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(jL)2
Fig. 7.2 Stability diagram.
(-)2> (III)
(7.62)
which corresponds to the shaded region II of yaw divergence as shown in Fig. 7.2.
In this case, the aircraft has a relatively large longitudinal stability as indicated by
Eq. (7.62) and a small directional stability as indicated by Eq. (7.61). Thus, if a
point lies in region I, then the aircraft experiences a divergence in pitch and, ifit
lies in region II, it will diverge in yaw or sideslip.
We have two regions, III and IV, where the aircraft is stable. Region :UI cor-
responds to those cases where the roIJing velocit}r Po is smaU, and region IV
corresponds to large rolling velocities. Let us consider what happens when a given
aircraft starts rolling at a steady rate. Initially, let us assume that the roll rate is
small so that this condition corresponds to the point P ,in region III. Note that the
slope of the line connecting point P to the origin is equal to the ratio (WO/C.Op)2. As
the rate of roll increases, we approach the origin along the straight Iine OP. Be-
cause this aircraft has a higher short-period frequency compared to the Dutch-roll
frequency, at some value of roll rate Po, the st7raight line OP willintersect region
II, indicating that the ai:rcraft will diverge in yaw or sideslip. On the other hand, if
it has a higher Dutch-roll frequency compared to the short-period frequency,it will
experience a divergence in pitch as shown by the line OPi intersecting region I.
The narrow region around the origin in which the aircraft becomes stable at
extremely high roll rates corresponds to the case of spin stabilhation. This is
(t)2
INERTIA COUPLING AND SPIN
GJl) 2
Fig.7.3 Stability diagram modified because oifdamping terms.
637
the case of artillery shells and bullets, wluch are known to be flying through the
atmosphere at high velocities and at high roll rates without experiencing anyinertia
coupling problems. Generally, a body becomes spin stabilized about an axis ofleast
inertia. Usually, for modem combat aircraft, the axis ofleast inertia happens to be
the x-body axis about which the aircraft is rolling. So as the roll rate increases, the
aircraft becomes spin stabilized.
The stability diagram shown in Fig. 7.2 is sometimes known as Philip's stability
diagram.
In the above analysis, for simplicity, we have ignored acceleration and damping
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