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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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