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National Advisory Committee for Aeronautics, Report - A Summary of Lateral Stability Derivatives Calculated for Wing Plan Forms in Supersonic Flow

A compilation of theoretical mlues of the lateral-stability
derivatives for wings at supersonic speeds is presented in the
form of design charts. The wing plan forms for which this
compilation has been prepared include a rectangular, two
trapezoidal, two triangular, a fully-tapered wept—back, a swept-
baclc hexagonal, an u-nsuept hexagonal, and a notched triangular
plan form. A full set of results, that is, values for all nine of
the lateral-stability deriratiifes for wings, was available for the
first sin: of these plan forms only. The reasons for the incom-
pleteness of the results arailable for other plan forms are
discussed.

The values of the deriratires presented were obtained directly
from tabulated results in the reports referenced or were calculated
from erpressions presented in these reports. The expressions
for the derivatives were derired using linearized theory for
compressible flow. The calues presented, however, do not
represent exact linear-theory solutions in every case due to the
fact- that approximations and simpl'y‘ications were sometimes
necessary in the derivation of the expressions or in the calcula-
tions of the numerical results. The ejects of these approxim-
tions and simplifications on the accuracy and applicability of
the results are considered.

The calculation of the lateral-stability derivative coeffi-
cients (hereinafter referred to as the iateralstahility deriv—
atives) for thin wings at supersonic speeds has been ac-
complished for a number of plan forms and the results are
reported in references 1 through 18. These results are neces-
sarily incomplete in view of the fact that- there is an unlimited
number of plan forms that could be investigated. There
appears to be a sufficient quantity of results available, how-
ever, to warrant the preparation of a. summary. In fact,
some summaries, such as references 10 and 17, are already
available but the results presented in these reports are re—
stricted to a. fairly small number of plan forms or to a small
number of derivatives. It is the purpose of this report,
therefore, to assemble and present a. more extensive set of
numerical results than was heretofore available. These
results will be limited to the thin-airfoil, inviscid-flow solu-
tions obtained from application of the linearized theory of
compressible flow. They will be presented in the form of
design charts showing the variations of the derivatives 1 with
Mach number, aspect ratio, and other plan-form parameters.