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National Advisory Committee for Aeronautics, Report - Method for Calculating Lift Distributions for Unswept Wings with Flaps or Ailerons by Use of Nonlinear Section Lift Data.

A method is presented which allows the use of nonlinear
section lift data in the calculation of the spanurise lift distribu-
tion of unswept uings with flaps or ailerons. This method
is based tlpo-n lifting-line theory and is an extension to the
method described in. NAOA Rep. 865. The mathematical
treatment of the discontinuity in absolute angle of attack at the
end of the flap or aileron inrolres the use of a correction factor
which accounts for the inability of a limited trigonometric
series to represent adequately the spanuise lift distribution.
1-1 treatment of the apparent discontinuity in maximum sect-ion.
lift coeficient is also described. In order to minimize the
computing time and to illustrate the procedures inrolred,
simplified computing forms containing detailed examples are
gire-n for both symmetrical and asymmetrical lift distributions.
A few comparisons of calculated characterinics with those
obtained experi mentally are also presented.

Unswept—wing characteristics calculated by the method of
reference 1, in which nonlinear section lift. date. are used, have
been found to agree much closer with experimental data. in
the region of maximum lift coefficient than those calculated
by methods in which linear section lift curves are used. It
appears feasible that; the similar use of nonlinear section data
would yield improved results for unswept wings with flaps or
ailerons. The deflection of a partial—span flap or aileron,
however, causes discontinuities in the spanwise distribution
of the absolute angle of attack. If such discontinuities exist,
an excessively large number of spanwise stations must be
considered in order to obtain a solution by the method of
reference 1 or by any other method in which the lift dis-
tribution is approximated by a trigonometric series.

A different method of treatment of the discontinuity is there-
fore desirable. Developed herein is a new method of treat-
ment. involving the use of a correction factor which accounts
for the. inability of a limited trigonometric Series to represent
adequately the spa-nwise lift distribution of a wing with
partial-span flaps or ailerons deflected. This correction
factor is obtained with the aid of reference 2 and is used in
conjunction with the system of multipliers of reference 1 to
obtain the induced angle of attack from the spanwlse lift
distribution.