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National Advisory Committee for Aeronautics, Technical Notes - A Simple Approximate Method for Calculating Spanwise Lift Distributions and Aerodynamic Influence Coefficients at Subsonic Speeds

Several approximate methods for calculating lift distributions at
subsonic speeds are combined and extended to form a simple step-by-step
procedure for calculating symmetric and antisymmetric lift distributions
for arbitrary angle-of—attack conditions on swept and unswept wings.
Methods of estimating the required aerodynamic characteristics are
included, but any available theoretical or experimental results may be
used in several steps of the analysis to shorten the work and increase
the accuracy. The extension of the method to the calculation of aero-
dynamic influence coefficients and of spanwise moment distributions is
indicated.

An empirical method (ref. 1) for calculating spanwise lift distri-
butions on unswept wings has been used extensively in the past. In
modified form (ref. 2) it has been applied to the calculation of span-
wise lift distributions on swept wings. More recently, an improved
method of calculating the lift distributions due to twist has been
published (ref. 3).

In the present paper a limitation of the method of reference 3 as
applied to antisymmetric twists is indicated and removed. The methods
of references 1 to 3 are then combined with each other and with the
results of another investigation (ref. h) into a step-by-step procedure
which starts with the lift-curve slope and the additional lift distri—
bution and proceeds with the calculation of symmetric basic lift distri-
butions, the lift distribution due to roll, the rolling—moment coeffi-
cient due to roll, and, finally, antisymmetric lift distributions. The
additional lift“distribution is herein defined as the lift distribution
for constant angle of attack across the span with a lift coefficient
equal to l. The basic lift distribution is defined as the lift distri-
bution of a twisted wing at—zero (total) lift. Means of'calculating
the aerodynamic characteristics required in the method are contained in
this paper, but if any of these characteristics are known from other
sources they may be incorporated in the procedure with a resultant
saving in time and improvement of accuracy.