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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
comparison, these calculations were also done using the Aerodynamic Preliminary
Analysis System (APAS)8 and the APAS-results are included in Figs. 3.60 and 3.61.
  The APAS is an interactive, graphic user interface program for preliminary
aerodynamic analyses of airplane-type configurations.lt uses slender body theory
for subsonic/supersonic modeling of the fuselage. The surface singularity/panel
methods are used for wing and tail surfaces at subsonic/supersonic speeds. The
interference effects between fuselage ancl wing and between fuselage and tail
surfaces are modeled using a cylindricalinterference shell enveloping the fuselage.
The analysis for subsonic/supersonic Mach numbers is performed by the unified
distributed panel (UDP) program. For hypersoruc Mach numbers, APAS uses the
　
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