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Mach Number
b)
Fig. 4.33 C,r.g and Cmq for the aircraft of Example 4.10.
parameter k appearing in Eq. (4.554) was chosen equal to 0.8. The planform
efficiency parameter e was evaluated using Eq. (4.478) based on exposed aspect
rat"io At.We have r = 3 deg, zw = 1.27 rn, and span b = 17.3228 m. For ALE = 45
deg, A = 0.25, and Ae = 2.6893, we obtain from Fig. 4.25, (pciplk)cL =O.M =O =
-0.225. Similarly, the val_ues at other Mach numbers are obtained and the data are
curve :fitted to obtain the following expression:
( p~ ),,=o(;) = 0.3708 M3 _ 0.6662 M2+0.3128 M - 0.2325lrad
For supersonic speeds, Datcod data are used. Because the Datcom7 method is
quite involved, the details are not presented in the text. The calculated values are
curve fitted to obtain the following expression:
(C ) = -0.3806 M3 +3.422 M2 _ 10.1458 M +10.1346/rad
The contribution of the vertical tail was determined using Eq. (4.545), where the
lift-curve slope ay was evaluated at supersonic speeds using the methods discussed
in Chapter 3 and as explained in Example 3.8.
"
~
424 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
a)
Mach Number
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.
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a
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