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Knowing CLa.N and CLce.e at subsonic and supersonic speeds, we can now find
KN using Eq. (3.25).
Using Eq. (3.27), we obtain KWcB) = 1.17, which is applicable for both sub-
sonic and supersonic Mach numbers. We get KBcW) = 0.285 using Eq. (3.28) for
subsonic speeds. For supersonic speeds, we have to use the data of Fig. 3.18b for
KBtW) because pAe(l + A,t)[(tan A LE/p) + 1] > 4. These values of KB(W) were
curve fitted to obtain the following expression applicable for 1.2 S M < 4.0:
KBcW) = 0.0063 M2 _ 0.0645 M + 0.2362
With these values, we are now in a position to calculate the wing-body lift coeffi-
cient using the following equation:
Sexp
CLa.WB = [KN + KW(B) + KBcW)lC S
Calculaiion of Cma,WB. We have
Cmcr.WB = (Xcg - Xac.WB)CLa.WB
where
STATIC STABILITY AND CONTROL
(-,,. ) =( )NCL.a.N+(lar)W(B)CLa,.W(B)+(l:t;'j-)B(W)CLcr.B(W)
CLcr.WB
We have
C~,:r.W(B) = K W(B)C~cr. SS
C~a,.B(W) = KB(W)C~a.e SS
Because we have calculated K WcB), K BcW),
and CU,,W(B) using the above relations.
241
and CLu,e, we can evaluate Ctcr.B(W)
For subsonic speeds (0 < M <. 0.80), using Eq. (3.36), we obtain
(-,, N=-0.51
r
For supersonic speeds (1.2 P S M < 5.O),the calculated values using data ofFig.3.lla
and Eq. (3.37) were curve fitted to obtain the following expression:
1.0171M2 + 0.1295 M - 1.1364
(-,,. N = -0.0
Furthermore, we note that
(-)W,B, - (-,..) W
Then, using the data of Fig. 3.19b and curve fitting the values, we obtain
;367 M3 _ 0.4810 Mh + 0.2214 M + 0.4918 (0 S M < 0.80)
-,,,) w = 0.33f
= -0.0121M2 +0.0837 M +0.5342 (1.4 < M S 5.0)
Now we have to e'valuate (Xac]Cre)B(W). We have Ae - 2,6893. Therefore, for
all subsonic Mach numbers, we find that pAe < 4. Therefore, we need to use
interpolation. For pAe - 4, using the data of Fig. 3.20 and Eq. (3,39), we obtain
(XaclCre)B(W) = 0.3748. For pAe -. O, using Fig. 3.21, we obtain (Xac/Crt)B(W) =
0.40. With this, we get the following interpolation formula for subsonic speeds
and O < pAe S 4,
).4 - 0.0063 pAt (0 < M S 0.8)
-...) B,W, = 0.4
where p = -jc~-.
242 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
For supersonic speeds, with ALE - 45 deg, Ae - 0.1705, and At - 2.6893, we
find that pAe(l + Av )[1 +1]p tan A.LE J > 4. Therefore, for supersonic speeds, we
use Fig. 3.22b because the given configuration has no afterbody. The calculated
values were curve fitted (least square) to obtain the following expression:
-0.0108 M2 + 0.0819 M +0.2807 (1.2 < M < 4.0)
-...) B,W, = -(
Having calculated all the required parameters, we can now obtain the slope of
the pitching-moment coefficient from subsonic to supersonic s]peeds. Note that
some of the calculated parameters have a discontinuity across the transonic Mach
numbers from 0.8 to 1.2. For such cases, a smooth interpolation was used.
The calculated values of CU.WB, Xac,WCB), and Cma.WB at various subsonic and
supersonic Mach numbers are shown in Figs. 3.60 and 3.61. For the purpose of
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