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u a~U~ = -p Uo SCD - 2p Uo2S U(., :. ) (4.431)
With u = AU/Uo and Cx = Fx/~:pUo2S,Eq. (4.431) simplifies to
Cxu - -2CD - CDu (4.432)
Next, let us suppose that the aircraft is disturbed in pitch angle O. Then, from Eq.
(4-427),
a AFx aF
dAO - ~d2 =-W,os0o (4.433)
or
Cx0 - -CL cos0o (4.434)
Next, consider the forces in the Oz direction, we have
Fzo - W cos 0o - Lo = O (4.435)
382 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Fz = Fzo + AFz
- W cos(8o + AO) - L
= w cos(0o + AO) - (Lo + AL)
Proceeding in a similar fashion as before, we can show that
Czu = -2CL - CLu
Czo -. -CL siri 0o
(4.436)
(4.437)
(4.438)
(4.439)
(4.440)
Now suppose the aircraft is disturbed in angle of attack. The forces acting on the
airplane in the disturbed state are shown in Fig. 4.17b. We have
so that
F.ro - -Do + T - W sin Oo -. 0 (4.441)
F, - Fxo + AF;. (4.442)
- L sin Acy - D cos Aar + T - W sin 00 (4.443)
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