Theoretical span load distributions and rolling moments for sideslipping wings of arbitrary plan form in incompressible flow Page: 4 of 18
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THEORETICAL SPAN LOAD DISTRIBUTIONS
AND ROLLING MOMENTS FOR SIDESLIPPING WINGS OF ARBITRARY
PLAN FORM IN INCOMPRESSIBLE FLOW 1
By M. J. QUEIJo
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 differentiation 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 differentiation 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 CI/CL
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-
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
C,,; 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
I Supersedes NACA Technical Note 3605 by M. J. Queijo, 1955.
indicated a rapid decrease in load and experiments indicated
a rapid increase. The method of reference 1 does predict
the rapid tip-load change with sideslip which has also been
observed for unswept wings. Examination of reference 1
indicated that the basic concepts employed therein could be
used in the calculation of span loads and rolling moments
for swept wings in sideslip, provided sweep effects could be
taken into account.
The purpose of the present report is to derive a method,
using the basic concepts of reference 1 and introducing a
means to account for sweep effects, which permits the calcu-
lation of the span load distribution and rolling moment for
any wing in sideslip. The method requires that the span
load distribution at zero sideslip angle be known. Since
this information is available for a large variety of wings
(see refs. 4 to 7, for example), this restriction is not believed
to be serious.
The basic concepts used herein permit the determination
of the span load and the resulting rolling-moment coefficient
of a wing in sideslip by use of either an integration method
and a continuous spanwise circulation distribution or a series
summation in combination with a stepped circulation distri-
bution. Both methods are developed lerein.
aspect ratio, b2/S
wing lift coefficient due to angle of attack,
Wing lift due to a
willg rolling-momlellt coefficient,
Wing rolling moment
c chord, parallel to plane of symmetry
c average chord, S/b
Ct chord at inboard end of a vortex
II I11111111 III
I -II -- I--- -I
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Queijo, M. J. Theoretical span load distributions and rolling moments for sideslipping wings of arbitrary plan form in incompressible flow, report, October 6, 1955; (digital.library.unt.edu/ark:/67531/metadc60662/m1/4/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.