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-o
-: -0.5
-:1 -1
o -1.5
:.J
:l
o
6
a
Jl
o
taper ratio=0.25
..........'.:7...'.:." ....::
┏━━━━━━━━━━━━━━━━━━━┓
┃... ....:.:.*. .................... ┃
┃ x " ': ┃
┗━━━━━━━━━━━━━━━━━━━┛
234
::J
T:i
o
- A=O
---~ A = 30"
-.-.~ A - 45o
...... A = 60"
taper raiio=0.5
Aspect Ratio=2.0
Aspect Ratia=4.0
6
:l
c:
~}
Aspect Rac10=6.0
Fig. 4.22 rfhe parameter (CLa)e for supersonic speeds.r
where the fuselage apparent mass coefficient (k2 - ki) can be obtained using the
data presented in Fig. 4.6.
For supersonic speeds,
(C2ce)B = (CNa)B
(4.533)
where (CNa)B can be estimated by approximating the given fuselage either as a
tangent-ogive or a cone-cylinder, whicheveris closer, and using Fig. 4.10 or 4.11.
Estimation of C z. This derivative is a measure of the time-lag effects on the
pitching moment when the aircraft experiences a change in the angle of attack
with respect to time. As said before in our discussion on CLd, the horizontal tail
contribution is usually the most significant one. From Eq. (4-523), we have
Cu(t) = a,(SS),7,[, (t) -/w +,, - :a (,(t) - UZ.)] (4.534)
c
l. .
, ,"
' \. .
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C,:
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C:
l
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'l':
. :'I:
':7' ,:
i .,
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402 PERFORMANCE, STABfLITY, DYNAMICS, AND CONTROL
Taking moments about the center of gravity,
Cnu(t)=-a,(SSt:),7,[cy(t)-/ID+/t-~( (t)'-U-)] (4.535)
The derivative Cmd iS defined as
8Cm
C..:=a(,u.) . (4.536)
Differentiating Eq. (4.535) with respect to a and simplifying,
(Crrur)t
-2a, V,,7,(: ) (1:)
(4.537)
For airplane configurations wich long fuselages and short aspect ratio wings,
the contribution of the wing-body combination can be quite sigruficant. For such
configurations, the total value of Cma for the complete airplane is given by
Cma : (Cmd)WB + (Cmd)t (4.538)
The wing-body contribution can bc estimated using the following expression/
(Cma)WB = [KWcB)+KB,W,j(SS )(C.,).
+(Cm*)BSS,2 7,ad (4.539)
where (Cn a)e iS the contribution of the exposed wing and (Cma)B iS that of the
isolated body.
For both subsonic and supersonic speeds]
(Cma)e = (C:na.)e+ (-: )(C,,)e (4.540)
where Xcg.U is the distance of the center of gravity from the leading edge of the
exposed wing, positive aft (see the insert at the top of Fig. 4.2(}), and (CLa)e iS to
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