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 derivatives. With theinclusion ofthese terms, the stability boundar:ies are modified
as shown by the solid lines in Fig. 7.3. Thus, we observe that the narrow region
around the origin where the aircraft becomes spin stabilized now connects to the
stable region of small rolling velocities. By properly choosing the values of coo
and co.y, it is possible to avoid the instabilities irt pitch and yaw as shown by
the straight line OP. As the roll rate increases, the aircraft simply becomes spin
stabilized. However, we must remember that this analysis is based on several
simplifying assumptions pertaining to the airplane's mass(inertia distribution and
aerodynamic characteristics.
7.2.3  Prevention of Inertia Coupfing
        For an aircraft prone to divergencein yaw, we can improveits resistance toinertia
coupLing by increasing the level of static directional stability Cnp or by increasing
the inertia in roll Ir  relative to the inertia in pitch Iy. These methods call for major
oh-4
638           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
modifications and have to be considered early in the design cycle. As we know, the
vertical tailis the major contributor to the static directional stability parameter Cnp.
Therefore, to increase C ip, we have to incrcase the vertical tail area and vertical tail
arm. However, this may cause some problems in spiral stability. Thus, a tradeoff
is involved in deciding how much directional stability can be pernutted on a given
aircraft. The second option calls for distributing more mass into the wings such as
placing fuel tanks in the wings. Also, we can have a larger wing span or a higher
aspect ratio. This explains why the earlier aircraft that had a short bulky fuselage
 and high aspect ratio wings did not experience inertia coupling problems.
    Similarly, for an aircraft prone to pitch divergence, we can increase its resis-
tance to inertia coupling by increasing the static longitudinal stabilit)r level Cma
 or increasing the inertia in roll  Ix relative to the inertia in yaw Iz. The main fac-
 tors affecting the longitudinal stability parameter C     are the horizontal tail area,
 horizontal tail moment arm, and the location of the center of gravity. The designer
 has to make a proper selection of these variables. However, the second option is of
 very limited valuein this case because we cannotincrease Ix withoutincreasing Iz.
         Another option is to use a feedback control system, which wiU increase both the
 damping in pitch and damping in yaw. Referring to Fig. 7.3, we observe that.this
 will result in widerung the area, which connects regions I and III. However, we
  will not be going into the design of such a feedback control system. The interested
 reader may refer elsewhereJ for additionalinformation on this subjecL     .
                                          Example 7.1
       To illustrate the above theory, we consider the following aircraft.6 The data given
in Ref. 6 is an FPS (foot-pound-second) system, whicl        , convertel
as given in the following: mass -  ,0872 x  , _-~w}x~~~:5:;4881:3edltj04jkg,m"j:
Iy = 7J417 x l04 k~Dr2,1z = 8.7850 x l04 kg/,m~::       Sar5ar7 mSC.j
mean aerodynamic chord c = 3.442 m,wing span b =                       :nr - ~0.095,
Cmq = -3.5, Cmct - -0.36, Cip - 0.057, Cyp = -0.28, CLa : 3.85, and
 CIP = -0.255. All the derivatives are per radian.
       For fiight at a velocity of 210.6168 m/s and a dynamic pressure of 9432.4 N/m2,
 examine the stability o9this aircraft in steady rolling maneuvers.
I I)=87 x850 l04_l.4881xl04
 Iy )    7.7417x~0~
                   -. 0.9425
(I  I,'   = 7.7417 x l04 -1.4881x l04
                        8~850 x~0~
             - 0.7118
The pitch divergence and yaw divergence boundaries are shown in Fig. 7.4.
　
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