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National Advisory Committee for Aeronautics, Report - Some Effects of Nonlinear Variation in the Directional Stability and Damping in Yawing Derivatives on the Lateral Stability of an Airplane

A theoretical investigation has been made to determine the
(feet of nonlinear stability clericatices on the lateral stability
of an airplane. Jfotions were calculated on the assumption
that the directional-stability and the damping-inqawing
derivatives are functions of the angle of sideslip. The. applica-
tion of the Laplace transform to the calculation, of an airplane
motion when certain types of nonlinear deriratices are present is
described in detail. The types of nonlinearities assumed
correspond to the condition in» which the ralnes of the directional-
stability and damping-inflawing derimtices are zero for small
angles of s-irleslip.

The results of the investigation indicated that under certain
conditions the nonlinear stability derivatives assumed in. the
analysis caused a motion which had dfierent rates of damping
for the large and small amplitudes of motion, with Avery little
damping at the small amplitudes. In general, the period of the
resultant oscillation increased with time.

Recent flight tests of several airplanes designed for high-
speed high-altitude flight have indicated neutrally damped
lateral oscillations of small amplitude generally referred to
as snaking. Tfpon examination of the flight records, the
decrement of the oscillatory motion is found in some cases
to be different for the large and small amplitudes of motion
with a neutrally stable oscillation occurring at the -all
amplitudes. One_of the explanations offered for the cause
of this type of motion is that some of the stability derivatives
are nonlinear; that is, the derivatives have diEerent values
for the largeand small amplitudes of motion. The non-
linearity could be caused by boundary—layer efiects or flow
separation due to poor fairing'at the junction of the-tail
surfaces.

The present report represents a preliminary investigation
of the effect of the presence of two nonlinear stability
derivatives, the directional-stability derivative 0“,, and the
damping—in—yam'ng derivative C,” on the motion of an air-
plane.