES FOR
'". 2,.
* . ' 'il \. "
l ;>.) TWO SUPERSONIC FIGHTER AIRPLANES AS DETERMINED
FROM FLIGHT AND WIND-TUNNEL TESTS By Harold L. Crane, Milton D. McLaughlin, and Jack A. White Langley Research Center Langley Field, Va.
ATlONAL AERONAUTICS AND
SPACE ADMINISTRATION
WASHINGTON April 1959 "
W
NATIONAL AERONAUTICS AND SPACE AaMINISmTION TECH LIBRARY KAFB, NY .
COMPARISON O F CONTROL-FMED STABILITY DERIVATIVES FOR TWO SLTPERSONIC FIGmER AIRPLANES A S D E - FROM FLIGHT AND WIND-TUNNEL TESTS* By Harold L. Crane, Milton D. McLaughlin, and Jack A. White The principal control-fixed stability derivatives of two f i g h t e r airplanes operating in the clean condition have been obtained from f l i g h t t e s t s at an a l t i t u d e of 35,000 f e e t at Mach numbersup t o 1.44 f o r one airplane and up t o 1.23 fortheotherairplane. The s t a t i c d e r i v a t i v e s werecompared with those determined from wind-tunnel r e s u l t s after the tunnel data were adjusted for the effects of differences in configura- tion,aeroelasticdistortion, and mass flowthroughtheengine. After theseadjustments were m a d e , the static derivatives determined from the wind-tunnel results usually proved t o be an adequate indication of the derivatives of thefull-scaleairplane.
INTRODUCTION The principal control-fixed stability derivatives of twomodern fighter airplanes have beendetermined from the characteristics of the short-period longitudinal and lateral o s c i l l a t i o n s measured i n flight.
The purposeof t h i s paper is to present the stability derivatives obtained from t h e f l i g h t t e s t s of these t w o airplanes and, insofar as possible, t o compare the stability derivatives determined from flight with those previously determined from wind-tunnel measurementsof t h e two airplane configurations. The r e s u l t s are presentedfor a Mach number rangeof approximately 0.7 t o 1.44 for airplane A and 0.7 t o 1.23 for airplane B.
The f l i g h t data were obtained at an a l t i t u d e of approximately 33,000 feet t o minimize the required correction ofwind-tunnel results for the aero- e l a s t i c d i s t o r t i o n of the airframe.
Vitle, Unclassified.
v
The longitudinal derivatives were determined by use of theapproxi- mate mathematicalexpressions which may be found i n variouspapers.(See r e f . 1, f o r example. ) The l a t e r a l d e r i v a t i v e s have been determined from I the flight records by the time-vector method which has been described i n previouspapers.(Seerefs. 2 t o 4.) The s t a t i cd e r i v a t i v e s which
%
were available from N A S A wind-tunnel r e s u l t s (refs. 5 and 6) obtained rl i n t h e Langley8-foottransonictunnels and the Langley 4- by &-foot G I supersonic pressure tunnel are compared to the values obtained from the flightdata. The wind-tunnel r e s u l t s have been adjusted, whenever the correction was appreciable, in accordance with the estimated flexibility and/orenginemass-flow characteristics of each airplane which were supplied by the manufacturers.
Additional results of t h e f l i g h t measurements of handling qualities of airplane. A are presented i n reference 7.
SYMBOLS AND COEFFICLENTS The r e s u l t s of t h i s i n v e s t i g a t i o n a r e r e f e r r e d t o t h e s t a b i l i t y system of axes, which i s defined as a three-dimensionalright-hand orthogonalsystem of axes intersecting at the airplane center of gravity in which the X- and Z-axes l i e i n t h e plane of symmetry. The X - a x i s i s the projection of the relative airstream onto the XZ-plane of symmetry.
The Y- and Z-axes are perpendicular to the X-axisand t o eachother.
lateral acceleration, g u n i t s "Y normal acceleration, g u n i t s "Z b wing span, f t C wing chord, f t
-
C mean aerodynamic chord of wing, f t
-
mean aerodynamic chord of t a i l , f t l i f t c o e f f i c i e n t , W/qS CL acL
lift-curveslope, -, per radian
cLa dU Rolling moment rolling-moment coefficient, qSb ac, damping-in-rollderivative, A, per radian " $ 1 , r a t e of change ofrolling-moment coefficient with yawing ac,
angular-velocity factor, A , 'per radian
C effective-dihedral derivative, -
l 8
aP
Pitching moment pitching-moment coefficient, qSC C s t a t i c margin, mean chord units T"cL " , perradian
4%)
acm
longitudinal-stabilityderivative, -, perradian
aU Yawingmoment yawing-moment coefficient, Cn G b r a t e of change of yawing-moment coefficient with rolling
. angular-velocity factor, - , per radian
r a t e of change of yawing-moment coefficient with yawing cnr
angular-velocity factor, - , per radian
.
r directional-stability derivative, - ? ' c n per radian I
aP
rate of change of yawing-moment ofchange ' coefficient with rate of angle-of-sideslip factor,
, per radian
2v
Lateral force lateral-force coefficient, CY
ss
rate of change of lateral-force coefficient with rolling cyP
ac, -
angular-velocity factor, - , per radian
rate of change of lateral-force coefficient with yawing a c , ,
angular-velocity factor, - per radian
.
rate of change of lateral-force coefficient with angle of
cyP
per radian rate of change of lateral-force coefficient with rate of
change of angle-of-sideslip factor, - ? per radian
a(@) 2v
d
differential operator, - D
vt d , acceleration due to gravity, ft/sec moment of inertia about Y stability axis nondimensional radius of gyration in r o l l about X stability axis nondimensional radius of gyration in yaw about Z stability axis KZ
Kxz nondimensional product-of-inertia parameter
M Mach number m mass of airplane, W/g, slugs P period of damped natural frequency, sec P rolling velocity, radians/sec
9 dynamic pressure, $, lb/sq f t ; pitching velocity, radian/sec
P
4 = -, dq radians/sec
d t r yawing velocity, radians/sec
r = - . dr, radians/sec 2
d t S wing area, sq f t time required for transient oscillation to damp t o one-half T1/2 amplitude, sec t tine, sec
v airspeed, ft/sec
W weight of airplane, l b Y s i d e foFce or l a t e r a l f o r c e , l b aerodynamic component of sideforce due to angle of s i d e s l i p yP . .
aerodynamic component of side force due t o l a g i n s idewash
Yb
weight component of side force due t o angle of bank
v
irlertial componentof side force due t o yawing velocity U angle gf attack of airplane, angle between reference body X - a x i s and s t a b i l i t y X - a x i s , deg ' du
6, = - radians/sec
d t '
P angle of sideslip, deg o r radians P mass density of air, slugs/cu f t wing down), radian Y i angle of bank (positive with right 4 f angle of yaw (positive with nose right), radian CI relative-density factor, m/pSb DESCRIFTION O F THE AlRpLANEs Airplane A is a high-wing, low-tail fighter airplane with the wing having 42' of sweepback of thequarter-chordline. Photographs of the t e s t a i r p l a n e a r e shown i n f i g u r e 1, a three-viewdrawing of the air- plane i s given i n f i g u r e 2, and pertinent dimensionsof the physical characteristics of theairplanearepresentedintable I. The airplane normally employs equipment t o provideautomaticstabilizationaboutthe roll and yaw axes and a l s o t o provide interconnection of rudder and aileron controls during manual operation, but this equipment was turned off duringthepresenttests. The t e s t s were conducted in the cruise configuration(flaps and gearup). A t subsonic and transonicvelocities, theso-calledcruise droop was employed, as is customary, t o improve the cruise and maneuver performance. Cruise droop consists of deflection of the leading-edge flap on the wing which produces an effective camber i n t h e w i n g . The deflection of theleading-edgeflap i s 6.8O and 7.0° for theinboard and outboardsections,respectively. (See f i g . 2. ) Airplane B is a midwing fighter airplane with the wing having 35' of sweepback of thequarter-chordline. The horizontal $ail is mounted s l i g h t l y lower thanthe wing. A three-viewdrawing of theairplane i s shown i n f i g u r e 3, the pertinent dimensions of the physical character- i s t i c s of theairplanearepresentedintable 11, andphotographs of airplane B axe shown in figure 4. For flight with flaps retracted, 4 longitudinal control was provided by anall-movablehorizontal tail. With the flaps extended, additional pitch control w a s provided by a geared elevator. Lateral control w a s provided by flaperons(spoilers) mounted .
ahead of theflaps. The ruddercontrol was conventional.Althoughthe airplane was equippedwith a yaw damper which operated the rudder, the yaw damper was turned off and the data presented herein were 'for the airplane in the clean condition and with power f o r l e v e l f l i g h t .
TEST CONDITIONS Wind T u n n e l The wind-tunnel data which were used herein for comparison with f l i g h t - t e s t r e s u l t s were obtained from references 5 and 6. The d a t a f o r Mach numbers up t o 1 . 2 were obtained in the Langley8-foottransonic tunnels whereas t h e d a t a f o r a Mach number of 1 . 4 were obtained in the Langley 4- by 4-footsupersonicpressuretunnel. The scale of t h e model of airplane A ( r e f . 5 ) w a s 0.042 andof airplane B ( r e f . 6) w a s 0.067.
The t e s t Reynolds number w a s approximately 2,000,000 over t h e t e s t Mach number range for both configurations.
The models were mounted on a sting. The tareforcealongthelongi- tudinal body axis w a s adjusted so t h a t t h e magnitudecorresponded t o t h a t which would be produced by a pressure at the model base equal t o t h e free- stream staticpressure.Stinginterference and buoyancy corrections were considered t o be negligible. A t subsonicspeeds,thewallinterference e f f e c t s were alsoconsideredto be withintheaccuracy of thedata. For Mach numbers between 1.03 and 1.12, the effects of wall-reflected dis- turbances were considered t o be large, and no measured data were used i n t h i s speedrange. A t othersupersonicspeeds,theeffects of w a l l - reflected disturbances were considered t o be small and were neglected.
In neither case was the model configuration exactly the same as t h e testairplaneconfiguration. The principaldifferences between t h e model configuration and airplane A were in the longitudinal fuselage dimensions.
Thesechanges consistedmainly of a fuselage extension on the airplane of approximately 2 f e e t (at f u l l scale) behind the horizontal tail.
Since the t a i l length w a s not changed by this modification, no adjust- ment of the tunnel data for configuration discrepancies has been m a d e inthepresentpaperforthe model of airplane A. The wind-tunneldata presented herein for the mo,del of airplane B havebeen adjusted for dif- ferences in t a i l length and area of t h e v e r t i c a l t a i l between t h e wind- tunnel model and the airplane by adjusting the increment between t a i l - o n and t a i l - o f f wind-tunnel data f o r t h e changes inconfiguration. The area of t h e v e r t i c a l t a i l of the airplane was 23 percent greater than that which was represented by t h e model. The t a i l length w a s 6 percent greater.
These were the only known significant differences between airplane B and the wind-tunnel model.
* Flight The f l i g h t t e s t s were made by initiating small longitudinal or lateral disturbances from trimmed l e v e l f l i g h t at an a l t i t u d e of approxi- mately 35,000 f e e t . Examples of theshort-periodoscillations which resultedare shown i n f i g u r e s 5 and 6. The testcenter-of-gravityranges - were 27.5 t o 28percent c forairplane A and 24 t o 25 percent F f o r airplane B. A table of approximate trim l i f t coefficientsfollows:
C , f o r -
T-
L M Airplane A Airplane B "" 0.36 0.7 .8 0.30 - 9 9 23 25 1.0 .16 .21 1.1 .12 .18 . 1 0 1.2 9 15 "" -09 1.3 "" 1.4 9 07
t
FLIGHT INSTRUMENTS AND ACCURACY Standard NASA instruments were used i n both airplanes to record airspeed, altitude, three components of angular velocity and acceleration, l a t e r a l and normal componentsof linear acceleration, angles of attack and sideslip, and controlpositions. The p i t o t - s t a t i c headand the s i d e s l i p and angle-of-attack vanes were a l l mounted on a nose boom as
shown i n f i g u r e s 1 , 2, and 4 . All records i n eitherairplane were
synclzronized at 0.1-second intervals by a comon timing circuit.
The turnmeters used to measure angular velocities and accelerations were referenced to the body axes of the airplane. Alinement errors were less than 0.5' for the turnmeters and linear accelerometers. Because the accelerometers were necessarily mounted away from the center of gravity, the linear-acceleration data were corrected for the effects of angular acceleration. The turnmeters and accelerometers are considered to be accurate to within approximately + L O percent of the scale ranges.
by The indicated angles of.sideslip and angles of attack, measured vane-type sensors, were corrected by the vector methods of reference 2 for yawing-velocity and pitching-velocity effects, respectively. The corrections to the vane readings for rolling velocity were considered to be negligible. The vanes were mass balanced and had essentially flat frequency response characteristics over the frequency range of airplane motions. The vane indications were statically accurate to about k0.1'.
The differences in instrument l a g were considered when the phasing and amplitude of the various measured quantities were determined from the flight records.
The scale ranges, sensitivities, and dynamic characteristics of the instruments used to measure the dynamic response of airplanes A and B are presented in the following table: ~ ~ _ _ Approximate S e n s i t i v i t y p e r Natural frequency,
Measured scalerange inch of f i l m l r I, CPS
. ~ . ~ - ~ _ _ q u a n t i t i e s Lirplane A -lane B Airplanes A and B iirplane A lirplane B l i r p l a n e B "
a, deg . . . . . . . -10 t o +30 11.3 10.5 10 t o 20 1 0 t o 20 c o . 1 c o . 1
10.6 10 t o x) 10 t o 20 c o . l c o . 1 0, deg . . . . . . . +40 9.7 0.65 p, r a d i a n s l s e c . . . +4 3.8 3.9 18.5 18.5 0-57
p, radians/sec2 . . k6 or a+10 6.0 10.0 0.68 0.65
7 7.1 0.50 0.48 18.5 0.60 q, r a d i a n s l s e c . . . 20.5 9.5 0 - 59 4, r d i a n s / s e c 2 . . +O. 8 0.76 0.78 0.65 0.68 7 7
r, radians /sec . . . . 0.49 0.48 14.25 0.60 0.61
20.5 9.5 e, r d i a n s / s e c 2 . . 0.68 0.65 0.79 0 - 79 7 7.0 b i - 3 1.0 14 I 2 0.67 0.99 0.7 sZ, g u n i t s . . . .
24 0.69 3.5 3.6 25.5 0.7 +o. 5 1.0 1.0 13.5 13- 5 0.66 0.7
I'
2' " ~ - units * *. * - aAirc&me B.
bAccelerometers of two s e n s i t i v i t i e s wereused.
'Conditions at s e a l e v e l .
METHOD Longitudinal Stability Derivatives
The longitudinalderivatives C% and Cms. + C% were determined
by substituting the measured values of period and damping of the short- period longitudinal oscillation in the following expressions: These expressions have previouslyappearedinotherreports. (See r e f . 1, f o r example.) The lift-curveslope, which is needed in thesolution of the damping derivative, was determined from t h e f l i g h t measurements of t h e amplitude r a t i o ofnormal acceleration to angle of attack during the short-periodoscillation. The moment of i n e r t i a w a s determined as a function of airplane loading from calculated data furnished by the manufacturers. A f i r s t approximation of the derivative a C aCL was m/
determined by t a k i n g t h e r a t i o of t o c
c% La'
Lateral Stability Derivatives The time-vector method was used for determining the lateral stability derivatives from f l i g h t measurements. The l a t e r a l e q u a t i o n s ofmotion in vector form, based on those of reference 4 but including rate of change of s i d e s l i p terms, are as follows: 1 1 In the three lateral equations ofmotion, threedegrees of freedom, eachwiththe same frequency and dazqing characteristics, are involved i n each equation: namely, sideslip,roll, and yaw. The motions repre- sented by these three equations have the same damping rate, and the phase angles remainconstant;thus, forvectorrepresentation,thevarious C y .
amplitude and phase relations axe invariantwithtime. The
B
terms are not considered directly in the present evalua-
and C Z b
tion.Intheapplication of the yawing-moment equation(eq. (3) ) , Dp
i s assumed t o be equal and opposite t o DJr. Thisassumptionhas a negligible effect on theaccuracy of the solution of this equation and
permitsevaluation of the combined derivative Cnr - Crib*
The l a t e r a l s t a b i l i t y d e r i v a t i v e s and theequations of motion employed I n the present analysis are referenced to the stability system of axes. Inasmuch as t h e f l i g h t data arereferencedtothe body axes, the flight data were transferred from the body axes t o t h e s t a b i l i t y axes by the method described in reference 2.
The vector methodof references 2 and 3 was employed for the determi-
nation of Cnp, Cn, - Crib, C z P y and . Experience has shown t h a t
c2P the values of and cyr may often be neglected in calculating the three representative flight records were determined from the manufac- turer'sdesignvalues of thesederivatives. These vectors proved t o be verysmall, and t h e i r s u m was negligible. It w a s therefore assumed throughoutthepresentanalysisthat and Cyr were equal t o zero.
cYP It w a s also necessary to assume values for one derivative in order to solve each moment equation. Estimated values of Cn and C z r furnished P by themanufacturers were used inasmuch as these quantities determine vectors of minor importance to the equilibrium of moments.
Since CY and c y , were found t o be negligible, it was possible
P t o determine by means of the following simplified equation derived from equation ( 1 ) : c L or d i r e c t l y from the measured lateral acceleration as follows:
"yw
%p = pss
In addition,since all three terms of equation ( 4 ) were available from measurements, these data were checked for consistency with the lateral- accelerometer data. A graphical illustration of a vectorsolution of equations ( 4 ) and (ha)for one t e s t record i s shown i n f i g u r e 7. It will.
be noted that the vector diagram did not close until adjustments were made to the measured data.
Both a correction in phaseangle and a change i n amplitude of one of the vectors representing the inertia terms were required to close the vector diagram of figure 7. It was assumed thatthediscrepancy was much more l i k e l y t o be due t o some sidewash e f f e c t at the vane than $0 an errorinthe measurement of angular velocity. Therefore, the p and p vectors were adjusted as needed tosatisfytheequationwhile b/p was
held constant. The amplitudes of p and 6 were thereby reduced about
10 percent for airplane A and as much as 25 percent for airplane B t o satisfy the side-force equation with the result that the values determined
for C y czp, and c were increased i n the same r a t i o . The required
P ' nD adjustments of the phaseangle of the p vectors were typically 5 ' and
sometimes as much as loo. Phase discrepancies of t h i s magnitude primarily
affectthedetermination of C and couldcauseerrors
- Cnrj and 2P
of 50 percent or more in these derivatives.
General Discussion The control-fixed stability derivatives obtained from measurements made inflightarepresentedinfigures 8 t o 13. The s t a t i c d e r i v a t i v e s are compared withvaluesobtained from wind-tunnel measurements. The f a c t t h a t t h e f l i g h t r e s u l t s a r e for 1 g operation at a pressure altitude of approximately 35,000 feet tends to minimize the effects of aeroelastic distortion which mustbe considered when comparing s t a b i l i t y d e r i v a t i v e s from f l i g h t and tunneltests. However, ininstancesin which the dis- tortion effects based on estimates by themanufacturers, became as large as 5 percent of thevalue of a derivative, the wind-tunnel results have been adjustedaccordingly. The estimates of f l e x i b i l i t y e f f e c t s assumed
r
the fuselage to be r i g i d but the wingand t a i l surfaces to be flexible.
Adjustments were made f o r changes in lift-curve slope of the t a i l SLIT- face as well as f o r changes in the lift-curve slope and t h e aerodynamic- center position of the wing.
The wind-tunnel t e s t s f o r a i r p l a n e A did not simulate the engine mass-flow effects.Therefore,theappropriatederivativesobtained from thewind-tunnel t e s t s have been adjusted for mass-flow e f f e c t s by the method used in reference 2. During the tunnel tests of the model of airplane By mass-flow throughthefuselageductsapproximatedtheflight values w e l l enough t o make further adjustments for mass-flow e f f e c t s unnecessary.
Longitudinal Stability Derivatives The longitudinal stability derivatives CLa7 c m , 7 CWL7
and Cms + ClndL which were determined from f l i g h t measurements arepre-
8 and 9 forairplanes A and B y respectively. Wind- sentedinfigures tunnelvalues for the static derivatives obtained from references 5 and 6 arealso shown. For airplane A, thewind-tunnel and flightvalues of cLa are in reasonable agreement. However, a comparison of the pitching-moment derivativesrevealspoorer agreement. The wind-tunnel resultsindicate a somewhat lower degree of longitudinal stability than do t h e f l i g h t r e s u l t s ( a decrement of 5 percent in the static margin) and a l a t e r t r a n - s o n i c s t a b i l i t y change which occurred a t a Mach number of approxi- mately 0.90 as compared t o t h e f l i g h t value of 0.85. The cruise droop w a s used f o r the subsonic flight tests butnotforthewind-tunnelresults shown infigure 8. However, wind-tunnel testsincludingthecruise droop were available f o r a more limitedrange of Mach numbers, and these data showed that the cruise droopcaused a rearwardaerodynamic-center s h i f t of about 0.01F compared with the discrepancy of 0.OgF between flight and tunnelresults. Thus f a r , no explanation has been found f o r t h e d i f - ference between wind-tunnel and flight values of c r i t i c a l Mach number.
The t o t a l t r a n s o n i c aerodynamic-center s h i f t was indicated to be about - 15 percent c in either case.
For airplane B, the lift-curve slope measured i n f l i g h t w a s approxi- mately 5 percent lower thanthewind-tunnelvalue. The f l i g h t and wind- tunnel values for pitching-moment derivatives shown i n figure 9 had approximately parallel trends with Machnumber although the wind-tunnel resultsindicated a 5 t o 10 percentsmallerstatic margin. The transonic aerodynamic-center s h i f t was about 35 percent of the mean aerodynamic chord for airplane B.
1 4 Reference 8 presents longitudinal-stability data for airplane B obtained in the 8-foot wind tunnel of the Cornell Aeronautical Laboratory.
The variation of s t a t i c margin with Machnumber as determined from the data of reference 8 was i n d i c a t e d t o f a l l between the values shown for f l i g h t and wind-tunnel results obtained at LangleyResearchCenterover most of the test Machnumber range.
As wouldbe expected,theslope of t h e l i f t curve of airplane A which a 42’ sweptback wing was somewhat lower than that of airplane B which had a 3 5 O sweptback wing. The transonicaerodynamic-center s h i f t w a s a t least twice as great for airplane B as for airplane A, but the fact that the m a x i m u m r a t e of change of aerodynamic-center position with Mach num- ber was about the same for either airplane was apparently more significant t o t h e p i l o t . The l e v e l of the pitch damping for airplane B was also greater than for airplane A andapproximatelydoubled in the transonic range,whilethe damping for airplane A decreased gradually with increasing Mach number. Closer examination of the results f o r a i r p l a n e B (fig. 9 ) indicated that the improved transonic and supersonic pitch damping of airplane B onlyoccurred when t h e p i l o t r e l e a s e d t h e s t i c k or relaxed s l i g h t l y h i s g r i p on t h e s t i c k and thus permitted the bobweights t o move the control as a function of the normaland angular acceleration.
The phasing was such that the damping i n p i t c h was thereby improved. The resulting motion of t h e s t i c k was usuallynotnoticed by t h e p i l o t . The stick force required to oppose the bobweights was only 4 o r 5 pounds.
(See f i g . 5 . ) Lateral Stability Derivatives The l a t e r a l s t a b i l i t y d e r i v a t i v e s C
CYp ’
2P’
., which were determined from f l i g h t measurements, are pre-
and cnr - CnB
sentedinfigures 10 t o 13 forairplanes A and B. The valuesassigned t o Cn and C f o r use in this evaluation are also shown i n f i g - P ures 12 and 13 and a r e based on the estimates o’f themanufacturers.
Values determined in transonic and supersonic wind tunnels for ‘nB 9 C2$ and c y B are a l s o shown f o r comparison withtheflightresults.
These wind-tunnel derivatives have been corrected for estimated aero- e l a s t i c d i s t o r t i o n andmass-flow effects whenever the estimated correc- tions were appreciable. Note t h a tt h e wind-tunnel values of Cn P and C 2 are at nearlythe same level as thederivatives measured i n B f l i g h t . However, theshort-rangetrendswith Mach number indicated by t h e f l i g h t and wind-tunnel r e s u l t s were sometimes quite different (as
inthecase of C z P or Cnp forairplane B) . The moderate amount of
s c a t t e r which i s present in the flight results could conceal some of the .
short-rangetrendsindicated by the wind-tunnel tests. The flightvalues were usually about 20 percent smaller than the wind-tunnel values.
Of CYp It is i n t e r e s t i n g t o n o t e t h a t a l l t h e measured lateral derivatives
except the damping-in-yaw derivative - CnB were approximately of
'nr equal magnitude for airplanes A and B and were not subject t o l a r g e varia-
tionwith Mach number. The values of Cnr - Cni determined i nf l i g h t
for airplane A decreased gradually from approximately -0.6 t o approxi- mately -0.4 withincreasing Mach number. The valuesforairplane B were more e r r a t i c and the yaw damping w a s much less with the level of
Cnr - Cni
approximating -0.1. It should be emphasized t h a t t h e l a t e r a l s t a b i l i t y derivatives were measured withthe yaw-damping devicesturnedoff. "he assigned values of C and C which were based on estimates of the
nP 2, '
manufacturers, were a t approximately the same level for airplanes A and B a t t h e minimum t e s t Mach number but had dissimilar trends with increasing Mach number.
CONCLUDING REMARIG Stability derivatives determined from data obtained a t t h e Langley 8-foottransonictunnels and the Langley 4- by 4-footsupersonicpressure tunnel for models of airplanes A and B, when corrected for mass-flow e f f e c t s and aeroelastic distortion, usually agreed with the stability derivatives of thefull-scaleairplaneswithinacceptable limits. How- ever,thedirectional-stabilityderivative and the effective-dihedral CnP for airplane B were indicated by thewind-tunnel r e s u l t s derivative cZP t o have more erratic variation with Mach number than was measured i n f l i g h t .
Another discrepancy between f l i g h t and wind-tunnel results occurred i n the longitudinal-stabilitydata. The flightresultsforbothairplanesindi- cated a 5 percent greater stability margin thanthetunnelresults. I n addition, the transonic stability break for airplane A occurred a t a Mach number of 0.85 i n f l i g h t compared with a Mach number of 0.90 i n the wind tunnel.
There were many s i m i l a r i t i e s between the measured values of the s t a b i l i t yd e r i v a t i v e sf o rt h e two airplaneconfigurations. However, i n some cases the stability derivatives measured i n f l i g h t f o r t h e two air- planeconfigurations had markedly differenttransonictrends. For example,
L
thetransonicaerodynamic-centershift was considerably greater for air- plane B than for airplane A. The pitch damping of airplane A decreased r slowly with increasing Machnumber while t h a t of airplane B increased.
However, the larger part of theapparent improvement i n t h e p i t c h damping of airplane B a t Mach numbers between 0.95 and 1.23 was caused by control motionproduced by the response-feel system when the pilot relaxed his grip on the stick during the pitching oscillation. With yaw dampers %urned off, airplane B had l e s s damping i n yaw than airplane A, and at
transonic speeds, the values of C n - Crib f o r airplane B fluctuated
r e r r a t i c a l l y between small positive and negative values.
Langley Research Center, National Aeronautics and Space Administration, Langley Field, V a . , October 27, 1958.
, 1. Wolowicz, Chester H.: Dynamic LongitudinalStabilityCharacteristics of a Swept-Wing Fighter-Type Airplane at Mach Numbers Between 0.36 and 1.45. NACA RM H56H03, 1957.
2. Wolowicz, Chester H.: Time-Vector Determined Lateral Derivatives of a Swept-Wing Fighter-Type Airplane With Three Different Vertical Tails at Mach Numbers Between 0.70 and 1.48. NACA RM ~ 5 6 ~ 2 0 , 1956.
3. Larrabee, E. E.: Application of the Time Vector Method t o t h e Analysis of Flight T e s t Lateral Oscillation Data. FRM No. 1 8 9 , Cornell Aero.
Lab. Inc. , Sept. 9, 1953.
4. Klawans, Bernard B., and White, Jack A.: A Method Utilizing Data on the Spiral, Roll-Subsidence, and Dutch Roll Modes f o r Determining Lateral Stability Derivatives From Flight Measurements. NACA TN 4066,
1957 -
5. Pierpont, P. Kenneth: Transonic Wind-Tunnel Investigation of S t a t i c Longitudinal and L a t e r a l S t a b i l i t y and Control Characteristics and D r a g Rise of a RepresentativeFighterAirplane. N A S A MEMO 12-14-58LY 1958. * 6. Bielat, Ralph P.: A Transonic Wind Tunnel Investigation of thePer- formance and of t h e S t a t i c S t a b i l i t y and Control Characteristics of a Modelof a Fighter-Type Airplane WhichEmbodies P a r t i a l Body Indentation. N A S A MEMO 12-13-582, 1958.
7. Kraft,Christopher C . , Jr., McLaughlin, Milton D . , White, Jack A . , and Champine, Robert A. : Flight Measurements of Some of theFlying Q u a l i t i e s and Stability Derivatives of a Supersonic Fighter Airplane.
NASA MEMO lO-7-?8Ly 1958.
8. Cochi, R. J.: Transonic Wind Tunnel Tests of a 1/21Scale Model of the Grumman Design 98J Airplane. Rep. No. AA-ll40-W-2(Contract No. SC-123 P. 0. ~ 8 7 0 8 2 ) ~ vols. I and 11, ser. V I , Cornell Aero.
Lab. , Inc . , July 1957.
. .
TAELE I . - PERTINETI D I M R E I O N S OF AlRPLRNE A Uiing (notincluding leading-edge chordsxtension) : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ea, s q f t span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35.67 Aspectratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Taper r a t i o 0.247 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sweepback of quarter-chord line, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Di.dral, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-5.0 Geometric wing incidence, r e l a t i v e t o fuselage reference b e : Cruise apd high speed, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-1.0 Take-offand l a n h l n g , deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.0 Wing-hinge-point location,percent C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39.58 Mean aerodyaamic chord, in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4 Airfoil section parallel to plane of symmetry: Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NACA 65A 006 Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ ~ ~ 6 5 ~ 0 0 5 Deflections of leading-edge droop: Inboard section: Landingand take-off, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cruise, deg 6.75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 .ghspeed, deg Outboard section: Landing and take-off, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cruise, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.0 High speed, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 Chord-extension area(bothsides),sq ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.33 Center-sectioninboardflaps: Area (both sides), sq f t 13.44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Deflection for landing and take-off, deg .. 20.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Deflection for cruise and higbspeed, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 Ailerons: Chord, percent of ving chord: Outboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28.0 Inboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23.5 Area, s q f t 20.78 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Deflections: High speed and cruise, deg *15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Take-offand landing: Both ailerons drooped as flaps, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 As ailerons, deg 4.45 t o -15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vertical stabilizer (based on areaextending to horizontal-tall centerline. not includingdorsal): Area. sq f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.75 . . . . . . . . . . . . . . . . . . . . . . . . Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Sweepback of quarter-chordline. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45.0 Taper ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.25 Mean aerodynamicchord. in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U4.8 T a i l length. from 25 percent F t o 25 percent Ft. in . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
173.1 Airfoilsection: . . . . . . . . . . . . . . . . . Modified NACA 65AOO5.3 Root . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . Modified NACA 65AOd1 Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rudder : .ea. s q f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.56 Chord. constant. in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.28 Maximum deflections: High-speed and cruise. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f6.0 Take-off and landing. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f17.0 Horizontal-tail (based on areaextending t o fuselagecenter line) : Area. sq f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93.4 Span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.1 . . . . . . . . . . . . . . . . . . . . . .
Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.148 . . . . . . . . . . . . . . . . . . . . . .
Sweepback of quarter-chordline. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geometric dihedral. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.417 Mean aerodynamicchord. in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73.4 Tail length from25 percent F t o 25 percent ct. in . . . . . . . 204.8 . . . . . . . . . . . . . . . . . . . . . .
Maximm deflections: Trailing edge down. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Trailingerne u p . deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Airfoil section: Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NACA 65~006 Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NACA 65A004 Weightand balance: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center-of-gravity rmge (for tests). C 26.5 to 27 Ueight: Take.off. l b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26, 077 Test range, l b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-. . . . 24,503 t o 20. 000 Range of moment of i n e r t i a of airplane about X s t a b i l i t y axis, slug-ft2 . . . . . . . . . . . . . . . lJ.,400 t o 10. 600 Range of moment of inertia of airplane about Y stability axis, slug-ft2 . . . . . . . . . . . . . . .
89, 500 t o 82. 500
Range of moment of inertia of airplane about 2 s t a b i l i t y axis, slug-ft2 . . . . . . . . . . . . . . .
97, 250 to 90, OOO Range of product of inertia referred to X and 2 s t a b i l i t y axes,slug-ft2 . . . . . . . . . . . . . . . .
5. 203 t o 500 !
TABLF, I1 . . PERTINENT DIMEIEIONS OF AIReLANE B
Wing:
. . . . . 250
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 31.625
Span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.5
. . . . .
Sweepback at quarter-chordline. deg . . . . . . . . . . . . . . .
Dihedral. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -2.5
Incidence.deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
. . . . . . . . . . . . . . . . . . . . . . . . . 98.38
Mean aerodynamicchord. in A i r f o i l s e c t i o n p a r a l l e l t o p l a n e ofsymmetry:
Wingroot . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modified NACA 6 5 ~ 0 0 6
Wing t i p . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modified NACA 65AOO4
Slatarea. sq f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.8
S l a tt r a v e l . deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Flap area. sq ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35.82
Flaptravel (down). deg . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Flaperonarea(total).sq f t . . . . . . . . . . . . . . . . . . . . . . . . 21.3
Flaperon travel(up). deg . . . . . . . . . . . . . . . . . . . . . . . . . .
V e r t i c a l s t a b i l i z e r : Area (exposed f i n ) . s q ft . . . . . . . . . . . . . . . . . . . . . . . . . . .
45.1 Span. from fuselagereferenceline. f t . . . . . . . . . . . . . . . . . . .
Sweepback of quarter-chordline. deg . . . . . . . . . . . . . . . . . . . .
45.5 0.286 Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Airfoil section . . . . . . . . . . . . . . . . . . . . . . . . Modified NACA 16.005.625
Rudder :
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1
Travel (clean condition). deg . . . . . . . . . . . . . . . . . . . . . . . . +5
Horizontal tail: Area (exposed). sq f t . . . . . . . . . . . . . . . . . . . . . . . . . . .
65.5
span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.167
Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-5
Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.4
Sweepback of quarter-chordline. deg . . . . . . . . . . . . . . . . . . .
Dihedral. deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
Mean aerodynamicchord. i n . . . . . . . . . . . . . . . . . . . . . . . .
55-13 .
ct (Ft based on Taillength from 25 percent t o 25 percent
including fuselage area). in . . . . . . . . . . . . . . . . . . . . . . 151.23
Meximum deflections: Trailing edge down. deg . . . . . . . . . . . . . . . . . . . . . . . . .
Trailing edge u p . deg . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Airfoil section:
Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NACA 6 5 ~ 0 0 6
Tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NACA 65A004
Weight and balance:
Center-of-gravity range (fortests).percent C . . . . . . . . . . . . . . . 24 t o 25
Weight :
Take.off. l b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20. 000
Test range. l b . . . . . . . . . . . . . . . . . . . . . . . . . . . 18. 000 t o 16. 000
Range of moment of i n e r t i a about the X stability axis. slug-ft2 . . . . . 6. 500 t o 6. 300 Range of moment of inertia about the Y s t a b i l i t y axis. slug-ftz . . . . 44. 400 t o 41. 000 Range of moment of i n e r t i a aboutthe Z stability axis. slug-ft . . . . 49. 000 t o 43. 800 Range of product of inertia r e f e r r e d t o the X and Z s t a b i l i t y
axes. slug-ft2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .2. 900 t o .2. 500
.
.
( b ) Rear view. L-57-2102 Figure 1. - Concluded.
8 5 . 6
L
!
L
- 227.2 -
Figure 2. - Three-viewdrawing of airplane A. A l l l i n e a r dimensions are i n inches. (For detailed dimensions, seetable I.)
Ct C
t - 379.5 - 1
Figure 3 . - Three-view drawing of airplane B. All linear dimensions are in inches. (For detailed dimensions, see table 11. ) (b) Rear view.
L-57-2256 Figure 4.- Photographs of airplane B.
r
.- - I a 8 I O Time, sec Figure 5.- Time history of a short-period longitudinal oscillation of airplane B a t a Machnumber of 1.0 and an altitude of 35,000 feet.
(Traceamplitudes have been enlarged up t o f i v e times from the film records. )
-.5 I-: m
> " c 0 - W
' -.02
. I -. I Time, sec Figure 6.- Time history of a short-period directional oscillation of air- plane B at a Machnumber of 1.15 and an altitude of 35,000 feet.
(Trace amplitudes have been enlarged upto ten times fronb the film records. ) Figure 7.- Sample side-force vectordiagram which illustrates the adjust- ment of the p and fi vectors t o satisfy the side-force equation..
Wind tunnel """"" Windtunnel interpolated 0- --Flight . - . -. . .
-. 2 " - - --..- 1 ""- "-- ~~~ ~ " /
E"
-Q'
0 -00-0" -. 4 . .
-. 6 7 . . 5 j . .
. ..
" .
I .o 1.2 1 . 3 I 1 . 5 Mach number , M Figure 8.- Longitudbal stability derivatives for airplane A.
Wind tunnel - - - " - - - - Wind tunnel interpolated .
0- - - Flight Mach number, M Figure 9 . - Longitudinal stability derivatives for airplane B.
L
Wind tunnel - - - - -- -- - - Wind tunnel interpolated 0 - --Flight
I
-. I -. 2 -. 3 ..- .6 . 7 .8 .9 1.0 1.1 1.2 1.3 1.4 I Mach number , - M Figure 10.- S t a t i c l a t e r a l s t a b i l i t y d e r i v a t i v e s f o r airplane A.
.4 .3 .2
" ""_
""
-"
-
.I Wind tunnel - - - - - - - - - - Wind tunnel interpolated 0- --Flight -1.2 . 7 .9 I .o 1 . 1 1.2 1.3 1 . 4 1.5 Mach number , M Figure 11.- S t a t i c l a t e r a l s t a b i l i t y d e r i v a t i v e s f o r a i r p l a n e B.
Estimated 0 - - - Flight measured " ~~ .~ . ~ . ~ . .
- .2 c a
e
I " " .. "" ~. . .
z . I a L V " 0 6 . 7 .a .9 1.0 1 . 1 1.2 1.3 1.4 I Machnumber , M Figure 12.- Rotary and damping derivatives f o r airplane A.
W ' .4 ..
-0- L W -. 4 0.
.Q
-.a ' c -1.2 Estimated 0 - - - Flight measured c .- rn e L -. 4 a , Q V - -. 8 Mach number , M Figure 13.- Rotary and damping derivatives for airplane B.
NASA - Langley Field, Va. L-1-36