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National Advisory Committee for Aeronautics, Report - Theoretical Calculations of the Pressure, Forces, and Moments at Supersonic Speeds Due to Various Lateral Motions

SUMMARY

Velocity potentials, pressure dishibutions, and stability de-
rivatives are derived by use of supersonic linearized theory for
families of thin isolated vertical tails performing steady rolling,
steady yawing, and constant-lateral—acceleration motions. Ver—
tical-tail families (half-delta and rectangular plan forms) are
considered for a broad Mach number range. Also considered
are the vertical tail with arbitrary sweepbaclc and taper ratio at
Mach numbers for which both the leading edge and trailing edge
of the tail are supersonic and the triangular vertical tail with a
subsonic leading edge and a supersonic trailing edge. For pur—
poses of completeness, analogous expressions and derivatises for
sideslip motion obtained primarily from other sources are
included.

Expressions for potentials, pressures, and stability derivatives
are tabulated. Curves which determine the stability derivatives
for half-delta and rectangular tails are presented which enable
rapid estimation of their values for given values of aspect ratio
and Mach number. In order to indicate the importance of end—
plate efi'ects, several comparisons are shown of the derived results
(based on a zero-end-plate analysis) with those corresponding to
a complete-end—plate analysis.

INTRODUCTION

Detailed knowledge of the loading, forces, and moments
acting on vertical tails undergoing various maneuvers is a
necessary prerequisite for determining the lateral dynamic
behavior of aircraft. The information presently available is,
in many instances, insufficient to enable reliable estimates to
be made of the vertical—tail contributions to airplane stabil—
ity at supersonic speeds. Aside from calculations for several
“slender” configurations, theoretical results to date have
been concerned, for the most part, with tail configurations
either subject to a constant sideslip attitude or performing
a steady rolling motion (see refs. 1 to 13).

For the sideslip motion, the effects of Mach number and
aspect ratio on the aerodynamic loads of a number of tail
configurations with both one and two planes of cross-sec-
tional symmetry have already been investigated extensively.
The same effects on tail arrangements in a rolling motion