Palmer, William E

English

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NACA 
RESEARCH MEMORANDUM 
A WlliD- TUNNEL INVESTIGATION OF THE lJJW -AMPLITUDE 
DA1I1PllJG IN YAW AND DIRECTIONAL STABILITY 
OF A FUSELAGE - TAIL CONFIGURATION 
AT MACH NUMBERS UP TO 1.10 
By William E . Palmer 
Langley Aeronautical Laboratory 
Langley Field, Va. 
NATIONAL ADVISORY COMM ITTEE 
FOR AERONAUTICS 
WAS HI NGTON 
May 16, 1957 
Declassified Ju 22 1 
https://ntrs.nasa.gov/search.jsp?R=19930089662 2020-06-17T05:07:36+00:00Z

I 
A NACA RM L57C15 
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
RESEARCH MEMORANDUM 
A WIND-TUNNEL INVESTIGATION OF THE LOW-AMPLITUDE 
DAMPING IN YAW AND DIRECTIONAL STABILITY 
OF A FUSELAGE-TAIL CONFIGURATION 
AT MACH NUMBERS UP TO 1.10 
By William E. Palmer 
SUMMARY 
A low-amplitude free-oscillation investigation was made at zero 
angle of attack of the damping in yaw and directional stability of a 
fuselage-tail configuration through a range of reduced frequency from 
about 0.03 to 0.11 and Reynolds numbers from about 4 x 106 to 22 x 106 
based on body length at Mach numbers up to 0.94. Limited additional 
tests were made at Mach numbers up to 1.10. 
The results indicate that the damping in yaw decreased appreciably 
at Mach numbers above 0 . 8 and became a minimum near Mach numbers of 1.0. 
At the higher test Mach numbers, the damping increased to a value at 
least as great as that at subsonic speeds. The directional-stability 
parameter decreased rapidly at high subsonic speeds. 
INTRODUCTION 
Certain high-speed aircraft configurations have experienced a lack 
of damping of low-amplitude oscillations in yaw at high subsonic Mach 
numbers. (See ref. 1, for example.) This undamped lateral oscillation 
is difficult to control and reduc~s ' the eff-iciency of the aircraft as a 
gun platform. 
The purpose of the present investigation is to determine the effect 
of Mach number and Reynolds number on the oscillatory damping in yaw and 
directional stability of an airplane model through a range of reduced 
frequency at zero angle of a ttack . The configuration chosen for the 
i nvestigation was a f uselage-tail model of a research airplane which is 
known t o be subject to snaking oscillations at transonic speeds. 
2 NACA RM LS'7C1S 
SYMBOLS 
The data are referred to the stability axes, the origin of which is 
taken as the longitudinal location of the ~uarter-chord point of the 
mean aerodynamic chord of the normal wing position of the model tested. 
The symbols are defined as follows: 
a 
b 
C 
value of damping, ft-lb/radian/sec 
assumed wing span, 2 ft 
mechanical spring constant, ft-lb/radian 
Yawing moment 
~Sb 
Cn~ :=: 
I Z 
k 
M 
yawing moment of inertia of model, ft-lb-sec2 
reduced-fre~uency parameter, rub/2V 
Mach number 
tunnel stagnation pressure, in. Hg 
dynamic pressure, ! pv2, lb/s~ ft 
2 
'"\ 
NACA RM L57C15 3 
R Reynolds number based on body length 
yawing velocity, dW/dt, radians/sec 
r yawing acceleration, d2w/dt2, radians/sec2 
S assumed wing area, 0.663 sq ft 
Tl / 2 time to damp to one-half amplitude, sec 
t time, sec 
V free-stream velocity, ft/sec 
~ angle of sideslip, radians 
~ d~/dt, radians/sec 
ill circular frequency, radians/sec 
p mass density of air or Freon-12, Ib-sec2/ft4 
angle of yaw (equal to -13 for wind tunnel), radians 
Subscripts: 
f tare value due to mechanical friction 
value measured during oscillatory motion 
00 undi sturbed free-stream conditions 
APP ARATUS AN]) MODEL 
The tests wer e made i n the Langley l ow-turbulence pressure tunnel. 
The tunnel can accommodate tests in a i r at pressures of 1 to 10 atmos-
pheres at Mach numbers up to 0 . 4 and in Freon-12 at pressures of 1/10 
t o 1 atmosphere at equivalent air Mach numbers from 0.4 to 0.94. Slots 
i n the ceili ng and f l oor of the test secti on can be opened to permit 
test s up to a Mach number of approximately 1.1 in Freon. Freon as a 
test medium gives "the added advantage of permitting lower oscillating 
frequencies for a given reduced f r equency. 
The mG J.<o2., "Thich is chown ':"n f igure 1., was sting mounted in the 
t.unrGl. It is a · /~4-sccj.e mode- of the Bell X- I airplane. Inasmuch 
4 NACA RM L57C15 
as wings have little effect on damping ' in yaw or directional stability 
at zero angle of attack, the model was tested without wings. Horizontal 
and vertical tails of the model had NACA 65-008 airfoil sections paral-
lel to free stream. 
The model was supported at its center of gravity by means of flex-
ure plates which permitted freedom in yaw with restraint in pitch and 
roll. Electrical strain gages were attached to these flexure plates to 
record on pen-tyPe recorders the time history of the yaw deflections as 
the model oscillated freely. An initial displacement of 10 in yaw was 
produced by an eccentric cam and a direct-current motor located in the 
model nose and attached to the sting. A photograph of the model with 
nosepiece off is shown in figure 2. At a given Mach number and Reynolds 
number, the frequency of oscillation was varied by use of three inter-
changeable pairs of flexure plates identified herein as flexure plates 
1, 2, and 3, which had mechanical spring constants C of 217, 100, and 
26 foot-pounds per radian, respectively. 
TESTS 
The tests consisted of de~lecting the model 10 in yaw and then 
releasing it. The resulting free oscillation was recorded against time. 
These tests were made through a range of reduced frequency (mb/2V) by 
variation of the free-stream velocity, stagnation pressure, and spring 
constant of the yaw flexure plates. (See fig. 3(a).) The range of 
test Reynolds number and Mach number converted to equivalent air Mach 
number by the method of reference 2 is shown in figure 3(b). A slight 
variation in stagnation pressure from test to test caused small varia-
tions in Reynolds number at each nominal pressure. The model angle of 
attack was 00 for the entire test. 
EFFECTS OF TECHNIQUE 
The test technique used in this investigation was selected at a 
time when more positive methods of measuring aerodynamic damping were 
unavailable. The technique is severely limited in accuracy in those 
test ranges where the model motion is influenced by such factors as: 
(1) turbulence in the free stream, (2) resonant conditions in the free 
stream caused by presence of the tunnel walls (ref. 3), (3) tunnel-wall 
reflected shock waves, and (4) sting flexibility. 
Unpublished tests made with a hot-wire anemometer in the Langley 
low-turbulence pressure tunnel show that the level of airstream turbu-
lence in this tunnel is low throughout the Mach number range with the 
NACA RM L57C15 5 
test section slots either open or closed. On the basis of these results, 
it is believed that the low level of airstream turbulence in the low-
turbulence pressure tunnel did not appreciably affect the damping trends 
determined. 
The conditions for resonance of the airstream between tunnel walls 
have been predicted theoretically in reference 3. For the present tun-
nel test conditions, the critical condition of resonance occurs near a 
Mach number of unity. The theory was developed, however, for the two-
dimensional case. Inasmuch as the chord length of the lifting surface 
of the vertical tail was small in comparison with the tunnel width (1:10) 
and the aspect ratio of the lifting surface was only 2, it appears prob-
able that the effects of resonance of the airstream on model response 
would be minor for the present investigation. 
Calculations on the position of the bow-shock reflections from the 
tunnel walls (ref. 4) indicate that reflections strike the nose of the 
model forward of the maximum body diameter only at Mach numbers of 1.03 
to 1.05. Since the model was located in the center of the tunnel and 
was performing oscillations of small amplitude, the reflected waves 
would be expected to strike the model on opposite sides at nearly the 
same longitudinal location and with about the same strength. The effect 
of shock reflections on model response is believed negligible, there-
fore, even in the range of Mach number from 1.03 to 1.05. 
In order to obtain adequate amplitude of oscillations while main-
taining scale-model afterbody shape, sting diameter at the base of the 
model was quite small and resulted in a relatively flexible sting 
(fig. 1). Initial displacement of the model by the eccentric cam pre-
stressed the sting so that a sting oscillation resulted when the cam 
was released for each test. Although the model was mechanically coupled 
to the sting through the relatively weak flexure plates, oscillation of 
the model on the sting caused very little sting excitation because the 
mass center of gravity of the model was maintained on the oscillation 
axis and because of the divergence between the resonant frequencies of 
the model and of the sting support. Oscillograph records verified the 
small response of the sting when the model was oscillated. A dynamic 
analysis made of the first-order effects of the above factors on the 
measured damping indicated that sting response due to initial model dis-
placement and to model-sting coupling could affect the measured values 
of damping from approximately 3 to 20 percent. This possible error in 
measurement would not, of course, affect the trends of measured damping 
as presented in this paper. 
It is recognized that the preceding effects on aerodynamic damping 
measured with the free-decay oscillation technique will become more pro-
nounced as the actual model damping decreases. 
L 
6 NACA RM L57Cl5 
REDUCTION OF DATA 
Determination of the damping-in-yavT and directional-stability 
derivatives by use of the free-oscillation techni~ue is discussed i n 
reference 5. In nondimensional form, they may be expressed, respec-
tively, as 
and 
where the subscript f denotes wind-off test values. The values of a 
and af are determined from the relation 
Wind-off test runs were made with various parts of the model 
removed in order to determine the variation of ar with fre~uency 
for each flexure plate. Values of ar for use in the damping-in-yaw 
e~uation were then interpolated at the wind-on fre~uency. 
The values of spring constant C for the three flexure plates were 
determined from static calibration. The value of I Z for the model waS 
then determined from the wind-off tests by use of the expre s sion 
RESULTS AND DISCUSSION 
Damping in Yaw 
Figure 4 shows the variation of 
(Cnr) (I) - (Cn~) (I) wit n Mach number for 
the damping- in-yaw paramet er 
the various :'l..;:xt...Te ;.18.-:'\;:,5 anu 
NACA RM L57C15 7 
stagnation pressures. The scatter of test points is an indication of 
the accuracy of the data based on repeatability and appears to be gener-
ally within ±0.05. Within this accuracy, there appears to be no effect 
of Reynolds number (stagnation pressure). Increasing the reduced fre-
quency (from flexure plate 3 to 1) generally reduced the damping in 
yaw. It should be noted, however, that this apparent trend is contrary 
to theory (ref. 6) and is almost within the estimated accuracy of the 
data. The most important trend to be noted is the change in damping 
with Mach number as the Mach number approaches unity. The damping 
begins decreasing at a Mach number of 0.8 and decreases progressively 
to near the closed-tunnel choke Mach number of about 0.94. For the one 
test at a Mach number of 1.0 at a stagnation pressure of 19 inches mer-
cury (tunnel slots open), the aerodynamic damping in yaw was apparently 
sufficiently negative to offset the tare damping of the system so that 
the model experienced a sustained oscillation of about ±lo. A negative 
value of aerodynamic damping probably results from the turbulent energy 
in the airstream which, although very low, can influence the model 
motion when the model aerodynamic damping approaches zero. At Mach 
numbers of 1.05 and 1.10, the damping increased to a value equal to 
or greater than that measured at subsonic speeds. 
Directional Stability 
Variation of the directional-stability parameter with Mach number 
is shown in figure 5 for the various flexure plates and stagnation pres-
sures. There was an increase in the stability parameter (Cn~)m + 
(k2Cnr)m with a decrease in reduced frequency. The indicated increase 
in stability at Mach numbers up to 0.85 includes the effect of decreasing 
reduced frequency (fig . 3(a)). The actual increase with Mach number is 
therefore less than that shown in figure 5 although some increase would 
be expected from the Mach number effect on lift - curve slope of the ver-
tical tail. The decrease in stability at Mach numbers from 0 . 85 to 0.95 
is due to the force break on the 8-percent - thick vertical tail in this 
Mach number range. 
Within an estimated accuracy based on repeatability of ±0.03, there 
is no effect of change in Reynolds number (stagnation pressure) on the 
directional- stability parameter for the range of test conditions. 
CONCLUSIONS 
A low-amplitude free-oscillation investigation was made at zero 
angle of attack of the damping in yaw and directional stability of a 
8 NACA RM L57C15 
fuselage-tail configuration through a range of reduced frequency from 
about 0.03 to 0.11 and Reynolds humber from about 4 X 106 to 22 X 106 
at Mach numbers up to 0.94. Limited additional tests were made at Mach 
numbers up to 1.10. The results indicate the following: 
1. The damping in yaw decreased appreciably at Mach numbers above 
0.8 and became a minimum near Mach numbers of 1.0. Further increase in 
Mach number to l.lO increased the damping to a value at least as great 
as that measured at subsonic speeds. 
2. The directional-stability parameter decreased rapidly at Mach 
numbers from 0.85 to 0.95. 
3. An increase in reduced frequency caused a decrease in damping 
in yaw and a decrease in directional stability for the test frequency 
range. 
4. Within the accuracy of the data, the damping in yaw and direc-
tional stability were not affected by change in Reynolds number. 
. --
Langley Aeronautical Laboratory, 
~ . 
National Advisory Committee for Aeronautics, 
Langley Field, Va., March 5, 1957. 
A NACA RM L57C15 
REFERENCES 
1. Drake, Hubert M., and Clagett, Harry P.: Effects on the Snaking 
Oscillation of the Bell X-l Airplane of a Trailing-Edge Bulb on 
the Rudder. NACA RM L50KOla, 1951. 
2. Von Doenhoff, Albert E., Braslow, Albert L., and Schwartzberg, 
9 
Milton A.: Studies of the Use of Freon-12 as a Wind-Tunnel Testing 
Medium. NACA TN 3000, 1953. 
3. Runyan, Harry L., Woolston, Donald S., and Rainey, A. Gerald: Theo-
retical and Experimental Investigation of the Effect of Tunnel Walls 
on the Forces on an Oscillating Airfoil in Two-Dimensional Subsonic 
Compressible Flow. NACA Rep. 1262, 1956. (Supersedes NACA TN 3416.) 
4. Moeckel, W. E.: Approximate Method for Predicting Form and Location 
of Detached Shock Waves Ahead of Plane of Axially Symmetric Bodies. 
NACA TN 1921, 1949. 
5. 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.) 
6. Fisher, Lewis R., and Wolhart, Walter D.: Some Effects of Amplitude 
and Frequency on the Aerodynamic Damping of a Model Oscillating 
Continuously in Yaw. NACA TN 2766, 1952. 
'1 
c . =f ~\~ 
0> 
t-- -------- 26.58 --------------1 
C\J 
I/) 
I' 12 . 34-----~ 
Eccentric Cam Motor 
Figure l.- Sketch of model. 
~ 
Sting 
Yow Flexure Plates. 
(All dimensions in inches.) 
~ of Madel 
t:; 
~ 
o 
;J> 
~ 
t-t 
\Jl 
?3 
I--' 
\Jl 
~ 
Figure 2.- Photograph of the model with nose piece off. L-94895 
~ 
~ 
~ 
t"" 
VI 
~ 
I-' 
VI 
I-' 
I-' 
12 
.12 
Flexure plate 
1..\ 1 0 
2 0 
c )\ 3 0 
\ 
\\ Slots open, • 
.11 
.10 \' 
\\ \', . 09 
t~ \ \ 
[b\~, 1\ ~ .08 
\\ f\ '\ ~ l:--
\ " \\ '\ i'" . 07 
<\ 1\ <, ~ \~ 
"-
"'" 
\~ ~ "-I, 
IDb 
2V .06 
< 
--...... f-_ ~U , 
"" '\ • "" • 
.05 
< ~ ~, b ; 
" "---
\ I I 
. 04 
~ 
" 
\ 
'> > 
. 03 
.02 
f--
Pro' in . HS 
8 
--
I- 19 - - --
28 ---. 01 
I I I 
.6 . 8 l. 0 
Mach number, M 
(a) Reduced frequency. 
-
-
-
or; 
... ~ 
I1J 
.0 § 
c 
m 
'" H 0 
~ 
I1J 
or; 
1. 2 
NACA RM L57C15 
22 XlO 6 I~ 
20 
18 
16 
14 
12 
10 
8 
6 
4 
2 
o 
.4 
j} ') Flexure plate 
-1 V 1 0 2 0 
-l' 3 0 
-,~ Slots open, . 
!.? 
WI ,C'~~ 
I:: 
/ ~ ...... /l /~ t/~~ 
I[ / 
• / 1/ ~ 1/ ;C~ 
r: / 
« 
r:~~ ~ ~ 
~ ~ :..-
~ p--
Pro' in. HS 
I--
8 --
19 - - --
-
28 ---
.6 .8 1.0 1.2 
Mach number, M 
(b) Reynolds number. 
Figure 3.- Variation with Mach number of the reduced frequency and 
Reynolds number for various flexure plates and stagnation pressures. 
(Symbols are for identification and not actual data pointe., 
-l 
01 ' 
1 0 I I I +1+ I Flexure plate 
1 0 
2 0 
30 
I I 
I 
-.1 "0," 0p,O, .. 
\ -.2 \ 
-· 3 hf=:i~~~r-~tT-=+~~-+:rt---+-.t=:::r+~Ati-LJ 
(Cnr ) - (C~) r-~~~t---t---t---i---i-~1---~--~---t---t---t--tt---+--~--~--~L-~--~L-~ (1) (1)1 
-.41 1 I Poo =' 8 in.' Hg I I I I Poo ~ 19 i~ . Hg 1 I ~ I I I Poo ~ 28 ~. Hg I I 
- .5 I~ __ ~ __ ~ __ ~ __ ~ __ ~=-~ __ ~ __ ~ __ ~ __ ~ __ ~ __ ~ __ -L __ -L __ -L __ -L __ -L __ ~ __ ~ __ ~ 
.4 .6 .8 
Mach number, M 
1. 0 
. 4 .6 . 8 
Mach number, M 
1.0 
.4 
1. 2 
.6 . 8 1.0 
Mach number, M 
Figure 4.- Variation with Mach number of the damping-in-yaw parameter for various stagnation 
pressures and flexure plates. 
~ 
> 
~ 
~ 
~ 
t-t 
V1 
--.J 
Q 
I-' 
V1 
I-' 
\)J 
14 
.2 
.1 
o 
.2 
.1 
o 
.2 
.1 
o 
.4 
NACA RM L57C15 
I I 
Pco = 8 in. Hg 
0 
~~ .i. -"" ~ ~ ~ ." 
1 U 1<:. 
- ~ -OF. ~  ( ~ 
c 1 ~o 
PO) = 19 in. Hg ... ~ ~ , 
, 
~ - _\ --I <': ~ t --r- .. ....,.-~ 
~ t--4;: • p--g~ ~: ( I- -~ ~--C --"" 
~ 1\--
~ 
PO) = 28 in . Hg 
~ Flexure plate 1 0 ~ ~~ .~ /~ ~~j 2 0 
--
em ir-1 
l . ... E J L-o I~ -;; 3 0 
Ie ~ Slots open, • 
I I 
.6 .8 1.0 1.2 
Mach number, M 
Figure 5.- Variation with Mach number of the directional-stability 
parameter for various flexure plates and stagnation pressures. 
~v.M·~angle1i Field. v~. 


A Wind-tunnel Investigation of the Low-amplitude Damping in Yaw and Directional Stability of a Fuselage-tail Configuration at Mach Numbers up to 1.10

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