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National Advisory Committee for Aeronautics, Technical Notes - Theoretical Calculations of the Lateral Force and Yawing Moment Due to Rolling at Supersonic Speeds for Sweptback Tapered Wings with Streamwise Tips

Theoretical results are obtained, by means of the linearized theory,
for the lateral force and yawing moment due to combined angle of attack
and roll. The thin wings considered are tapered and have leading and
trailing edges which are each swept at a constant angle; the tips are
parallel to the center section. Further restrictions are that the leading
edges are supersonic (the velocity component normal to the leading edge is
supersonic) and the Mach lines from either tip do not intersect the remote
tip. The trailing edges may be either supersonic or subsonic provided
that the taper ratio is equal to or less than one.

Design curves are presented which permit rapid estimation of the two
stability derivatives, rate of change of lateral force and yawing moment
with roll CI? and Cnp, respectively, for given values of aspect ratio,
taper ratio, Mach number, and leading-edge sweep. These design curves
are given relative to the body axes with the origin located at the pro-
jection of the leading edge of the tip section on the center section.

The conversion to stability axes with moments about an arbitrary-axis can
be accomplished by use of a simple formula given herein.

One of the important derivatives required in the prediction of the
lateral stability of airplanes is the rate of change of yawing moment
with roll. Theoretical results for this derivative CnP and also for
the derivative expressing the rate of change of lateral force with
roll 61 at supersonic speeds have been reported in a number of papers
for thin wings having particular plan forms. These papers include
references 1 and 2 for triangular plan forms, reference 3 for rectangular
wings, reference h for wings of zero taper ratio having sweptback, sub-
sonic leading edges, and reference 5 for sweptback tapered wings with
streamwise tips and subsonic leading edges (the component of velocity
normal to the leading edge is subsonic).

In the present paper, the linearized theory is used to obtain the
derivatives an and 01b for thin wings at supersonic speeds. The
wings considered have conventional taper ratios, the leading and trailing
edges are each swept at a constant angle, and the tips are parallel to
the center section. The results are valid only for a range of super-
sonic speeds for which the leading edge is supersonic (the component of
velocity normal to the edge is supersonic). The trailing edges may be
either supersonic or subsonic provided that subsonic edges do not affect
the tip edges. A further restriction is that the Mach lines from either
tip do not intersect the remote tip.