Document
EFFECTS OF WING DIHEDRAL A N D PLANFORM
ON STABILITY CHARACTERISTICS
OF A RESEARCH MODEL AT
MACH NUMBERS FROM 1.80 TO 4.63
by Muurice 0. Feiyn una? James F. CumpbeZZ
LungZey Reseurch Center
LungZey Stution, Humpton, Vu.
N A T I O N A L AERONAUTICS AND SPACE A D M I N I S T R A T I O N WASHINGTON, D. C. JULY 1965 NASA TN D-2914 TECH LIBRARY UFB. NM EFFECTS O F WING DIHEDRAL AND PLANFORM ON STABILITY CHARACTERISTICS O F A RESEARCH MODEL AT MACH NUMBERS FROM 1.80 TO 4.63 By Maurice 0. Feryn and J a m e s F. Campbell Langley Research Center Langley Station, Hampton, Va.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sole by the Cleoringhouse for Federal Scientific and Technicol Information Springfield, Virginia 22151 - Price $3.00 L EFFECTS OF WING DIHEDRAL AND PLA"0RM ON STABILITY CHARACTERISTICS O F A RXSEAFCH MODEL AT MACH N U M B E R S F R O M 1.80 TO 4.63 By Maurice 0. Feryn and James F. Campbell Langley Research Center An investigation has been made t o determine the e f f e c t s of wing geometric dihedral and planform on t h e s t a b i l i t y characteristics of a wing-body-tail Geometric dihedral angles were s e t a t 3 O , Oo, and - 3 O f o r the research model.
31' and 73' swept-leading-edge wings investigated. Tests were performed a t angles of a t t a c k from about - 4 O t o 24O, a t angles of s i d e s l i p from about -4' t o 8O, a t Mach numbers from 1.80 t o 4.63, and a t a Reynolds number per foot of 3.0 x 106.
The d i r e c t i o n a l s t a b i l i t y was increased by positive geometric dihedral and decreased by negative geometric dihedral f o r both the t a i l - o n and t a i l - o f f con- figurations, p a r t i c u l a r l y a t t h e high angles of a t t a c k and high Mach numbers as a r e s u l t of dynamic-pressure e f f e c t s induced on the fuselage afterbody. Posi- t i v e effective dihedral was increased by positive geometric dihedral and decreased by negative geometric dihedral. The highly swept wing with subsonic leading edges provided l a r g e r negative values of effective dihedral than did t h e wing with lower sweep and supersonic leading edges. The amount of geometric dihedral used i n these t e s t s had l i t t l e o r no e f f e c t on the aerodynamic char- a c t e r i s t i c s i n pitch.
INTRODUCTION A large research e f f o r t i s now being made on a i r c r a f t such a s t h e multi- mission f i g h t e r , t h e supersonic transport, and vehicles of even higher Mach number which a r e capable of f l i g h t i n t o the hypersonic speed region. Because of t h e inherent l o s s of l i f t on s t a b i l i z i n g surfaces with increased Mach number, the 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 these a i r c r a f t a r e becoming a serious problem not only i n cruise-flight conditions but a l s o i n maneuvering conditions a t higher angles of attack. Some of the f a c t o r s affecting the s t a b i l i t y of air- c r a f t at supersonic speeds have been discussed i n references 1 t o 5. Although considerable data have been obtained concerning the e f f e c t s of two of these factors (geometric dihedral and wing planform) on the aerodynamic character-
istics in pitch and sideslip at low Mach numbers (refs. 6, 7, and 8, for
example), only a small amount of information is available at the higher super- sonic Mach numbers (ref. 9 , for example).
A n investigation has been made on a wing-body-tail model to determine the effects of geometric dihedral and wing planform on the stability character- istics of aircraft at high supersonic Mach numbers, and the test results are presented herein. The model was tested with and without a vertical tail and
with two wing planforms - a swept wing with 7 3 ' of leading-edge sweep and a
trapezoidalwing with 31' of leading-edge sweep. The tests were performed in
the Langley Unitary Plan w h d tunnel at Mach numbers from 1.80 to 4.63, at
angles of attack from about - 4 ' to 24O, and at angles of sideslip from about
-40 to 80. The Reynolds number per foot for these tests was 3.0 x 106.
SYMBOLS The lateral force and moment data are referred to the body-axis system, and the longitudinal force and moment data are referred to the stability-axis
system. The reference moment center was located 17.15 inches behind the nose
of the fuselage on the body center line. The data were reduced with the use of the geometric dimensions of the swept wing.
The symbols used are defined as follows: wing span, ft section chord, ft mean geometric chord, ft Drag
drag coefficient, -
@ W Lift
lift coefficient, -
SS, Pitching moment pitching-moment coefficient, q S $ Rolling moment rolling-moment coefficient, qswb
effective-dihedral parameter, 3, per deg
ap
Yawing moment yawing-moment coefficient , s%b
mn
d i r e c t i o n a l - s t a b i l i t y parameter, -, per deg
Side force side-force coefficient, ss, K Y
side-force parameter, -, per deg
l i f t - d r a g r a t i o , - CL
CD Mach number free-stream dynamic pressure, lb/sq f t reference wing area, 1.19 sq f t angle of attack, deg angle of s i d e s l i p , deg wing geometric dihedral angle, deg APPARATUS AND TESTS Model Drawings of the research model a r e presented i n figure 1.
The investiga- t i o n was conducted on an ogive-nose cylindrical body i n conjunction with trapezoidal- and swept-planform wings and a v e r t i c a l t a i l ; no horizontal t a i l was used on the model. The trapezoidal-planform wing had 31° leading-edge sweep, a 4-percent-thick circular-arc a i r f o i l section i n t h e streamwise direc- t i o n , a planform area of 1.33 square f e e t , and an aspect r a t i o of 3.007.
The swept wing had 730 leading-edge sweep, an NACA 65A004 a i r f o i l section i n the streamwise direction, a planform area of 1.19 square f e e t , and an aspect r a t i o of 1.313. The geometric dihedral f o r each wing could be s e t a t angles of 3 O , Oo, and - 3 O .
The c y l i n d r i c a l portion of the c i r c u l a r body was constructed of wood and f i b e r glass with a s t e e l core, and t h e nose was made of s t a i n l e s s s t e e l .
,.- , ,,. . . . .. .
Tunnel Tests were conducted i n both t h e low and high Mach number t e s t sections of Plan wind tunnel, which i s a variable-pressure continuous- t h e Langley Unitary Each test section i s approximately 4 feet square and 7 feet long.
flow tunnel.
sections a r e t h e asymmetric sliding-block type The nozzles leading t o t h e t e s t t h a t permit a continuous variation i n Mach number from about 1.5 t o 2.9 i n t h e t e s t section and from about 2.3 t o 4.7 i n the high Mach number low Mach number t e s t section.
T e s t Conditions The stagnation temperatures and pressures f o r t h e various t e s t Mach num- bers are as follows: .. __i_ S t agnat i on Stagnation temperature, OF number pressure, p s i a 12.65
14.86
17.62 21.41 40.00 4.63 54 74 The Reynolds number per foot w a s constant a t 3.0 X 106 f o r a l l tests. The stagnation dewpoint w a s maintained a t -30° F i n order t o avoid condensation e f f e c t s .
The configurations were t e s t e d through an angle-of-attack range from about -4' t o 24' and through an angle-of-sideslip range from about -4' t o 8'.
Data f o r t h e configuration with and without t h e v e r t i c a l t a i l were obtained f o r both wing planforms a t geometric-dihedral angles of 3 O , O o , and -3'.
I n order t o obtain turbulent flow over t h e model, t r a n s i t i o n s t r i p s com- posed of No. 60 carborundum grains set i n a p l a s t i c adhesive were used on a l l configurations. These s t r i p s were 1/16 inch wide and were placed 1/2 inch 1/2 inch from the leading edge i n a from the nose on t h e cylindrical body and streamwise direction on the wing and t a i l surfaces.
Measurements Aerodynamic forces and moments were measured by means of a six-component e l e c t r i c a l strain-gage balance housed within t h e model. The balance was r i g i d l y fastened t o a s t i n g support which was i n t u r n attached t o t h e tunnel The balance-chamber pressure w a s measured by means of a single support system.
static-pressure o r i f i c e located i n t h e balance cavity.
I
Accuracy The accuracy of the individual measured quantities. based on calibrations and repeatability of data. is estimated to be within the following limits:
%I . 0002
CD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
*o . 002
CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M.001 cz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
k0.0004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 0004
C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 002
cy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
k0.10 a, deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
k0.10 p , deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
%) . 015
M = 1 . 8 0 to 2.86.
*o . 050
M = 3.95 and 4.63 . . . . . . . . . . . . . . . . . . . . . . . . .
Correcti ons Angles of attack were corrected for tunnel-flow angularity. and angles of attack and sideslip were corrected for deflection of the balance and sting
support due to aerodynamic loads . The drag data were adjusted to correspond
to free-stream static conditions at the base of the model .
PRFSENTATION OF RESULTS The results of the investigation are presented in the following figures: Typical aerodynamic characteristics in sideslip:
Trapezoidal-wing configuration. tail on . . . . . . . . . . . . . . . . . 2
Swept-wing configuration . . . . . . . . . . . . . . . . . . . . . . . . 3
Effect of geometric dihedral on sideslip parameters:
Trapezoidal-wing configuration. tail off . . . . . . . . . . . . . . . . 4
Trapezoidal-wing configuration. tail on . . . . . . . . . . . . . . . . . 5
Swept-wing configuration. tail off . . . . . . . . . . . . . . . . . . . 6
Swept-wing configuration. tail on . . . . . . . . . . . . . . . . . . . . 7
Effect of wing planform and Mach number on the variation of the slope of
the lateral-stability parameter with angle of attack . . . . . . . . . . 8
Effect of geometric dihedral on aerodynamic characteristics in pitch:
Trapezoidal-wing configuration. tail on . . . . . . . . . . . . . . . . . 9
Swept-wing configuration. tail on . . . . . . . . . . . . . . . . . . . . 10
DISCUSSION Sideslip Characteristics Typical aerodynamic c h a r a c t e r i s t i c s i n s i d e s l i p a t t h e higher angles of 2 and 3 f o r the trapezoidal- and swept-wing a t t a c k a r e presented i n figures configurations, respectively. These figures a r e presented primarily t o show t h e l i n e a r i t y of t h e data since a l l s i d e s l i p parameters presented herein were obtained from incremental r e s u l t s of tests made throughout t h e angle-of-attack range a t s i d e s l i p angles of about 0 ' and 4'. The r e s u l t s with the exception of some of the Cn data f o r the swept-wing configuration ( f i g . 3 ( a ) , f o r It i s believed, example) a r e r e l a t i v e l y l i n e a r f o r s i d e s l i p angles up t o 4O.
however, t h a t even though the values presented i n t h i s paper f o r the Cnp swept-wing configuration a t t h e higher angles of a t t a c k may not be quantita- t i v e l y exact, the comgarisons shown a r e valid.
The e f f e c t s of wing geometric dihedral on t h e s i d e s l i p parameters f o r the
trapezoidal-wing configuration a r e shown i n figures 4 and 5 f o r the v e r t i c a l
t a i l off and on, respectively. For t h e t a i l - o f f condition, positive geometric dihedral tends t o increase t h e d i r e c t i o n a l s t a b i l i t y , whereas negative geomet- r i c dihedral tends t o decrease the d i r e c t i o n a l s t a b i l i t y a s the angle of a t t a c k increases. This e f f e c t becomes increasingly s i g n i f i c a n t with increase i n Mach number, p a r t i c u l a r l y a t the higher angles of attack. The variations i n CnP with geometric dihedral angle a t t h e higher angles of a t t a c k a r e associated with the change i n dynamic pressure over the r e a r of the model caused by incre- of flow i n s i d e s l i p mental changes of wing l i f t due t o t h e l a t e r a l component This e f f e c t i s such t h a t positive dihedral provides a l o c a l ( r e f . 10).
increase i n l i f t f o r the windward wing with an attendant s t a b i l i z i n g increase i n dynamic pressure over the afterbody. Negative dihedral provides an opposite e f f e c t .
Increasing t h e geometric dihedral from - 3 O t o 3 O leads t o an almost l i n e a r increase i n positive e f f e c t i v e dihedral a t a l l t e s t angles of a t t a c k and Mach numbers. There i s , however, a decrease i n t h e a b i l i t y of geometric dihedral t o produce e f f e c t i v e dihedral with increasing Mach number a t low angles of attack.
With the v e r t i c a l t a i l on, the trapezoidal-wing configuration generally displays small changes i n d i r e c t i o n a l s t a b i l i t y with wing dihedral a t t h e lower angles of a t t a c k . However, a t t h e higher test angles of a t t a c k t h e r e s u l t s a r e similar t o those f o r t h e configuration with t h e t a i l off i n t h a t positive geometric dihedral of t h e wing produces t h e greatest d i r e c t i o n a l s t a - b i l i t y and negative geometric dihedral produces t h e l e a s t . There i s l i t t l e or no difference i n t h e e f f e c t of geometric dihedral on f o r t h e configura- C z p t i o n with or without t h e v e r t i c a l t a i l , although it may be noted t h a t a t the higher Mach numbers the e f f e c t i v e dihedral varies only sliatly with angle of a t t a c k f o r the t a i l - o n case.
The effects of geometric dihedral on t h e s i d e s l i p parameters of t h e swept- .g configuration a r e shown i n figures 6 and 7 f o r t h e v e r t i c a l t a i l off and respectively. The e f f e c t s of geometric dihedral on Cnp f o r t h e swept-wing configuration a r e about t h e same a s those previously discussed f o r t h e trapezoidal-wing configuration. A s noted i n t h e data of figure 7 f o r t h e swept-wing Configuration, t h e large decrease i n directional s t a b i l i t y with angle of attack a t t h e lower t e s t Mach numbers i s o f f s e t a t t h e higher Mach numbers by the increased dynamic pressure induced by t h e wing on t h e afterbody.
a t low angles of attack, t h e config- Thus, i n s p i t e of t h e decrease i n CnP uration maintains positive directional s t a b i l i t y throughout t h e angle-of-attack range. I n the t e s t Mach number range planform does not greatly a f f e c t t h e directional s t a b i l i t y of t h e configuration.
Geometric dihedral of the swept wing produces e f f e c t s on similar t o those already noted f o r t h e trapezoidal-wing configuration, although t o a con- siderably l e s s e r degree. The Cz variation with a i s considerably more P negative a t low angles of a t t a c k f o r t h e swept wing ( f i g . 6 ) than f o r the trapezoidal wing ( f i g . 4 ) , p a r t i c u l a r l y a t t h e lower Mach numbers. To i l l u s - t r a t e t h i s f a c t more effectively, t h e slope i s shown i n figure 8 a s a CzPU function of Mach number f o r both wing planforms. This figure indicates t h a t i s much smaller i n absolute value f o r t h e trapezoidal-wing configuration C z P , than f o r t h e swept-wing configuration, and has only a s m a l l decrease (becoming l e s s negative) over the Mach number range. The swept-wing configuration has r e l a t i v e l y large negative values of a t t h e lower Mach numbers but these values decrease rapidly up t o a Mach number of about 3.40 and then show l i t t l e change with further increase i n Mach number. This e f f e c t of wing planform on may be explained by t h e differences i n the wing-panel lift-curve slope c z P U f o r the two wings. The trapezoidal wing has a leading-edge sweep of 31° so t h a t large portions of t h e wing are supersonic a t a l l test Mach numbers (leading edge swept ahead of Mach l i n e s ) . When t h i s configuration i s side- slipped, t h e l o c a l Mach number increases f o r the windward wing and decreases f o r t h e leeward wing. Since t h e lift-curve slope of a wing decreases with increase i n supersonic Mach number, t h e windward wing loses l i f t , and t h e lee- ward wing gains l i f t ; thus, less negative values of a r e attained. The swept wing, on t h e other hand, has a leading-edge sweep of 7 3 O and t h e e n t i r e wing i s subsonic a t Mach numbers up t o about 3.40, and large portions a r e sub- sonic even up t o t h e highest t e s t Mach number. Thus, t h e windward wing i n s i d e s l i p f o r t h i s configuration would have an increase i n lift-curve slope for i t s subsonic portion, whereas t h e leeward wing would have a decrease i n lift- curve slope.
This combination would lead t o more negative values of CzPa than f o r t h e trapezoidal-wing configuration. The decrease i n C a t t h e 2Pa higher Mach numbers f o r the swept wing i s caused by more of t h e windward wing becoming supersonic.
Longitudinal Characteristics The e f f e c t s of geometric dihedral on t h e aerodynamic c h a r a c t e r i s t i c s i n p i t c h a r e presented i n figures 9 and 10 f o r t h e trapezoidal- and swept-wing configurations, respectively. These data show t h a t t h e amount of geometric dihedral used f o r these t e s t s has l i t t l e or no e f f e c t on the p i t c h character- i s t i c s of t h e configurations. I n addition, t h e r e a r e e s s e n t i a l l y no e f f e c t s of planform on t h e l i n e a r i t y of the l i f t and pitching-moment curves with angle of attack, although, a s expected, the l i f t - c u r v e slope f o r the trapezoidal- wing configuration i s somewhat greater than t h a t f o r the swept-wing configuration.
CONCLUSIONS A n investigation made t o determine t h e e f f e c t s of wing geometric dihedral and planform on the 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 wing-body-tail model a t Mach numbers from 1.80 t o 4.63 indicated t h e following conclusions: 1. The d i r e c t i o n a l s t a b i l i t y was increased by positive geometric dihedral and decreased by negative geometric dihedral for both t h e t a i l - o n and t a i l - o f f configurations, p a r t i c u l a r l y a t the high angles of a t t a c k and Mach numbers a s a r e s u l t of dynamic-pressure e f f e c t s induced on t h e fuselage afterbody.
2. Positive e f f e c t i v e dihedral was increased by positive geometric dihe- d r a l and decreased by negative geometric dihedral.
3 . The swept wing with t h e high sweep angle and the subsonic leading edges provided l a r g e r negative values of e f f e c t i v e dihedral than did the trap- ezoidal wing with t h e lower sweep angle and t h e supersonic leading edges.
4. The amount of geometric dihedral used i n the wing configurations of these t e s t s had l i t t l e or no e f f e c t on the aerodynamic c h a r a c t e r i s t i c s i n pitch.
Langley Research Center, National Aeronautics and Space Administration, Langley Station, Hampton, Va., March 23, 1965.
a
FEFERENCES 1. Spearman, M. Leroy: Some Factors Affecting the Static Longitudinal and Directional Stability Characteristics of Supersonic Aircraft Configurations. NACA RM L57E24a, 1957.
2. Spearman, M. Leroy; and Henderson, Arthur, Jr.: Some Effects of Aircraft Configuration on Static Longitudinal and Directional Stability Character- istics at Supersonic Mach Numbers Below 3 . NACA RM L55L15a, 1956.
3. Robinson, Ross B . : Effects of Vertical Location of the Wing and Horizontal Tail on the Static Lateral and Directional Stability of a Trapezoidal- Wing Airplane Model at Mach Numbers of 1.41 and 2.01. NACA RM ~58~18,
4 . Spearman, M. Leroy: Investigation of the Aerodynamic Characteristics in
45O Sweptback-Wing Airplane Model With Various
Pitch and Sideslip of a
Vertical Locations of the Wing and Horizontal Tail - Effect of Wing
M = 2.01.
Location and Geometric Dihedral for the Wing-Body Combination, NACA RM ~55~18, 1955.
5. Spearman, M. Leroy; and Robinson, Ross B.: Investigation of the Aerodynamic
Characteristics in Pitch and Sideslip of a 45O Swept-Wing Airplane Con-
figuration With Various Vertical Locations of the Wing and Horizontal
Tail - Static Lateral and Directional Stability; Mach Numbers of 1.41
and 2.01. NACA RM L57J25a, 1957.
A n Approximation to the Effect of Geometric Dihedral on 6. Purser, Paul E . : the Rolling Moment Due to Sideslip for Wings at Transonic and Supersonic Speeds. NACA RM L52BOl, 1952.
7. Kuhn, Richard E.; and Draper, John W.: Wind-Tunnel Investigation of the
Effects of Geometric Dihedral on the Aerodynamic Characteristics in Pitch and Sideslip of an Unswept- and a 4 5 O Sweptback-Wing-Fuselage Combina- tion a t High Subsonic Speeds. NACA RM L53F09, 1953.
8. Boatright, William B.: Experimental Investigation of Effects of Wing Plan Form and Dihedral Angle on Sideslip Derivatives of Sweptback-Wing- Body Combinations at Supersonic Speeds. NACA RM ~58~08, 1958.
9. Fuller, Dennis E.; and Feryn, Maurice: Effect of Wing Height and Dihedral
on Stability Characteristics of a 76O Swept Wing Body at Mach Numbers
From 1.60 to 4.63. NASA TM X-1023, 1964.
1 0 . U l m a n n , Edward F.; and Ridyard, Herbert W.: Flow-Field Effects on Static Stability and Control at High Supersonic Mach Numbers.
NACA RM L55Llga, 39.10
4 17.15 - 4
1 . 6 4 1 I I 8.59 G e o m e t r i c d i h e d r a l F u s e l a g e a Figure 1.- Model drawing. (All dimensions in inches unless otherwise specified.)
0.75 Jpoo 7
I S t a . S t a .
5.24 17.15 / / M o m e n t c e n t e r
730 ' 7 0 ° , '
~- ~ ~- I-- _ _ -
1 -5.00 2
-20.00 S w e p t w i n g c a . S t a .
15.58
I
3 1 ' M o m e n t c e n t e r - @ - - T r a p e z o i d a l w i n g Figure 1.- Concluded.
.02 .02 .04 - -
-6 - 4 - 2 0 2 4 6 a l o
P , d e g (a) M = 250; a = 17O.
F i g u r e 2.- Typical aerodynamic characteristics in sideslip f o r trapezoidal-wing configuration. Tail on.
.04 .02
- .02
- . 0 4
.02 c l
- .02
- . 0 4
C Y
- .1
- .c
- 6 - 4 - 2 0 2 4 6 a 10
P , d e g (b) M = 4 . 6 3 ; a = 174 Figure 2- Concluded.
.02 c 1
- .02
- .04
- . L
-6 - 4 - 2 0 2 4 6 8 10 P , d e g (a) M = 1.80; a z 120.
F i g u r e 3.- Typical aerodynamic characteristics in sideslip f o r swept-wing configuration.
- . . .. I . . .
I
.06 .04 .02 ,.02 .04 .06 .02
- .02
- .04 .1 C Y
- .1
- .2 - 6 - 4 - 2 0 2 4 6 8 1 P , d e g (b) M = 1.80; a zz 17O.
Figure 3.- Continued.
.06 .04 .02
Cn o
- .02
- .04
- .06
.02 - .02
- .04
.1 CY
- .1
- . C
-6 - 4 - 2 0 2 4 6 8 10 B , d e g ( c ) M = 2.86; a = 120.
Figure 3.- Continued.
I
.06 .04 .02 C n
- .02
- .04
.02 c l
- .02
- . 0 4 .1 C Y
- .1
.-
- 6 - 4 - 2 0 2 4 6 8 lo B,de!J (d) M = 286; a = 170.
Figure 3.- Concluded.
,002
crl
P
..002 .002 C
P
- '.004 CY
B
-.02 -
a -4 0 4 8 12 16 20
a, d e g (at M = 250.
Effect of geometric dihedral on sideslip parameters f o r trapezoidal-wing configuration. Tail off.
F i g u r e 4.- .oo;
ctl
P C
-.002 .002 C -.002 - .004 CY
P
-.02
-a -4 0 4 a 12 16 20
(b) M = 286.
Figure 4.- Continued.
.ooi
cnP 0
-.002 ,002
c'P 0
-.002
.a -4 0 4 8 12 16 20
a, deg (c) M = 3.95.
Figure 4.- Continued.
.002 c n p 0 -.002 .002 C -.002 C Y
P
-.02 -8 -4 0 4 8 1 2 1 6 20 a, deg (d) M = 4.63.
Figure 4.- Concluded.
CY
P
(a) M = 2.50.
Effect of geometric dihedral o n sideslip parameters f o r trapezoidal-wing configuration. Tail on.
Figure 5.- .010 .008 .006 .004 .002 -.004
cyB
-.02 -0 -4 0 4 8 12 16 20 a, deg (b) M = 286.
Figure 5.- Continued.
.008 .006 .002 -.002 -.02
-
8 -4 0 4 8 12 1 6 20 a, deg (c) M = 3.95.
Figure 5.- Continued.
.. .. .. ..-. __ .. .
.OOE .004
cnP
.002 .002
cyP
-.02
-a -4 0 4 8 12 16 20
a, deg m (d) M = 4.63.
Figure 5 . - Concluded.
-.I CY
B
(a) M = 1.80.
Figure 6.- Effect of geometric dihedral o n sideslip parameters for swept-wing configuration. Tail off.
a, deg (b) M = 216.
Figure 6.- Continued.
C Y
P
(c) M = 250.
Figure 6 . - Continued.
(d) M = 286.
Figure 6.- Continued.
C Y
P
(e) M = 3.95.
Figure 6.- Continued.
CY ( f ) M = 4.63.
Figure 6.- Concluded I I S w e p t w i n g 20 2 4 28 - 8 - 4 0 4 8 1 2 a, d e g (a) M = 1.80.
Effect of geometric dihedral o n sideslip parameters f o r swept-wing configuration. Tail on.
Figure 7.- 0 4 8 1 2 1 6 20 2 4 28 a, d e g (b) M = 216.
Figure 7.- Continued.
a, d e g (c) M = 2.50.
Figure 7.- Continued.
- I -8 - 4 0 4 8 12 16 20 a, d e g (d) M = 2.86.
Figure 7.- Continued (e) M = 3.95.
Figure 7.- Continued.
... . . . . . . ...
0 4 8 1 2 1 6 20 24 - 4 a, d e g (f) M = 4.63.
Figure 7 . - Concluded.
M Figure 8.- Effect of w i n g planform and Mach number on t h e variation of t h e slope of t h e lateral-stability parameter w i t h angle of attack.
I.'.
i I I
i
I
I I L/D
r
I 0 0
I
0 3 0 -3
- l I
I
- * I I/ I
" I I 1
I/
-3 1, ~
!
ri
- 4 1
I,
I
- 5 I I
!
~ I" II
il
CL (a) M = 250.
Figure 9.- Effect of geometric dihedral o n aerodynamic characteristics in pitch for trapezoidal-wing configuration. Tail on.
- v -.2 -.l 0 .1 . 2 .3 . 4 .5 .7 .8 CL ( a ) Concluded Figure 9.- Continued.
I I I ,f I I L/U 0 0 - 1 .32 n 3 0 -3 -2 .20 -3 .24 - 4 .20 - 5 .16
A
/ A
T r a p e z o i d a l w i n g .12 .00 .04 - .1 .1 .2 .3 , .7 .8 CL (b) M = 286.
Figure 9.- Continued.
4 1
r, d e g I , 3 ..
C L (b) Concluded.
Figure 9.- Continued.
1 2 C Q (c) M = 3.95.
Figure 9 . - Continued.
(c) Concluded.
Figure 9 . - Continued.
.
.
L / O 1 -1 -2 -3 I24 - 4 , 2 0 I 16 - 1 2 -08 so4 (d) M = 4.63.
Figure 9 . - Continued.
T r a p e z o i d a l i\ w i n g , . 3 .5 .6 Id) Concluded.
Figure 9.- Concluded.
.6 . 7 . E 0 .1 . 2 .3 .4 C L (a) M = 1.80.
Figure 10.- Effect of geometric dihedral o n aerodynamic characteristics in pitch f o r swept-wing configuration. Tail on.
(a) Concluded.
Figure 10.- Continued.
L/D (b) M = 216.
Figure 10.- Continued.
4 9
1111111111 I 1 1 1 1 1 1 1 1 1 1 I I I I I I 111.1111.11111 (b) Concluded.
Figure 10.- C o n t i n u e d L /o .28 - 2 4 .20 .16 .12 .08 - 0 4 (c) M = 250.
Figure 10.- Continued.
( c ) Concluded.
Figure 10.- Continued.
. - ._ . . .. - . .... . . .. . .. . , -,. ,- ._.._..I - . I . 11.11 I I I, 1 1 1 . I., I , . I I I I 111 I .,..,.,,,, I I I. , I .24 .20 .16 .I2 c g .08 .04 , o -.2 -.1 0 .1 .2 .3 .4 .5 .6 . 7 CL (d) M = 286.
Figure 10.- Continued CL (d) Concluded.
Figure 10.- Continued.
L/O .16 .12 .08 .04 : o CL (el M = 3.95.
Figure 1 0 . - Continued.
(e) Concluded.
Figure 10.- Continued 08 c g (f) M = 4.63.
Figure 10.- Continued.
. . .
- . 2 -.l 0 .1 .2 . 3 . 4 .5 C L (f) C o n c l u d e d Figure 10.- Concluded.
NASA-Langley, 1965 L-4292 I “The aeronautical and space activities of the United States shall be
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