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                               -  -0.0019 + 0.000068cr
where a is in degrees. Summing the wing and tail contributions, we have
                         Cip = cr(0.000068 - 0.00314CLu) - 0.0016
where ct is in degrees and CUr (per degree) was calculated as shown in Fig. 3.60.
     At supersoruc speeds. we have
(Clp)WcB) = -0.061CN (g73) [l+;t.(l+A,E)] (1+ A2  ) (    ~-)
 X[-, +(-, )4'3]+r(Crp+A~p)+(ACtp)z.
where CNa iS per radian, ALE is in radians, and f' is in degrees. We have ALE  -
45 deg  = 0.7853 rad and A  -  0.1705. From the solution of Example 3.2, we have,
for the the wing at M - 2.0, CNa -. 1.81/rad.
    Using Eq. (3.372), we obtain Cip/r = 5.4043 * 10-4 Ctp.
  Using Datcoml for the wing at 1.4 < M < 4.0 (see Chapter 4 for more
information on CiP), wc get
CIP = A(-0.0025 Mz +0.0283 M - 0.1154)
STATIC STABILITY AND CONTROL
311
With A = Ac - 2.8396 and M = 2.0, we get Ctp = -0.1954. With chis, we get
Cip] F = 1.0560 :k l0-4.
    From calculations performed earlier for M - 0.7, we have
                                AC'p, = -0.0000261/deg2
                   :r
                                   (ACtp)zw - 0.0009105
Substituting and simplifying, we get
     (C,p)WtB) = -0.061CX (~78~) [1+0.1705 * (1 + 0.7853)] (1 + O 72853)
     X (~)+ _;.:b_796 +(,)4'3l+35(1.0560*10_4
              - 0.0000261) + 0.009105 - -0.001725CN + 0.000816
    From the solution ofExample 3.8, for M  - 2.0, we have ay -  1.8338lrad, k =
On6, (i+[au/ap])~ =  1.2012, Sv/S - 0.1909, z, - 3.8290 m,/u = 7.7561 m,
and b - 17.3228 m. Substituting these values in Eq. (3.374), we get
                                          (Cip)v  - -0.001233 + 0.000044ct
where a is in degrees. Then, summing up wing and tail contributions,
                    Clp = ct(0.000044 - 0.001725CLa) - 0.000417
where a is in degrees and CLu iS given in Fig. 3.60. Thus, we observe that this
vehicle has adequate lateral stability at subsonic and supersonic speeds. It should
be remembered that these results are based on crude approximation of vertical tail
contribution to lateral stability at supersonic speeds.
3.7 Summar\t
    In this chapter, we have studied the concepts of static stability and control. The
airplane was assumed to be a rigid body and possess a vertical plane of symmetry.
The aerodynamic forces and moments were assumed to be linear functions of angle
of attack/sideslip and control surface deflections. We assumed that the longitudinal
control deflections do not produce lateral-directional forces or moments and vice
versa. The effect of power was ignored. Under these assumptions, it was possible
to assume that the longitudinal and lateral- directional motions of the airplane are
indepcndent of each other, and we could study the associated concepts of static
stability and control separately.
      The static stability is the inherent capability (open-loop stability) of the airplane
to counter a disturbance in angle of attack or sideslip. The stability with respect
to a disturbance in angle of attack is called the longitudinal stability. We have two
types ofstabilities, lateral and directional, with respect to a disturbance in sideslip.
Usually, the lateral and directional motions are always aerodynamically couple9:
Everything else remairung the same, the location of the center of gravity has a
312          PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
significant influence on the level of the static Iongitudinal stability. The center of
　
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