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     The spin is not of any tactical value for a military aircraft. Also, it serves no
 useful purpose in civil aviation. The spin is different from a spiral dive. What
  distinguishes a spin from the spiral dive is the low air speed and operation of the
INERTIA COUPLING AND SPIN
t
\
Y-- SpinAxis
 1
  i
Fig.7.10    Schematic diagram of a spinning airplane.
647
wings well beyond the stalling angle. In a spiral dive, the airplane is not stalled
and the air speed is continuously increasing. Further, the spin axis is much closer
to the airplane center of gravity than the axis of the spiral dive. The airplane has
a much higher yaw rate in a spin compared to that in a spiral dive. Typical yaw
rates for straight-wing light general aviation airplanes are about 120-150 deg/s in
a developed spin.
      The spin may be in either direction,i.e., to the right or to the left. However, both
 the right and left spins may not be identical because of the effect of rotating engine
masses or the propellers. The spin may be due to an inadvertent stall or could
be intentionally initiated by stalling the airplane and applying prospin controls.
Initially, the pitch, roll, and yaw rates oscillate, but these oscillations decay if the
airplane establishes a steady spin,in which case all the parameters tend to assume
constant values.
648          PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
       The spin may be erect or inverted.ln erect spin, the roll (as seen visually by the
pilot) and yaw (as indicated by the turn indicator needle) are in the same direction.
In an inverted spin, the two are in opposite directions.
        The characteristics of the steady-state spin.differ between the types of airplanes.
No two ai:rplanes spin in the same way. Even airplanes of the same type may spin
differently. Also, the spin is affected to a considerable degree by the amount of
control deflections used to initiate a spin entry.
         Basically, there are two types oferect spins. The firstis the steep spin in which the
 angle of attack is around 30 deg so that the nose is approximately 60 deg below the
horizontal plane. The otheris the flat spin in which the angle of attackis 60 deg or
 more. The attitudes ofthe airplane in steep and flat spins are shown in Fig. 7.11. The
steep spin is the slower of the two. In flat spin, the rate of rotation is considerably
a) Steep spin
b) Flat spin
Fig. 7.11    Airplane attitudes in spin.
INERTIA COUPLING AND SPIN                          649
higher. The recovery from the steep spin is relatively easier, whereas recovery from
a flat spin may be qrute difficult. Usually, a steep spin preceeds a flat spin.
         The airplane spin is not very amenable for theoretical analysis because of nonlin-
ear,inertial cross coupling between the longitudinal and lateral degrees offreedom.
Furthermore, the aerodynamics ofthe spinning airplane are extremely complex be-
cause of extensive fiow separation over the wing and tail surfaces. Owing to these
 di:fficulties, most ofthe investigations ofairplane spin have been traditionally based
on experimental studies using static and dynamic testing in wind tunnels, rotar3t
balance tests, flying model tests in vertical spin tunnels, outdoor radio-controlled
model tests, and full-scale airplane flight tests.u Even with this kind of experi-
mental aerodynamic database,it is not always possible to obtain a good correlation
between the observed and the predicted spin behavior.
     However, if we restrict ourselves to the study of the developed or steady-state
spin, it is possible to get some physical understanding of -various factors that influ-
ence the spinning motion and use the semiempirical approach based on strip theory
to get approximate estimates ofthe aerodynamic coefficients of a steadily spinrung
airplane.13-15 In a steady-state spin, the balance of forces is necessary, but tlus fact
alone does not guarantee that the steady-state spin will be established. It is the bal-
ance between the inertial and aerodynamic moments that is of crucial importance
to the establishment of a steady-state spin. Even for the case of steady-state spin,
it is not easy to analytically determine the equilibrium spin modes because 1) a
simple and comprehensive analytical aerodynamic modefof the spinning airplane
　
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