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Li = qr(ly - Iz)
Nt = pq(lx - ly)
670 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
In the above equations,'the values of p, q, and r are in rad/s. Substitution gives
M, - 4359.5633 Nm
Lt = -425.9929 Nm
' Nr = -86.6869 Nm
For steady-state spin, the sum of aerodynamic and inertial moments is zero.
Therefore,
Mu o - -4359.5633 Nm
Laero - 425.9929 Nm
Naero - 86.6869 Nm
Converting to coefficient form, we get
M aero
Cm.aero = qSc
- -0.2299
/acro
Ct.acro = qSb
- 0.003
N w~,
C^ m=qS,
- 0.0006
7.8 Summar\r
In this chapter, we have discussed two classes of flight where the longitudinal
and latcral-directional motions of the airplane are strongly coupled. The first case
was the inertia coupling or roll coupling problem where a steadily rolling aircraft
experiences instability as the roll rate is increased. We obsewed that an aircraft
having a higher level of directional stability compared to longitudinal stability ex-
periences a divergence in pitch, whereas an aircraft deficient in directional stability
is susceptible to a yaw divergence. The roll rates at which an aircraft experiences
either of these two instabilities depend on its inertia characterisitics. As the roll
rate is further increased, the aircraft becomes stable again, but this time it is spin
stabilized about its longitudinal body axis.
The other class of problems we considered is the air Jlane spm. The autorota-
tional tendency of the unswept wings at stall is the driving mechanism for light
general aviation airplanes to enter into a spin. Whether the steady-state spin is es-
tablished depends on the balance between the aerodynamic and inertia moments.
If such a balance is not achieved, the spin remains oscillatory. The wing tilt plays
an important role in the establishmentYof a steady-state spin. The magnitude and
sign of the inertia-rolling and yawing moments depend or7the wing tilt Also, the
INERTIA COUPLING AND SPIN
671
wing tilt affects the sideslip, thereby affecting the aerodynamic rolling and yaw-
ing moments. The application of opposite rudder followed by a forward stick is
the standard recovery procedure for most of the light general aviation airplanes.
However, the use of ailerons for recovery depends on the mass and inertia char-
acteristics of the airplane. On some airplanes, prospin ailerons assist recovery,
whereas on others it may be the opposite. Modifying "e outboard leading edge of
the wing considerably helps improve the spin resistance. Also, some modifications
to aft fiiselage geometry such as rounding the bottom surface or installing strakes
increases the damping effect of the fuselagein spin.
References
IPhilips, W. H., "Effect of Steady Rolling on Longitudinal and Lateral Stability:' NACA
TN 1627, June 1948.
2Pinsker, W. J. G., "The Theory and Practice ofInertia Coupling:' Joumal of the Royal
Aeronautical Society, Vol. 73, Aug. 1973, pp. 695-702.
3Gates, O. B., Jr., and Woodling, C. H., "A Theoretical Analysis of the Effects of Engine
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