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RESEARCH MEMORANDUM
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A SUMM_ARY O F THE LONGITUDINAL AND LATERAL STABILITY AND CONTROL CHARACTERISTICS OBTAINED FROM ROCKET-MODEL
TESTS O F A SWEPT-WING FIGHTER-TYPE AIRPLANE
AT MACH NUMBERS FROM 0.5 TO 1.9
I
I
By Grady L. Mitcham Langley Aeronautical Laboratory Langley Field, Va.
DI'BFEIA T O T,ERQI.J :sJKl ::.Yfm l ; f , / 2 3 / 6 ~
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
WASHINGTON I F e b r u a r y 27, 1957 i !
i
i
NATIONAL A D V I S O R Y COMMI- F O R AERONAUTICS RESEARCH MEMORANDUM C O N T R O L CHARACTERISTICS OBTAIIED FROM R O C K E T - M O D E L TESTS O F A SWEPT-WING FIGBIER-TYPE AIRPLANE - 1 AT MACH NUMBERS FROM 0.5 TO 1.9 A f l i g h t investigation has been conducted by means of rocket models of a swept-wing fighter-type airplane t o determine drag coefficients, longitudinal. and l a t e r a l s t a b i l i t y derivatives, effects of aeroelasticity on rolling effectiveness, and the effect of the engine j e t exhaust on the trim characteristics over the Mach number range from 0.5 t o 1.9.
The jet-engine simulator caused a decrease i n trim angle of attack of approximately 1.270 and a decrease i n trim-lift coefficient of 0.07.
A positive increment i n pressure coefficient was caused by the j e t on the side and bottom of the fuselage. As the distance downstream of the j e t e x i t increased, the increment on the bottom of the fuselage increased, whereas the increments on the side decreased t o a negative peak.
The drag r i s e begins a t a Mach number of 0.90. The minimmi-drag coefficient (including base and internal drag) has a value of 0.02 a t a Mach number of 0.87, an increase t o 0.070 a t a Mach number of 1.1 and then a gradual increase t o a value of 0.074 a t a Mach number of 1.83.
There was a reduction i n s t a t i c longitudinal s t a b i l i t y at the higher l i f t coefficients a t subsonic speeds. Dynamic longitudinal s t a b i l i t y was indicated throughout the speed range.
The horizontal tail was an effective control throughout the speed range. The dihedral effect was adequate. The r o l l -ing was nearly constant through the speed range and agreed with some theoretical values.
The aeroelastic losses i n rolling effectiveness varied from about 6 percent a t 35,000 feet t o about 27 percent a t sea level a t a Mach rimer of 0 . 5 and from about 20 percent a t 35,000 f e e t t o about 84 percent a t sea level NACA RM ~ 5 6 ~ 1 9 As a result of the current interest in airplanes that fly at super- sonic speeds, the Pilotless Aircraft Research Division of the Langley Aeronautical Laboratory has conducted an investigation to determine some of the aerodynamic characteristics of a twin-engine, swept-wing, fighter- type airplane by utilization of the rocket-propelled-model technique.
The primary purposes of this investigation were to determine drag coefficients, longitudinal and lateral stability derivatives, effects of aeroelasticity on the rolling effectiveness, and the effect of the engine jet exhaust on the trim characteristics, since the engine exits are located below and well forward of the all-movable horizontal stabi- lizer and tail.
This paper summarizes the flight-test results obtained from the six models used to determine the desired aerodynamic information over the Mach number range from 0 . 5 to 1.9.
SYMBOLS A cross-sectional area, sq ft A , jet exit area, sq in.
a total damping factor longitudinal-accelerometer reading normal-accelerometer reading
wg
transverse-accelerometer reading "t/g b wing span, ft E mean aerodynamic chord, ft chord-force coefficient, positive in a reasward direction, c a2 W 3
--
g Sw 9
drag coefficient, CN sin a + CC cos a
C~ NACA R b I ~ 5 6 ~ 3 . 9
- - PO)
base-drag coefficient, C ~ , b base area q%~ internal-drag coefficient 'D, i C ~ , m i n minirmnn-drag coefficient Ringe moment hinge-moment coefficient, qStEt
l i f t coefficient, CN cos a, - Cc s i n a
C~
/ c l i f t coefficient for minimum drag coefficient
~)cD,min \ pitching-moment coefficient about center of gravity %I pitching-moment coefficient about center of gravity a t zero o angle of attack and horizontal-tail deflection
cm = acm/i($), per raiiian
cmk = >C /a(%), ZV,: per radian
Cm + C pitch-darrrping derivative 9 a normal-force coefficient, positive toward top of model from C~ an W 1
- - -
model center line, €5 S , q incremental change i n pressure coefficient due t o power-on,
Cp,power-on - Cp,power-off
(PI - PO)
pressure coefficient, coefficient of rolling moment due t o r o l l i n g velocity,
acz
- e r radian
dig)'
c o e f f i c i e n t of r o l l i n g moment due t o yawing v e l o c i t y , ac 1
-, p e r radian
ac 2
coefficient of r o l l i n g moment due t o s i d e s l i p , -, per r a d i a n
&P c o e f f i c i e n t of yawing moment due t o r o l l i n g velocity, 'cn
-, p e r r a d i a n
c o e f f i c i e n t of yawing moment due t o yawing velocity, ac c o e f f i c i e n t of yawing moment due t o s i d e s l i p , 2, p e r r a d i a n aP c o e f f i c i e n t of yawing moment due t o sideslipping velocity, side-force c o e f f i c i e n t
c o e f f i c i e n t of s i d e force due t o s i d e s l i p , 3, p e r radian
dB t h r u s t , l b a c c e l e r a t i o n due t o gravity, 32.2 f t / s e c moment of i n e r t i a about body r o l l a x i s , slug-ft2 moment of i n e r t i a about body p i t c h axis, s l u g - f t 2 mor-ent of i n e r t i a about body yaw axis, slug-ft2 product of i n e r t i a , slug-ft2 length, f t Mach number a *..*.
Me e x i t Mach number m mass of model, slugs
m '
s t a t i c t e s t couple applied a t 0.945b/2 i n a plane p a r a l l e l t o the model center l i n e and perpendicular t o the wing chord plane, in-lb period of short-period oscillation, see; or t e s t load applied a t station 26.38 zeaslured &erg the @.07-=ercent chord l i n e
i n figure 44, l b
r o l l i n g angular velocity, radian/sec free-stream s t a t i c pressure, lb/sq f t j e t e x i t s t a t i c pressure, lb/sq ft l o c a l s t a t i c pressure, lb/sq ft average base s t a t i c pressure, lb/sq f t wing-tip helix angle, radians dynamic pressure, lb/sq ft Reynolds number yawing angular velocity, radians/sec; or i n figure 6 radius of equivalent body of revolution, f t wing area including intercept, sq f t free-stream s t a t i c temperature, OR time, sec time t o damp t o one-half q l i t u d e , sec . . ... . . .. . .. .. . . . 0 . . 0 .
0 . 0 . 0 . . ... e.. ...
. . . . . . . . . . . . . . .. . .
0 . 0 . ... 0 . .
:*: * . ; .c1.lr, ...
• 0 . NACA RM ~56K19 V velocity, f t / s e c equivalent l a t e r a l velocity, f t / s e c V e W weight of model, l b w mass flow through duct, slugs/sec mass of a i r flowing through a stream tube of a r e a equal t o t h e w inlet-cowl a r e a under free-stream conditions, slugs/sec s t a t i o n (measured from nose), f t x angle of a t t a c k of fuselage reference l i n e (at model center a of g r a v i t y ) , deg I3 angle of s i d e s l i p , deg f l i g h t - p a t h angle, measured with respect t o a h o r i z o n t a l plane, radians J s p e c i f i c heat r a t i o a t j e t e x i t 7 e 6 h o r i z o n t a l - t a i l deflection, p o s i t i v e t r a i l i n g edge down, deg; o r i n f i g u r e 44 d e f l e c t i o n of 48.07-percent chord l i n e of wing r e s u l t i n g from applied load P, i n .
d e f l e c t i o n of each a i l e r o n measured i n a plane perpendicular t o 'a t h e a i l e r o n hinge l i n e , deg '/P f l e x u r a l - s t i f f n e s s parameter i n . /lb E i n c l i n a t i o n of p r i n c i p a l a x i s , deg wing angle of t w i s t i n a plane p a r a l l e l t o t h e model center l i n e 8' and perpendicular t o t h e wing chord plane, radians angle between fuselage center l i n e and horizontal, radians 8'/m1 t o r s i o n a l - s t i f f n e s s parameter, radians/in-lb P air density, s l l ~ g s / c u ft
@ r o l l angle, radians
NACA R l l ~56K1-9 fraction of rigid-wing rolling effectiveness retained by the
9 '
f l e x i b l e wing 9 angle of yaw, radians frequency of t h e Dutch r o l l oscillation, radians/sec w phase angle of side-force coefficient t o angle of sideslip, R
%
r d f mx luzless otherwise noted phase angle of r o l l r a t e t o angle of sideslip, radians unless R P otherwise noted Subscripts: w w i n g t t a i l
- ~ C L - - -- h C h
Derivatives a r e q r e s s e d i n t h i s manner: CL - 3 Ch8 ha, a and s o forth.
A dot over a symbol indicates t h e f i r s t derivative with respect t o time, and two dots indicate t h e second derivative with respect t o time.
Tne syrnbol I ( represents the absolute magnitude of the amplitude
of a quantity and i s always taken t o be positive.
All the measured quantities and aerodynamic derivatives are referred t o t h e system of body axes which assumes the X-axis corresponds t o the fuselage reference l i n e . (see f i g . 1. ) DESCRIPTION O F MODEIS Model A The fuselage of model A was constructed of s t e e l bulkheads with p l a s t i c hatches and wooden fairings forming the contoured body lines.
The wing Both the wing and t h e horizontal t a i l had swept plan forms.
thickness vazied from 6.67 percent chord a t t h e root t o 5.71percent chord a t the t i p . The a i r f o i l sections were NACA 65~007 and NACA 65~006 a i r f o i l s modified by extending the chord 5 percent forward of t h e . . ... . . .. . . . . . . . . ... 0 .
0 . 0 . 0 . . ...
0 . .
0 . 0 .
e . 0 NACA RM ~ 5 6 ~ 1 9 . . ... . . . ..
16. 04-percent-chord l i n e and adding 1.67 percent p o s i t i v e camber. There was lo of p o s i t i v e incidence between t h e wing and t h e model center l i n e .
> -+ The horizontal s t a b i l i z e r was f i x e d a t a d e f l e c t i o n of -1.2O. Duralumin p l a t e s and mahogany f i l l e r s made up t h e wing panels, and s t a l l p l a t e s were Two pulse rockets were located a t about 70 percent of each semispan.
i n s t a l l e d forward of the canopy t o d i s t u r b t h e model i n p i t c h . The model same a s t h a t shown i n f i g u r e 1 with t h e exception of was e s s e n t i a l l y the t h e wing root i n l e t s which were f a i r e d over on model A t o f a c i l i t a t e i n s t a l l a t i o n of the rocket-motor simulator i n t h e engine ducts which was used t o sirnulate t h e j e t exhaust c h a r a c t e r i s t i c s of t h e t u r b o j e t engines.
These f a i r e d i n l e t s can be seen i n t h e photographs shown a s f i g u r e 2.
Sirciulation of j e t exhaust was accomplished by use of two s o l i d - propellant rocket motors designed according t o t h e method of reference 1.
The simulator shown i n f i g u r e 3 was i n s t a l l e d i n s i d e t h e engine ducts.
The ducts terminated e x t e r n a l t o and under t h e fuselage. The f i n a l angle on t h e curved b o a t t a i l s of t h e engine ducts was about 250. The simulator i n s t a l l a t i o n was designed t o simulate t h e P r a t t & Whitney 557 engine exhaust c h a r a c t e r i s t i c s a t maximum r a t e d power (sonic e x i t , afterburner The simulator on) a t a Mach number of 1.5 and an a l t i t u d e of 35,000 f e e t .
f l i g h t - t e s t performance d a t a corrected t o an a l t i t u d e of 35,000 f e e t and f u l l scale by t h e method of reference 1 a r e presented i n t a b l e I with t h e 557 design values f o r comparison.
A sketch showing t h e o r i f i c e locations where t h e f l i g h t pressure measurements were taken i s presented a s f i g u r e 4.
Model B The o v e r a l l construction of model B was e s s e n t i a l l y t h e same as t h a t of model. A with t h e exception of t h e pulsed horizontal s t a b i l i z e r and t h e i n t e r n a l ducting. A three-view drawing i s shown i n f i g u r e 1 and a photograph a s figure 5 . The a r e a d i s t r i b u t i o n and equivalent body of revolution a r e shown i n f i g u r e 6. This information i s included f o r pressure-drag c o r r e l a t i o n a t a llach number of 1.0.
The horizontal s t a b i l i z e r was s o l i d duralumin and operated i n abrupt Operation was r~ovenents between angles of approximately -2O and -7'.
achieved by a hydraulically actuated piston. A motor-driven cam operating an e l e c t r i c solenoid was used t o control t h e flow of t h e h y d r a ~ l i c f l u i d t o t h e piston and t o insure proper timing of t h e pulsing operation.
Hinge morlents were measured by means of a d e f l e c t i o n beam attached between the push rod of the control system and t h e torque rod which a c t u a t e d t h e horizontal s t a b i l i z e r . Deflection i n t h e beam was propor- t i o n a l t o t h e moment i n t h e torque rod which ckmged t h e inductance i n t h e instrument.
The wing root i n l e t was unswept and incorporated a boundary-layer bleed. Internal ducting consisted of two separate ducts running through the model with a mininnun cross section near each duct exit. A t o t a l - p e s s - u e rake was UO-uited siightiy Torward of t h i s minimum section t o obtain data t o be used i n the calculation of internal drag a t supersonic Mach numbers. A f a i r i n g was installed i n each duct i n order t o duplicate the location and cross-sectional area of the engines and accessory housings. The internal ducting did not duplicate t h a t of the full-scale airplane; however, the exit-to-entrance area r a t i o w a s such as t o regulatp the mass flow t o approximate the engine requirements a t supersonic speeds.
Since t h e afterburner base cf the iiio&l &id not dilpiicate t i a t 02 the full-scale airplane, it was necessary t o deternine the base drag of t h e Six manifold static-pressure tubes were used t o determine the nodel.
average static-pressure variation over the f l a t base of one of the after- burners. The model contained no sustainer rocket motor.
Model C The constmctional and geometrical characteristics of model C were essentially t h e same a s model B with the exception of t h e horizontal s t a b i l i z e r which w a s fixed at a deflection of - 0 . 4 ~ t o trim model C a t a low positive l i f t coefficient. The model was disturbed l a t e r a l l y by six small rockets, mounted i n t h e nose, whose t h r u s t produced a short l a t e r a l acceleration. The timing of these pulses placed two of them i n the supersonic speed range and the remainder i n the transonic and high subsonic ranges.
The geometric and mass characteristics of models A, B, and C are given i n tables I1 and 111, respectively.
blodels D, E, and F Models D, E, and F consisted of 10-percent-scaled reproductions of the assumed full-scale airplane wing mounted on pointed cylindrical bodies 9 inches i n diameter with a cruciform arrangement of d e l t a t a i l f i n s .
The basic model wings (not including wing f i l l e t area which is achieved by a trailing-edge chord-extension at t h e root) had an aspect r a t i o of 4.281 and a taper r a t i o of 0.284 and were swept back 36.84O a t the 20-percent-chord line. A photograph of one of the models and a dimen- sioned sketch are shown i n figures 7 and 8, respectively.
The models were t e s t e d with a fixed aileron deflection. The wing of model D was of very s t i f f construction with an aileron deflection The wings of models E and F, on which the ailerons were deflected of 25O.
15O and 25O, respectively, approximated the scaled-down s t i f f n e s s char- a c t e r i s t i c s of t h e full-scale airplane wing.
NACA RM ~ 5 6 ~ 1 9 A telemeter which transmitted time h i s t o r i e s of t h e primary d a t a a s t h e models t r a v e r s e d t h e Mach number range was i n s t a l l e d i n models A, B, and C. For models D, E, and F spinsondes were used t o obtain t h e p r i - mary data, which were r o l l i n g v e l o c i t y .
A rawinsonde r e l e a s e d a t t h e time of f i r i n g recorded t h e free-stream temperature and s t a t i c pressure over t h e a l t i t u d e range covered by each t e s t . The v e l o c i t y and p o s i t i o n i n space of t h e models were determined by a CW Doppler r a d a r s e t and a r a d a r t r a c k i n g u n i t .
TESTS Simulator Ground Tests Three s t a t i c f i r i n g s of t h e s u s t a i n e r motor f o r model A were made, and t h r u s t , chamber pressure, and e x i t s t a t i c pressure were measured.
These t e s t s were used t o show t h a t proper simulation would be achieved; they a l s o served t o c a l i b r a t e t h e v a r i a t i o n of e x i t - s t a t i c pressure with chaxi~er pressure. This c a l i b r a t i o n enabled c a l c u l a t i o n of t h r u s t i n f l i g h t .
F l i g h t Tests Flight t e s t s of t h e models were conducted a t t h e Langley P i l o t l e s s A i r c r a f t Research S t a t i o n at Wallops Island, Va. The models were accel- e r a t e d t o t h e i r maximum Mach numbers, which corresponded t o about M = 2.0 f o r models A, B, and C and about M = 1.2 f o r models D, E, and F, by means of booster rocket motors which separated upon c e s s a t i o n of thrusting. A photograph of model B p r i o r t o launching i s shown a s f i g u r e 9. The Reynolds number range covered by t h e t e s t s i s given i n f i g u r e 10. The d a t a presented h e r e i n were obtained during t h e coasting phase of f l i g h t , with t h e exception of model A f o r which power-on d a t a were obtained a t M = 1.5. The r a t i o of j e t s t a t i c pressure t o f r e e - stream s t a t i c pressure f o r t h e power-on p o r t i o n of t h e f l i g h t varied from 3.5 t o 4.0 a s shown i n f i g u r e 11.
NACA m 1 ~ 5 6 ~ ~ 9
Longitudinal St.& i l i t , y Free o s c i l l a t i o n s of model I3 were created by pulsing the horizontal t a i l i n an approximate square-wave motion which resulted i n changes i n normal acceleration, angle of attack, and hinge moment. The longitudinal-
~..+~h,'l,'+,, nvnl-mi r -4' khCS2 osz-jlla?--ons is base& on *--- ------ -* *
L) uuu.LAL uy - ~ u y 0L.a , , I u w u d ~ ~ s c e s UL s r ~ e - don i n pitch. The basic equations of motion used i n the analysis are a s follows : I n order t o simplify the analysis and t o permit the determination of equations f o r t h e more important aerodynamic derivatives a number of assumptions are necessary. It i s assumed t h a t during the time i n t e r v a l over which each calculation is made the following conditions exist: The forward velocity i s constant and t h e aerodynamic forces and moments vary l i n e a r l y with the variables a , 6, and 8. In t h e appendixes of ref- erences 2 and 3 c m be found a more detailed discussion of the methods used i n reducing the data from a f l i g h t time history t o the parameters presented i n t h i s paper and the assunptions made i n and the limitations of the t e s t technique.
Some of the control characteristics and damping data obtained from t h i s t e s t are incomplete between Nach numbers of 0 . 8 0 and 1.07 because the conditions of damped oscillations and l i n e a r variation of aerodynamic forces and noclents with angle of attack discussed i n references 2 and 3 are not s a t i s f i e d i n t h i s speed range.
Corrections f o r model pitching and yawing velocities by the method described i n reference 4 were made t o t h e air-flow indicators t o obtain angles of attack and angles of sideslip. A l l coefficients, with t h e exception of hinge moments (which were based on t h e t o t a l horizontal-tail area) and pressure coefficients, were computed based on t h e theoretical wing area ( f i l l e t area excluded), and a l l angles were measured r e l a t i v e t o t h e fuselage reference l i n e . (see f i g . 1. ) NACA RM ~ 5 6 ~ 1 9 The t o t a l pitching-moment c o e f f i c i e n t s were c a l c u l a t e d by t h e f o l - lowing equations: The angular a c c e l e r a t i o n i n p i t c h was obtained from t h e following r e l a t i o n : The quantity 6 was obtained by d i f f e r e n t i a 5 i n g t h e measured a curve and t h e quantity f- w a s calculated from t h e measured a c c e l e r a t i o n s at t h e model c e n t e r of gravity.
A choking s e c t i o n and a t o t a l - p r e s s u r e rake i n s t a l l e d i n t h e duct e x i t made it possible t o determine mass-flow r a t i o and i n t e r n a l drag
based on free-stream and duct-exit conditions. ( s e e r e f . 5 . ) The i n t e r - -
n a l drag presented h e r e i n was calculated i n t h e following manner:
- - - 1 k(' - 'exit) - % x i t ( p e x i t - p0)]
C ~ , i q s , Calibration of t h e v a r i a t i o n of e x i t s t a t i c pressure with chamber pressure i n s t a t i c t e s t s enabled c a l c u l a t i o n of t h e t h r u s t i n f l i g h t by use of t h e following equation: Comparison of t h e vacuum impulse ( t h e f i r s t term of t h e preceding equation i n t e g r a t e d over t h e burning time) i n t h e s t a t i c t e s t s with t h a t i n f l i g h t indicated a t o t a l impulse of approximately 1 0 percent more i n f l i g h t . The impulse v a r i a t i o n i n t h r e e s t a t i c t e s t s was l e s s than 3 percent; thus, an adjustment of t h e f l i g h t chamber pressure d a t a was The measured chaniber pressure was proportionally adjusted indicated.
and t h e r e s u l t i n g t h r u s t used i n conjunction with t h e accelerometer meas- urements t o determine t h e power-on drag c o e f f i c i e n t . The power-on l i f t c o e f f i c i e n t s were a l s o corrected t o a zero t h r u s t condition.
L a t e r a l S t a b i l i t y + Throughout t h e t e s t , model C executed a continuous l a t e r a l motion which.showed l i t t l e damping; thus t h e time t o damp t o one-half amplitude was considered i n f i n i t e . O s c i l l a t i o n s of small amplitudes were a l s o d .
.* present i n t h e traces of angle-of-attack and l i f t coefficient, which indicated i n e r t i a coupling between longitudinal and l a t e r a l motions.
Although t h e e f f e c t s of the l a t e r a l motion on the longitudinal motion were w o r t a n t i n producing or modifying the longitudinal motion, t h e longitudinal motion produced a secondary e f f e c t on t h e l a t e r a l motion which was within the accuracy of the l a t e r a l s t a b i l i t y measurements.
O n t h i s b a s i s t h e computations were based on t h e following equations f o r t h r e e degrees of f'reedom: Side force: Rolling moment: Yawing moment : W
I n t h e side-force equation the gravity terms -(@ cos 8 + I ) s i n 8 )
ss
have been omitted. This assumption i s v a l i d f o r rocket-propelled models since the models have low wing loadings and are flown through rather dense air at high speeds so t h a t the values of the gravity terms are very small.
Also, i n the lateral-force equation all the aerodynamic terms are combined
i n t o one term referred t o a s Cy or the t o t a l l a t e r a l force. ,This assump-
t i o n i s valid since the t o t a l l a t e r a l force was measured by a transverse accelerometer and includes the contributions of r o l l i n g angular velocity, yawing angular velocity, and sideslip angle. It was f u r t h e r assumed t h a t
was equal t o % P I I n the rolling-moment and yawing-moment equa-
c~
P
tions, t h e assumption has been made t h a t fi = -r i n order t h a t t h e
yawing- and sideslipping-velocity derivatives may be combined t o reduce the number of unknown aerodynamic terms.
The l a t e r a l equations of motion written i n the form t o analyze the data by the vector method a r e given i n figure 12. More detailed discus- sions of the application of the time vector m y be found i n references 6, 7, and 8. The time vectors, such as the example given i n figure 12 f o r one solution, constitute a three-degree-of-freedon analysis by using basic notional information such as the representative curves of t h e variation of side-force coefficient with aagle of sideslip. The primary vectorial NACA R M ~ 5 6 ~ 1 9 d a t a necessary f o r t h e a n a l y s i s and obtained from t h e f l i g h t time h i s - t o r y a r e as follows: t h e Dutch r o l l frequency, t h e d q i n g f a c t o r , t h e undamped natural c i r c u l a r frequency, t h e phase d i f f e r e n c e between t h e r o l l r a t e and t h e angle-of-sideslip o s c i l l a t i o n s , and t h e amplitude r a t i o of t h e r a t e of r o l l t o angle of s i d e s l i p . The phase angles include cor- r e c t i o n s required by t h e frequency response c h a r a c t e r i s t i c s of t h e r o l l r a t e gyro.
The method allows t h e determination of two d e r i v a t i v e s i n each degree of freedom, whereas t h e t h i r d must be otherwise determined. The cross derivatives C 2 and Cn were assigned two values t o show t h e e f f e c t r P A more of s e l e c t i n g them a s t h e d e r i v a t i v e s not found i n t h e a n a l y s i s .
complete discussion on t h e evaluation of t h i s t e s t technique i s given i n reference 8.
The frequency of t h e Dutch r o l l motion w a s a l s o used t o compute by the following equation, which was w r i t t e n f o r one degree of f r e e - C P dom i n yaw: shown by t h e two methods i s a measure of t h e and t h e difference i n C n ~ e f f e c t of neglecting t h e product of i n e r t i a terms. The i n c l i n a t i o n of t h e p r i n c i p a l axis, measured t o be -4.2O, was used t o compute t h e product of i n e r t i a .
ACCURACY The estimated probable e r r o r s i n t h e b a s i c q u a n t i t i e s measured a r e shown i n t a b l e IV. The s t a b i l i t y d e r i v a t i v e s presented i n t h i s paper a r e dependent upon some o r all of t h e s e measured q u a n t i t i e s . A n a n a l y s i s by t h e methods of references 6 and 8 of t h e probable e r r o r s i n some of t h e derivatives due t o t h e probable e r r o r s quoted i n t a b l e IV i n d i c a t e s t h e following e r r o r s a t M = 1.7 and M = 0.85: Mach n w e r 1.7 0.85 lvlach number 1.7 0.85
, p e r c e n t . 25 25
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . and C l , percent It5 k8
B C"P
C , p e r c e n t . . . . . . . . . . . . . . . . . . . . . . . . fl4 EL7
2~
C - G ; , p e r c e n t . . . . . . . . . . . . . . . . . . . . . + 15 k25
nr data f o r models D, E, and F have not been corrected f o r The pb/2V the e f f e c t s of r o l l i n g moment of inertia. Reference 9 shows t h i s cor- rection t o be small except i n the transonic region, where r o l l i n g accel- erations become large. For t h i s reason, the accuracy l i n i t s i n t h e tran- sonic region (0.88 < M < 1.00) are about +20 percent, whereas a t subsonic and supersonic speeds the accuracy is about It10 percent.
Base- and internal-drag data were obtained from pressure measurements and therefore have different possible errors than the drag values based on acceleration measurements. The maximum possible errors i n both of these quantities due t o instrunent inaccuracy would be so small t h a t they would not change any three-decimal-place drag values used.
It i s believed t h a t the data presented i n t h i s report provide a good indication of t h e variation of the s t a b i l i t y derivatives with Mach number and t h e absolute values of these derivatives are a t l e a s t as accurate o r b e t t e r than indicated above.
RESULTS AND DISCUSS I O N L i f t and Trim Characteristics .
Lift.- Coefficients are based on t o t a l wipg area, excluding wing
-
f i l l e t area, a s shown i n figure 1. L i f t characteristics a s a function of angle of attack f o r some representative Mach numbers are given in figure 13(a). These values of CL represent the range covered a t t h e indicated Mach numbers. The variation of CL with a is essentially l i n e a r over t h e CL and M range covered by the t e s t s with the excep- t i o n of M = 0.86 where an abrupt break occurs a t CL = 0.75. Values of lift-curve slope CL taken over the l i n e a r portion of these p l o t s a a r e presented i n figure 13(b).
0 . 0.. . e.. . .e 0 . . . 0.. 0 .
0 . 0 . 0 . . 0 . . 0 . . ...
. . . . . .. . . . .
0 0 e . . • NACA RM ~56Kl-9 2 - ..
The power-on and power-off values of ' C ? : 'abtained from model A i n La addition t o unpublished tunnel r e s u l t s a r e presented f o r comparative pur- poses with t h e r e s u l t s obtained from model B . Data presenting t h e v a r i a - t i o n of CL with a from model A a r e l h i t e d i n b o t h l i f t range covered and quantity since t h e primary purpose of t h e i n v e s t i g a t i o n was t o d e t e r - mine t h e e f f e c t of t h e engine j e t exhaust on t h e drag and trim character- i s t i c s of t h e configuration. The d a t a from model A i n d i c a t e t h a t t h e r e C due t o f a i r i n g over t h e might have been some reduction i n power-off L, i n l e t s ; however, i n general, t h e agreement between t h e t h r e e sources i s considered good. There a r e no unusual v a r i a t i o n s o r t r e n d s i n l i f t - c u r v e slope over t h e Mach number range covered.
The f l i g h t time h i s t o r y of normal a c c e l e r a t i o n showed t h e presence of high-frequency o s c i l l a t i o n s a s t h e model pitched t o t h e higher l i f t c o e f f i c i e n t s below M = 0.93. These o s c i l l a t i o n s a r e believed t o repre- sent t h e b u f f e t - i n t e n s i t y r i s e , which occurred a t about a t CL = 0.59
M - 0.93 and CL - 0.65 a t M - 0.86 with t h e maximum amplitude being
ACL = 0.1. As a r e s u l t of t h e high frecpency of t h e o s c i l l a t i o n s (115 cps) and s i n c e obtaining b u f f e t information was not a primary purpose which can be obtained from of t h i s t e s t , t h e minimum amplitude of ACL t h e instrumentation used i s 0.03.
Trim.- The e f f e c t of power on t h e t r i m - l i f t c o e f f i c i e n t and angle The measured t r i m angle of a t t a c k with of a t t a c k i s shown i n f i g u r e 14.
respect t o t h e fuselage reference l i n e i s presented f o r both t h e power-on and t h e power-off portions of t h e f l i g h t . The values of power-on trim- l i f t c o e f f i c i e n t were obtained by correcting t h e measured-lift c o e f f i - c i e n t s f o r t h e t h r u s t component along t h e l i f t a x i s . Power-on produced a decrease i n trim angle of a t t a c k of approximately 1.1' and a t r i m - l i f t - c o e f f i c i e n t decrease of about 0.06 a t a Mach number of about 1.5. The model t h r u s t a x i s was below t h e center of g r a v i t y producing a pitch-up moment, thus a l l e v i a t i n g t o some extent t h e pitch-down e f f e c t induced by t h e j e t exhaust. With t h e t h r u s t a x i s through t h e center of g r a v i t y t h e model change i n trim with power on would have been s l i g h t l y g r e a t e r .
The decrease i n trim angle of a t t a c k corrected t o t h r u s t through t h e center of g r a v i t y was approximately 1.27' with a decrease i n t r i m - l i f t c o e f f i c i e n t of approximately 0.072. During power-on, burning of t h e pro- p e l l a n t caused a gradual s h i f t i n t h e center-of-gravity location. The power-off d a t a f o r t h e r e s t of t h e f l i g h t a r e f o r a center-of-gravity location of 17.8 percent c .
The jet-off pressure c o e f f i c i e n t s f o r t h e various o r i f i c e l o c a t i o n s shown i n f i g u r e 4 a r e presented i n f i g u r e 15. The d i s c o n t i n u i t y and temporary increase i n several of t h e c o e f f i c i e n t s a t a Mach number of about 1.5 a r e believed t o have been caused by i n t e r m i t t e n t burning of NACA RM ~ 5 - 9 propellant remnants. Orif ice qpi!&q @ lhorizontal stabilizer) is omitted a t high Mach nurribers due t o the fact t h a t this pressure varied with angle of attack and since it was measured intermittently it was impossible t o get a complete time history. None sf the ~ % b s r pressures appeared t o be influenced by changes i n angle of attack encountered.
Figure 16 shows the incremental change in pressure coefficient caused
by the j e t exhaust (5 = - Cp,power-off) for the power-on
porkion of the flight. Measurements prior t o power-on were used for In figure 16(a) a general increase i n pressure along the Cp,power-off.
bottom of the fuselage i s indicated with the most forward orifice showing l i t t l e change and the most rearward orifice showing the greatest increase.
Pressure coefficients on the side of the fuselage (fig. 16(b)) indi- cated that power-on caused an increase near the j e t and a gradual decrease t o a high negative change approximately two jet diameters t o the rear of the j e t exit. The base annulus pressures were increased considerably but the portion of the annulus inboard showed about 35 percent l e s s increase This effect is than the outboard portion of the annulus (fig. 16(c) ) .
believed t o be caused by the influence of the fuselage-tail-pipe juncture i n the vicinity of the base. Power-on produced an approximate change i n
pressure coefficient aCp = 0 . 1 1 for o r i f i c e number 8 (horizontal sta-
b i l i z e r ) but it i s not possible t o determine w h a t the change would have been with no angle-of-attack change. The small range of the r a t i o of
jet-exit s t a t i c pressure t o free-stream s t a t i c pressure ( f i g . 11) encoun-
tered i n f l i g h t precludes the determination of the effect of pressure r a t i o on any of the data presented; however, it i s noted that several of the incremental changes follow the same trend as the pressure ratio.
Basic drag.- The basic drag data from model B are presented in the These curves are for various Mach form of lift-drag curves i n figure 17.
numbers and l i f t ranges 8nd the drag values include both internal and base The mass-flow ratios a t which the t e s t s were conducted are given drag.
i n figure 18.
Minimum drag.- The variations of the lift coefficient for minimum
drag, t C ~ ) Cg,mjn and the minimum-drag coefficient CDymin as determined
from the lift-drag curves of figure 17 are presented as a function of Mach I include both internal
~ number i n figures 19 and 20. The values of CD,rnin
and base drag. Values of CD, and C D , ~ are also presented i n f i g - A t the higher horizontal-tail deflections the model did not ure 20.
oscillate t o minimum drag.
NACA RM ~ 5 6 ~ 1 9
Between M = 0.82 and M - 0.87, CD,min i s constant a t about
0.020. The drag r i s e occurs a t Bl = 0.90 t h e Mach number at which
(
and a t M = 1.10, CD,min has a value of 0.070. The drag dM continues t o increase gradually with Mach number and a t M = 1.83 has a value of CDjrnin = 0.074.
Base drag.- The base-drag d a t a were obtained from t h e base-pressure survey taken on t h e e x i t of t h e afterburner on model B. The base-drag c o e f f i c i e n t varied from about 0.001 a t subsonic speeds t o about 0.002-at supersonic speeds.
I n t e r n a l drag.- The values of internal-drag c o e f f i c i e n t determined from model B and presented i n f i g u r e 20 a r e n e a r l y a constant value of 0.005 from M = 1 . O 1 t o M = 1.84. N o subsonic values could be obtained s i n c e the duct became unchoked below M = 1.0; however, other t e s t s have shown the internal-drag l e v e l remains about t h e same a t subsonic and supersonic speeds f o r cases where t h e v a r i a t i o n i n mass-flow r a t i o i s small.
Jet e f f e c t s on drag.- The v a r i a t i o n of power-on and power-off drag c o e f f i c i e n t s with time at CL = 0.11 i s shown i n f i g u r e 21. The power- o f f data were obtained j u s t previous t o simulator f i r i n g and cannot be d i r e c t l y compared with t h e drag d a t a discussed from model B i n t h e pre- ceding paragraphs since t h e i n l e t s were f a i r e d over on model A. The power-off d a t a presented i n f i g u r e 21 a r e corrected t o zero base drag, and during power-on t h e base-drag c o e f f i c i e n t was n e g l i g i b l e . This drag comparison is not t h e difference i n t h e a i r p l a n e drag power-off and power-on, but shows t h e e f f e c t of t h e j e t exhaust on t h e e x t e r n a l drag.
The power-off total-drag c o e f f i c i e n t would b e g r e a t e r by t h e base-drag c o e f f i c i e n t and a l s o would involve a change i n i n l e t drag from a low i n l e t drag a t maximum mass flow t o a high i n l e t drag a t zero m a s s flow.
The d a t a indicate t h a t t h e power-on drag c o e f f i k i e n t i s equal t o o r a s much as 1 0 percent l e s s than t h e power-off drag c o e f f i c i e n t . This v a r i a t i o n i s believed t o b e due t o inaccuracies i n t h e determination of t h r u s t .
The average power-on drag i s l e s s than power-off, b u t t h e incre- ment i s within t h e accuracy of t h e data.
Longitudinal S t a b i l i t y S t a t i c . - The 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 c h a r a c t e r i s t i c s of t h e configuration with open ducts, model B, a r e shown i n f i g u r e s 22 t o 24.
A l l moment d a t a were taken about t h e center-of-gravity l o c a t i o n a t
-
Some representative curves of pitching-moment coefficient C, as a function of f o r various t a i l deflections and 3lach numbers are pre- CL
-
sented i n figure 22.
A t Mach numbers above 1-09 t h e curves presented i n f i g n c 22(a) are l i n e a r f o r the CL range covered; however, a t M = 1.09 there i s a s l i g h t change i n pitching-moment slope a t CL = 0.05. Fig- ure 22(b) shows t h a t at M = 0.94 and M = 0.95 there is a change i n slope beginning a t CL = 0.10. The curve a t M = 0.85 shows an almost Ilr;es.x- ~ ~ i ~ ~ l a t i o i i of Cm with CL in the lift range from CL = 0.56 t o t h e point where an abrupt change i n slope occurs a t CL = 0 . 8 3 . These pitching-moment curves a t the subsonic Mach numbers, where a large l i f t range w a s covered, indicates a reduction i n s t a b i l i t y a t the higher l i f t coefficients. The measured periods P of the short-period longitudinal o s c i l l a t i o n s resulting from t h e abrupt control movement are given i n fig- ure 23. These values were used t o calculate the longitudinal s t a b i l i t y parameter \ by the following relation:
The values of Cm, i n conjunction with C L ~ were used t o compute
aerodynamic-center values f o r comparison with those obtained from the slopes of t h e pitching-moment curves which are shown i n figure 24.
The slopes of t h e pitching-moment curves were taken over the l i n e a r portion of the curves ( f i g . 22). The aerodynamic center moved from a location of 62 percent mean aerodynamic chord a t M = 0.88 t o its most r e w a r d location of 85 percent mean aerodynamic chord a t about M = 1.40 and then decreased t o a value of 81 percent mean aerodynamic chord a t M = 1.72.
The aerodynamic-center location w a s obtained a t several isolated times from the f l i g h t time history of model A. These data are plotted i n figure 24 f o r comparison. The data i n general show good agreement with those from model By but because of the s c a t t e r of t h e data it i s f e l t t h a t t h e e f f e c t of t h e j e t exhaust on t h e center of pressure should not be interpreted from these data.
Basic pitching moment.- The basic pitching-moment coefficient Cm a t zero t a i l deflection and zero angle of attack i s shown i n figure 25.
The wing of t h e model had lo of positive incidence r e l a t i v e t o the model center l i n e , which was used as the reference i n t h i s t e s t . Since most of the tunnel data used the wing as the reference, figure 25 shows
C,o
computed by using a = 0' . r e l a t i v e to t h e wing a s well a s t o t h e model center l i n e . Unpublished wind-tunnel data are plotted f o r comparison . . 0.. 0 .
...............
. . . . . . . . . . . . . . . .
. . . . . . . . . .
. . . . . . . .
20 NACA RM ~ 5 6 ~ 1 9 ............
and the agreement i s good a t supersonic speeds. A value of C, was computed a t M = 0.88 by using rocket-model values of and CL, CmcL and unpublished wind-tunnel values of control effectiveness. The agree- ment between t h i s value of C and the tunnel value a t M = 0.90 i s
mo
good.
calculated f o r 0' wing angle of attack vary from Values of Cm- Damping i n pitch.- The damping-in-pitch characteristics are given by the parameters
t and $ + C , d which are presented i n figures 26
and 27, respectively. These parameters were determined from an analysis of the r a t e of decay of the transient short-period oscillations resulting from abrupt horizontal-tail movements. Figure 27 shows a decrease i n M = 0.90 and 1.02 followed by a gradual increase pitch damping between t o M = 1.40 and a more rapid increase between M = 1.40 and M = 1.75.
Pitch-damping data from the rocket t e s t of a model having a horizontal t a i l of aspect r a t i o 4.33 ( r e f . 10) show the sane general variation of with Mach number. The configuration t e s t e d i n t h i s investiga-
% +
t i o n was dynamically stable without any unusually large reductions i n damping i n pitch over the speed range covered.
The horizontal s t a b i l i z e r , however, did not remain a t a fixed angle but oscillated about a mean trim l i n e i n phase with a as a r e s u l t of the high hinge moments a t supersonic speeds. The maximum A6 of t h i s oscillation was i n the order of 0.5' with an average value of about 0.25'.
The s t a t i c derivatives were corrected f o r t h i s effect; however, no dynamic corrections were made f o r t h i s effect.
Longitudinal control effectiveness.- The effectiveness of the a l l - movable horizontal t a i l of aspect r a t i o 3.30 i n producing l i f t and pitching moments i s given i n figures 28 and 29. The l i f t coefficient per degree of t a i l deflection C has a value of 0.0103 a t about M = 1.05 and L6 decreases gradually with increase i n Mach number u n t i l a t M = 1.70 the value of C i s 0.0070. Pitching-moment effectiveness C & varies L6 from -0.036 at M = 1.00 t o a value of -0.023 a t M = 1.70.
Two other longitudinal-control effectiveness p a m e t e r s , the change i n trim angle of attack per degree of t a i l deflection Au/A~ and the r a t e of change i n t r i m - l i f t coefficient with t a i l deflection ACL/A6, are presented as functions of Mach number i n figures 30 and 31, respectively.
The h o r i z o n t d t a i l i s an effective pitch control throughout the Mach number range covered. A l l the effectiveness parameters show gradual variations with Mach number.
Hinge moments.- The hinge-moment characteristics of t h e horizontal t a i l i n t h e form of t h e variation of hinge-moment coefficient with angle of attack C and t h e variation of hinge-moment coefficient with tail ha deflection Chg are given i n figures 32 and 33. The parameter
ch, 1
was obtained from t h e l i n e a r portion of p l o t s of Ch against a (approxi- mately 0' t o 4') and was determined by the method discussed in Chs reference 2. The horizontal t a i l was hinged a t 26.5 percent of t h e t a i l mean aerodynamic chord and had an unswept hinge l i n e . Figure 32 shows that cha varies from a value of 0.0020 a t M = 0.82 t o cha = -0.0075 a t M = 1.55 and a t M = 1.72 had a value of -0.0055. Figure 33 shows a steady decrease i n C from -0.0170 at M = 1.07 t o Ch = -0.0073 B Lateral S t a b i l i t y The l a t e r a l derivatives obtained from model C, with t h e exception I of the rolling-effectiveness parameter pb/2V, a r e all presented as groups of data points. The r e s u l t s give a visual estimation of the accuracy of I determining each derivative. Also shown are t h e e f f e c t s of neglecting the cross derivatives and t h e product-of-inertia terms, as explained i n t h e "Analysis" section. Two sections of t h e time history which show some of the quantities measured and t h e lack of damping of t h e $ oscil- l a t i o n a r e shown i n figure 34. The vectorial data necessary t o obtain the l a t e r a l s t a b i l i t y derivatives by t h e time-vector method are presented i n t h e following figures: variation of side-force coefficient with angle of s i d e s l i p a t various Mach nmibers ( f i g s . 35 and 36), the Dutch r o l l I frequency ( f i g . 37), t h e phase difference between t h e r o l l r a t e and t h e angle-of-sideslip oscillations and between the side-force coefficient
and t h e angle-of-sideslip oscillations ( f i g . s), and t h e amplitude r a t i o
of t h e r a t e of r o l l t o angle of sideslip ( f i g . 39).
Static. - The dihedral-effect derivative ( f i g . 40) shows l i t t l e
c z ~
chmge i n value with change of C and indicates the dihedral e f f e c t 2 r w a s adequate.
(fig. 41) is shown f o r the two The s t a t i c l a t e r a l s t a b i l i t y 'na C The values of C methods of computation and f o r the change i n n$ 9.
based on a one-degree-of-freedom analysis of the periods are s l i g h t l y . . 0.. 0 . ...............
. . . . . . . . . . . . . . . .
. . . . . . . . . .
. . . . . . . .
22 o . e . . . . . . . . . NACA RM ~56K.19 The d i f f e r e n c e d i f f e r e n t from those found by t h e vector computations.
i s a measure of t h e e f f e c t of neglecting t h e product-of-inertia terms.
The change i n C has a n e g l i g i b l e e f f e c t on C n~ * Dynamic.- The roll-damping d e r i v a t i v e C i s presented i n f i g u r e 42, 2~ where t h e apparent s c a t t e r i s mainly a r e s u l t of t h e v a r i a t i o n of $ i n f i g u r e 38. Theoretical values a r e shown a s computed from references 1 1 and 12. The r o l l damping remained near t h e same l e v e l throughout t h e speed range and agreed with t h e t h e o r e t i c a l v , d u e s .
Presented i n f i g u r e 43 i s t h e dynamic-lateral-stability d e r i v a t i v e which shows a g r e a t e r e f f e c t of t h e change i n C The deriv-
Cnr - CnB
n ~ '
a t i v e Cnr - C n i remains negative throughout t h e speed range, b u t - t h e
The reason f o r l i t t l e o r no damping model motion showed l i t t l e damping.
observed i n t h e model motion was t h e r e s u l t of l a r g e r o l l coupling due t o t h e r e l a t i v e l y l a r g e product of i n e r t i a . For t h e angle of a t t a c k of t h i s t e s t t h e out-of-phase yawing moment contributed by t h e product-of- i n e r t i a term i s of opposite s i g n and l a r g e r magnitude than t h a t contrib- uted by Cnr - C n i ( s e e f i g . 1 2 ) .
p b / 2 ~ . - The s t i f f n e s s c h a r a c t e r i s t i c s Effect of a e r o e l a s t i c i t y on E, and F a r e compared with t h e scaled-down of t h e wings of models D, s t i f f n e s s c h a r a c t e r i s t i c s of t h e assumed f u l l - s c a l e a i r p l a n e wing i n f i g u r e 44.
The v a r i a t i o n of t h e rolling-ef f e c t i v e n e s s parameter p b / 2 ~ with Plach number i s shown i n f i g u r e 45. These p b / 2 ~ values have been cor- r e c t e d by t h e method of reference 13 f o r t h e s m a l l wing and t a i l incidence angles r e s u l t i n g from construction t o l e r a n c e s . Included i n f i g u r e 45 i s t h e rigid-wing r o l l i n g effectiveness which was estimated by cross p l o t t i n g t h e data f o r 25O a i l e r o n d e f l e c t i o n against 8 ' /m' and making a s t r a i g h t l i n e extrapolation t o 8'/m' = 0.
Flexible-wing r o l l i n g effectiveness a t sea l e v e l and 35,000 f e e t was estimated from t h e d a t a f o r 25O a i l e r o n d e f l e c t i o n by assuming t h a t t h e i s proportional t o t h e dynamic
l o s s i n r o l l i n g effectiveness 1 - @
pressure q. The v a r i a t i o n of 1 - @' and q with Mach number f o r t h e
flexible-wing model with 25G a i l e r o n d e f l e c t i o n at t e s t a l t i t u d e s i s shown in f i g u r e 46. Estimated flexible-wing r o l l i n g effectiveness a t sea l e v e l and 35,000 f e e t i s compared with estimated rigid-wing r o l l i n g effectiveness i n f i g u r e 47. Figure 47 shows t h a t t h e l o s s i n r o l l i n g effectiveness due t o a e r o e l a s t i c i t y v a r i e d from about 6 percent a t 35,000 f e e t t o about 2 ( percent a t s e a l e v e l at a Mach number of 0.5 and from about 20 percent a t 35,000 f e e t t o about 84 percent a t s e a l e v e l a t a Mach number of 1.2.
0 . 0 .
. . ... 0 . . 0 .
NACA RM ~ 5 6 ~ 1 9 : . t - 0. . 0 . .. .. . . .. ... . 0. .
Results fromthe flight t e s t s of models of a fighter-type aiqlme i n the Mach number M range from 0.5 t o 1.9 indicate the following con- clus ions : 1. The jet-engine simulator caused a decrease i n trim angle of attack of approximat.ely 1 , 2 p a d a <&ease I r , trli;i-lift coefficleiit, of G.07.
2. The pressure coefficient for the base annulus was increased, but the increase was smaller on the portion of the annulus adjacent t o the fuselage.
3 . Pressure coefficients on the side and bottom of the fuselage As the distance down- indicated a positive increment near the jet exit.
stream of the j e t exit increased, the increment on the bottom of the fise- lage increased, whereas the increments on the side decreased t o a negative peak.
4. The drag r i s e begins a t M = 0.90. The minimum-drag coefficient (including base and internal drag) has a value of 0.02 a t M = 0.87, an increase t o 0.070 a t M = 1.1, and then a gradual increase t o a value of 0.074 a t M = 1.83.
5. The s t a t i c longitudinal s t a b i l i t y is reduced a t the higher l i f t coefficients a t subsonic speeds.
6. The aerodynamic-center location i s a t 62.0 percent mean aero- M = 0.88 and reaches i t s most rearward position of 85.0 dynamic chord a t percent mean aerodynamic chord a t M = 1.4.
7. The pitch-damping parameters indicated that the configuration possessed dynamic longitudinal stability without any unusually large reductions over the speed range covered.
8. Variation of horizontal-tail effectiveness with Mach rider from 1.00 t o 1.70 was gradual and the tail remained an effective control f o r producing forces and moments throughout the speed range.
9. The pitching-moment coefficient a t o0 wing angle of attack and
O0 t a i l deflection decreases from a positive value of 0.076 a t a Mach nmber of 1.06 t o 0.048 a t a Mach number of 1.77.
10. The r o l l damping remained near the same level throughout the speed range tested and agreed well with some theoretical values.
11. There was an adequate dihedral effect.
NACA RM ~ 5 6 ~ ~ 9 12. The cros , were not determined, b u t t h e i r e f f e c t s on hown t o be small.
13. The l o s s i n r o l l i n g effectiveness due t o a e r o e l a s t i c i t y varied from about 6 percent a t 35,000 f e e t t o about 27 percent a t s e a l e v e l at and from about 20 percent a t 35,000 f e e t t o about 84 percent a t M = 0.5 sea l e v e l a t M = 1.2.
Langley Aeronautical. Laboratory, National Advisory Committee f o r Aeronautics, Langley Field, Va., October 31, 1956.
NACA RM ~ 5 6 ~ 1 9 1. DeMoraes, Carlos A., IZaggicbotho~, Willim K . , jr., and Falanga, Ralph A.: Design and Evaluation of a Turbojet Exhaust Simulator, Utilizing a Solid-Propellant Rocket Motor, f o r Use in Free Flight Aerodynamic Research Models.
W A RM ~34115, 1954.
2 ; Y i t c h a , G r e L., Stz'v-ens, Zoseph E., and Harris, Harry P. : Aero- dynamic Characteristics and Flying Qualities of a Tailless Triangular- Wing Airplane Configuration -4s Obtdned Fr3m Flights of Rocket- Propelled Models a t Wansonic and Low Supersonic Speeds. NACA (supersedes NACA RM LgL07. ) TN 3753, 1956.
3. G i l l i s , Clarence L., Peck, Robert F., and Vitale, A. James: Preliminary Results From a Free-Flight Investigation a t Trmsonic and Supersonic Speeds of t h e Longitudinal Stability and Control Characteristics of an Airplane Configuration with a Thin Straight Wing of Aspect Ratio 3.
NACA RM L9fC25, 1950.
4. Ikard, Wallace L.: An Air-Flow-Direction Pickup Suitable f o r Telem- otering Use on P i l o t l e s s Aircraft. NACA TN 3799, 1956. (supersedes NACA RM ~ 5 3 ~ 6 . ) 5. Faget, Maxime A., Watson, Raymond S,, and B a r t l e t t , Walter A,, Jr.: Free-Jet Tests of a 6.5-~nch-~iameter Ram-Jet Engine a t Mach Nuibers of 1.81 and 2.00. NACA RM ~ 3 0 ~ 0 6 , 1951.
6. Mitchell, Jesse L., and Peck, Robert F.: Investigation of t h e Lateral S t a b i l i t y Characteristics of the Douglas X-3 Configuration a t Mach Numbers From 0.6 t o 1 . 1 b y Means of a Rocket-Propelled Model. NACA RM ~54120, 1955.
7. D'Aiutolo, Charles T., and Henning, Allen B.: L a t e r d S t a b i l i t y Char- a c t e r i s t i c s a t Low L i f t Between Mach Nuribers of 0.85 and 1.15 of a Rocket-Propelled Model of a Supersonic Airplane Configuration Having a Tapered Wing With Circular-Arc Sections and 40' Sweepback. NACA RM L55A31, 1955.
8. G i l l i s , Clarence L., and Chapman, Rowe, Jr.: Effect of Wing Height and Dihedral on the Lateral S t a b i l i t y Characteristics a t Low Lift of a 45' Swept-Wing Airplane Configuration As Obtained From Time- Vector Analyses of Rocket-Propelled-Model Flights a t Mach Numbers From 0.7 t o 1.3. NACA RM ~ 5 6 ~ 1 7 , 1956.
9. Sandahl, Carl A., and Marino, Alfred A.: Free-Flight Investigation of Control Effectiveness of Full-Span 0.2-Chord Plain Ailerons at High Subsonic, Transonic, and Supersonic Speeds To Determine Some Effects of Section Thic weepback. NACA RM L7D02, 1947.
. . . . . . .
. . .. . a. . .
. . . . . .
NACA RM ~ 5 6 ~ 1 9 . . . . . . . . . .
-*.. , +
10. Peck, Robert F., and Hollinger, James A.: A Rocket-Model Investiga- tion of the Longitudinal S t a b i l i t y , Lift, and Drag Characteristics of the Douglas X-3 Configuration With Horizontal T a i l of Aspect Ratio 4.33. NACA RM L53Fl9a, 1953.
11. Malvestuto, Frank S., Jr . , Margolis, Kenneth, and Ribner, Herbert S . : Theoretical L i f t and Damping i n Roll a t Supersonic Speeds of Thin Sweptback Tapered Wings With Streamwise Tips, Subsonic Leading Edges, and Supersonic Trailing Edges. NACA Rep. 970, 1950. (supersedes NACA TN 1860. ) 12. Martin, John C., and Jeffreys, Isabella: Span Load Distributions Resulting From Angle of Attack, Rolling, and Pitching f o r Tapered
Sweptback Wings With Streamwise Tips - Supersonic Leading and
Trailing Edges. NACA TN 2643, 1952.
13. Strass, H. Kurt, and Marley, Edward T.: Rolling Effectiveness of A l l - Movable Wings a t Small Angles of Incidence a t Mach Numbers From 0.6 t o 1.6. NACA RM L5lH03, 1951.
NACA R M ~ 5 6 ~ ~ 9 COMPARISON BETWEEN P F K F O R M A N C E S O F S m O R
AND PRATT & WHITNEY J 5 7 TUIiBOJE'I' ENGINE
( ~ i m u l a t o r performance corrected t o f'ull scale and a l t i t u d e of 35,000 feet; all data f o r one enginq - Turbojet Rocket simulator design J
J e t stagnation temperature, %' abs
. . . 4,000
3, 200 Specific heat r a t i o . . . . . . . . . .
1-25 1.27 Ratio of j e t stagnation t o free-
. . . . . . . . stream s t a t i c pressure
6.3 t o 7.2 7.10 J e t thrust, l b . . . . . . . . . . . . .
15,200 t o 15,900 15,600 Average j e t gross weight flow,
lb/sec . . . . . . . . . . . . . . . . 120 122
J e t e x i t area (afterburner condition), sq ft . . . . . . . . . .
3 99 3.98 NACA RM ~56K19 TABLE I1 PHYSICAL CHARACTERISTICS O F M O D E L S A. B . AND C Wing:
. . . . . . . . . . . . . . . . Area (theoretical). sq ft
Span. f t . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . Aspect r a t i o
. . . . . . . . . . . . . . .
Mean aerodynamic chord, ft
. . . . . . . . . . . . . . . . . . . . . . . Taper r a t i o
. . . . . . . . . . . . . Sweepback of leading edge, deg
. . . . . . . . . . . . . Sweepback of t r a i l i n g edge. deg
Incidence angle (with respect t o model center l i n e ) . deg
. . . . . . . . . . . . . . . . . . . Dihedral angle, deg
a ~ o o t thickness (theoretical). percent chord . . . . . . .
. . . . . . . . . . . . . . &Tip thickness, percent chord
Horizontal t a i l :
. . . . . . . . . . . . . . T o t a l area. sq f t . . . . . . . . 1.17
Span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . 1.97
Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . . 3.30
. . . . . . . . . Mean aerodynamic chord. ft . . . . . . . . 0.62
Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . 0.46
. . . . . . . Sweepback of leading edge. deg . . . . . . . . 39.80
Sweepback of t r a i l i n g edge. deg . . . . . . . . . . . . . . . 20.93
. . . . . . . . . . . . . Dihedral angle. deg 26.50 . . . . . . . .
. . . . . . . . . . . . Root a i r f o i l section NACA 65A007 (modified)
NACA 65~006 (modified)
. . . . . . . . . . . . . Tip a i r f o i l section
chord t o Tail length (25 percent wing mean aerodynamic
. . . . . . . . 3.69
25 percent t a i l mean aerodynamic chord) . .
Fuselage : . . . . . . . . . . . . . . . . . . . . . . . . .
Length. f t 8.38
. . . . . . . . . . . . . . . . . . . . . Width (maximum). f t 0.96
. . . . . . . . . . . . . . . . . . . . Height (maxinun). f t 0.88
. . . . . . . . . . . . . . 0.66
Maximum cross-sectional area. sq ft b ~ u c t s (one side):
. . . . . . . . . . . . . . . . . . . . . . ~ n l e t area. sq ft 0.0625
. . . . . . . . . . . . . . . . . . . . . . 0.0474
Exit area. sq ft Area a t compressor face (excluding area blocked
. . . . . . . . . . . . . . . by accessory housing). sq f t 0.0802
Vertical t a i l :
. . . . . . Area above fuselage (dorsal excluded). sq ft
. . . . . . . . . . . . . . . . . . . . . . . . Span. ft
. . . . . . . .
Mean aerodynamic chord (theoretical). ft Aspect r a t i o (theoretical) . . . . . . . . . . . . . . .
Sweepback angle a t leading edge. deg . . . . . . . . . .
Sweepback angle a t t r a i l i n g edge. deg . . . . . . . . . . . .
airf'oil ROO. s . . . . . . . . . . . . . . . . . . . . . . . NACA
Tip a i r f o i l section . . . . . . . . . . . . . . . . . . NACA
&Root and t i p a i r f o i l sections are NACA 65~007 and 65~006. respec- tively. modified by extending the chord 5 percent forward of the 16.04- percent-chord l i n e and adding 1.67 percent positive camber .
b ~ c t s were f a i r e d over on model A .
e m e m . e m m e me. . e . . 0.
i we . e m . . . . . 0 . e m m e
NACA RM ~sICl-9
e m . .. e m
.
0. e m .. . om. m e
TABLE I11 WEIGHT AND BALANCE DATA FOR MODELS A, B, AND C * Moment of inertia, Center-of -gravity slug-f t 2 Wing loading, Weight, position, Model , l b lb/sq ft percent E I z Ix IY Rocket f u e l included i n model
----- ----
A 21.2 55-30 489.75 85.3 Models without rocket f u e l
----- ----
A 17.80 32-64 455.81 79.3
----- --- -
B 16. 90 405.25 54.95 70.5
"c 46.30 66.0
47.78 3.57 17 30 379.40 a~riclination of principal a x i s was -4.2'.
NACA RM ~ 5 6 ~ ~ 9 .
TABLE I V ESTIMATED ACCURACIES O F VARIOUS MFASURED QUANTITIES [ A l l increments may be p o s i t i v e or n e g a t i v d
Estimated accuracy at -
r Quantity Mode 1 M = 1.7 bi = 0.85 M, percent 1.0 2- 5 A, B, C
-----
1.0 M, percent D, E, F q, percent 2.0 5-0 A, B, C
-----
q, percent 3 0
D, *, F
W, percent 5 5 A, B, C IX, percent 3-5 3 5 A, B, C 2.0 2.0 Iy, percent A, B, C 2 . 0 IZ, percent 2.0 A, 5, C 8.0
8. o
% IXZ, percent
5 5 a, deg A, B, C 5 5 P , deg B, C .2 .2 B 6, deg . O O ~ .10 P, sec B
, percent
C 3.0 3 0 2.0 2.0 c
lyl, percent
W, percent 2 5 C 2- 5 3.0 C 3.0
%, deg
a ~ r i m a r i l y due t o estimated accuracy of p r i n c i p a l axis i n c l i n a t i o n (112O) Figure 1.- Three-view drawing of models B and C . Model A is essentially similar except for wing root inlets, which were faired for installation of rocket-motor simulator. Broken lines indi- cate plan form of theoretical wing. All dimensions are in inches.
( a ) Side view. L-88336. 1 (b) Top view. L-88337. 1 Figure 2.- Photographs of model A.
e t r i c a l about & Figure 3.- Sketch of rocket simulator. All dimensions are in inches.
Model F.S. 91.65, R.F! 2.89 F. S. 88.72, R.F! 2.59
Ref. plane zero - ducting
Figure 4.- Pictorial layout of orifice locations.
Figure 5.- Photograph of model B.
NACA RM L56KLg Model L (a) Equivalent body of revolution.
(b) Area distribution.
Figure 6.- Area distribution and equivalent body of revolution of models B and C.
Figure 7.- Photograph of typical model D, E, and F.
L-87108.1 Figure 8 . - Sketch of configurations D, E, and F. All dimensions are in inches.
NACA R M ~ 5 6 ~ ~ 9 L-86652. 1 Figure 9.- Photograph of model-booster combination on launcher.
.......
...............
. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . .
4 0 ............. NACA RM ~ 5 6 ~ 1 9
Figure 10.- Reynolds number variation with Mach number for all tests.
NACA RM L56KLg p direction Sideforce eauation:
rnvlbl, rnv13.l - rnvl+la -Id = 0
-- qSlPI qs IPI q S l P I I P I Figure 12.- Typical vector solution; body-axis system.
0. . a . . 0 . 0. . 0.. . 0. . 0.
0 . . a . . 0 . . . 0 . 0 . 0 .
... . . . 0 . 0 0 . 0 0 .
Rolling-moment equation : Figure i2.- Continued.
. . 0.. 0 .
...............
. . . . . . . . . . . . . . . .
....
.......
. . . . . .....
44 . . e . . e . . NACA RM ~ 5 6 ~ 1 9
Yawing -moment equation Figure 12.- Concluded.
(a) Lift coefficient as a f'unction of angle of attack.
Figure 13.- Lift characteristics of model B.
(a) Concluded.
Figure 13. - Continued.
(b) Variation of lift-curve slope with Mach number.
Figure 13.- Concluded.
(a) Trim-lift coefficient.
(b) Trim angle of attack.
Figure 14.- Power-on and power-off variation of trim conditions with Mach number.
a a a a a • a a a- • -am a . m a a a m a . a * . . a .
a a . a . a .
m a . . a . a . . a . a . 0 .
a m . a a o a a a * .
a - a .
. a . a . a a . . . * a NACA RM ~ 5 6 ~ 1 9 49 M (a) Orifices 1, 2, 3, and 4 (bottom of fuselage).
(b) Orifices 5, 6, znd 7 (side of fuselage).
(c) Grifices 8, 9, and 10 (horizontal stabilizer and nacelle base).
Figure 15.- Power-off pressure-coefficient variation with Mach number.
NACA RM ~ 5 6 ~ 1 9 t. .OC ( a ) O r i f i c e s 1, 2, 3, and 4 (bottom of f u s e l a g e ) .
8 . 0 8 . 4 8 . 8 9 . 2 9 . 6 10.0 1 o . h 10.8 11.2 1 1 . 6 t. see ( b ) O r i f i c e s 5 , 6, and 7 ( s i d e of f u s e l a g e ) .
( c ) O r i f i c e s 8, 9, and 1 0 ( h o r i z o n t a l s t a b i l i z e r and base).
Figure 16.- Variation with time of t h e incremental change i n pressure c o e f f i c i e n t due t o power e f f e c t s .
. . . * * * * * * * a m * . . .
a . ** . a 0 * . . a .
NACA RM ~ 5 6 ~ ~ 9 e k e a -
Figure 17.- Variation of dreg coefficient with lift coefficient from
model B . Drag coefficient includes internal and base drag.
NACA RM L56~19 (b) 8 = -5*5c.
Figure 17.- Concluded.
NACA RM L56K19 Figure 18.- Duct mass-flow ratio.
Figure 19.- L i f t c o e f f i c i e n t f o r minirmun drag.
Figure 20. - Drag c o e f f i c i e n t a s a f'unction of Mach number (from model B) .
Figure 21.- The variation of power-on drag coefficient with time for a lift coefficient of 0.011.
shown for comparison.
Power-off external drag coefficient for CL = 0.11 (a) M 2 1.0.
Center of gravity Figure 22.- Variation of pitching-moment coefficient with lift coefficient.
at 0.169;; model B.
(b) M < 1.0.
Figure 22.- Concluded.
M3del B.
Figure 23.- Period of the longitudinal oscillation.
Figure 24. - Aerodynamic-center location.
- Rocket-model test
0 Calculated with rocket-model data A Unpublished tunnel data (aw, = 0') Figure 25.- Basic pitching-moment coefficient.
Figure 26. - Time t o damp t o half amplitude. Model B.
Figure 27.- Pitch-damping parameter. Center of gravity at 0.169c'; model B.
,8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 M Figure 28.- Control lift effectiveness.
Model B.
Ti'
...
Center of gravity at 0.:169c'; model B.
Figure 29.- Control pitching effectiveness.
Figure 3 . - Change in angle of attack per degree of tail deflection.
Figure 31.- Change in lift coefficient per degree of tail deflection.
.....
. .
'1 .
Figure 72.- Effect of Mach number on Cb. Model B.
l .
.
. *
.
. .
.
e . .
. l
. .
...
. .
.....
.....
. .
.
.....
e....
e . .
l .
.....
. l
l ..
Figure 33.- Effect of Mach number on Chg. Model B.
- i m e , s e c 3 , rad \ 3ec 4 -10 0, 9 d e g 4 . 1 1 .
-4 I I _
-
r i
-
/ \ /-',
/ / /
. \, \, a, 0 \, /) \</ '-1 e e F, ," ,"
\/
- -4 1 1 . 1 1 1 1 . 6 11.6 12.C 1 . 1.4 12.6 1 . 13.0 15.2 T i r e , s e c Figure 34.- Time history of some of the quantities measured.
Model C.
NACA RM ~ 5 6 n g Figure 35.- Variation of side-force coefficient with angle of side slip.
Model C.
NACA RM ~ 5 6 ~ 1 9 Figure 36.- Side force due to angle-of-sideslip derivative. Model C.
NACA RbT ~56Ki-g w, 12 r a d i a m sec
1 . 0 1 *2
Figure 37.- Frequency of Dutch roll oscillations. Model C.
NACA RM L56KLg Figure 38.- Phase angles of r o l l r a t e and side-force c o e f f i c i e n t t o angle of s i d e s l i p . Model C.
Figure 39.- Amplitude r a t i o of r o l l r a t e t o angle of sideslip. Model C.
Figure 40.- Dihedral-effect derivative.
Model C .
NACA RM L ~ ~ K I - 9 Figure 41.- Static lateral stability. Model C.
- Reference 11
--- Reference 1 2
Figure 42.- Roll-damping derivative.
Model C.
NACA Rl4 ~ 5 6 ~ 1 9 Figure 43.- Dynamic-lateral-stability derivative. Model C.
NACA RM ~ 5 6 ~ 1 9 a rl
A
<
a 2
(d d k \ .)
-2 1
o 4 8 12 16 2 o
Span perpendicular to model center line, in.
4 8 1 2 16 20
Distance along 48.07-percent-chord line, In.
Figure 44.- Stiffness characteristics of model wings coqared with scaled stiffness airplane wing.
NACA RM ~ 5 6 ~ 1 9
. Rigid wing (83 t ima ted )
- - - Stiff wing, ea=250
model D,
-- Flexible wing, 6 , = 1 5 O model E
wing, 6 , ~ 2 5 ~ m n A a l ?7 Figure 45. - V a r i a t i o n of rolling e f f e c t i v e n e s s parameter p b / 2 ~ with Mach number.
NACA R M ~ 5 6 ~ ~ 9
q and 1 - @ I f o r t h e f l e x i b l e -
Figure 46. - V a r i a t i o n w i t h Mach number of
wing model w i t h 25' a i l e r o n d e f l e c t i o n .
NACA RM L S K l g . 1 6
. 12
.08 35,000 feet +.
*4 * 6 * 8 1 *O 1 . 2
1.4
M
Figure 47.- Comparison of rolling effectiveness of the flexible wing at
sea level and 55,000 feet with rigid-wing rolling effectiveness.
8 , = 2 5 ' .
NACA - Lnngley Field. V 4