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National Advisory Committee for Aeronautics, Technical Notes - The Influence of the Aerodynamic Span Effect on the Magnitude of the Torsional Divergence Velocity and on the Shape of the Corresponding Deflection Mode

This paper deals with the limiting case of the bend— U
ing— ~torsion flutter problem which occurs when the _flutter . _
frequency has the value zero. This aspect of the problem__d
has been formulated and dealt with, as a firoblem_ of _._ M-“
static torsional instability, by H. Reissner (reference
1) in 1926. Reissner- 3 treatment, as well as th.e later
work on the general flutter problem by Theodorsen (ref-
erence 2), Loring (reference 3), and Ble'akney (reference
4) assumes expressions f_or the relevant_ air forces a_t
each section of the wing which correspond to th_e assump—
tion of two—dimensional flow.

The purpose ofmthe present paper-is to investigate
the effect of this simplifying assumption by giving a
procedure for the analysis of the torsional-divergence
problem_which takes into.account the aerodynaMic span
effect. The developments are based on the theory of tor—
sion of straight rods and on.lifting—line theory for the
spanwise distribution of lift.

A rapidly convergent process of iteration is devised
for the soluti_on of the equations of the_ two theories for
an elastically twisted wing. The method is applied to
some typical examples and it is found that for a wing
with an aspect ratio of about six the aerodynamic span
effect modifies the torsional~divergence velocity obtained
with the assumption of air forces of the'two- dimensional
theory by l? to 40 percent, depending _on the elastic and
plan—form characteristics of the wing.

This investigation, conducted at the Massachusetts
Institute of Technology, was sponsored_ byl_and conduc_ted
with financial assistance frOm, the National Advisory
Committee for Aeronautics.