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National Advisory Committee for Aeronautics, Technical Notes - Preliminary Study of the Damping Factor in Roll

The following paper was submitted by the writers as a thesis
to the Department of Aeronautical Engineering, at the Massachusetts
Institute of Technology. It constitutes a general theoretical
discussion of the damping factor in roll, together with the re—
sults of wind tunnel tests on.the continuous rolling of a U.S.A.
30 airfoil. Two general formulas are derived for the damping of
roll, each of which contains unavoidable indeterminate functions
Certain of these functions have_been evaluated from the test data.
of chief interest is the deduction that the actual damping as ex-
perienced in flight differs from the damping as theoretically
calmilated my a function of the wing-tip pressure distribution,
which is in turn largely influenced by the form of the wingetip
and by the rolling velocity. Finally, it has been‘shown that in
the damping equations 53; may be substituted for 53;: even
under full flight conditions, without serious error.

The damping of an airplane in roll is an exceedingly compleg ”g
problem and one which it may never be possible to solve completely,__
but if we can form some idea of the magnitude of the principal
factors involved and of their importance in practical flying, a
mathematically complete solution can be dispensed with. Our int—
erest in the damping coefficient is mainly as a guide to the de:
termination of stability and as an indication of the forces en—
countered in maneuvers.

The damping coefficient itself is made up of many components, __
arising from the several elements concerned: wings, fuselage, tail,
etc. As long, however, as we confine our tests to the complete
airplane, we have no means of analyzing the source of the magni~
tude of the basic elements of damping. The chief contributor to
these elements, the wing, is itself affected by a series of com—
plications. Dihedral, stagger, taper and aspect ratio are only a M_
few of the complicating factors. In view of the foregoing, there: _
fore, this report will be confined principally to the str