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National Advisory Committee for Aeronautics, Technical Notes - Influence of Leading Edge Suction on Lift Drag Ratios of Wings at Supersonic Speeds

A method based on linearized twory is presented for calculat-
ing the theoretical suction force at the subsonic leading edges of
a family of wings at supersonic speeds. The method is used to
determine the optimum sweepback angles for the tips of trapezoidal
wings and to determine the effect of curvature of the tip contour
on the lift-drag ratio of wing regions influenced by the tip. The
effect of skin friction is included. The possible gain in lift-
drag ratio from "proper tip design of trapezoidal wings increases
as the sweepback of the wing is increased. Results indicate that
appropriately curved tip boundaries will give higher lift-drag
ratios in the region affected by the tip than the best trapezoidal
wing.

The two-dimensional theory of thin airfoils at subsonic speeds
gives a resultant force normal to‘ the wing surface if only pressure
forces on the wing surface are considered, which implies a net drag.
For this theory, however, the velocity components become infinite
at the leading edge. Evaluation of the effect of this singularity
yields a suction force that exactly cancels the drag and thus sat-
isfies the momentum requirement that the resultant force vector be
normal to the direction of flight (reference 1).

The procedure used to derive the suction force is not
restricted to two-dimensional wings and indicates that such a.
force may occur along any edge at which the normal congaonent of
the velocity becomes infinite. . In the linearized theory for thin
wings flying at supersonic speeds, such a singularity exists along
leading edges swept behind the Mach angle. It has therefore been
proposed by Brown (reference 2) that a leading-edge suction force,
which tends to counteract the wave drag, exists along subsonic
leading edges of wings flying at supersonic speeds. The magnitude,
of this force is calculated in reference 2 for triangular wings
swept beyond the Mach angle. The reduction in drag predicted by
the concept of leading-edge suction force has been shown by
Vincenti to occur experimentally for triangular wings swept beyond
the Mach angle.