282
PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Substituting the mass and aerodynamic characteristics of the general aviation
airplane, we get the approximate transfer functions of the general aviation airplane
for aileron and rudder inputs as follows.
For the roll subsidence mode,
A~(s) 0.1342
A8a~s~ = s~0~46s+0038. . 7)
Aq3(s) 0.0118
A8~s~ = s~0 0046s+0.0387)
(6.280)
(6.281)
'1
588 PERFORMANCE,STABILITY,DYNAMICS,ANDCONTROL
For the Dutch-roll approximation,
Ap(s) __ 0.0076s (6.282)
A8a~s~-. 76~:;~7tf
Ayr(s) -- ._0.00'76s _0.002 (6.283)
A8a~s~-6. 76.6~~76.
A[3(s) __ 0.0024S2+0.16s . (6.284)
A8r~S~-6. .76~.6~~76.
Arjr(s)=. _0.1582s-0.0294 (6.285)
A78r(S)=6. 76-.t~7f16.
For the spiral approximation,
Ap(s)_ 0.0021s2+0.0016s
~8(s~= ood0: -J:0-4S
Ap(s) _ 0.0097s
A8o~s~=-.6~fT.T. ~04S
Ap(s)_ = 1.8204 x l0~4 SZ +8.6321 x 10-4S
A8r~S- ~7~7~=G-
Ayj(s) . 0.0061
~ ))=-6. -7. To4S
A8 (s '
(6.286)
(6.287)
(6.288)
(6.289)
We note that
p(s) = s A~(s) (6,290)
r (s) = sAp(s) (6.291)
n zurplane and the final
Usmg the above transfer functions of the g~tatralt~fesatioof the lateral_directional
va}ue theorem (see Chapter 5), the steady-st Ls a step input can be obtained.
variables Ap, A4, and p for a grven input such as :
However, this is left as an exercise to the reader.
6.3.4 Lateral.Oirectional Frequency Response
~elateral_directionalfrequency responrseol:tsouaileron and rudderinputs is ofinter-
est oecause the pilotinput to these two contrrol surfaces can be considered as a signal
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