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o 5 10 15 ZO Z5 30 35 40 45
a, deg
a) Statjc lateral stability parameter
0 10 20 30 40 50
a0, dL,j
b) Roll damping parameter
Fig. 8.33 Variation oflateral stability and roll damping parameters with angle of
attackY (Courtesy AGARD.)
and negative (stabilizing) at high values of roll angle as shown in Fig. 8.33b.
The roll angle ~ is the mean roll angle about which the forced oscillation roll
damping data are obtained. As stated,24 the roll damping parameter obtained by
forced oscillation tests on the 80-deg delta wing is not sensitive to the oscillation
frequency. This implies that hysteresis is not the cause of wing rock of the 80-deg
delta wing. The hysteresis, if present, would make the roll damping depend on
frequency of oscillations. In view of this, the principal cause of the wing rock of
the single-degree-of-freedom, free-to-roll, 80-deg delta wing model is believed to
be the nonlinear variation of roll damping with roll angle or sideslip.
The normal force, even though not having a direct effect on the wing rock
motion, has an interesting variatiori during the wing rock as shown in Fig. 8.34.
The frequency of the normal force is almost twice that of the roll angle, whereas
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704 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
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20 30 40 ' 50
.Time, s
Time, s
Fiig. 834 Variatrion of normal force and side force coef6cients during wing rock of
80-deg delta wing.n
the side force has the same frequency and phase as the roll angle. According to the
static data,27 the normal force coefficient should vary between 1.28 (~ = O) and
0.8 (4 -. 4max = 28 deg). However, the mean value of the dynamic normal force
is around 0.65 (Fig. 8.34b), which is far less than the expected average value of
1.04 for the static range of 0.8-1.28.
The physical mechanism responsible for the complex variations ofaerodynamic
characteristics during wing rock is not very clear. However, to get an idea of the
fiow physics, let us take a look at the histogram of Ci vs ~ and try to correlate it
with available fiow visualization data.
The histogram of Cz vs 4 for one limit cycle of wing rockis shown in Fig. 8.35.
Also shown in this figure is the corresponding histogram with sideslip as the
STABILITY AND CONTROL PROBLEMS AT HIGH ANGLES OF ATTACK 705
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25 -15
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a. deg
Fig. 835 Histogram of rolling moment coefficient z, (Courtesy AGARD.)
independent variable. The sideslip angle was evaluated using Eq. (8.2). The time-
varying rolling moment coefficient Ci(t) can be obtained from the measured roll
angle time history as follows:
Ci(r) = ;LS4b
(8.3)
Usually, 4 is determined using numerical differentiation or curve fitting to the
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