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National Advisory Committee for Aeronautics, Technical Notes - Theoretical Spanwise Lift Distributions of Low-Aspect-Ratio Wings at Speeds Below and Above the Speed of Sound

The spanwise lift distributions of wings of low aspect ratio but of
arbitrary plan form and angle—of—attack distribution have been analyzed
4 by two well-established concepts: the virtualemass concept and the
Weissinger method» Both concepts have been found to yield the same
simple integral expression for the spanwise lift distribution in terms
of the spanwise angle—of—attack distribution. Tables and figures of
lift distributions of low-aspect-ratio wings have been preSented.
Within certain limitations these distributions are independent of the
plan forms For plan forms with leading edges swept back behind the Mach
cone, the results of the analysis are applicable at supersonic speeds.

For wings of very low aspect ratio, of the order of l or less, at
small angles of attack the flow may be assumed to be esentially two—
dimensional in planes normal to the stream direction. (See reference 1.)
In the present paper this concept is shown to lead to a simple formula-
tion of the problem of calculating the Spanwise lift distribution of
wings of very low aspect ratio for various angle—of—attack distributions
in terms of conditions at the widest section of the wing. The same
problem is also formulated as a limiting case of the Weissinger
L-method. (See reference 2.) Some comparisons are drawn between the
assumptions and limitations of the two approaches.

Spanwise lift distributions have been calculated for angle-of—
attack distributions which correspond to several symmetrical and
antisymmetrical twists, as well as to the deflection of flaps and
ailerons of various spans.- The results are presented in a table and in
several figures.

According to the theory of reference 1 the disturbance set up by
wings of low aspect ratio at small angles of attack is essentially two-
dimensional in planes perpendicular to the free stream. The lift on a
spanwise strip of width dx may then be obtained from the time rate of
change of the vertical momentum of the virtual mass associated with the
given two-dimensional flow.