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Chapter 3.
From Eq. (4.525), we observe that the acceleration derivative (CLd)r depends on
the tail volume ratio Vi and the downwash velocity gradient (de/dct). Recall that
Vi increases with an increase in tail area and tail length. The downwash gradient
400 . PERFORMANCE, STABILITY, DY.NAMICS, AND CONTROL
depends on the aspect ratio, sweep, and taper ratio of the wing. The higher the
wing aspect ratio, the lower the value of the downwash gradient.
For airplane configurations with long fuselages and short aspect ratio wings,
the contr:ibution of the wing body combination can be quite significant. For such
configurations, the total value of the derivative Cue is given by
CLtt = (CLcr)WB+(CUr)t ' (4.526)
The wing-body contribution (based on wing area S and mean aerodynamic chord
c-) can be estimated using the following expressionl
' (Cue)WB = LKWcB) + Kncw,l(SS )(C n)e
+(C ce)BS s- 7rad (4.527)
where (CL")e iS the contribution of the exposed wing and (Cr"re)B is that of the
isolated body. These two parameters can be determined as follows.
For subsonic speeds]
(C~ct)e = 1,5 (-., )e(CLa)e + 3CL(g)/rad (4.528)
Thelift-curve slope ofthe exposed wing (CU)e can be estimated using the methods
discussed in Chapter 3 using exposed wing area, exposed taper ratio, and exposed
aspect ratio. The function CL(g) can obtained using the following expression,
which is curve fit to the Datcom data:7
C~(g) = ( 2pA ) (0.0013 r4 _ 0.0122 r3 +0.0317 r2 + 0.0186 r - 0.0004)
. (4.529)
where -c - pAe, Ae is the exposed win )ect ratio, and 8 = ^f/= M2.
For supersonic speeds, the Datcon09paspetdure for evaluating (CLcr)e iS quite
involved and is not presented here. Instead, we have performed calculations us-
ing Datcom/ data for some typical wing planforms and presented these data in
Fig. 4,22. It may be observed that the taper ratio has ver)r little :(nfluence, whereas
the leading<edge sweep and aspect ratio have a large effect on (CLcr)e.
The parameter (CLd)B at both subsoruc and supersonic speeds (based on
SB,maxl f ) iS given by7
(CLa)B =2(C2cr)B(S V I ) (4.530)
For subsonic speeds,
(C;n)B = (C~a)B ( SV,,.) (4.531)
(CLa.)B = 2(k2 - k,)(SV:,, ) (4.532)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATNES 401
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