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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
-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. .
, ,"
' \. .
::*,. ,
C,:
~,l
C:
l
Jir:
'l':
. :'I:
':7' ,:
i .,
. ..
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)
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