A theoretical study of lateral stability with an automatic pilot Page: 1 of 13
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REPORT No. 693
A THEORETICAL STUDY OF LATERAL STABILITY WITH AN AUTOMATIC PILOT
By FREDERICK H. IMLAYSUMMARY
The influence of automatic operation of the aileron and
rudder controls on the lateral stability of an airplane is
discussed. The control deflections are assumed to be
proportional to the deviations and to the rates of deviation
of the airplane from steady-flight conditions. The effects
of changes in the types of deviation governing control ap-
plication are considered.
For one simple method of control in which the aileron
deflection is proportional to the angle of bank and the
rudder deflection is proportional to the angle of yaw, the
effect of lag in control application is studied and regions
of stability with and without lag are given. For the simple
control with lag, curves are included that -show the vari-
ations in the roots of the stability equation with changes in
the amount of control applied.
It is concluded that, although the simple control pro-
vides a satisfactory means of varying most of the lateral-
stability characteristics, the stability in azimuth will al-
ways be poor for such a control. Modification of the
simple control by deflecting the ailerons in proportion to
the angle of yaw appears to offer a promising method of
improving the azimuth stability.
INTRODUCTION
The automatic control of aircraft has long been of
interest and, as a result, considerable literature exists
on the subject. Much of the published work, however,
is confined to descriptions of devices proposed or em-
ployed to overcome the mechanical problems en-
countered in various specific types of automatic pilot.
Theoretical treatments of the application of automatic
control to aircraft have mainly consisted of general
discussions of the differential equations of motion for
the controlled airplane. Relatively few writers have
presented data to show the influence of definite types of
automatic control on the characteristics of specific air-
planes. Such an investigation for longitudinal motion
was made at New York University and the results are
presented in reference 1.
In the present study, the influence of various methods
of automatic control on the lateral stability of an air-
plane has been analytically determined. For the pur-
poses of the investigation, a hypothetical airplane ofaverage physical form was considered. The theoretical
treatment employed is based primarily on well-known
methods and assumptions used in studies of lateral
stability. An outline of the general method of theo-
retical treatment used is given in the appendix to-
gether with definitions of the symbols involved.
AIRPLANE USED AS BASIS OF CALCULATIONS
Physical characteristics.-The airplane chosen as a
basis of computations is the hypothetical average air-
plane discussed in reference 2. The characteristics,
including the control characteristics, are similar to
those of the Fairchild 22. As the properties assigned
to the airplane are based on the average for many con-
ventional airplanes, it should be possible to apply the
general conclusions reached to all conventional designs.
The forces and the moments acting on a given air-
plane as a result of known linear and angular velocities
of the airplane relative to the air can be determined
from the nondimensional stability derivatives of the
airplane, which are fixed by its physical form. For
the study of automatic control, it has been found con-
venient to make use of similar nondimensional control
derivatives, expressing the forces and the moments
acting on the airplane as a result of control deflections.
Values of the stability and the control derivatives for
the average airplane are given in tables I and II for
various flight conditions; these values are useful in
comparing the characteristics of the airplane treated
in this investigation with those of other airplane de-
signs. The value 0.35 for the lift coefficient CL is
assumed to represent the condition of cruising flight;
1.0, the gliding condition; and 1.8, low-speed flight
with flaps down. Table II also contains values of the
velocity V along the flight path and values of the time-
conversion factor r(=m/pSV).
TABLE I
STABILITY DERIVATIVES FOR THE AVERAGE
AIRPLANE
CIL ,, 4 , Z, n, tni n,
0.35 -0.140 -1.42 -4.43 0.905 0.960 -0.169 -0.744
1.0 -.200 -1.83 -4.46 2.60 1.02 -.416 -.916
1.8 -.415 -2.73 -4.56 4.65 1.31 -.574 -1.81
273
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Imlay, Frederick H. A theoretical study of lateral stability with an automatic pilot, report, March 4, 1940; (https://digital.library.unt.edu/ark:/67531/metadc66353/m1/1/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.