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level (speed of sound r. 1100 ft/s). Let the flight path be contained in the equator
(A = 0). This flight velocity corresponds to a flight Mach number of approximately
1.34. With A - 0 in Eq. (4.268), we have
92e x ?2e x Re = k.Ref22
IQe X g2e X Rel = ReS2~
With Re ~ 2.097 x 10J ft and
SZe = 24~60 (2;7;)
- 7.2722 * 10-s rad/s
(4.274)
(4.275)
(4.276)
(4.277)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 367
we obtain
IS2e x ~e X Rel - 2.097 x 107a.2722 *10-5)2 (4.278)
- 0.11089 ft/SZ
Similarly, from Eq. (4.269), with A - 0,
2S2e x Ve = 292e(- Je Voz + ke Voy)
21S2e x Vel ~ 2S2e Vo
N 2(7.2722 *10-5)1466.37
(4.279)
(4,280)
(4.281)
(4.282)
~ 0.2133 ft/S2 (4.283)
Thus, the errors caused by ignoring the Earth's rotation about its own axis are
relatively small for typical aircraft motions at subsonic and supersonic speeds.
However, these errors can become significant if the 11ight velocity increases.
With these assumptions, Eq. (4.259) reduces to
F = m (ao)e (4.284)
= t,z (Vo)e
(4.285)
= , (:V, )e . (4.286)
Using the moving axes theorem, we have
(ddV, )e = (ddJ, )b+Wl.b X Vo (4.287)
With (Vo)b = lb U + ib V + kb W and 7.o~,b = t70lb = 7b p + 7bq + kbr, we have
(ddV, ), = 7b U + jb V + kb W (4.288)
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PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL2(121)
