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┃.. y- .: .-..-. .. , . ┃
┃ . . }l( ┃
┗━━━━━━━━━━━━━━━━━┛
Aspect Rat10=6.0
234
Mach Number
Ng.4.20 The parameter (C~). atsupersonic speeds:'
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 395
where Xm : XcA, the moment reference point (measured from fuselage leading
edge), and VB iS the fuselage volume. The fuselage apparent mass coefficient term
(k2 - ki) can be obtained using the data presented in Fig. 3.6. Note that (CLq)B
is based on SB,max/f and (CLat)B iS based on Vg/3, where SB,max iS the maximum
cross-sectional area of the fuselage, t f is the total length of the fuselage, and VB
is the volume of the fuselage.
The body contribution at supbys7onic speeds (based on maximum cross-sectional
area and body length) is given b
(CLq)B = 2(CNct)B (1 - -f )
(4.496)
where the slope of normal force coefficient (CNa)B can be estimated using the data
given in Fig. 3.10, which is based on maximum cross-sectional area of the body.
Estimation of Cmq. This denvative is a measure of the pitching moment in-
duced because of a pitch rate experienced by the aircraft and is kriown as the
damping-in-pitch derivatrve. This is one of the most important longitudinal dy-
namic stability derivaLives of the aircraft. Generally, the contribution of the aft-
located horizontal tail is damping in nature and by far is the largest because of its
long moment arm from the center of gravity. The contribution of the wing-body
is generally small but can be significant if the fuselage is long and the wing has
a small aspect ratio. The contribution of the horizontal tail can be estimated as
follows.
As we have seen earlier, because of the pitch rate, the tail angle of attack and the
lift coefficient increase. The corresponding increase in pitching-moment coeffi
cient is given by
With
We get
AC,n, = -a, (qj.) ( SS ) -7, (1:)
r a cm
Cmq = a(~-)
(Cmq)t =
-2a,( S )-7,(/:)2
= -2at V,,7,(1:)
(4.497)
(4.498)
(4.499)
(4.500)
For aircraft configurations with long fuselage and small aspect ratio wings, the
contribution of the wing-body combinat:ion may become significant. For such
configurations, the total value of the damping-in-pitch der:ivative is given by
Cmq = (Cmq)WB + (Cmq)t
(4.501)
PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
The wing-body contribution can be estimated using the following expression:7
(Cmq)WB = [K W(B) + KB,W)] SS ( : )2(C,rrq)e
+(Crrrq)BSS (l:)27rad (4.502)
where (Cmq)e and (Cmq)B are the contributions of the exposed wing and body,
respectively.
For subsonic speeds]
(Cmq)e = [-:, ., ](,, q)e.M =0.2 (4.503)
where
(Cmq)e.M =0.2 = -0.7Cia,cos Ac/4 A(0.5g +2g2) + (24 ) +1]
C5
(4.504)
cl = A3 tan2 Ac/4
3
C2'= B
C3 = AB +6 cos Ac/4
04 = A+6 cos Ac/4
C5 - A+2 cos Ac/4
(4.505)
(4.506)
(4.507)
(4.508)
(4.509)
-_-
B = J~:: M2 cos:! Ac/4 (4.510)
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