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NASA TM X-1207 TRANSONIC AERODYNAMIC DAMPING AND OSCILLATORY STABILITY IN YAW AND PITCH FOR A MODEL O F A VARIABLE-SWEEP SUPERSONIC TRANSPORT AIRPLANE By B r u c e R. Wright and Benjamin T. Averett Langley R e s e a r c h Center Langley Station, Hampton, Va.
NATIONAL AERONAUTICS AND SPACE ADMlN I STRATI ON F o r s a l e by t h e C l e a r i n g h o u s e for F e d e r a l Scientific and T e c h n i c a l Information
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TRANSONIC AERODYNAMIC DAMPING AND OSCILLATORY STABILITY I N YAW AND PITCH F O R A MODEL O F A VARIABLE-SWEEP SUPERSONIC TRAIGPORT AIRPLANE By Bruce R. Wright and Benjamin T. Averett Langley Research Center SUMMARY Wind-tunnel measurements were made i n the Langley 8-foot transonic pressure tunnel t o determine t h e aerodynamic damping and o s c i l l a t o r y s t a b i l i t y i n yaw and p i t c h f o r a model of a variable-sweep supersonic transport airplane (designated SCAT 15). A l l t e s t s were made at an o s c i l l a t i o n amplitude of 1 ' with the use of a forced-oscillation technique f o r angles of a t t a c k from - 2 O t o 16O. The yaw tests were made a t Mach numbers from 0.40 t o 1.20 with corresponding Reynolds numbers, based on t h e mean aerodynamic chord of t h e f u l l y swept wing, from 3.1 x lo6 t o 5.8 x lo6. The p i t c h t e s t s were made only at a Mach number of 0.80 a t a Reynolds number of 5.0 x lo6.
For t h e model with t h e wing panels swept 2 5 O , t h e yaw damping w a s p o s i t i v e and generally w a s l i n e a r with angle of a t t a c k a t subsonic Mach numbers f o r t h e lower angles of attack. Both the damping and s t a b i l i t y i n yaw increased with increase i n v e r t i c a l - t a i l s i z e . Above an angle of a t t a c k of about 12O, however, addition of v e r t i c a l tails decreased t h e damping and r e s u l t e d i n negative damping a t a Mach number of 0.80.
For a wing-sweep angle of 75' at t h e lower angles of attack, t h e damping and s t a b i l i t y i n yaw were p o s i t i v e and increased with v e r t i c a l - t a i l s i z e . Above about 6 O , t h e yaw damping and s t a b i l i t y parameters were very e r r a t i c and showed no systematic variations. Positive damping i r i p l t c h m2 p s i t i ~ e values of t h e Oscillatory-longitudinal-stability parameter were exhibited f o r a l l angles of a t t a c k at a Mach number of 0.80 f o r a wing-sweep angle of 2 5 O .
Removal of t h e engine nacelles produced appreciable e f f e c t s on t h e yaw parameters at t h e higher angles of a t t a c k . Only s l i g h t e f f e c t s on t h e yaw damping and s t a b i l i t y parameters were determined f o r t e s t s with engine i n l e t s plugged at Mach numbers of 0.95 and 1.20 f o r a wing-sweep angle of 7 5 O .
INTRODUCTION A commercially successful supersonic transport airplane must have suitable performance, stability, and control characteristics in the design cruise condi- tion and all other flight conditions. Therefore, in order to provide research information for the development of a successful supersonic commercial transport airplane, the National Aeronautics and Space Administration has undertaken a program to determine experimentally the aerodynamic characteristics of a number of proposed configurations.
Presented herein are the transonic aerodynamic damping and oscillatory- stability characteristics in pitch and yaw of one of the supersonic commercial air transport configurations designated SCAT 15. This configuration had a variable wing geometry in order to meet the requirements of both high- and low- speed flight. Both fixed and variable-sweep wing panels were employed. The fixed wing panel had a sweepback angle of 7 5 O at the leading edge. The leading edge of the variable-sweep portion of the wing was swept back at an angle of 25O for low-speed flight, and this portion merged with the fixed portion to form an arrow wing for supersonic flight.
The vertical and horizontal tails were mounted on the tips of the fixed wings as shown in figure 1.
The static-stability characteristics for the SCAT 15 configuration are pre- sented in reference 1. The dynamic-stability tests presented herein were made in the Langley 8-foot transonic pressure tunnel at an oscillation amplitude of lo with the use of a forced-oscillation technique for angles of attack from -2O to 1 6 ' with the model at zero sideslip. The Mach number for the yaw tests was varied from 0.40 to 1.20 with corresponding Reynolds numbers, based on the mean 6 6 of the fully swept wing, from The aerodynamic chord 5.1 x 10 to 5.8 x 10 .
reduced-frequency parameter was varied from 0.0152 to 0.0626 for the yaw tests.
Pitch tests were made only at a Mach number of 0.80 at a Reynolds number of 5.0 X 10 because of instrumentation difficulties. The reduced-frequency param- eter was varied from 0.0145 to 0.0237 for the pitch tests.
Yaw tests were made with two sizes of vertical tails as well as with the vertical tails removed. Provisions could not be made to obtain the proper mass- flow rate for the engine inlets. Consequently, tests were made with the cylin- drical engine inlets open, with the inlets plugged, and with the engine nacelles removed in order to provide a qualitative indication of the effect of engine inlets on the yawing dynamic-stability parameters.
SYMBOLS The aerodynamic parameters are referred to the body system of axes Origi- nating at the oscillation center Of the model as shown in figure 1. The International System Of Units (SI) is used herein with U.S. Customary Units given parenthetically. (See ref. 2 for relationships between these systems.)
The reference dimensions are based on the geometric characteristics of the model with the wings fully swept (excluding the horizontal tails) regardless of the actual test wing-sweep position.
b model wing span of fully swept wing, 0.406 meter (1.333 ft) damping coefficient about Y-axis and Z-axis of body, CY,CZ meter-newton-second ft-lb-see respective ly , radian
( rad )
-
C mean aerodynamic chord of fully swept wing, 0.397 meter (1.303 ft) (see fig. 1) f frequency of oscillation, cycles per second moment-of-inertia coefficient about Y - a x i s and Z-axis of body,
IY 9 =z
meter-newton-second2 ft-1b - sec
respectively ,
radian ( rad ')
torsional-spring coefficient about Y-axis and Z-axis of body, KY ' K Z meter-newton respectively, radian & k u.31 in yaw, radians
reduced-frequency parameter, - in pitch and -
2v 2v M free-stream Mach number
pitching velocity , radians/second
free-stream dynamic pressure, newtons/meter2 ( lb/ft2) 8,
-
R Reynolds number based on c r yawing velocity, radians/second s --_ w i r l g - ~ l m f c m ~ r e z of f u l l y swept wing, 0.170 meter2 (1.828 ft2) maximum torque required to oscillate model in pitch and in yaw, TY JZ respectively, newton-meter (lb-ft )
v free-stream velocity, meters/second (ft/sec )
U angle of attack, degrees or radians; mean angle of attack, degrees angle of sideslip, degrees or radians P phase angle between % and 0, degrees maximum angular displacement i n p i t c h of model with respect t o
s t i n g , radians
degrees leading-edge sweep angle of wing panel, phase angle between TZ and $, degrees maximum angular displacement i n yaw of model with respect t o s t i n g , radians angular velocity, 2xf, radians/second Pitching moment pitching-moment c o e f f i c i e n t , G S E Yawing moment yawing-moment c o e f f i c i e n t , %USb
, per radian
p e r radian
acn , per radian
&n
Cnp = -, per radian
a P
damping-in-pitch parameter, p e r radian C% + C m i
Cma - k % % oscillatory-longitudinal-stability parameter, per radian
damping-in-yaw parameter, per radian
cnr - Crib cos a
oscillatory-directional-stability parameter, per radian CnP COS u + k Cn; A dot over a quantity denotes the f i r s t derivative w i t h respect t o time.
The expression cos a appears i n t h e directional parameters because these parameters a r e expressed i n terms of the body system of axes.
DESCRIPTION OF APF'ARATUS Model 1.
Design dimensions of the model of t h i s investigation a r e shown i n figure Detailed c h a r a c t e r i s t i c s of the model are contained i n reference 1. The model was aerodynamically similar t o the proposed SCAlc 15 airplane except f o r a f t - fuselage modifications necessary t o accommodate t h e support s t i n g and o s c i l l a - The t i o n mechanism. The fixed wing had a leading-edge sweep angle of 75'.
variable-sweep portion of the wing had a leading-edge sweep angle of 25' f o r t e s t s at low Mach numbers, and t h i s portion merged with t h e fixed portion t o form an arrow wing with a sweep angle of 7 5 O f o r t e s t s at the higher Mach num- The v e r t i c a l and horizontal tails were mounted on t h e t i p s of the fixed bers.
wings. Provisions were made f o r t e s t i n g the model with v e r t i c a l t a i l s of two different s i z e s as well as with t h e v e r t i c a l tails removed. Although the non- operating engine i n l e t s on the model were normally open t o allow airflow, some t e s t s were made with t h e i n l e t s plugged and with the engine nacelles removed.
The model was made of magnesium and the v e r t i c a l tails were made of stain- Even though the t e s t model was considered rigid, possible e l a s t i c l e s s s t e e l .
d i s t o r t i o n may have occurred because of the r e l a t i v e l y t h i n wing panels.
Three-dimensional roughness consisting of No. 60 carborundum grains w a s applied The s i z e t o t h e model t o assure t h e existence of a turbulent boundary layer.
G ~ K Z locatio:: sf t h e three-dimensional roughness - were computed by the method of reference 3 .
O s c i l l a t ion-Balance Mechanism The forward portion of the oscillation-balance mechanism i s shown i n the photograph presented on page 6. Since the amplitude of the o s c i l l a t i o n i s small t h e r o t a r y motion of an e l e c t r i c motor i s used t o provide e s s e n t i a l l y sinusoidal motion of constant amplitude t o the balance through the crank and Scotch-yoke mechanism. Although constant amplitudes of 1/2O, lo, and 2 ' can be obtained by using d i f f e r e n t cranks, an amplitude of 1 ' was used f o r these tests. The o s c i l - l a t i o n center w a s located at the model station corresponding t o t h e proposed mass of the configuration. 1.)
center of (See f i g .
..
Assembled oscillation balance mechanism- Displacement bridge Mechanical spring Model- mounting
surface 2
‘m,i/iTorque bridge L-63-1969.1 A s shown i n t h e photograph, t h e strain-gage bridge which is used t o meas- ure the torque required t o o s c i l l a t e t h e model i s located between t h e model- mounting surface and the pivot axis. The torque-bridge location e l m n a t e s the e f f e c t s of pivot-bearing f r i c t i o n . Although t h e torque bridge i s located for- ward of the pivot axis, compensating c i r c u i t s s h i f t t h e e l e c t r i c a l centers of the bridge t o t h e pivot axis so t h a t a l l torques are measured w i t h respect t o axis of the o s c i l l a t i o n balance.
the pivot A mechanical spring, which i s attached t o the fixed sting, i s mounted within the o s c i l l a t i o n balance and i s connected t o t h e front end of t h e o s c i l l a - t i o n balance through an H-shaped flexure. The mechanical spring allows t h e model-balance system t o be o s c i l l a t e d a t t h e frequency of velocity resonance.
Although, with the forced-oscillation balance, the model may be o s c i l l a t e d a t frequencies from about 4 t o 30 cps, as explained i n reference 4, the most accurate measurement of the damping coefficient is obtained a t velocity reso- nance. As shown i n t h e photograph, a strain-gage bridge i s attached t o t h e mechanical spring t o provide a signal which i s proportional t o t h e angular displacement o f t h e model w i t h respect t o t h e sting.
.
Wind Tunnel The t e s t s were made i n t h e Langley 8-foot transonic pressure tunnel. The t e s t section of t h i s single-return closed-circuit wind tunnel i s about 2.2 meters square (about 7.1 f e e t square) with t h e upper and lower w a l l s s l o t t e d t o permit continuous operation throughout the transonic speed range. Test- section Mach numbers up t o about 1.30 can be obtained by controlling t h e speed of t h e tunnel-fan drive motor. The Mach number d i s t r i b u t i o n i s uniform through- out t h e t e s t section, with t h e m a x i m u m deviation from t h e average free-stream Mach number on t h e order of 0.01 at t h e higher Mach numbers.
The sting-support system is designed t o keep t h e model near t h e center l i n e of t h e tunnel through an angle-of-attack range from -20 t o 1 6 ' when used i n con- junction with t h e oscillation-balance mechanism of these tests.
TEST CONDITIONS The t e s t s were made at an o s c i l l a t i o n amplitude of 1 ' with t h e use of the previously described forced-oscillation technique f o r angles of a t t a c k from -2' t o 1 6 ' with t h e model at zero s i d e s l i p .
The Mach numbers f o r t h e y a w tests were varied from 0.40 t o 1.20 with corresponding Reynolds numbers, based on t h e mean aerodynamic chord of t h e f u l l y swept wing, from 3.1 x 106 t o 5.8 x lo6.
L @ The reduced-frequency parameter varied from 0.0152 t o 0.0626 f o r t h e yaw 2v t e s t s . Because of instrumentation d i f f i c u l t i e s , t h e p i t c h tests were made only
at a Mach number of 0.80 at a Reynolds number of 5.0 x 10 6 . The reduced-
frequency parameter & f o r t h e pitch t e s t s varied from 0.0145 t o 0.0237. The
2v data are presented i n figures 2 t o 5 f o r the various t e s t conditions as indi- cated by t h e following t a b l e : 2j Large 0.40 5.1 x 1 0 6 Small .4u 3.1 Removed .40 25 3.1 Large .80 25 5.0 SlIlall .80 25 5.0 .80 Removed 25 5.0 75 Large * 95 5.5 Small .95 5.5 Removed 75 .95 5.5 1.20 75 Large 5.6 1.20 75 Small 5.6 Removed 1.20 75 5.6 Large .95 5.5 Plugged Large 75 .95 5.5 Nacelles removed Large .95 5.5 1.20 75 Large 5.6 1.20 Plugged Large 5.6 Nacelles removed Large 1.20 75 5.6 0.80 5.0 x lo6 5 25 open Large MEASUREMENTS AND REDUCTION OF DATA Strain-gage bridges are used to measure the torque required to oscillate the model and the angular displacement of the model with respect to the sting.
The signals are amplified and passed through mechanically coupled but electri- cally independent sine-cosine resolvers which rotate with constant angular velocity at the frequency of model oscillation. Each signal is resolved by the sine-cosine resolver into two components which are read on damped digital volt- meters. Details of the electronics used are given in reference 4.
Fromthe computed values of the maximum torque required to oscillate the model in y a w T z , the maximum angular displacement in yaw of the model with respect to the sting $i, the phase angle h between T z and $, and the angu-
lar velocity of the forced oscillation (LI (as explained in ref. 4 ) , the
damping coefficient for this single-degree-of-freedom system was computed as TZ sin h
c z =
(4
Also, the spring-inertia parameter was computed as TZ COS h
% - 1 9 2 =
k
where Q is the torsional-spring coefficient of the system and I z is the moment-of-inertia coefficient of the system about the Z-axis of the body.
For these tests, the damping-in-yaw parameter was computed as ( 3 ) and the oscillatory-directional-stability parameter was computed as 2 T cos A T cos h
COS u + k C n ; , = -
(4)
CnP
%Sb [( ! ! ) w i n d on ( 9 ) w i n d of fl
is independent of oscillation frequency and The value of
(*' " ) w i n d off
is determined at the frequency of the wind-off velocity resonance, because, as explained in reference 4, maximum accuracy is obtained at the frequency Of . .
i s a function of the velocity resonance. The value of
(Tz io' ')wind off
o s c i l l a t i o n frequency and, therefore, i s determined f o r each t e s t value of the wind-on frequency.
From the computed values of t h e maximum torque required t o o s c i l l a t e t h e
3, the m a x i m u m angular displacement i n p i t c h of t h e model w i t h
model i n p i t c h respect t o the s t i n g 0, t h e phase angle 7 between TY and 0, and the angu- cu, the system c h a r a c t e r i s t i c s i n p i t c h l a r velocity of the forced o s c i l l a t i o n were computed as Ty s i n 1 1 ( 5 ) cy =
ruo
and For these t e s t s , the damping-in-pitch parameter was computed as and t h e oscillatory-longitudinal-stability parameter w a s computed as
2 kys ") - (" ys ") ] ( 8 )
cma - c% =--
wind on wind o f f %Ise w a s determined at t h e
As f o r t h e yaw t e s t s , t h e value of (" 2 11)
wind off frequency of t h e wind-off velocity resonance, and the wind-off and wind-on Ty COS --- - . I " v e ~ e determined at t h e same frequency of o s c i l l a t i o n . v d - n of - RESULTS AND DISCUSSION Directional Results m e e f f e c t s of v e r t i c a l tails on the dynamic-stability c h a r a c t e r i s t i c s i n y a w f o r t h e model with t h e wing panels swept 2 5 ' are presented i n f i g u r e 2 f o r Mach numbers of 0.40 and 0.80. A t angles of a t t a c k below about 6 O , the damping i n yaw w a s p o s i t i v e (negative values of Cnr - Cnd cos a) and generally l i n e a r with angle of a t t a c k f o r both Mach numbers; the o s c i l l a t o r y - d i r e c t i o n a l .
s t a b i l i t y was positive positive values of CnP COS u + k2Cn5) f o r a l l configu-
(
rations but t h e one with t h e v e r t i c a l t a i l s removed. Both t h e damping and sta- b i l i t y i n yaw increased with t h e addition of v e r t i c a l tails, with a g r e a t e r Above an angle of a t t a c k of about 12O, increase f o r t h e l a r g e r v e r t i c a l t a i l .
however, addition of t h e v e r t i c a l t a i l s produced an adverse e f f e c t of decreased damping f o r both Mach numbers, and at a Mach number of 0.80 negative damping Although resulted f o r t h e configurations with large and s m a l l v e r t i c a l tails.
t h e flow phenomenon producing t h i s negative damping i s not understood at present, negative damping may be associated with wing-separation e f f e c t s on t h e v e r t i c a l tails.
The e f f e c t s of t h e v e r t i c a l tails on t h e dynamic-stability c h a r a c t e r i s t i c s i n yaw f o r t h e model with t h e wing panels swept 7 5 O a t Mach numbers of 0.95 and 1.20 a r e presented i n figure 3 . A t angles of a t t a c k up t o about 6 O , t h e yaw damping and s t a b i l i t y were positive and increased with an increase i n t h e v e r t i c a l - t a i l s i z e .
Above about 6 O , the variations of t h e yaw damping and sta- b i l i t y parameters with angle of a t t a c k were very e r r a t i c and indicated t h e prob- able presence of large areas of flow separation. The region of negative damping t h a t was present a t t h e high angles of a t t a c k f o r t h e model with t h e wing panels swept 25' at Mach numbers of 0.40 and 0.80 did not e x i s t f o r t h e model with t h e panels swept 7 5 O a t Mach numbers of 0.95 and 1.20.
A s mentioned previously, t h e proper mass-flow rate through t h e simulated engine i n l e t s could not be obtained f o r t h i s model. In order t o provide a qualitative indication of t h e e f f e c t of the engine-inlet configuration on t h e directional dynamic-stability c h a r a c t e r i s t i c s at Mach numbers of 0.95 and 1.20, investigations were made with t h e i n l e t s open, with t h e i n l e t s plugged, and with engine nacelles removed f o r the model with t h e wings swept 75'. A s shown i n figure 4, removal of the engine nacelles produced appreciable e f f e c t s at t h e higher angles of attack. Although these e f f e c t s were e r r a t i c and showed no systematic variation, they indicated t h e importance of simulating t h e engine nacelles on a i r c r a f t configurations of t h i s type. Simulation of t h e exact amount of airflow, however, was l e s s important than expected, as indicated by the f a c t t h a t plugging the i n l e t s had only a s l i g h t e f f e c t on t h e d e t a i l e d damping o r s t a b i l i t y o r the trends at Mach numbers of 0.95 and 1.20.
Longitudinal Results Because of instrumentation d i f f i c u l t i e s longitudinal data were obtained only f o r M = 0.80 f o r t h e configuration with a wing-panel sweep of 2 5 O , l a r g e v e r t i c a l tails, and engine i n l e t s open i n these tests. Positive damping i n p i t c h ' negative values of Cms + C%) and near zero o r p o s i t i v e ( s t a b l e )
(
values of t h e o s c i l l a t o r y - l o n g i t u d i n a l - s t a b i l i t y parameter were exhibited f o r a l l angles of a t t a c k a t t h e o s c i l l a t i o n - c e n t e r l o c a t i o n used ( f i g . 5 ) .
I 10 .
CONCLUDING R E M A R K S Wind-tunnel measurements were made i n t h e Langley 8-foot transonic pressure tunnel t o determine t h e aerodynamic damping and o s c i l l a t o r y s t a b i l i t y i n yaw and p i t c h f o r a model of a proposed variable-sweep supersonic transport airplane designated t h e SCAT 15.
For t h e model with t h e wing panels swept 25O, t h e yaw damping w a s positive and generally remained l i n e a r with angle of a t t a c k f o r angles below about 6'.
A t Mach numbers of 0.40 and 0.80 both the damping and s t a b i l i t y increased with an increase i n t h e v e r t i c a l - t a i l s i z e . Above an angle of a t t a c k of about 12O, however, addition of t h e v e r t i c a l tails produced t h e adverse e f f e c t of decreased o r negative damping f o r . t h e subsonic t e s t Mach numbers.
The model with t h e wing panels swept 75' w a s t e s t e d i n yaw at Mach numbers A t angles of a t t a c k up t o about 6O, t h e damping and s t a b i l i t y of 0.95 and 1.20.
were positive and increased with an increase i n t h e v e r t i c a l - t a i l s i z e . Above about 6O, t h e variations of t h e yaw damping and s t a b i l i t y parameters were very e r r a t i c and inconsistent.
Pitch tests were made f o r t h e model with a wing-panel sweep of 25O, large Positive v e r t i c a l tails, and engine i n l e t s open f o r a Mach number of 0.80.
damping i n p i t c h and positive o r near zero values of t h e o s c i l l a t o r y - longitudinal-stability parameter were exhibited f o r a l l test angles of attack.
Removal of t h e engine nacelles produced appreciable e f f e c t s at t h e higher angles of a t t a c k f o r t h e configuration t e s t e d i n yaw with t h e wings swept 75'.
These e f f e c t s indicate t h e importance of simulating t h e engine nacelles for dynamic-stability t e s t s of a i r c r a f t configurations of t h i s type. Tests with t h e engine i n l e t s plugged indicated only a s l i g h t e f f e c t on t h e y a w damping o r sta- b i l i t y at Mach numbers of 0.95 and 1.20.
Langley Research Center, National Aeronautics and Space Administration, Langley Station, Hampton, V a . , November 1, 1965.
.
REFERENCES 1. Henderson, W i l l i a m P.: Low-Speed Aerodynamic C h a r a c t e r i s t i c s of a Supersonic Transport Model With a Blended Wing-Body, Variable-Sweep Auxiliary Wing Panels, and Outboard T a i l Surfaces. NASA T M X-993, 1964.
2. Mechtly, E. A.: The I n t e r n a t i o n a l System of Units - Physical Constants and
Conversion Factors. NASA SP-7012, 1964.
3 . Braslow, Albert L.; and Knox, Eugene C.: Simplified Method f o r Determination of C r i t i c a l Height of Distributed Roughness P a r t i c l e s f o r Boundary-Layer Transition at Mach Numbers From 0 t o 5 . NACA T N 4363, 1958.
4. Braslow, Albert L. ; Wiley, Harleth G. ; and Lee, Cullen Q. : A Rigidly Forced Oscillation System f o r Measuring Dynamic-Stability Parameters i n Transonic and Supersonic Wind Tunnels. NASA TN D-1231, 1962. (Supersedes NACA RM L58A28.)
X 0 L r , ; e v e r t i c a l tails 0 Small v e r t i c a l ts-ils 0 V e r t i c d t:>,ils rerrioved
c"r- C" cos
B per radian Angle of attack ,a,deg (a) M = 0.40; R = 3 . 1 X lo6; k = 0.0432 to 0.0626.
Figure 2.- Effect of vertical tails on dynamic-stability characteristics in yaw for model w i t h engine inlets open. A = 25'.
.
0 Lari<e vertical tails 0 Small v e r t i c a l tails 0 Vertical tails removed
C , l C ' C O S Q
"B
per radian -1 -2 .2
C ~ ~ C O S Q + k2Cn* r
per radian -4 0 4 8 i 2 :5
Angle of attack ,a,deg
(b) M = 0 . 8 0 ; R = 5 . 0 X lo6; k = 0.0175 to 0.0319.
Figure 2.- Concluded.
0 Large v e r t i c a l tails 0 S m 1 1 vertica.1 tails 0 Vorticc.1 tails r m o v e d -1 Cnr- Cn COS Q B - 2 per radian -3 -4 -5 CnBCOS a + k2Cn; per radian Angle of attack ,a ,deg (a) M = 0.95; R = 5 . 5 x lo6, k = 0.0163 to 0.0310.
= 7 5 ' .
Figure 3.- Effect of vertical tails on dynamic-stability characteristics i n yaw for model with engine inlets Open.
0 Lid,r,.;e v e r t i c a l tails 0 Sm-211 v e r t i c a l tvils 0 Vcrticnl fails rr,movcd -1 Cnr-C 'COS(L -2 nP per radian -3 -4 -5 .2 -7 '4 0 4 8 12 16 20 Angle of attack ,a,deg (b) M = 1.20; R = 5.6 X lo6; k = 0.0154 to 0 . 0 2 6 0 .
Figure 3.- Concluded.
-1 -2 C " I C 'COS Q nP per radian -3 -4 -5 CnBCOS a + k 2 C , ; per radian (a) M = 0.95; R = 5.5 X lo6; k = 0.0193 to 0.0310.
Figure 4.- Effect of engine inlets on dynamic-stability characteristics in yaw for model w i t h large vertical tails. A = 75' a 0 En'ine i n l c t s oren 0 Cn-ine i n l e t s nlu-,;ed 0 ?n .ir.e n-cellcs rcrroved Cnr-C COS Q "B per radian CnBCOS Q + k*C,; per radian . L -4 0 4 8 12 16 20 Angle of attack ,a,deg (b) M = 1.20; R = 5 . 6 X lo6; k = 0.0152 to 0.0280.
Figure 4.- Concluded.
c .
/
-2 - 4
( 5
c +c
mq mti per radian -6 -8 - 10 .4 Cma- k2Cm 9 .2 per radian Mean angle of attack,a,deg lo6: Figure 5.- Dynamic-stability characteristics in pitch for model w i t h large vertical tails and engine inlets open. A = 25O; M = 0.80; R = 5.0 k = 0.0145 to 0.0237.
x) NASA-Langley, 1966 L-4748 lications inclvde , handbooks, so I