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t, s
Fig. 6.24 Unit-step response (lateral-directional) of the general aviation airplane:
roll rate.
Dbiai = -Cypb:(Cip Cnr - Clr Cnr) + C),*(CiBCnrb{ - C,p Izl - IxZI Cnp
- Cu Cnpb:t) + b21Cyp(Ctp Cnr - Ctr Cnp) + bi (mi - bi Cvr )
x(CLp Cnp - Clp Cnp) (6.245)
E8iar = Cy4bi(CipCnr - Cnp Clr) (6.246)
The transfer function for angle of yaw is given by
A p(s)
A8a~s~ =
mis - bi Cyps - ~yB
-(Clp + bi CiBs.)\
-(Cnp + bi CnBs)
-(bi C),pS + C).d)
--Cipbis + Ix1S2
-CnpbiS - /z1S2
Cy8a
Cl8a
Cnbt,
Alar
(6.247)
Let Nl/,./s" denote the determinant in the numerator. Expanding, we get
Nlr;.Bo = Arr S3 + BrpS2 + Cy;s + Dv; (6.248)
!
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-
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