388
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PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Flight Path
_/_h _
Fig.4.18 Forces acting on an airplane during a pull-out maneuver.
For the disturbed flight,
Fx -. Fxo + AFx -. -(Do + AD) - W sin(0o + AO) + T
\ U)?-
Fz -- Fzo + AFz = -(Lo + AL) + W cos(0o + AO) - ( v~ [(Uo +RAf/
so that
AFx -. -AD - W cos 0o AO
AFz = -AL - W sinOoAO - (V;~) [2URAU ]
Proceedingin a similar way as we did for the small disturbance equations ofmotion
for a steady flight in a vertical plane, we obtain
Cxu - -2CD - CDu
xcr : -CDa
Cx0 - -CL COS 0o
Cxct - -CDd - 0
Cxq = -CDq - 0
Czu = -2CL - CLu - 2tTl,iqo
zct : -Cln
zd - -CLdt
Czq = -CLq
Cz8 - -CL siri0o
The expressions for other lateral-directional stability derivatives essentially remain
the same as those derived earlier for steady ffight. However, we have to note that
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 389
all the stability derivatives have to be evaluated for curved flow conditions to sim-
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