PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL4(40)

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it will precess in a direction perpendicular to a plane containing both the vectors
r and p. Hence, in this case, the angular velocity vector of precession will be
along positive y-axis (Fig. 7.19), which corresponds to a noseup pitching motion.
Similarly, if the gyroscope in Fig. 7.18a is disturbed by a torque that imparts it a
yawing velocity r, it will pitch in a noscdown directio: Thus: the net gyroscopic
action will be the difference between these two induced pitching motions.
   Generally, Iz >/ so that the inertia pitching couple is positive or nose up
that tends to flatten the spin attitude. For equilibrium, the aerodynamic pitching
moment must be negative or nose down. At angles of attack well above the stall,
the nosedown aerodynamic pitching moment mainly comes from the horizontal
tail with wing making very little contribution.
     Balance of rolkng moments.    As we have seen earlier, unswept wings have
a strong autorotative tendency at stall. As a result, for angles of attack beyond
      N1
the stalling angle, the aerodynamic rolling moment for airplanes having unswept
wings is generally prospin. Another factor that contributes to the development
658            PERFORMANCE, STABILITY, DYNAMfCS, AND CONTROL
        , -.
       ,    I
        .     .
              ,
       ,     .
       .       I
       .       l
       .        .
- - --.
                                  .
 . -- -N .J-
--------}
a) Gyroscope aligned along x-axis
-------
-/- - -
           I
        '--- - --
   , --
       --- .
         .
     .
          - --
                                ,- --l
    / '\,
---_-----:

-------------.."
b) Gyroscope aligned along y-axis

-_ - - - --)
-'-.-:.-'--.
----- --
c) Gyroscope aligned along z-axis
Fig. 7.18    Gyroscopic representation of a spinrung airplane.
=  ( 022 ) sin 2a siri X (Iz - Iy)
(7.128)
Thus, if X  - 0, the inertial-rolling moment is zero. Because the wing tilt d:irectly
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        .
　
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