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National Advisory Committee for Aeronautics, Report - Theoretical Antisymmetric Span Loading for Wings of Arbitrary Plan Form

A simplified ang—snrface theory that includes ejects of
compressibility and spanwise mriation of section lift-curve slope
is used to provide charts with which antisymmetric loading due
to arbitrary antisymmetric angle of attack can be found for
wings hazing symmetric plan forms with a constant spanwise
sweep angle. of the quarter-chord line.
to the flexible wing in roll. Aerodynamic characteristics due to
rolling, deflected ailerons, and sideslip of wings with dihedral
are comidered. Solutions are presented for straight-tapered
wings for a range of swept plan forms.

Reference 1 has been for many years the stande reference
for estimating the stability and control characterisfics of
wings. The lifting-line theory on which this work was
based gave generally satisfactory results for straight wings
having the aspect ratios considered; however, the use of wing
sweep combined with low aspect ratio has made an extension
of this work desirable. fitting-line theory cannot ade-
quately account forthe increased induction efl’scts‘ due to
sweep and low aspect ratio; consequently, it has been found
necessary to turn to the more complex lifting—surface theories.

Of the many possible procedures, a simplified lifting-
surface theory proposed by Weissinger and further developed
and extended in reference 2 has been found especially suited
to the rapid computation of characteristics of wings of
arbitrary plan form; Comparisons with experiment have
generally verified the theoretical predictions. In reference
2, this method has been used to compute for plain, unflapped
wings, the aerodynamic characteristics dependent on sym-
metric loading. The same simplified lifting-surface theory
can be extended to predict the span loading resulting from
antisymmetric  distribution of the wing angle of attack.
From such loadings the damping moment due to rolling,
the rolling moment due to deflected ailerons, and the rolling
moment due to dihedral angle with the wing in sideslip can
be determined.