Study of effects of sweep on the flutter of cantilever wings Page: 17 of 25
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STUDY OF EFFECTS OF SWEEP ON THE FLUTTER OF CANTILEVER WINGS
FiLuE 11.-Theoretical flutter-speed coefricent as a function of the ratfo of bending to torbin
frequency for the rotated model 30B at four angles of sweep and with a constant mass-
density ratio (---7.8)-
constant length-chord ratio but decreasing aspect ratio (fig.
13), and (2) sheared back with constant aspect ratio and
increasing length-chord ratio (fig. 15). A study of these two
figures suggests that the length-chord ratio rather than the
aspect ratio Area/ may be the relevant parameter in
determining corrections for finite swept wings. (Admit-
tedly, effects of tip shape and root condition are also in-
volved and have not been precisely separated.)
Figure 16, which refers to the same sheared wings as figure
15, shows the ratios of experimental to predicted flutter fre-
quencies. The trend is for the ratio to decrease as the angle
of sweep increases. Table I shows that the flutter frequency
fJ obtained with VR and used as a reference in a previous
section of the report is not significantly different from the
frequency ft predicted by the present analysis.
A few remarks can be made on estimates.of over-all trends
of the flutter speed of swept wings. As a first consideration
the conclusion may be made that, if a rigid infinite yawed
Fmuan 12--Ratio of theoretical flutter frequency to torsional frequency as a function of the
ratio of bending to torsion frequency for the rotated model 30B at two angles of sweep and
with a constant mass-density ratio (1-37.8)-
0 o0 20 30 40 50 60
FIGUra I.-Rato of experimental to theoreteally predicted flutter speed as a function of
sweep angle for two rotated models.
wing were mounted on springs which permitted it to move
vertically as a unit and to rotate about an elastic axis, the
flutter speed would be proportional to I/cos A. A finite
yawed wing mounted on similar springs would be expected
to have a flutter speed lying above the curve of 1/cos A
because of finte-span effects. For a finite sweptback wing
clamped at its root, however, the greater degree of coupling
between bending and torsion adversely affects the flutter
speed so as to bring the speed below the curve of 1/cos A
for an infinite wing. This statement is illustrated in figure
17 which refers to a wing (model 30B) on a rotating base.
The ordinate is the ratio of flutter speed at a given angle of
sweep to the flutter speed calculated at zero angle of sweep.
A theoretical curve is shown, together with experimentally
determined points. Curves of 1/cos A and 1/ cos are
shown for convenience of comparison. The curve for model
30D (not shown in figure 17) also followed this trend quite
closely. The foregoing remarks should prove useful for
making estimates and discussing trends but are not intended_
to replace more complete calculation. In particular, men-
tion may be made, for example, that a far-forward location
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Barmby, J G; Cunningham, H J & Garrick, I E. Study of effects of sweep on the flutter of cantilever wings, report, January 1, 1951; (digital.library.unt.edu/ark:/67531/metadc60354/m1/17/: accessed November 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.