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                   ,
   2m
 mi - --.                               (4,421)
           p UoS
     Iy
Iyl  =  ;-p U 2S~                                                    (4,422)
380              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
L
T, Uo
  a
  zo
a) Airplane in steady flight
                                   
  \ ~---    &,                     
┏━━━━┳━━━━━━━━━━━┓
┃        ┃                      ┃
┣━━━━╋━━━━━━━━━━━┫
┃        ┃                      ┃
┣━━━━╋━━━━━━━━━━━┫
┃jr .    ┃r\l,        Horizonta ┃
┗━━━━┻━━━━━━━━━━━┛
     zo
b) Airplane disturbed ui angle of attack
                                                                                             \-~ A +
c) Airplane disturbed in bank angle
Fig.4.17    Airplanein steady and disUnrbed flight condiOons.
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 381
axis or the zero-lift line, whereas 0o is the angle between the local horizontal and
the velocit)t vector or the flight path.
    Now let us evaluate various derrvatives like Cxu, Czu, etc., appearing in Eqs.
(4.417-4.419).
     The forces acting on the airplane are lift L, drag D, thrust T, and weight W as
shown. For steady equilibrium flight,
                              Fxo = T ~ Do - W sin0o = o                    (4.423)
 and, for disturbed flight,
                         Fx - Fxo + AF.r                                            (4.424)
                                       - T - D - W sin(0o + AO)                                  (4.425)
                                       = T - (Do + A/:5) - W sin(0o + AO)                   (4.426)
so that
                                                AFx = -AD - W cos OoAO                               (4.427)
　
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