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b)
Fig. 4.34 Cr.& and Cm~e for the aircraft ofE}:ample 4.10.
The calculated values of Cyp are presented in Fig. 4.35a.
Clp: The estimation ofwing contribution to Cip at subsonic speeds was evaluated
as discussed above in connection with the determination of Cyp.
For supersonic speeds, Datcom7 data are used to calculate (C.lp)W. Tlus method
is not discussed in the text because it is quite involved. The calculated values are
curve fitted to obtain the following expression:
(Clp)W = (-0.0025 M2 + 0.0283 M - 0.1154) Ae/rad
where Ae is the exposed wing aspect ratio and, for /his case, Ae - 2.6893.
The vertical tail contribution at subsonic speeds is evaluated using Eq. (4.579)
with zu - 3.8290 m,ly :7.7561 m, and b -. 17.3228 m.We have already explained
theproc ure ofcalculating Cyp,v.
The calculated values of Cip at subsonic and supersonic speeds are presented in
Fig. 4.35b.
Cnp:
Cnp = (Cnp)W + (Cnp)V
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 425
-L
~
h
a)
a
g
A
o
a)
-o
e!
k
o
a
d
c
o
Alpha=4
b)
c)
Fig. 4.35 C,p, Cip, and C,,p for the aircraft of Example 4.10.
Cyr:
Cyr = (Cyr)V
At subsonic speeds, the vertical tail contribution is evaluated using Eq. (4.599).
Because no general method is available for supersonic speeds, to get a crude es-
timate of Cyr, Eq. (4.599) is also used at supersonic speeds with ay evaluated at
supersonic speeds. The calculated values are presented in Fig. 4.36a.
Clr:
CLr = (Clr)W + (Clr)V
At subsonic speeds, the wing contribution is evaluated using Eq. (4.613). From
Fig. 4.28, we o~tain (Clr/CL)CL =O,M =O = 0.3. With this, we can calculate Cu for
subsonic speeds.
l:~'
c,
e!
a
o-
*6
"a!
T:i
O
;l
".",{
i~
q!
{.:.
~
.
-*
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r.
y
:!
;}
'v.
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.:
Jr
o
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ad
7
El
o
At subso:tuc speeds, the wing contribution is evaluated using Eq. (4.594). The
vertical tail contribution is evaluated using Eq. (4.598). At supersonic speeds,
Datcom/ data are used. The details of this method are not given in the text.
The calculated values are presented in Fig. 4.35c.
342 PERFORMANCE, STABIUTY, DYNAMICS, AND CONTROL
Now,
C70l.b X Lr' =
Then,
or
Similarly,
>
zb
p
Cll
Jb
q
C12
kb
r
C13
(4.152)
= lb(C13q - C12r) - jb(C13p - Ciir) + kb(C12P - Ciiq) (4.153)
ddt .= (CII + C13q - C12r)rt, + (C12 + Ciir - C13P) jb
+ (C13 + C12P - Ciiq)k,
-0
where
Cll = C12r - Ct3q
C12 = C13 p - Ciir
C13 = Ciiq - C12P
C21 = C22r - C23q
C22 - C23 p - C21r
C23 = C21q - C22P
C31 - C32r - C33q
C32 - C33p - C31r
C33 = C3iq - C32P
(4.154)
(4.155)
(4.15 6)
(4.157)
(4.158)
(4.15 9)
(4.160)
(4.161)
(4.162)
(4.163)
(4.164)
C11 C12 < -r q
- C21 C22 'g'j,l[_q -. -,P] ,4.165,
C31 C32 ( p 0
C;, = Cb S2lb
gZtbt = [_q
(4.166)
(4.167)
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