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National Advisory Committee for Aeronautics, Technical Notes - An Improved Approximate Method for Calculating Lift Distributions due to Twist

A new method is presented for calculating the lift distribution due
to twist which gives a much closer approximation than the empirical
method of Schrenk (NACA TM 9MB) and requires about the same amount of
computing. The new method, based on lifting—line theory, makes use of
the lift distribution due to angle of attack and takes into account the
aspect ratio of the wing. The twist may be that of the washout incor-
porated in the wing design, of aeroelastic deformations, of deflected
flaps or ailerons, or of downwash induced by another lifting surface or
by the jet boundary of a wind tunnel. Examples are presented for the
four main types of twiSt: symmetrical, antisymmetrical, continuous, and
discontinuous. The applicability of the method to swept wing; is also v
presented.

For many purposes it is desirable to calculate quickly an approxi-
mate spanwise lift distribution on a wing due to its twist. The twist
may be that of the washout incorporated in the wing design, of aero-
elastic deformations, of deflected flaps or ailerons, or of downwash
induced by another lifting surface or by the jet boundary of a wind
tunnel. One approximation, which has been used extensively in the past,
is that of Schrenk (reference 1) modified by fairing out discontinuities
as suggested in references 2 and 3. Although Schrenk's approximation may
be adequate for some purposes, it is not as accurate as often desired
since it does not-take into account the aspect ratio of the wing and
weights the twist angle arbitrarily according to the spanwise chord dis~
tribution. The ability to obtain a closer approximation with about the
same amount of computing is therefore desirable. The_method presented
herein has been developed to provide such an approximation.

Gdaliahu, using lifting—line theory, has rigorously proved in refer-
ence A that the average angle of attack of a twisted wing can be obtained
by a spanwise integration of the local angle of attack Weighted according
to the additional spanwise load distribution. The average angle multi-
plied by the three-dimensional lift-curve slope gives the lift coeffi—
cient. These results are proved herein in a somewhat different manner.
It is also shown herein that the moment of the lift distribution of a'
twisted wing can be closely approximated by a simple expression.