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Valuesof(pc:,p/;)gdofo'typicalwingplanform-s toestimate(/;):
} general method is available U
Forsupersoni ';e;lis;er:oin9Datcomlcalculationswereperformedforq/
Usingtheinformationg entedinFig.4.26.
wing planforms and are presenr
.'.
:,
F;
.:
;u
t::
p:
c
\w.
fr
.-
P :.
. .'
'-L
406 PERFORMANCE, STABILrFY, DYNAMICS, AND CONTROL
Taper Ratio = 0.5
A, deg
~ A=2
--N- A=4
~.-.- A = 6
Taper Ratlo = 0.25
-0.1
p~ -0.3
-0.4
Taper Ratlo ~ 1.0
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┃ ┃
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┃ "" "" " " " ".... ┃
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┃- - - - - f- ┃
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o 20 40 60
A, deg
Fig.4.25 The parameter (pcrplk)cL=o at subsoruc speeds.;
Estimation of qp. This derivativeis a measure ofthe rolling momentinduced
due to a roll rate experienced by the aircraft and is called the damping-in-roll
derivative. This is one of the most import.ant lateral-directional dynamic deriva-
tives. The major contribution comes from the wing and the v. ertical tail, and the
contributions of the fuselage and horizontal tail are usually small and can be ig-
nored. However, the contribuOon of the horizontal tail can become significant ifit
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
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