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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
is not available and 2) the equations of motion are coupled and nonlinear. An
example of determining the steady-state spin modes using the static and dynamic
wind-tunnel test data may be found elsewhere.16
In this chapter, we will discuss various factors that influence the balance be-
tween inertia and aerodynamic moments and also discuss various methods of spin
recovery. Finally, we will discuss some of the recent methods for improving the
spin resistance of airplanes.
7.5 Equations of Motion for Steady-State Spin
The equations governing the spinning motion are the complete six-degree-of-
freedom equations [Eqs. (7.1-7.6)]. For simplicity, we ignore t~e product ofinertia
t.erm Ixz, With this assumption, Eqs. (7.1-7.6) assume the following form:
Fx =m(U +qW -rV)
Fy=m(V+Ur-pW)
Fz = m(W + pV - Uq)
L = plx + qr(lz - Iy)
M = qly +rp(lx - Iz)
N = r Iz + pq(ly - Ix)
(7.74)
(7.75)
(7.76)
(7.77)
(7.78)
(7.79)
In a steady-state spin, the spin axis is nearly vertical, and the center of gravity of
the airplane moves downward in a helical path around the spin axis with a constant
velocity. Let Uo denote the velocity of descent. Resolving the velocit)r vector Uo
650 PERFORMANCE, STABILI-fY, DYNAMICS, AND CONTROL
Fig. 7.12 Forces acting on an airplane in steady-state spin.
in the body axes system, we have
U - Uo cosa
W - Uo sina;
(7.80)
(7.81)
where a is the angle of attack. Because the descent velocity is in a vertical direc-
tion, ce is the angle between the chordline and the vertical as shown in Fig. 7.12.
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