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National Advisory Committee for Aeronautics, Technical Notes - Motion of the Two Control Airplane in Rectangular Flight After Initial Disturbances with Introduction of Controls Following an Exponential Law

An airplane in steady rectilinear flight was assumed
to experience an initial disturbance in rolling'br yawing
velocity. The equations of motion were selved to see if
it were possible to hasten recovery of a stable airplane
or to secure recovery of an unstable airplane by the spa
plication of a single lateral control following an exponen~
tial law.

The sample computations indicate that. for initial
disturbances complex in character, it would'be difficult
to secure correlation with one type of exponential control.
The possibility is visualized that two-control Operation
may seriously impair the ability to hasten recovery or
counteract instability.

An investigation was recently made for the National
Advisory Committee for Aeronautics of the motion of the
two~control airplane (i.e., one with either aileron or
rudder control eliminated) in rectilinear flight following
initial disturbances due to gusts or other causes.

The general plan of attack was as follows. An air—
plane in steady rectilinear flight was assumed to experi—
ence an initial disturbance in rolling velocity or yawing
velocity. Its motion without application of the controls
was found (by the use of operator methods) and appropri~
atoly plotted. Then a single control (either rudder or
aileron) was assumed as being applied in a simple fashion
realizable by a pilot. The equations of motion were again
solved, and the results plotted. From the solutions of
the equations and from the curveS, it was sought to answer
the following questions:

1. Under such types of initial lateral disturbances,
is it possible to hasten recovery substantially in the
case of a stable airplane by the application of only a
single_lateral control?

2. Under such types of initial lateral disturbances,
is it possible to secure recovery in the case of an un~
stable airplane by the application of only a single latu
eral control?

The curves obtained as a result of typical calcula—
tions and qualitative answers (which appear to be of some
degree of general applicability) to the foregoing ques-
tions are presented in this note.