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National Advisory Committee for Aeronautics, Report - Calculated Spanwise Lift Distributions, Influence Functions, and Influence Coefficients for Unswept Wings in Subsonic Flow

Spanim'se lift distributions have been calculated for nineteen
unswept wings with various aspect ratios and taper ratios and
with a variety of angle-of-attack or tim'st distributions, including
flap and aileron deflections, by means of the Weissinger method
with eight control points on the semispan. Also calculated
were aerodynamic influence coeflicients which pertain to a
certain definite set of stations along the span, and several
methods are presented for calculating aerodynamic influence
functions and coeflicients for stations other than those stipulated.

The information presented herein can be used in the analysis
of untwisted wings or wings with known twist distributions, as
well as in aeroelastic calculations involving initially unknown
twist distributions.

In the design and development of an airplane, a knowledge
of the spanwise lift distribution on the wing is important in
predicting the structural loads and the stability character-
istics. For high-speed airplanes having flem'ble wings, the
calculation of the spanwise lift distribution is an aeroelastic
rather than a purely aerodynamic problem. In aeroelastic
calculations means are required for calculating the span-
wise lift distribution for angle-of—attack (or twist) distribu-
tions which are initially unknown. Aerodynamic influence
functions or coefficients constitute the most convenient of
these means.

As used in this report, the term “aerodynamic influence
function’ ’ refers to a function which, when multiplied by the
spanwisc angle—of-attack or twist distribution and integrated
over the span, yields the lift (per unit span) at some station
on the wing. This function may be considered to be lift
distributions on the given wing corresponding to angle~of-
attack distributions given by delta (impulse) functions. In
a mathematical sense this function is the Green’s function for
whatever equation is used to relate lift distributions to angle-
of—attack distributions.