曝光台 注意防骗
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by whjich the aircraft is rotate7about the z-body axis. Then the angles X, Oy, and
ct are related by the following expression:r'
SillOy - -cos a- sin X (7.90)
To get a physical understanding of tlus relation, consider the two extreme cases
ofa = 0 and a - 90 deg. At a = 0, the spinning motion is all rolling because the
x-body axis co:incides with the vertical spin axis. The z-body axis is now in the
horizontalplane. So the rotation X about the z-body axis is numerically equalto Oy.
654 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
For ce - 90 deg, the airplane is in a fiat spin, and the spinning motion is all yaw
about the z-body axis, which now coincides with the sp:in axis. Thus, any amount
of rotaLion about the z-body axis does not give any wing tilt because ffie wings are
in the horizontal plane for all values of X. Hence, the Oy = 0 for a ~ 90 deg.
The angular velocity vector S-2 now has the following components in the body
axes system:
p - s2 cos cr cos X
q - -c2 cos ct sin X
r -. 92 sina
7.5.1 Balance of Forces
.Arith U = V = W = O, Eqs. (7.74-7.76) reduce to
Fx = m(q W '- r V)
Fy = m(Ur - pW)
Fz = m(pV -Uq)
(7.91)
(7.92)
(7.93)
(7.94)
(7.95)
(7.96)
Substituting for U, V, W from Eqs. (7.80-7.82) for p, q, r from Eqs. (7.91-7.93)
and ignorin9 X (cOs x - 1, sin X - 0), we get
Fx - m C22R sincr
Fy =0
Fz = _m C22R cosa
(7.97)
(7.98)
(7.99)
Ignoring power effects and resolving the aerodynamic and gravity forces acting
on the airplane, we get
L sin af - D cos cr + W cos av = mC22R sin cy
-L cosa - D sin a + W sin ar = -mSl2R cos a
(7.100)
(7.101)
Multiply Eq. (7.100) by cos ct and Eq. (7.101) by sin a and add the two equations
to obX;
D-W
With this, substitution in either Eq. (7.100) or (7.101) gives
L = IT2~2R
(7.102)
(7.103)
It so happens that we could have arrived at these simple relations directly by look-
ing at Fig. 7.12. However,in this process of deriving these results using equations
of motion, we have obtained some understanding of the lanematics of the spinning
motion.
With
D -. 2lp U02SCD
L = ~pU02SCL
(7.104)
(7.105)
we get
INERTIA COUPLfNG AND SPiN
UO -
R=(2 )pUo2SC
From Eqs. (7.67) and (7.68), we have
CL - CR COS Ct
CD = CR siri CL
655
(7.106)
(7.107)
(7.108)
(7.109)
Suppose we could determine the angle of attack and spin rate from some other
criteria, then we could use Eqs. (7.106) and (7.107) to determine the descent
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