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National Advisory Committee for Aeronautics, Technical Memorandum - A Simple Approximation Method for Obtaining the Spanwise Lift Distribution - Schrenk

In this paper a simple approximation method is pre-
sented for rapidly computing the lift distributions of
arbitrary airfoils. The numerical results are compared
with those obtained by an exact method and for many pur-
poses show a satisfactory degree of accuracy. The latter.
for all practically occurring cases, can be estimated at
the start of the computation work with the aid of the com-
parison examples given. ’

The method described below enables the approximate
determination of the lift distributions in a few minutes
with an accuracy sufficient for many purposes. 'It is also
characterized by.a certain simplicity which is useful in
the clarification of many questions and is in accord with
the engineer‘s point of view. Finally. the method is ap-
plicable to cases for which all other methods are entirely
unsuitable (for example. wines with end plates).

Similar methods, as the author subsequently found.
have already appeared elsewhere. The surprising accuracy
of such simple methods is, however, generally unrecognized.
so that a presentation of comparison computations which
provide a measure of the degree of accuracy obtainable.
should lead to an extended application of the method.

The autho ~wishes to express his appreciation to his
ce-workcr at Gottingen. Mr. N. Eiorth. for carrying out
the laborious computations required for the comparison.

The plausible assumption is made that the real lift
distribution lies between an ideal distribution independ-
ent of the wing shape and a distribution determined in a
simple manner by the wing shape. The ideal distribution
is that with minimum induced drag and constant induced
downwash velocity - that is, for the usual monoplane, the
elliptic distribution; while the distribution dependent
on the the shape is proportional to a t at each position
of the wing.