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National Advisory Committee for Aeronautics, Technical Notes - Span Load Distributions Resulting from Constant Angle of Attack, Steady Rolling Velocity, Steady Pitching Velocity, and Constant Vertical Acceleration for Tapered Sweptback wings with Streamwise Tips - Subsonic Leading Edges and Supersonic Trailing Edges

On the basis of linearized supersonic-flow theory, the theoretical
spanwise distributions of circulation (which are proportional to the
span load distributions) resulting from constant angle of attack,
steady rolling velocity, steady pitching velocity, and constant verti-
cal acceleration were calculated for a series of thin, sweptback,
tapered wings with streamwise tips. The analysis is valid at those
speeds for which the wing is wholly contained betWeen the Mach cones
springing from the wing apex and the trailing edge of the root section,
that is, subsonic leading edges and supersonic trailing edges. An
added restriction is that the Mach cones emanating from the leading
edges of the wing tips must not intersect on the wing. ‘

Fornmlas for the spanwise distributions of circulation are given
in closed form. Numerical results are presented as a series of design
charts from which the desired loading may be obtained for given values
of aspect ratio, taper ratio, Mach number, and leading—edge sweepback.
The axis of pitch is taken at the wing apex although, by use of the cal-
culated results and a simple transformation, span load distributions for
steady pitching velocity may be readily obtained for arbitrary location
of the pitch axis. Variations of the spanwise distributions of circula-
tion with the various plan-form parameters, Mach number, and axis-of-
pitch location are also presented for illustrative purposes.

A knowledge of the spanwise loading or spanwise distribution of
circulation (which is proportional to the spanwise loading) is of great
value in solving aerodynamic problems and performing aerodynamic calcu—
lations. For example, it has been shown that the upwash and sidewash
downstream of an airfoil are largely determined by the spanwise circu—
lation except in the region directly behind the trailing edge. In addi-
tion to the estimation of flow fields and evaluation of forces and
moments on the surface itself, the spanwise distribution of circulation
may/also be applied to problems in aerodynamic loads and aeroelasticity.
In view of these considerations, a series of charts giving the spanwise
distributions of circulation for a variety of wing plan forms at various
Mach numbers will serve many useful purposes.