Lichtenstein, Jacob H

Williams, James L

English

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COI4flDE NTIAL
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RM L58B26 
NACA 
RESEARCH MEMORANDUM 
LOW-SPEED INVESTIGATION OF THE EFFECTS OF FREQUENCY AND 
AMPLITUDE OF OSCILLATION IN SIDESLIP ON THE LATERALb. 
•1, 
STABILITY DERIVATIVES OF A 60° DELTA WING, A
c,1 45° SWEPTBACK WING, AND AN UNSWEPT WING 
By lacob H. Lichtenstei.n and James L. Williams
C', 
Langley Aeronautical Laboratory 	 . i 
Langley Field, Va.	
..°/ 
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C.,' 
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CLASSIFIED DOCU9SSN'F 
This material contains Information affecting the National Defense of the United States within the mg 
of the espionage laws, TIUe 18, U.S.C., Secs. 793 and 794, the transmission or revelation of which,any 
manner to an unatitherized person Is prohibited by law. 
NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
WASH I NGTOt1 
Tune 5, 1952 
CON Fl DENTIAL
https://ntrs.nasa.gov/search.jsp?R=19930090030 2020-06-17T06:43:01+00:00Z
NACA RN L58B26	 coIAI 
NATIONAL ADVISORY CO'ri FOR AERONAUTICS

RESEARCH MEMORA.NDUM 
LOW-SPEED ThIVESTIGATION OF TEE EFFECTS OF FREQUENCY AND 
AMPLITUDE OF OSCILLATION IN SIDESLIP ON TILE LATERAL 
STABILITY DERIVATIVES OF A 600 DELTA WING, A 
1i7° SWEPTEACK WING, AND AN UNSWEPT WING 
By Jacob H. Lichtenstein and James L. Williams 
SUMMARY 
A low-speed investigation has been conducted in the Langley sta-. 
bility tunnel to study the effects of frequency and amplitude of side-
slipping motion on the lateral stability derivatives of a 600 delta wing, 
a 1.i-7° sweptback wing, and an unswept wing. The investigation was made 
for values of the reduced-frequency parameter of 0.066 and 0.218 and 
for a range of amplitudes from ±2° to ±6°. 
The results of the investigation indicated that increasing the 
frequency of the oscillation generally produced an appreciable change 
in magnitude of the lateral oscillatory stability derivatives in the 
higher angle-of-attack range. This effect was greatest for the 600 delta 
wing and smallest for the unswept wing and generally resulted in a more 
linear variation of these derivatives with angle of attack. For the 
relatively high frequency at which the amplitude was varied, there 
appeared to be little effect on the measured derivatives as a result of 
the change in amplitude of the oscillation. 
IWRODUCTION 
At the present time, there is considerable interest in stability 
derivatives measured by various oscillation techniques. The results of 
such tests are of interest mainly because of the very large effects of 
frequency and amplitude on the stability derivatives. There is consider-
able literature on oscillation-in-yaw tests; some typical results for 
wing-alone and complete-model configurations are given, for example, 
C0'IDENTIAL
2	 CONFIDENTIAL	 NACA RM L58B26 
in references 1, 2, and 3. Results of some oscillation in pure yawing 
tests are presented in reference i-. Some preliminary free-danrping 
oscillation-in-sideslip tests on -wins alone are presented in reference 5, 
and forced-oscillation tests of a 6o" delta complete model are presented 
in reference 6. 
The purpose of this investigation was to obtain information about 
the effects of frequency and. amplitude of pure sideslipping oscillations 
by the forced-oscillation technique on the stability derivatives of a 
600 delta wing, a k5° swept wing, and an unswept wing. The frequencies 
of oscillation used in the tests-were 1 and 3.31 cycles per second 
(wb/2V of 0.066 and 0.218) and the amplitude of oscillation varied. 
from ±2° to ±6°.
SYMBOLS 
The data are presented in the form of coefficients of forces and 
moirients which are referred to the stability system of axes with the-
origin at the projection on the plane of symmetry of the quarter-chord 
point of the mean aerodynamic chord. The positive direction of forces, 
moments, angular displacements, and velocities are shown in figure 1. 
The coefficients and symbols used are defined as follows: 
CL lift coefficient,	
Lift 
qS' 
drag coefficient,	 Drag 
qS 
Cm pitching-moment coefficient, - 
• qSc 
- M 
_2L C 7, . rolling-moment coefficient, 
•	
-
qSb 
C yawing-moment coefficient, - 
qSb 
Mx rolling moment, ft-lb 
pitching moment, ft-lb
yawing moment, ft-lb 
q
	 dynamic pressure, j)V, lb/sq ft 
CONFIDENTIAL 
NACA RM L58B26	 CONF]IENTIAL	 3 
p	 mass density of air, slugs/cu ft 
V	 free-stream velocity, ft/sec	 - 
S	 area of wing, sq ft	 - 
b	 span of wing, ft 
mean aerodamic chord, 2 fb/2c2dy, ft 
c	 chord, ft 
X,Y,Z	 stability-axis system 
y	 distance along Y-axis, ft 
a	 angle of attack with respect to wing-chord plane, deg 
angle of sideslip, degrees unless otherwise specified 
= , radians/sec 
Ac/)I	 sweepback of quarter-chord line 
angular velocity, 2irf, radians/sec 
f	 frequency, cps 
=	 per radian 
C = -i, per radian 
=_
Ii.	 CONFIDEWPIAL	 NACA RM L58B26 
reduced-frequency parameter 
2V 
Subscript: 
U)	 mean oscillatory parameter 
MODELS AND APPARATUS 
The models used in this investigation were the same as those used 
in the tests of references 1, 11-, and 5 . A sketch of the models is shown 
in figure 2. These models consisted of an unswept wing (Ac/l i. = 0) and 
a 11-5° sweptback wing (Ac/li. = 11-5°), both of aspect ratio 1I and taper 
ratio of 0.6, and a 600 delta wing of aspect ratio 2.31. Each of the 
wings was made from 3/ il--inch-thick plywood with a circular leading edge 
and a beveled trailing edge; the airfoil section, therefore, was essen-
tially a flat plate. The trailing edge of the wings was beveled to give 
a trailing-edge angle of 10 . Photographs of the three wings mounted 
in the tunnel are shown in figure 3. 
The forced-oscillation-in-sideSliP apparatus used for the present 
tests was the same as that used for the oscillation tests described in 
reference 6; and the data-reduction method and apparatus are described 
in reference -I-. Since the apparatus is adequately described in the 
references mentioned, no further description of the apparatus will be 
made herein.
TESTS AND CORRECTIONS 
Tests 
The tests were conducted in the 6- by 6-foot test section of the 
Langley stability tunnel at a dynamic pressure of 211 . . 9 pounds per square 
foot and a Mach number of 0 .13 . The Reynolds numbers, based upon the 
wing mean aerodynamic chords, were 0.7 x 106 for the unswept and swept 
wings and 1.6 x io6 for the delta wing. 
The forced-oscillation-in-sideSliP tests were made for each of 
the wings as shown in the following table: 
CONFIDENTIAL
NACA RM L58B26	 CONFIDTIAL	 5 
Configuration a.	 range, deg f, cps f3,	 deg 
Unswept wing 0 to about 16 1.00 3.31
0.066 
-	 .218
±2 
±2,	 ±4-, ±6 
4-5	 swept wing 0 to about 30 1.00 3.31
.066 
.218
±2 
±2,	 ±1i, ±6 
600 delta wing 0 to about 1.00 3.31
.066 
.218
±2 
±2, ±1, ±6
The values of	 used in the investigation are believed to be 
2V 
within the range of those which may be encountered by an airplane. 
No static tests were made and the static longitudinal and lateral 
data were taken from reference 5. 
Corrections 
Jet boundary corrections to the angle of attack had already been 
applied to the static data of reference 5 and the same corrections to 
the angles of attack have been applied to the data described herein. 
The dynamic data have been corrected for a variation in angularity of 
the airstream as the model osëillated back and forth. No other cor-
rections have been applied to the data because it is believed that, in 
general, the corrections are small; however, the support-strut inter-• 
ference may have some effect at the higher angles of attack. 
RESULTS AND DISCUSSION 
The static test data were taken from reference 5. The lift, drag, 
and pitching-moment coefficients for the three wings are presented herein 
for convenience in figure 14, and the static lateral stability data are 
presented in figures 5, 6, and 7 as the zero frequency data. The oscil-
lation data are presented in figures 5, 6, and 7 for the 60° delta, the 
1 0
 swept wing, and the unswept wing, respectively. The static longitu-
dinal data have been discussed in reference 5 and therefore no discussion 
will be made herein.
CONFIDENTIAL 
6	 C0NFIDET1TIAL	 NACA RM L58B26 
600
 Delta Wing 
Effect of frequency.- The effects of changes in the frequency of 
oscillation at a maximum amplitude of ±2° on the four stability deriva-
tives (Cn. , C	 , C 1	 , and C 1	 \ are shown in figure 5(a). 
\.	 13,u)	 f3,w 
The effects of frequency manifest themselves by an appreciable change 
in magnitude of the derivative with changes in frequency at the high 
angles of attack and relatively little change in magnitude at the low 
angles of attack. Increasing the frequency of oscillation decreased 
the variations of the stability derivative with angle of attack. The 
results of these tests are similar to the results obtained in previous 
oscillation-in-sideslip tests (ref. 6) and oscillation-in-yaw tests 
(ref. 1). 
Effect of amplitude.- At an oscillation frequency of 3.31 cycles 
per second ( = 0.2l8) there appeared to be very little effect of 
varying the maximum amplitude of oscillation from ±2° to ±6° on any 
of the four stability derivatives (fig. 5(b)). This result is similar 
to that presented in reference 1 for oscillation-in-yaw tests where 
relatively minor effects also were found at the high frequencies, but 
considerable effects were found to exist at the low frequencies. 
)4 5 Swept Wing 
Effect of frequency.- The effects of changes in frequency of the - 
sideslip oscillation for the
	 swept wing are shown in figure 6(a).

An increase in the frequency generally decreased the variations of the 
derivatives with angle of attack for all four derivatives, Cn 
, C 1 . , and C 1 . The effects of frequency appeared more pro-
J3,w	 13,w	 j3,w 
nounced at the higher angles of attack; these effects are similar to 
those obtained for the 60° delta wing. This frequency effect is gener-
ally similar to that obtained previously for oscillation-in-yaw tests 
reported in reference 1. 
Effect of amplitude.- The effect of amplitude of oscillation 
(fig. 6(b)) for a reduced frequency of
	 = 0.218 shows very little

effect on any of the four stability derivatives. 
Unswept Wing 
Effect of freque.- The oscillatory data show the effects of fre-
quency at a maximum amplitude of sideslip of ±2° in figure 7(a). For 
CONFIDEWrLAL
NACA RM L78B26	 CONFIDENTIAL	 7 
the range of frequencies employed in these tests, there appeared to be 
a negligible effect of frequency on the yawing-moment acceleration deriv-
ative (Ca. \ throughout the angle-of-attack range and on the directional 
'	 f3,w) 
stability (C) up to a = 12°. Above a =	 the directional sta-

bility decreased as the frequency of oscillation increased. These results 
generally agree with those for the oscillation-in-yaw tests of 
reference 1. 
The effects of frequency on the rolling-moment acceleration deriva-
tive C 1	 were quite pronounced, with the low-frequency results exhib-
f3,U) 
iting a very erratic variation at the higher angles of attack and the 
high-frequency results a much smoother variation. The erratic variation 
of C 1	 at the low frequency probably results from the inherent stal-

t3,w 
ling characteristics of an unswept wing. There appeared to be no con-
sistent effect of frequency. The effect of frequency on the oscillatory 
dihedral parameter C 1	 appeared to be appreciable at some angles of 
13,u) 
attack but no consistent variation with frequency was obtained over the 
angle-of-attack range. 
Effect of amplitude. - The effect of amplitude at a value of 
= 0.218 appeared to be rather small on both yawing-moment and rolling-
moment derivatives. (See fig. 7(b).) 
CONCLUSIONS 
The results of some oscillation-in-sideslip tests performed on three 
flat-plate airfoil wings, a 600 delta wing, a 11-5° swept wing, and an 
unswept wing, indicate the following conclusions: 
1. Increasing the frequency of the oscillation generally produced 
an appreciable change in magnitude of the oscillatory stability deriva-
tives in the higher angle-of-attack range. This effect was greatest for 
the 600 delta wing and smallest for the unswept wing and generally 
resulted in a more linear variation of these derivatives with angle of. 
attack.
CONFIDENTIAL	 -
8	 CONFIDENTIAL	 NACA RM L58B26 
2. For the relatively high frequency at which the amplitude was 
varied (reduced-frequency parameter equal tb 0.218), there appeared to 
be little effect on the measured derivatives as a result of the change 
in amplitude of oscillation. 
Langley Aeronautical Laboratory, 
National Advisory Committee for Aeronautics, 
Langley Field, Va., February 12, 1958. 
1. Fisher, Lewis R.: Experimental Determination of the Effects of Fre-
quency and Amplitude on the Lateral Stability Derivatives for a 
Delta, a Swept, and an Unswept Wing Oscillating in Yaw. NACA 
RM L56A19, 1956. 
2. Campbell, John P., Johnson, Joseph L., Jr., and Hewes, Donald E.: 
Low-Speed Study of the Effect of Frequency on the Stability Deriva-
tives of Wings Oscillating in Yaw With Particular Reference to High 
Angle-of-Attack Conditions. NACA RM L55H 05, 1955. 
3. Bird, John, D., Fisher, Lewis R., and Hubbard, Sadie M.: Some Effects 
of Frequency on the Contribution of a Vertical Tail to the Free 
Aerodynamic Damping of a Model Oscillating in Yaw. NACA Rep. 1130, 
1953 . (Supersedes NACA TN 2657.) 
ti-. Queijo, M. J., Fletcher, Herman S., Marple, C. G., and Hughes, F. M.: 
Preliminary Measurements of the Aerodynamic Yawing Derivatives of 
a Triangular, a Swept, and an Unswept Wing Performing Pure Yawing 
Oscillations, With a Description of the Instrumentation Employed.. 
NACA RM L55L111-, 1956. 
5. Riley, Donald R., Bird, John D., and Fisher, Lewis R.: Experimental 
Determination of the Aerodynamic Derivatives Arising From Accelera-
tion in Sideslip for a Triangular, a Swept, and an Unswept Wing. 
NACA EM L55A07', 1955. 
6. Lichtenstein, Jacob H., and Williams, James L.: Effect of Frequency 
of Sid.eslipping Motion on the Lateral Stability Derivatives of a 
Typical Delta-Wing Airplane. NACA EM L57F07, 1957. 
CONFIDENTIAL
NACA RM L58B26	 CONFIDENTIAL	 9 
Y 
/ 
4 
I	 Yawing 
I- ________ 
Yaw referen
Rolling moment 
Li ft 
Pitching	 Rolling moment 
moment 
_ _-x-1'' 
Relative wind
Section A-A 
2 
Figure 1.- System of stability axes. Arrows indicate positive forces, 
moments, and angular displacements. Yaw reference is generally chosen 
to coincide with initial relative wind. 
CONFIDENTIAL
Circular leading edge-
I. 697_/ 
6.75
4.28 
36—
Mounting point Rounded tip 
2.8/ 
/1.25 
/8	 IJ\-Beve/ed portion 
10	 CONFIDENTIAL	 NACA EM L58B26 
/5.59
/
- Mounting point 
/	
I C'IPCUIOP leading edge 
31/8 /1 Beveled portion 
/	 I r	 4.28 
-	 -4 -'	 /8 
-'	 36
Delta wing 
Aspect ratio................... 2.3/ 
Leading-edge sweep angle, deg....... 60 
£'thedral angle, deg.............. 0 
Tw'st, deg..................... 0 
Airfoil section ............. F/at p/ate 
rea, sq.	 in................ 561.20 Span, in................... 36.00 
Mean aerodynamic chord, in ...... 20.79 
Mounting point 
c/4 
/.69,7 
6.75T4 
-.1'	 36 
Swept wing 
•	 .	 Aspect ratio............. 4.0 
Taper ratio.............. 0.6 
Circular leading edge 	 QuartercI0rd sweep angle, deg. .	 45 
-Rounded tip	 Dihedral angle, deg........ 0 
-Beveled portion
	
Twist, deg............. 0 
Airfoil section.......F/of plate 
Area, sq. in	 .......... 324 
Span, in	 ............ 36 
Mean aerodynamic chord, in.. . . 9.19 
linswept wing 
Aspect ratio............. 4.0 
Taper ratio...........
...	 0.6 Quarter-chord sweep angle, deg. .. 0. 
Dihedral angle, deg............. a. 
Twist,deg.................. 0 
Airfoil section........ Flat p/ate 
Area, sq. in............. 324 Span, in.............
-.	 36 
Mean cerodynomic chord, in.. .	 . 9 / 9
Circular leading edge
Center line	 /0.0 bevel 
-	 4.28
Section A-A 
Figure 2.- Sketches and geometric characteristics of the three wing

models investigated. All dimensions are in inches. 
CONFIDENTIAL 
I
II I 'IF 
NACA RN L78B26	 CONFIDENTIAL	 11 
(a) 600 delta wing.	 L-87320 
('b) 14 5
 swept wing.	 L-852l 
Figure 3 . - Photographs of the three wing models mounted on the oscil-
lation test rig in the 6- by 6-foot test section of the Langley 
stability tunnel.
CONFIDENTIAL
12	 CONFIDENTIAL	 NACA RM L58B26 
F 
(c) Unswept wing.	 L-87322 
Figure 3.- Concluded. 
CONFIDETflIAL
NACA RM L58B26	 CONFIDENTIAL	 13 
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CONFIDETTIAL 
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CONFIDENTIAL	 NACA RM L58B26 
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on the oscillatory yawing- and rolling-moment derivatives for the 
unswept wing.
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NACA RM L78B26	 CONFIDENTIAL	 19 
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Angle of attac.4 W, deg 	 Angle of a/tack, L2 deg
(b) Effect of amplitude of oscillation.

Figure 7.- Concluded. 
CONFIDEPIAL 
NACA - Langley Field, Vs.
CON Fl DENTIAL 
CON Fl DENTIAL


Low-Speed Investigation of the Effects of Frequency and Amplitude of Oscillation in Sideslip on the Lateral Stability Derivatives of a 60 D Delta Wing, a 45 D Sweptback Wing, and an Unswept Wing

Low-Speed Investigation of the Effects of Frequency and Amplitude of Oscillation in Sideslip on the Lateral Stability Derivatives of a 60 D Delta Wing, a 45 D Sweptback Wing, and an Unswept Wing

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