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 is comparable in size to the wing. In that case, the same approach as that used for
the wing can be used to estimate its contribution. With these assumptions,
Clp = (Clp)W + (CLp)V
(4.555)
      For aircraft with high-aspect ratio rectangular wings, an approximate estimation
of the wing contribution at low subsonic speeds can be done using the strip theory
as follows.
       Consider a rectangular wing in a uniform rolling motion with a roll rate  p about
the Ox axis as shown in Fig. 4.27a. Because of this rolling motion, the local angle
of attack of wing sections on the down-going (right) wing increases and that on the
up-going (left) wing decreases. Assuming that the steady~state angle of attack is
below the stall angle, we observe that the lift developed by the right wing increases
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 407
CVP
 a
clfP
 a
 Clt P
 a
Taper Ratio = 0.5
r~
L:
4
2
E
┏━━━━━━━━━━━━━━━━━━━━━━━━┓
┃                               ~                ┃
┃ '.  .:  .....j: A-6                            ┃
┃"'- "<                                          ┃
┃       ..                                       ┃
┃,. . . . .-. . . . . . ..                       ┃
┃    . :/7j;_'_::.L'."' .                        ┃
┃                    :--,             .\ . \ ':  ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━┛
234
Mach Numtx r
qIP
 a
Cw
 a
qr!
 a
A = 300
A = 45o
A : 60o
Taper Ratio = 1.0
Mach Number
Fig.4 26   The parameter (C,pla)w for supersonic speeds]
and that of the left wing decreases. This difference in lift gives rise to a restoring
or a negative rolling moment and is the aerodynamic mechanism that generates
the damping-in-roll because of the wing. Using strip theory, we can approximately
estimate the magnitude of this restoring moment and the damping-in-roll derivative
(Ctp)W as follows.
       The increase in the local angle of attack of an elemental wing strip  RT of width
dy at a spanwise distance y is given by
tan cxp = Zry
(4.556)
where Uo is the flight velocity. Assuming that the roll rate p is small, we obtain
so that
N  py
ap - Uo
ai(y) = a + a'p = cy + 7jY
(4.557)
(4.558)
pctt_
  k
408              PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
dL
                                                                         
                                                                         
                                                                         
　
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