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+ -b,C,r ddt + qt,(lzi - /).l) - Ixz,dd )Al = C18r A8r + C/8a A8a
- Cm"U - (Cmd CI dd + C, .) Aa + dd (ly, dd _ Cnq.,) AO
- C,n~e A8e + Cm8t A8t
(-Cnp - b,Cn~ dd )Ap + (_b,Cnpdd + qo(ly, - /xi) - Ixz, dd )A4
+ (-b,Cnr dd + Ixz,qo + Ixz, dd )A /, = C"8r A8r + Cn8a A8a
Now let us evaluate the forces and moments acting on the airplane following a
small disturbance during the pull-out. Referring to Fig. 4.18, we have
Fxo - -D - W sin0o + T -O
Fzo = ~L+ W cosO,, - (V~) (UR ) = 0
Mo -O
Fvo = Lo(RM) = No = 0
'y
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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
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