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National Advisory Committee for Aeronautics, Report - Correlation, Evaluation, and Extension of Linearized Theories for the Motion and Wheel Shimmy

An evaluation has made if the missing theories of linearized
tire motion and wheel shimmy. It is demonstrated that most of
the previously published theories represent varying degrees of
approximation to a summary theory developed herein which is a
minor modification of the basic theory of Von Schlippe and
Dietrich. In most cases where strong difl'erences exist between
the previously published theories and the summary theory, the
previously published theories are shown to possess certain
deficiencies

A series of systematic approximations to the summary theory
is developed for the treatment of problems too simple to merit the
use of the complete summary theory, and procedures are dis-
cussed for applying the summary theory and its systematic
approximations to the shimmy of more complex landing—gear
structures than have previously been considered.

Comparisons of the eaisting emperimental data with the
predictions of the summary theory and the systematic approxi-
mations provide a fair substantiation of the more detailed
approximate theories. Howwer, some discrepancies exist
which may be due to tire hysteresis ejects or other unknown
influences. Thus, further work may be needed to explain these
discrepancies.

In the ground maneuvering of aircraft equipped with
swiveling landing gears there sometimes arises the problem of
violent oscillations or shimmy of the landing gear which may
lead to failure of the gear. In the past this problem has been
handled largely by means of various measures based on
practical experience. However, this empirical approach has
not proved entirely adequate. Moreover, for radically
different types of complex flexible landing gears it is highly
doubtful Whether any empirical approach based purely on
past experience could always safely and optimumly take into
account all of the possible conditions which a landing gear
might be subjected to in actual operation.

A considerable amount of theoretical and experimental
work on wheel shimmy has been done, mostly in the past.25
years. Most of the existing papers on this subject are
listed in ref. 1, which also presents a historical discussion of
the development of the wheel-shimmy problem.) However,
most of these theoretical papers have not been correlated
with each other or with the available experimental data.