Document
MEMORANDUM
FLIGHT-DETERMINED STABILITY AND CONTROL DERIVATIVES O F A SUPERSONIC AlRPLANE WITH A LOW-ASPECT-RATIO UNSWEPT WING A N D A TEE-TAIL By William H . Andrews and Herman A. Rediess I Hiah-Speed Fliqht Station CLASSIFIED DOCIJMENT - TITLE UNCLZSSiI.ItD
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This material contains information affecting the National B f e n s e of the United S u b 8 rim Lbr RM* of the esplomge laws, n t l e 18, U.S.C., Secs. 783 and 794, the transmission or rewl8Uonof which i.Lllp.
manner to an unaukrized person I s prohlbited by law.
I
NATIONAL AERONAUTICS AND
SPACE ADMINISTRATION
WASHI NGTON
April 1959
CONFIDENTIAL
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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MEMORANDUM 2 -2 - 5 9H
FLIGHT-DETERMINED STABILITY AND CONTROL DERIVATIVES OF A SUPERSONIC AIRPLANE WITH A LOW-ASPECT-RATIO UNSWEPT WING AND A TEE-TAIL* By William H. Andrews and Herman A. Rediess SUMMARY A flight-test investigation of a supersonic airplane with a low- aspect-ratio unswept wing provided data in the trim angle-of-attack range for obtaining the longitudinal, lateral, and directional stability and control derivatives between Mach numbers of 0.88 and 2.08. The longitudinal-stability and three-axes control derivatives were determined by somewhat standard simplified methods, whereas the time-vector method was employed in the analysis of the lateral and directional stability derivatives.
The general correlation of the flight-determined derivatives with wind-tunnel results was good, except for a discrepancy in the absolute level of the effective dihedral derivative and the damping-in-roll derivative .
An improvement of,approximately 1 0 to 15 percent in the static directional stability was realized in the supersonic speed range by the installation of a ventral fin on the airplane.
In the region between a Mach number of 1.38 and 1.43, an abrupt loss in the directional damping to slightly unstable conditions was expe- rienced. At Mach numbers greater than 1.43, the damping was relatively low, but pos itive .
The application of the time-vector method of analysis to determine the lateral and directional derivatives was modified by incorporating the yawing velocity as a reference instead of the usual sideslip angle.
This modification tended to improve the reliability and reduce the labor involved in utilizing the method.
"ritle, Unclassified.
CONFIDENTIAL INTRODUCTION In recent years, flight-test investigations of high-performance airplanes have been guided by utilizing analog computers as flight simu- lators. To simulate the response characteristics of the airplane for various flight conditions, complete information pertaining to the stabil- ity and control derivatives of the test vehicle is required.
Wind-tunnel and free-flight rocket-model experiments have provided an extensive amount of derivative information on high-performance airplanes.
However, experience has indicated that it is desirable to substantiate model data and theory with full-scale flight-test data, especially when full-scale phenomena cannot be duplicated by model tests.
The purpose of this paper is to present a comprehensive coverage of the stability and control derivatives of a supersonic airplane with a low-aspect-ratio unswept wing in 1 g trimmed flight. The flight- determined derivatives were calculated from data obtained in the Mach number range of 0.88 to 2.08 between the altitudes of 38,000 and 42,000 feet. These data are compared with the wind-tunnel data pre- sented in references 1 to 9, as well as with unpublished wind-tunnel data.
In addition, the paper presents further experience in the determina- tion of the lateral and directional stability derivatives through the application of the time-vector method of analysis and indicates a means of improving the results derived from the method by utilizing a more reliable basic reference. Reference 10 employed sideslip angle as a reference in the analysis, whereas the present investigation utilizes yawing velocity as a basic reference.
The flight-test investigation was conducted at the NASA High-Speed Flight Station at Edwards, Calif.
SYMBOLS AND COEFFICIENTS The results of this investigation are referred to the body system of axes, inasmuch as the flight-test instrumentation is alined with these axes.
an normal acceleration, g units
% transverse acceleration, g units
b wing span, ft L i f t
l i f t c o e f f i c i e n t , -
;is
W trim 1 g l i f t c o e f f i c i e n t , -
cs
R o l l i n g moment rolling-moment c o e f f i c i e n t , Csb P i t c h i n g moment pitching-moment c o e f f i c i e n t ,
6s c
Yawing moment yawing-moment c o e f f i c i e n t , %Sb L a t e r a l f o r c e l a t e r a l - f o r c e c o e f f i c i e n t , QS mean aerodynamic chord, ft a c c e l e r a t i o n due t o g r a v i t y , f t / s e c p r e s s u r e a l t i t u d e , f t moment of i n e r t i a of a i r p l a n e about X-axis, s l u g - f t moment of i n e r t i a of a i r p l a n e about Y-axis, s l u g - f t d IY moment of i n e r t i a of a i r p l a n e about Z-axis, s l u g - f t ' product of i n e r t i a r e f e r r e d t o X- and Z-axes, s l u g - f t s t a b i l i z e r d e f l e c t i o n , p o s i t i v e when t r a i l i n g edge i s down, deg Mach number
mass of a i r p l a n e , w / ~ , s l u g s
p e r i o d o f damped n a t u r a l frequency o f a i r p l a n e , s e c r o l l i n g a n g u l a r v e l o c i t y , r a d i a n s / s e c r o l l i n g a n g u l a r v e l o c i t y f a c t o r , 2v -..
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P r o l l i n g angular acceleration, radians/sec 9 p i t c h i n g angular v e l o c i t y , radianslsec 4 p i t c h i n g angular a c c e l e r a t i o n , radians/sec
-
9 dynamic pressure, l b / s q f t r yawing angular v e l o c i t y , radians /sec r b
r ' yawing angular v e l o c i t y f a c t o r , -
2v r yawing angular a c c e l e r a t i o n , radians/sec S wing a r e a , s q f t time required f o r o s c i l l a t i o n t c damp t o h a l f amplitude, sec * l / 2 time, sec free-stream v e l o c i t y , f t / s e c weight of a i r p l a n e , l b angle of a t t a c k of a i r p l a n e , deg o r radians angle of s i d e s l i p , deg o r radians a i l e r o n d e f l e c t i o n , p o s i t i v e when l e f t a i l e r o n i s d e f l e c t e d down, deg t o t a l a i l e r o n d e f l e c t i o n , deg yaw damper d e f l e c t i o n , p o s i t i v e when d e f l e c t e d t o l e f t , deg 6 ~ d s i n Qd r a t i o of t h e a c t u a l damping t o c r i t i c a l damping, T time parameter, m/pVS mass d e n s i t y of a i r , slws/cu ft P 9 phase angle, deg C O N F I D E N T I A L damping angle, deg, tan- 1 0.1103P T' d e r i v a t i v e of c o e f f i c i e n t with respect t o subscript
C n }
C m a ~ m i t d e r i v a t i v e of c o e f f i c i e n t with respect t o sub- b
s c r i p t x -
2v
C m q ~ C% d e r i v a t i v e of - c o e f f i c i e n t with respect t o sub-
s c r i p t x C 2v The symbol ( i ( represents t h e absolute magnitude of an i quantity.
When employed in an equation, t h e equation i s considered t o be a vector equation.
The phase angle of a vector i r e l a t i v e t o a reference vector k i s i n d i c a t e d by t h e -subscripts i n Oik.
A dot over a l e t t e r i n d i c a t e s t h e d e r i v a t i v e with respect t o time.
The t e s t a i r p l a n e is a supersonic f i g h t e r powered by a t u r b o j e t engine equipped with afterburner; a three-view drawing i s shown i n f i g u r e 1.
The general physical c h m a c t e r i s t i c s c o n s i s t of a high-fineness- r a t i o , c i r c u l a r fuselage; low-aspect-ratio unswept w i n g ; and an all-movable h o r i z o n t a l t a i l mounted near t h e t o p of t h e v e r t i c a l t a i l . The wing has an a i r f o i l thickness of 3 percent and i s mounted with -10' d i h e d r a l . The v e r t i c a l t a i l i s swept 35' at t h e quarter chord and includes a conven- t i o n a l rudder and separate yaw-damper surface. After t h e i n i t i a l f l i g h t s of t h e airplane, a v e n t r a l f i n was i n s t a l l e d on t h e r e a r portion of t h e fuselage by t h e manufacturer t o improve t h e d i r e c t i o n a l s t a b i l i t y .
The l o n g i t u d i n a l and l a t e r a l controls c o n s i s t of i r r e v e r s i b l e hydrau- l i c systems. The a r t i f i c i a l f e e l f o r t h e l o n g i t u d i n a l system i s provided CONFIDENTIAL through a spring and bobweight combination; t h e l a t e r a l f e e l i s obtained t h r o w h a centering spring mechanism. D i r e c t i o n a l c o n t r o l i s obtained through a cable-actuated rudder without t h e a i d of power boost. A t h r e e - axes damper system w a s i n s t a l l e d i n t h e airplane; however, t h e damper systems were not a c t i v a t e d during t h i s program.
The physical c h a r a c t e r i s t i c s of t h e a i r p l a e a r e l i s t e d i n t a b l e I , and a comparison of t h e p e r t i n e n t physical c h a r a c t e r i s t i c s with those of t h e wind-tunnel models of references 1 t o 9 i s shown i n t a b l e 11.
The mass and i n e r t i a c h a r a c t e r i s t i c s a r e presented i n f i g u r e 2. The weight ranged between approximately 16,500 and 14,000 pounds; t h e center of g r a v i t y ranged between approximately 14 and 8 percent mean aerodynamic chord. The values of IX, Iy, and IZ were taken from t h e manufacturer's estimate and a r e referenced t o t h e body axes. The product of i n e r t i a was c a l c u l a t e d from t h e s e i n e r t i a values using an i n c l i n a t i o n of t h e p r i n c i p a l axes of 2.9O obtained from t h e manufacturer.
Standard NASA instruments were used t o record airspeed; a l t i t u d e ; angle of s i d e s l i p ; angle of a t t a c k ; normal and transverse a c c e l e r a t i o n s ; p i t c h , r o l l , and yaw v e l o c i t i e s and accelerations; and c o n t r o l surface d e f l e c t i o n s . The airspeed, a l t i t u d e , angle of a t t a c k , and s i d e s l i p angles were sensed on a nose boom. A l l instruments were synchronized a t 0.1-second i n t e r v a l s by a common timer.
The turnmeters used t o measure t h e angular v e l o c i t i e s and accelera- t i o n s were referenced t o t h e a i r p l a n e body axes and were mounted within 0.2' of these axes.
The ranges, s c a l e s of t h e recorded data, and dynamic c h a r a c t e r i s t i c s f o r angle-of-attack, s i d e s l i p , velocity, and a c c e l e r a t i o n instruments a r e : r Undamped n a t u r a l Scale of recorded d a t a Damping Function Range frequency, cps ( ~ e r i n . d e f l e c t i o n ) r a t i o -23 t o 34 10.5 10.40 0.65 a, deg
10.5 lo. 50
P , deg +-30 65 p, radians +2 19.0 2.20 .68 q, radians k.28 .61 6.5 .29 r, radians .66
+. 10
6 - 3 0 09 -1 t o 8 32.0 5.14 an7 @; -67 k.5 18.6 at,, g 56 65 CONFIDENTIAL Indicated s i d e s l i p angles and angles of a t t a c k measured by vane- type pickups were corrected f o r r o l l and yaw r a t e e f f e c t s and p i t c h r a t e e f f e c t s , r e s p e c t i v e l y . The pickups were mass damped and had dynamically f l a t frequency-response c h a r a c t e r i s t i c s over t h e frequency range of the a i r p l a n e .
A l l d a t a employed i n t h e a n a l y s i s were corrected f o r instrument phase l a g . P o s i t i o n corrections were applied t o indicated l i n e a r accel- erometer readings by t h e time-vector method ( r e f . 1 0 ) .
TESTS The general procedure employed t o obtain d a t a during t h i s i n v e s t i - g a t i o n w a s t o measure t h e a i r p l a n e response t o an abrupt c o n t r o l d e f l e c - t i o n a t s p e c i f i e d a l t i t u d e and Mach number conditions. So t h a t t h e applied methods of a n a l y s i s would y i e l d t h e b e s t r e s u l t s , considerable emphasis was placed on maintaining constant a l t i t u d e and Mach number, and control-fixed conditions during t h e t r a n s i e n t phase of t h e maneuvers.
The t e s t s were conducted over t h e Mach number range from 0.88 t o 2.08 a t an a l t i t u d e of 40,000 f e e t , with a d e v i a t i o n of +2,000 f e e t during t h e program. A l l d a t a were obtained a t t h e 1.0g ( f 0 . l g ) t r i m conditions presented i n f i g u r e 3.
The l o n g i t u d i n a l d a t a were obtained from abrupt triangular-shaped s t a b i l i z e r pulses ranging between -2' and -3' d e f l e c t i o n . The l a t e r a l and d i r e c t i o n a l d a t a were resolved from t h e abrupt a i l e r o n o r p i l o t - a c t i v a t e d yaw-damper input of rectangular shape. The a i l e r o n d e f l e c - t i o n s ranged from 25 percent t o f u l l d e f l e c t i o n . The yaw-damper d a t a During a presented a r e f o r f u l l d e f l e c t i o n of t h e damper surface.
p a r t i c u l a r maneuver only t h e c o n t r o l necessary t o produce t h e primary a i r p l a n e disturbance was deflected; a l l other c o n t r o l surfaces were maintained i n t h e f i x e d t r i m p o s i t i o n .
ANALYSIS AND DATA PRESENTATION Longitudinal The f l i g h t records, t y p i f i e d by t h e time h i s t o r i e s of f i g u r e 4, were
I % l
(, and amplitude r a t i o -
reduced t o t h e b a s i c values of P, T1/29
I " !
presented i n f i g u r e 5 . To determine t h e d e r i v a t i v e s CL,, Cm,, CONFIDENTIAL of figure 6, the basic data were substituted in the following simplified expressions: and The control effectiveness Cm (fig. 6) was calculated from data it obtained during the initial stabilizer input portion of the time history.
The peak acceleration and corresponding incremental velocity were sub- stituted in the following relation to obtain this parameter: The flight-determined derivatives and the wind-tunnel data used for comparison (fig. 7) were corrected to a center-of-gravity location of 10 percent mean aerodynamic chord.
Lateral and Directional The static and dynamic stability derivatives Cnp, (Cnr - Cni), C I , , Czp, and Cy were determined by the time-vector method. The
B
application of the method utilizes transient response time-history data from yaw-damper pulses similar to those included in figure 8 . From these data, the pertinent quantities of period, damping, amplitude ratio, and phase angles were determined and are summarized in figures 9 to 11.
Reference 10 includes an extensive discussion of the time-vector method and its limitations. In the present analysis, the results are referenced to the body axes instead of the stability axes system, and CONFIDENTIAL t h e amplitude r a t i o s and phase angles a r e measured with r e s p e c t t o t h e yawing v e l o c i t y . By using t h e yawing v e l o c i t y as a basic r e f e r e n c e , it was p o s s i b l e t o complete t h e a n a l y s i s without r e l y i n g on t h e measured s i d e s l i p angles, as was done i n references 10 and 11. When t h e s i d e s l i p angle i s employed a s a reference, d i f f i c u l t i e s a r i s e which r e q u i r e an i t e r a t i v e process i n t h e i n i t i a l phase of t h e a n a l y s i s . With t h e yaw v e l o c i t y a s a reference t h i s i t e r a t i o n i s eliminated, and t h e consistency and r e l i a b i l i t y of t h e r e s u l t s a r e believed t o be improved.
The equations of motion and r e p r e s e n t a t i v e time-vector diagrams are shown i n f i g u r e 12. I n t h e vector s o l u t i o n of t h e yaw and r o l l equa- t i o n s values of C were obtained from an estimate by t h e manufacturer,
np
and values of C were assumed on t h e b a s i s of unpublished wind-tunnel 1, data. Figures 13 and 14 show t h e flight-determined d e r i v a t i v e s .
The a i l e r o n and yaw-damper control-effectiveness d e r i v a t i v e s ( f i g . 15) were obtained by a method s i m i l a r t o t h a t employed i n t h e determination of t h e l o n g i t u d i n a l c o n t r o l e f f e c t i v e n e s s . The incremental r o l l i n g and yawing v e l o c i t i e s and corresponding peak a c c e l e r a t i o n s a s s o c i a t e d with t h e c o n t r o l input during a i l e r o n pulses and r o l l s were s u b s t i t u t e d i n t o t h e following s i m p l i f i e d equations t o obtain t h e a i l e r o n e f f e c t i v e n e s s : and Yaw-damper e f f e c t i v e n e s s w a s derived from t h e s u b s t i t u t i o n of t h e yaw v e l o c i t i e s and a c c e l e r a t i o n s in t h e expression: I n t h e comparison of t h e flight-determined d e r i v a t i v e s with wind- tunnel r e s u l t s ( f i g s . 16 t o 18) an attempt w a s made t o c a l c u l a t e t h e wing f l e x i b i l i t y c o r r e c t i o n s t o t h e wind-tunnel values of C , and C L by P P The c a l c u l a t i o n s t h e method o u t l i n e d i n appendix B of reference 11.
revealed t h a t t h e influence w a s i n s i g n i f i c a n t f o r t h e motion excursions CONFIDENTIAL # experienced by t h e a i r p l a n e during t h e investigation. The wind-tunnel values of Cn and Cy have been corrected f o r t h e e f f e c t s of v e r t i c a l - P D t a i l f l e x i b i l i t y by the' method of reference 12 and by u t i l i z i n g t h e manufacturer's estimated e f f e c t s of f l e x i b i l i t y on v e r t i c a l - t a i l effec- t i v e n e s s . The value of LCn due t o f l e x i b i l i t y varied between approxi- P mately 0.0003 t o 0.0008 per deg over a Mach number range from 0.90 t o 2.01.
The influence of t h e incremental s i d e f o r c e at t h e engine i n l e t r e s u l t i n g from t h e momentum change caused by turning t h e intake a i r i n t o t h e i n l e t duct was found t o be n e g l i g i b l e .
Analog Simulation I n a d d i t i o n t o t h e preceding analysis, an analog i n v e s t i g a t i o n was conducted t o assess t h e v a l i d i t y of t h e d e r i v a t i v e s . A simulation of the f l i g h t time h i s t o r y was obtained on a five-degree-of-freedom analog setup. The c o n t r o l input was programmed i n t o t h e machine through a p l o t t i n g t a b l e , and t h e r e s u l t i n g a i r p l a n e responses were compared with an overlay of t h e f l i g h t records. During t h e investigation, t h e f l i g h t - determined d e r i v a t i v e s were adjusted t o t h e values indicated by t h e s o l i d symbols of f i g u r e s 6, 13, and 15 i n order t o match t h e time h i s - t o r i e s of f i g u r e s 4 and 8.
DISCUSSION Longitudinal S t a b i l i t y
Basic d a t a . - The period, damping r a t i o , and amplitude r a t i o d a t a
of f i g u r e 5 i n d i c a t e no unusual deviations. In t h e transonic range, t h e period and damping r a t i o e x h i b i t r a p i d changes and a degree of s c a t - t e r which a r e usually associated with t h e aerodynamic behavior in t h i s region. The extent of t h i s behavior, discussed i n reference 13, i s a function of such f a c t o r s a s wing thickness, aspect r a t i o , and t a p e r r a t i o .
The period and damping r a t i o s vary from 2.3 t o 1.1 and 0.17 t o 0.90, respectively, over t h e speed range. Above M a 1.7 t h e s e q u a n t i t i e s increase over t h e minimum values mentioned.
F l i g h t derivatives.- The general trends of t h e s t a b i l i t y and c o n t r o l with t h e d e r i v a t i v e s ( f i g . 6) over t h e Mach number range appear uniform, In t h e transonic region C% exception of Cnh and (cmq + c ~ ) .
CONFIDENTIAL i n d i c a t e s t h e expected r a p i d increase between M = 0.89 and 0.92. The damping d e r i v a t i v e (cmq + c%) e x h i b i t s a gradual, but s i g n i f i c a n t , decrease between M = 1.05 and 1.25.
By observing t h e s o l i d symbols of f i g u r e 6, it i s evident t h a t only minor adjustments t o t h e flight-determined d e r i v a t i v e s were required t o obtain t h e analog simulation of t h e f l i g h t time h i s t o r i e s of f i g u r e 4.
Wind-tunnel comparison.- The general c o r r e l a t i o n between t h e wind- tunnel and flight-determined d e r i v a t i v e s of f i g u r e 7 i s good, e s p e c i a l l y i n t h e transonic region. The abrupt increase i n C% previously men- tioned appears t o be well confirmed by t h e e x i s t i n g wind-tunnel data i n t h i s region. The values of Cma from reference 1 show an appreciable deviation from t h e t r e n d of t h e f l i g h t r e s u l t s a t Mach numbers of 1.35 and 1.45. The reason f o r t h i s discrepancy i s not r e a d i l y apparent, inasmuch a s t h e same source of comparison shows good agreement a t t h e higher speeds.
L a t e r a l and D i r e c t i o n a l S t a b i l i t y Basic data.- The period of t h e t r a n s i e n t o s c i l l a t i o n shown i n f i g - ure 9 remains f a i r l y constant a t a value of approximately 1.6 seconds over t h e supersonic speed range, although a d e f i n i t e l o s s i n damping i s indicated between M = 1.38 and 1.43. Beyond M = 1 . 4 3 t h e damping increases s l i g h t l y , but s t i l l remains near zero.
A n attempt was made t o a s s o c i a t e t h e abrupt l o s s i n damping with t h e shock-wave i n t e r a c t i o n from various components of t h e a i r p l a n e .
Although a cursory analysis indicated t h a t shocks emanating from t h e wing t r a i l i n g edge i n t h i s speed range would probably impinge on t h e v e r t i c a l t a i l , t h e shock system can be s o complex ( r e f . 14) t h a t r e l a t i n g t h e l o s s i n damping t o any one shock system or phasing of any p a r t i c u l a r system becomes mere speculation. It is believed, however, t h a t t h e i n t e r f e r e n c e from various shock-wave p a t t e r n s may be t h e cause of t h i s phenomenon.
f i g u r e s 10 The v a r i a t i o n s of amplitude r a t i o and phase angles of and 1 1 show no unusual trends except i n t h e region, mentioned previously, range
between M = 1.38 and 1.43. The amplitude r a t i o s of - / Y / ~ / and
Ir l The r a t i o of v a r i e s from 2 t o 4 and 0.5 t o 0.3, respectively.
m
between 8 and 5.5, which i s somewhat higher than t h a t indicated by s e v e r a l comparable research a i r p l a n e s .
CONFIDENTIAL The degree of s c a t t e r exhibited by t h e amplitude r a t i o and phase angle d a t a is a minimum, with t h e exception of t h e roll-to-yaw phase angle which shows a maximum deviation from t h e mean of approxi- Opr mately f 7 O . This deviation occurs primarily i n t h e transonic region where t h e Mach number i s d i f f i c u l t t o c o n t r o l during t h e t r a n s i e n t phase of a t e s t maneuver. The consistency of t h e i s a t t r i b u t e d I rl t o t h e f a c t t h a t t h e s e q u a n t i t i e s were calculated from t h e transverse a c c e l e r a t i o n equation. It was possible t o obtain these q u a n t i t i e s i n t h i s manner, r a t h e r than by r e l y i n g on d i r e c t measurements, inasmuch a s t h e yawing v e l o c i t y was employed f o r t h e basic reference, a s discussed i n d e t a i l i n t h e a n a l y s i s section.
F l i g h t d e r i v a t i v e s . - The v a r i a t i o n of t h e s t a t i c - s t a b i l i t y deriva- t i v e s with Mach number presented i n f i g u r e 13 e x h i b i t s good consistency.
However, i n t h e evident s c a t t e r of t h e r e s u l t s it i s believed t h a t t h e d a t a between M = 1.38 and 1.43 i n d i c a t e a possible shock-wave e f f e c t .
From an observation of t h e l i m i t e d flight-determined d a t a C n ~ obtained without t h e v e n t r a l f i n , it appears t h a t an extrapolation of t h e r e s u l t s t o t h e higher speeds would agree favorably with t h e manu- It i s evident t h a t incorpora- f a c t u r e r ' s f l i g h t r e s u l t s ( s e e f i g . 13) .
t i o n of t h e v e n t r a l f i n on t h e a i r p l a n e increased by approximately Cn13
10 t o 13 percent over t h e supersonic speed range. ~ h k general t r e n d of
t h e v a r i a t i o n s of Cn and C z with Mach number f o r t h e configuration B B with t h e v e n t r a l f i n i n s t a l l e d i n d i c a t e s approximately a 60- t o 65-percent reduction in t h e s e parameters over t h e speed range t e s t e d .
The damping-in-yaw d e r i v a t i v e (Cnr - crib) remains f a i r l y constant
a t -1 over t h e speed range t o M = 2.08 ( f i g . 14). However, i n t h e region between M = 1.38 and 1.43 where t h e abrupt l o s s i n damping
(Cnr - cnB) increases t o -2, then abruptly drops
occurs ( f i g . g), t o -0.2 o r 0. The amount of s c a t t e r over t h e speed range is i n s i g n i f i - cant except i n t h e transonic region.
The damping-in-roll d e r i v a t i v e C v a r i e s from -0.6 t o -0.28 P between M = 0.95 and 2.08, and an abrupt decrease from -0.57 t o -0.42 occurs between M = 1.38 and M = 1.47.
and C were derived from t h e same Although t h e d e r i v a t i v e s C ' ~ IP vector diagram, t h e v a r i a t i o n of C with Mach number appears more c o n s i s t e n t than t h e v a r i a t i o n of C z . A study of t h e o r i e n t a t i o n of P the vectors representing C 2 and C 2 i n the r o l l equation ( f i g . 12) B P indicates t h a t a deviation of t h e phase angle Op, w i l l have a greater influence o n t h e m a g n i t u d e o f C t h a n o n C Consequently, t h e P '8' previously mentioned s c a t t e r i n i s reflected i n the r e s u l t s of C .
O P ~ P The aileron effectiveness C 2 and cross-control derivative C 6a n6a ( f i g . 15) indicate a nonlinear moment variation with aileron deflection up t o M z 1.4; however, t h i s is more evident a t M < 1. Over the t e s t Mach number range the control effectiveness decreases about 75 t o 80 per- cent. The C i s an appreciable positive value i n the transonic "6, region and decreases t o approximately zero with increasing Mach number.
The yaw-damper effectiveness indicates a loss of 75 percent Cn8yd between M = 0.95 and 2.08.
The s o l i d symbols of figures 13 t o 15 represent the values of the derivatives employed i n the analog simulation of the time h i s t o r i e s of figure 8. With the exception of a t M = 1.25, it can be seen t h a t C z B only minor adjustments of the flight-determined derivatives were required t o obtain good simulation r e s u l t s . The reason f o r t h e discrepancy i n a t M = 1.25 was not apparent.
C~~ Wind-tunnel comparison.- Generally, the agreement between the wind- tunnel and f light-determined C i s good ( f i g . 16). The ventral-on "B data a t M = 1.8 and 2.0 from the Ames 9 x 7 foot Unitary Plan wind tunnel are superimposed on the f l i g h t data. The incremental value from ventral-on t o ventral-off of 0.0008 per degree is approximately the same f o r the wind-tunnel r e s u l t s as f o r the f l i g h t r e s u l t s i n the high- speed range (see f i g s . 13 and 16) .
Comparison of the flight-determined r o l l derivatives and C Cl$ with wind-tunnel r e s u l t s ( f i g s . 16 and 17) indicates t h a t the f l i g h t data were consistently high over the e n t i r e speed range. It was con- cluded, a f t e r considering several possible sources of error i n the anal- ysis, t h a t an error could have been made i n t h e estimated moment of i n e r t i a IX. Consequently, the f l i g h t data were recalculated assuming a 20-percent reduction i n IX, and the r e s u l t s show a somewhat better comparison with the wind-tunnel data. This does not imply conclusively t h a t the estimated i n e r t i a s or the associated derivatives were incorrect, but it does appear t o be a possible explanation f o r the discrepancy shown.
The c o r r e l a t i o n of t h e unpublished wind-tunnel values of (cnr - cni)
of f i g u r e 17 with t h e flight-determined r e s u l t s , which were c a l c u l a t e d using t h e manufacturer's estimate of C shows g o ~ d agreement. After
"P'
t h e a n a l y s i s had been completed, unpublished wind-tunnel d a t a became a v a i l a b l e which included a v a r i a t i o n of C with Mach number ( f i g . 1 7 ) .
"P - These d a t a were incorporated i n a r e c a l c u l a t i o n of
and (cnr - cnj)
Cnp and t h e r e s u l t s a r e presented i n f i g u r e s 16 and 17, r e s p e c t i v e l y .
It can be seen t h a t t h e primary deviation from t h e o r i g i n a l l y computed Cn?
occurs i n t h e region between M = 0.95 and 1.5. The
and (cnr - cne)
values of Cn do not change appreciably; however, t h e r e c a l c u l a t e d P values of show poor c o r r e l a t i o n with t h e wind-tunnel r e s u l t s
('nr - C . )
P i n t h i s region.
The comparison of t h e c o n t r o l parameters of f i g u r e 18 shows good agreement between t h e flight-determined and wind-tunnel r e s u l t s , except f o r t h e values of C .
nea
C O N C L U S IONS Results of a f l i g h t - t e s t i n v e s t i g a t i o n t o determine t h e s t a b i l i t y and c o n t r o l d e r i v a t i v e s of a supersonic airplane, with a low-aspect- r a t i o unswept wing, between a Mach number of 0.88 and 2.08 i n t h e low angle-of-attack range l e d t o t h e following conclusions.
1. The l o n g i t u d i n a l damping i s r e l a t i v e l y constant; however, t h e l o n g i t u d i n a l s t a b i l i t y d e r i v a t i v e C% e x h i b i t s an abrupt increase between a Mach number of 0.88 and 0.92, then gradually decreases with f u r t h e r increase in supersonic Mach number.
and t h e e f f e c t i v e 2. The d i r e c t i o n a l s t a b i l i t y d e r i v a t i v e C n ~ d i h e d r a l d e r i v a t i v e decrease approximately 60 t o 65 percent between C% a Mach number of 0.88 and 2.08.
3. I n s t a l l a t i o n of a v e n t r a l f i n on t h e a i r p l a n e improved t h e d i r e c t i o n a l s t a b i l i t y by 10 t o 15 percent a t supersonic speeds.
4. An abrupt l o s s in t h e d i r e c t i o n a l damping w a s i n d i c a t e d i n t h e A t Mach numbers g r e a t e r region between a Mach number of 1.38 and 1.43.
than 1.43, t h e damping w a s r e l a t i v e l y low, but p o s i t i v e .
CONFIDENTIAL 5 . The a i l e r o n e f f e c t i v e n e s s d e r i v a t i v e w a s reduced by approxi- C28a mately 75 t o 80 p e r c e n t over t h e t e s t range and i n d i c a t e d an a p p r e c i a b l e n o n l i n e a r v a r i a t i o n of r o l l i n g moment w i t h a i l e r o n d e f l e c t i o n at Mach numbers l e s s t h a n 1.
6. The g e n e r a l agreement between t h e f light-determined d e r i v a t i v e s and t h e wind-tunnel r e s u l t s i s good, w i t h t h e exception o f a d i s c r e p a n c y i n t h e a b s o l u t e l e v e l of t h e e f f e c t i v e d i h e d r a l d e r i v a t i v e and t h e damping- i n - r o l l d e r i v a t i v e .
7. The i n c o r p o r a t i o n of t h e yawing v e l o c i t y a s a r e f e r e n c e i n s t e a d of t h e u s u a l s i d e s l i p a n g l e in t h e time-vector a n a l y s i s showed a tend- ency t o improve t h e d a t a r e l i a b i l i t y and reduced t h e l a b o r involved i n t h e a p p l i c a t i o n of t h e method.
High-Speed F l i g h t S t a t i o n , N a t i o n a l Aeronautics and Space Administration, Edwards, C a l i f . , October 29, 1958.
CONFIDENTIAL 1. Smith, Willard G. : Wind-Tunnel Investigation a t Subsonic and Super- sonic Speeds of a Fighter Model Employing a Low-Aspect-Ratio Unswept - Wing and a Horizontal T a i l Mounted Well Above t h e Wing Plane Longitudinal S t a b i l i t y and Control. NACA RM A54DO5, 1954.
2. Hieser, Gerald, and Reid, Charles F., Jr.: Transonic Longitudinal Aerodynamic C h a r a c t e r i s t i c s of a Fighter-Type Airplane Model With a Low-Aspect-Ratio Unswept Wing and a Tee-Tail. NACA RM L54Klga,
1956 -
3. Robinson, Ross B.: Longitudinal C h a r a c t e r i s t i c s of an Unswept-Wing Fighter-Type Model With External S t o r e s a t a Mach Number of 1.82 and Some E f f e c t s of Horizontal-Tail and Yaw-Damper-Vane Deflection on t h e S i d e s l i p Derivatives. NACA RM ~ 5 5 ~ 2 6 , 1956.
4. Spearman, M. Leroy, and Driver, Cornelius: Longitudinal and L a t e r a l S t a b i l i t y C h a r a c t e r i s t i c s of a Low-Aspect-Ratio Unswept-Wing A i r - plane Model a t Mach Numbers of 1.82 and 2.01. NACA RM ~ 5 6 ~ 0 6 , 1957.
5. Buell, Donald A . , Reed, Verlin D . , and Lopez, Armando E . : The S t a t i c and Dynamic-Rotary S t a b i l i t y Derivatives a t Subsonic Speeds of an ' Airplane Model With an Unswept Wing and a High Horizontal T a i l .
NACA RM ~56104, 1956.
6. Tinling, Bruce E.: Subsonic Aerodynamic C h a r a c t e r i s t i c s U p t o Extreme Angles of Attack of an Airplane Model Having an Unswept Wing and a High Horizontal T a i l . NACA RM A57KO5, 1958.
7 . Sleeman, William C . , Jr., and Wiggins, James W . : Experimental I n v e s t i - gation a t High Subsonic Speeds of t h e Rolling S t a b i l i t y Derivatives of a Complete Model With an Aspect-Ratio-2.52 Wing Having an Unswept NACA RM L54120, 72-Percent-Chord Line and a High Horizontal T a i l .
8. Arabian, Donald D . , and Schmeer, James W.: L a t e r a l S t a b i l i t y and Control Measurements of a Fighter-Type Airplane With a Low-Aspect- Ratio Unswept Wing and a Tee-Tail. NACA RM ~ 5 5 ~ 0 8 , 1956.
9. Smith, Willard G., and I n t r i e r i , Peter F.: Some E f f e c t s of Aileron Deflection on t h e S t a t i c L a t e r a l and Directional Aerodynamic Char- a c t e r i s t i c s of Four Contemporary Airplane Models. NACA RM A57E22,
1957 -
CONFIDENTIAL 10. Wolowicz, Chester H.: Time-Vector Determined L a t e r a l Derivatives of a Swept-Wing Fighter-Type Airplane With Three D i f f e r e n t Verti- c a l T a i l s a t Mach Numbers Between 0.70 and 1.48. NACA RM ~ 5 6 ~ 2 0 , 11. G i l l i s , Clarence L . , and Chapman, Rowe, Jr.: Effect of Wing Height and Dihedral on t h e L a t e r 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 a t Low L i f t of a 45' Swept-Wing Airplane Configuration a s Obtained from Time- Vector Analyses of Rocket-Propelled-Model F l i g h t s a t Mach Numbers from 0.7 t o 1.3. NACA RM ~ 5 6 ~ 1 7 , 1956.
12. Letko, William, and Riley, Donald R . : Effect of an Unswept Wing on t h e Contribution of Unswept-Tail Configurations t o t h e Low- Speed S t a t i c - and R o l l i n g - S t a b i l i t y Derivatives of a Midwing A i r - plane Model. NACA TN 2175, 1950.
13. Harris, William G. : A Wind-Tunnel Investigation at High-Subsonic and Low Supersonic Mach Numbers on a S e r i e s of Wings With Various Sweepback, Taper, Aspect Ratio, and Thickness. P a r t 2. Compari- son of L i f t and S t a b i l i t y Data. A . Tech. Rep. No. 6669. P a r t 2, Wright A i r Dev. Center, Dec. 1952.
14. Nielsen, Jack N . , and K a a t t a r i , George E.: The E f f e c t s of Vortex and Shock-Expansion F i e l d s on P i t c h and Y a w I n s t a b i l i t i e s of Supersonic Airplanes. b e p r i n t No. 743, I n s t . Aero. S c i . , June C O N F IDENT IAL TABLE I.- GEOMETRIC CHARACTERISTICS O F THE AIRPLANE Wing:
A i r f o i l s e c t i o n . . . . . . . . . . . . . . . . . . Modified biconvex
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . . . 196.1
Span. f t . . . . . . . . . . . . . . . . . . . . . . . . . . 21.94
Mean aerodynamic chord. f t . . . . . . . . . . . . . . . . .
9-55
Root chord. f t . . . . . . . . . . . . . . . . . . . . . . . 12.98
Tip chord. f t . . . . . . . . . . . . . . . . . . . . . . . . 4.89
Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . . . 2.45
Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . . . 0.378
Sweep a t 25 percent chord. deg . . . . . . . . . . . . . . . 18.1
Sweep a t t h e leading edge. deg . . . . . . . . . . . . . . . 2 7 - 3
Incidence. deg . . . . . . . . . . . . . . . . . . . . . . . 0
Dihedral. deg . . . . . . . . . . . . . . . . . . . . . . . . . -10.0
A i r f o i l t h i c k n e s s r a t i o . . . . . . . . . . . . . . . . . . . 0.0336
Leading-edge f l a p s (per s i d e ) -
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . . 8.50
llean chord. f t . . . . . . . . . . . . . . . . . . . . . . 1.012
Deflection l i m i t . deg . . . . . . . . . . . . . . . . . . . -30.0
Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plain
Trailing-edge f l a p s ( p e r s i d e ) -
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . .
11-53
. . . . . . . . . . . . . . . . . . . . . . llean chord. f t 2.52
. . . . . . . . . . . . . . . . . . . Deflection l i m i t . deg 45.0
. . . . . . . . . . . . . . . . . . . . . . . . . . . Type Plain
Ailerons ( p e r s i d e ) -
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . . 4.73
. . . . . . . . . . . . . . . . . . . . . . Mean chord. f t 1.716
span. f t . . . . . . . . . . . . . . . . . . . . . . . . .
2 - 7 5
Deflection . . . . . . . . . . . . . . . . . . . . . . . . f 13.0
T a i l : Horizontal t a i l .
A i r f o i l s e c t i o n . . . . . . . . . . . . . . . . . Modified biconvex
. . . . . . . 48.2
Area. s q f t . . . . . . . . . . . . . . . . .
Mean aerodynamic chord. f t . . . . . . . . . . . . . . . . 4.415
11.92 . . . . . . .
Span. f t . . . . . . . . . . . . . . . . . .
. . . . . . . 6.16
Root chord. f t . . . . . . . . . . . . . . .
. . . . . . .
Tip chord. f t . . . . . . . . . . . . . . . .
1.917
. . . . . . . . . . . . . . . . . . . . . . . 2.95
Aspect r a t i o
. . . . . . . 0.311
. . . . . . . . . . . . . . . . . Taper r a t i o
. . . . . . . 0.0493
Root thickness r a t i o . . . . . . . . . . . .
0.0261 . . . . . . .
Tip thickness r a t i o . . . . . . . . . . . . .
t o 0.23 T a i l length. 0.25 wing mean aerodynamic chord
. . . . . . . 18.72
hor i z o n t a l - t a i l mean aerodynamic chord. f t 10.12 . . . . . . .
Sweep at 0.25 mean aerodynamic chord. deg . .
5.0 t o -17.0 . . . .
. . . . . . . . . . . Deflection l i m i t s . deg
CONFIDENTIAL TABLE I.- G E O ! J . E T R I C CHARACTERISTICS OF THE AIRPLANE . Concluded V e r t i c a l t a i l .
. . . . . . . . . . . . . . . . .
A i r f o i l s e c t i o n IcIodified biconvex . . . . . . . . . . . . . . . . . . . . . . .
Area. s q f t 35.1
span. f t . . . . . . . . . . . . . . . . . . . . . . . . 5.46
Mean aerodynamic chord. f t . . . . . . . . . . . . . . . 6.88
Aspect r a t i o . . . . . . . . . . . . . . . . . . . . . . 0.849
Taper r a t i o . . . . . . . . . . . . . . . . . . . . . . . 0.371
T a i l length. 0.25 wing mean aerodynamic chord t o 0.25
v e r t i c a l - t a i l mean aerodynamic chord. f t . . . . . . . 1 3 . 13
Sweep at 0.25 mean aerodynamic chord. deg . . . . . . . . 35.0
Rudder -
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . . 4-3
span. f t . . . . . . . . . . . . . . . . . . . . . . . . 2.92
Average chord. f t . . . . . . . . . . . . . . . . . . . . 1- 375
Deflection l i m i t s . . . . . . . . . . . . . . . . . . . . +25
Yaw damper -
Area. s q f t . . . . . . . . . . . . . . . . . . . . . . .
1.0 Span. f t . . . . . . . . . . . . . . . . . . . . . . . . .
1.0 Average chord. f t . . . . . . . . . . . . . . . . . . . .
1.0 Deflection l i m i t s ) deg . . . . . . . . . . . . . . . . .
k20 Fuselage :
F r o n t a l area. s q f t . . . . . . . . . . . . . . . . . . . . . 2 5 . 0
Length. f t . . . . . . . . . . . . . . . . . . . . . . . . 51-25
Fineness r a t i o . . . . . . . . . . . . . . . . . . . . . . 9.09
Dive brakes ( p e r s i d e ) : Area. s q f t (projected f r o n t a l a r e a at maximum
d e f l e c t i o n ) . . . . . . . . . . . . . . . . . . . . . . . 4.13
Chord. f t . . . . . . . . . . . . . . . . . . . . . . . . . 2.50
D e f l e c t i o n l i m i t . . . . . . . . . . . . . . . . . . . . . 60.0
Weight :
. . . . . . . . . . . . . . . . . . . . . h p t y w e i g h t . lb 13. 237
. . . . . . . . . . . . . . . . .
T o t a l take-off weight. l b 18. 233 . .
Center.of.gravity.location, percent mean aerodynamic chord
Empty . . . . . . . . . . . . . . . . . . . . . . . . . . 17.40
Takeoff . . . . . . . . . . . . . . . . . . . . . . . . . 3-25
Note: For i n e r t i a c h a r a c t e r i s t i c s s e e f i g u r e 2 .
CONFIDENTIAL TABLE 11.- COMPAREON O F PHYSICAL CHARACTERISTICS O F WIND-TUNNEL M O D E L 5 WITH NLL-SCm AXEUNI - Test 6 4 8 References 1 2 7 9 3 5 airplane 0.040 0.086 0.086 0.085 0.040 0.0% 0.086 0.086 Model scale 1.00 0 . ~ 9 Wing: 196 191 190 . . . . . . . . . Area, s q f t 196.1 194 191 195 196 190 190 22 22 22 22 22 22 22 Span, f t . . . . . . . . . . 21.94 22 22 2.45 2.45 2.45 2.44 Aspect r a t i o . . . . . . . . 2.45 2.5 2.5 2.5 2.5 2.5 Mean aerodynemic chord, f t . . . . . . . . . . . .
9.5 9.3 9.3 9.4 9.5 9 . 3 9.5 9. 3 9.3 9.55 Sweep a t 25 percent chord, 18.2 19.1 1 8 5 18.1 18.5 deg . . . . . . . . . . . . 18.1 18.5 19 19 l g - 10 - 10 - 10 - 10 - 10 - 10 Dihedral, deg . . . . . . . . - 10 - 10 - 5 -5 0.38 0.384 0.384 Taper r a t i o . . . . . . . . . 0.38 0.377 0.377 0.385 0.378 0.385 0.385 Horizontal t a i l : 48 48.2 48 48 48 Area, s q f t . . . . . . . . . 48.9 48 117 49 47 M e m aerodynamic chord, 4.4 4.4 4.45 4.4 4.4 f t . . . . . . . . . . . . 4.42 4.45 4.4 4.4 4.3 11.6 12.0 11.9 11.9 12.1 11.9 span, f t . . . . . . . . . . 11.9 12.1 11.6 12.0 2.98 2.95 2.89 2.96 2.97 Aspect r a t i o . . . . . . . . 2.95 2.97 2.95 2.89 2.97
0 . 1 0.326 0.312 0.311 0 . 1 2 0.311 . 0.31 0.311
0.319 Taper r a t i o . . . . . . . . .
0.326 Sweep a t 25 percent 10 1 0 . U 10.1 10 10 10.3 10.1 chord, deg . . . . . . . . 10 10 10 T a i l length, f t (0.25 wing mean aerodynamic chord t o 0.25 horizontal-tail mean 16.7 16.7 18.7 18.0 16.7 16.9 18.3 aerodynamic chord) . . . . 16.8 16.7 16.7 Vertical t a i l : Area, s q ft . . . . . . . . .
35 29 37 31 % 34 35.1 30 37 34 Mean aerodynamic chord, 6.88 7.16 6.9 7.16 f t . . . . . . . . . . . .
7 7.0 6.9 8.7 7 6.9 0.78 1.1 0.85 0.8 0.849 0.86 1.1 0 . 8 0.997 Aspect r a t i o . . . . . . . .
0 . Q 0.46 0.462 0.38 0.463 0.4 Taper r a t i o . . . . . . . . . 0.38 0.4 0.378 0.371 0.37 Sweep a t 25 percent chord, deg . . . . . . . . . . . .
30 35 35 W 34.77 34.9 35 35 W 35 T a i l length, f t (0.25 wing mean aerodynamic chord t o 0.25 v e r t i c a l - t a i l mean 15.1 14.9 14.9 aerodynamic chord) . . . .
13 13 1 . 13 13.5 13 13 Vertical height (fuselage center l i n e t o vertical- 8.6 t a i l t i p ) . . . . . . . . .
7.4 8.5 7.6 8.7 7.9 8- 7 7.4 8.5 7 - 9 N o N o N o N o Yes N o Ventral on . . . . . . . . . Yes N o N o N o Note: Mode1 characteristics converted t o full-scale.
Figure 1.- Three-view drawing of the t e s t a i r p l a n e .
8 x lo4 Center of g r a v i t y , - percent c -.
-
7 14 -*I
:1 :I----
' 2 , ly, - -
I z I
slug-f t
-
4 - Figure 2.- I n e r t i a c h a r a c t e r i s t i c s of t h e t e s t a i r p l a n e a s a function of a i r p l a n e weight.
CONFIDENTIAL Figure 3.- Variation of t h e 1 g t r i m angle of a t t a c k and s t a b i l i z e r d e f l e c t i o n with Mach number.
hp = 40,000 f t .
g i Analog s ~ t i o n
1 I I 1 1 1 1
- ' A 4 6 8 1 ( 1 0 2 4 6 8 1 0 0 2 4 6 8 1 0
t , sec t, sec t, sec Figure 4.- Typical time histories of the longitudinal response characteristics of the test air- plane resulting from abrupt stabilizer deflection.
Figure 5 . - Variation of the longitudinal transient-response characteristics with Mach number.
1 6 , Analog elmulation . 0 8 4 & *
-*--
' L ; per deg 7----~~--~, n n - , C ,, 0 -
c m , ' -.02
per deg -.04 I I -0.
"0
0 I , -
0 0 OQ O 0
(cmq + CrnJ'- , 0 ( 3
tAwP
per r a d i a n
I
- 20
Figure 6.- Variation of the flight-determined longitudinal stability and control derivatives with Mach number.
C L ~ J per deg -.02 p e r deg -.04 -.06 .8 .9 1.0 1 . 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 M Figure 7.- Comparison of the flight-determined longitudinal stability and control derivatives with wind-tunnel results.
B , deg 0 - 2 L-- t, sec 1 , sec t, sec ( a ) Yaw-damper d e f l e c t ion.
Figure 8.- Typical time h i s t o r i e s of t h e l a t e r a l and d i r e c t i o n a l response c h a r a c t e r is t i c s of t h e t e s t a i r p l a n e r e s u l t i n g from abrupt yaw-damper d e f l e c t ions and a i l e r o n inputs.
simulation radian /sec -. 2
- 2
2 4 6 0 2 4 6 0 2 4 6 0 t, sec t, sec t, sec ( b ) Aileron d e f l e c t i o n .
Figure 8.- Concluded.
CONFIDENTIAL 3 -
~ I
I i I . .
h P P, sec i . ..
4- - . .
I I 0.
Figure 9.- Variation with Mach number of the lateral-directional period and damping characteris- tics of the test airplane.
Figure 10.- Variation with Mach number of t h e amplitude r a t i o s , M, and of t h e t e s t Irl I ' I I.rl a i r p l a n e a t i t s n a t u r a l frequency.
of t h e t e s t Figure 11.- Variation with Mach number of t h e phase angles Oa r, and Op,, t a i r p l a n e at its n a t u r a l frequency.
YAW E q v ~ r l o ~ ROLL EOWION TpArrsvrasE A C C E L C W I ~ N E ~ ~ A r l o v zr I > ! + 2-r 1 : ; - zsa - cL.;$ - G . 3 = = O lrl \ / P W - - 0.s22 P
(Ca;C,.) = - 1.51s
C,, = - 0.493 ?$.= - 262.4 Figure 12.- Representative time-vector diagrams employed i n t h e determination of t h e l a t e r a l - d i r e c t i o n a l s t a b i l i t y d e r i v a t i v e s . hp = 40,000 f t ; M = 1.245.
- ,008 n Manufacturer' flight t e s t - V e n t r a l ,ff
C" , Per d e g
Q Analog s i m u l a t l ~ n -C- -- ,004 I I 0 I Figure 13.- Flight-determined static lateral-directional stability derivatives.
r - c - Flight Analog simulation (cnr -Cnj) -- Manufacturer' s estimate - - d- - - Unpublished wlnd tunnel 0 v a ~2,; i ' i per radian c - 2 - A Cnp* per radian
Cz p'
- .4
per radian
C z , . '
per radian M Figure 14.- Flight-determined dynamic lateral-directional stability derivatives.
Flight R m g e Analog Simulation Ei, - 7" to 1 5 " - . . h per deg C 1 I 4 4 , * I # I I C n # . I < I 8,d' 1 ' per deg , , Figure 15.- Variation with Mach number of the flight-determined lateral-directional control- effectiveness derivatives.
.0 16 F l i g h t Wind Tunnel . - Figure 13 V Reference 4 .01 2 - . - - ished wind /r Unpublished - Ames 6 ' x 6' Off C% (Ames 0 Unpublished - Ames 9 ' x 7' 0n .008 ,004 Assuming 209 reduction i n IX -
- -
-- v 4 .--
r l / -
--
v
- - 2 -
- # Jb 0 ) 1 # ----1,-
-
- - 1
/---.
-
/
I
Figure 16.- Comparison of the flight-determined lateral-directional static stability derivatives with wind-tunnel results.
Wind Tunnel
F l i g h t 1
Figure 1 4 D Reference 5 Computed using 7 Reference 7 unpublished wind Unpublished - Ames 6 ' ~ 6' tunnel $ ( ~ m e s .'x 63 -- Manufacturer's estimate l h I I \ I per radian , - - Assuming 20$ reduction i n IX --
P .'
, per radian - 4
C l P * -.8 - .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 M Figure 17.- Comparison of the flight-determined dynamic lateral-directional stability derivatives with wind-tunnel results.
.oo I 2
~ 1 1 g h t i d e 7
R a y e % Reference - - - - - 25' t o 30' 1- 33.5 9
-
--
.0008
. .-
-
.
.
L,--- - - .
-
- -
\ -
-
-
-..
-
-
L- - ---
--'- - - . 0 0 0 4 - - , Assuming 206 reduction i n IX h- - - - - - b.
- -
- -
per deg - -
-
I 0- .0006 F l i g h t Wind Tunnel Reference Cn . , 5.4 S ~ d 20" D 8 .0004, per deg P v \
-
-
.0002 A V ' \ O 8 .9 1.0 1 . 1 1.2 1.3 1.4 1.5 1.6 17 1.8 1.9 2.0 2.1 M w Figure 18.- Comparison of the flight-determined lateral-directional control-effectiveness deriv- \D atives with wind-tunnel results.