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CILr is the sectional or two-dimensional lift-curve slope of the wing and can be
evaluated using the methods given in Chapter 3. The parameter 9 is defined in
Eq. (4.490). The value of (Cmq)e given by Eq. (4.503) is per radian and is based
on the exposed wing parameters Se and cZ:.
For supersonic speeds, we have7
(Cmq)e = (Cmq)e - 9(CLq)e (4.511)
where the parameter (~tlaqc)h mm valuated as follows.
For low supersonic hd rumbers when the wing leading edge operates under
subsonic conditions, which happens when the parameter P cot ALE < 1, the data7
:ed and are not presented here. The interested reader may refer to
Dar~tqou tm?-l mited
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 397
taper rat1o=0.25
---t-:..-.t.:.. ~.. -...-.
┏━━━━━━━━━━━━━━┓
┃€-:-:." "( "' ┃
┗━━━━━━━━━━━━━━┛
- - A = 30o
~-- - A = 45o
--.~--, A = 60o
taper rat1o=0.5
Aspect Rat1o-2.0
Aspect Rat1o-4.0
Aspect Rati0-6.0
~g- 4.21 The parameter (C:q)e at supersoruc speeds/
For higher Mach numbers when the wingleading edge operates under supersonic
Mach numbers or f3 cot ALE > 1,the parameter (Cmsq)Forarh~e evaluated using the
data presented in Fig. 4.21 for typical wing planfonns:'] ata on wing planforms
not covered here, the reader may refer to Datcoml
The body contribution at both subsonic and supersonic speeds is given by
(1- )-V( )]
(Cmq)B = 2(C:ncr)B 1 - Xml - VB1
where
Xm . Xc VB
Xm~ = lf ' Xcl = lf VB1 = SB n.lf
x. = : l," SB(x)xdx
(4.512)
(4.513)
(4.514)
Here, Xm = Xcg, the distance of the moment reference point from the leading edge
of the fuselage, VB iS the volume of the fuselage, and SB,max iS the maximum
cross-sectional area of the fuselage, The value of (Cmq)B given by Eq. (4.512)
l;
I:
:,t
rl
-.
g
c
y
IP
.
?-r
398 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
is based on the maximum cross-sectional area and square of the body (fuselage)
length]
For subsonic speeds,
(Cma)B = (Cmrr)B(S V ,f )
(4.515)
2(k2 -
(C,nr)B = ~k [,xo dSdxB(x)(xm -x)dx (4.516)
Here, k2 - ki is the fuselage apparent mass coe:fficient (see Fig. 3.6) and Xm - Xcg,
the distance of the moment reference point from the leading edge of the fuselage,
and xo is the axial location where the fluid flow over the fuselage ceases to be
potential. Approximately, this happens at the axiallocation where the local cross-
9ectional area SB(X) assumes a maximum rralue. In other words, x - xo when
SB = SB.max.
For supersonic speeds,
(C:ncr)B = (Cma)B
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