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Fig. 6.15 Free (longitudinaD response of the general aviation airplane to a distur-
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Fig. 6.16 Free (longitudinal) response of the general aviation airplane to a disfi:w-
bance in yaw rate.
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PERFORMANCE, STABILITY, DYNAMfCS, AND CONTROL
induces rolling and yawing motions, which also decay along with the sideslip.
However, the angle of yaw does not go to zero. Instead, it assumes a nonzero
steady-state value. This is due to the zero root, which makes the motion involving
yaw angle neutrally stable.
Figure 6.14 shows the free response to an initial disturbance of 5 deg in bank
angle. From a time-history plot for large values of time (not shown here), it is
observed that the disturbance in bank angle took as much as 500 s to decay to zero,
whereas the roll rate vanishes rapidly. The response following the heavily damped
roll subsidence mode is the Dutch roll during which the sideshp, bank angle, and
yaw rate display oscillatory behavior. Once the Dutch roll decays, the subsequent
motion is a slow convergence and is called spiral mode. During the spiral mode,
the bank angle and yaw rates decay to zero slowly. Once again,it is observed that
the angle of yaw assumes a nonzero steady-state value.
The free response to an initial disturbance in roll rate of 0.2 rad/s (Fig. 6.15)
is similar to the above case of disturbance in roll angle. The disturbance.in roll
rate quickly decays to zero, and all other variables, except angle of yaw, gradually
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