# Study of effects of sweep on the flutter of cantilever wings Page: 20 of 25

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APPENDIX B

DISCUSSION OF THE REFERENCE FLUTTER SPEEDFor use in comparing data of swept and unswept wings, a

reference flutter speed V1 is convenient. This reference

flutter speed is the flutter speed determined from the simpli-

fied theory of reference 7. This theory deals with tNwo-

dimensional unswept wings in incompressible flow and de-

pends upon a number of wing parameters. The calculations

in this report utilize parameters of sections perpendicular to

t le leading edge, first bending frequency, uncoupled torsion

frequency, density of testing medium at time of flutter, and

zero damping. Symbolically,

VR=bwcf(KXcxieatrc 2 )

Variation in reference flutter speed with sweep angle for

sheared swept wings.-The reference flutter speed is

independent of sweep angle for a homogeneous rotated wing

and for homogeneous wings swept back by keeping the length-

chord ratio constant. For a series of homogeneous wings

swept back by the method of shearing, however, a definite

variation in reference flutter speed with sweep angle exists

since sweeping a wing by shearing causes a reduction in

chord perpendicular to the wing leading edge and an increase

in length along the midchord as the angle of sweep is in-

creased. The resulting reduction in the mass-density-ratio

parameter and first bending frequency tends to raise the

reference flutter speed, whereas the reduction in semichord

tends to lower the reference flutter speed as the angle of

sweep is increased. The final effect upon the reference

flutter speed depends on the other properties of the wing.

The purpose of this section is to show the effect of these

changes on the magnitude of the reference flutter speed for

a series of homogeneous sheared wings having properties

similar to those of the sheared swept models used in thiis

report.

Let the subscript 0 refer to properties of the wing at zero

sweep angle. The following parameters are then functions

of the sweep angle:

b=bo cos A

cos A

248Since m is proportional to b,

brp 2

K= -= K cos A

Sinfilarly, since I is proportional to b,

0.56 I,

f, =--v- = (a)o(cos A)2

Also, because f, is independent of A,

h (cos A)'

An estimate of the effect on the flutter speed of these

changes in semichord and mass parameter with sweep angle

may be obtained from the approximate formula given in

reference 7,

V r, 0.5

VE - i 0.5+a+xm -=8 os A

This approximate analysis of the effect on the reference

flutter speed does not depend upon the first bending frequency

but assumesfh/f. to be small.

In order to include the effect of changes in bending-torsion

frequency ratio, a more complete analysis must be carried

out. Figure 20 presents some results of a numerical analysis

based on a homogeneous wing with properties at zero sweep

angle as. follows:x.,=50

x,.= 45

r '- 0.25

f,= 100bo=0.333

(D= 10

( -=0.4In figure 20 the curve showing the decrease in V, with A is

slightly above the /cos A factor indicated by the approxi-

mate formula.

Effect of elastic-axis position on reference flutter speed.-

As pointed out in the definition of elastic axis, the measured

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### Reference the current page of this Report.

Barmby, J. G.; Cunningham, H. J. & Garrick, I. E. Study of effects of sweep on the flutter of cantilever wings, report, September 9, 1948; (digital.library.unt.edu/ark:/67531/metadc60354/m1/20/: accessed June 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.