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National Advisory Committee for Aeronautics, Report - Theoretical Span Load Distributions and Rolling Moments for Sideslipping Wings of Arbitrary Plan Form in Incompressible Flow

SUMMARY

A method of computing span loads and the resulting rolling
moments for sideslipping wings of arbitrary plan form in in-
compressible flow is derived. The method requires that the
span load at zero sideslip be known for the wing under con-
sideration. Because this information is available for a variety
of wings, this requirement should not seriously restrict the
application of the present method. The basic method derived
herein requires a mechanical difierentiation and integration to
obtain the rolling moment for the general wing in sideslip.
For wings having straight leading and trailing edges over each
semispan, the rolling moment due to sideslip is given by a simple
equation in terms of plan—form parameters and the lateral
center of pressure of the lift due to angle of attack.

The mechanical difi'erentiation and integration required to
obtain the rolling moment for the general wing can be avoided
by use of a step-load method which is also derived. Charts are
presented from which the rolling-moment parameter 013/01,
can be obtained for wings having straight leading and trailing
edges over each semispan.

Calculated span loads and rolling-moment parameters are
compared with experimental values. The comparison indi-
cates good agreement between calculations and available experi-
mental data.

INTRODUCTION

The span load distributions and rolling moments of a wing
in sideslip are important in considering the structural and
dynamic lateral-stability requirements of an aircraft and,
hence, have been the subject of numerous experimental and
theoretical studies. Most of the studies have been limited
to the determination of the rolling moment due to sideslip
01"; however, a few studies have been concerned with the

span load distributions for wings in sideslip. (See refs. 1,
2, and 3, for example.) References 1 and 2 are theoretical
studies: reference 1, for unswept wings; and reference 2, for
sweptback wings. Comparisons between experimental and
theoretical span loads for unswept wings showed good
agreement (ref. 1). The few comparisons in reference 2
between theoretical and experimental span loads for swept
wings indicated fair agreement over most of the semispan
but poor agreement near the wing tip where the theory

lSupeIsedes NAOA. Technical Note 3605 by M. J. Quello, 1955.