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Under the assumptions of linearized theory, general methods of solutin are given for two- and three-dimensional steady-state and two-dimensional unsteady-state equations of compressible flow. The solutions depend in all cases on the use of Green's equivalent layer of sources, sinks, and doublets. Emphasis is placed on applications in supersonic wing theory, the singularities arising in the integrations being treated by Hadamard's finite part of the technique. Four examples of different character are discussed. In particular, the load distribution over a specific swept-back lifting surface is determined at a free-stream Mach number of one.
The experiments conducted with boron carbide and each of four metals showed that nickel, cobalt, and iron formed a bonding zone between the metal and the ceramic and that chromium showed satisfactory physical wetting characteristics on the ceramic.

Report

United States. National Advisory Committee for Aeronautics

Published: 1950

Total Pages: 26


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Reverse-flow theorems in aerodynamics are shown to be based on the same general concepts involved in many reciprocity theorems in the physical sciences. Reciprocal theorems for both steady and unsteady motion are found as a logical consequence of this approach. No restrictions on wing plan form or flight Mach number are made beyond those required in linearized compressible-flow analysis. A number of examples are listed, including general integral theorems for lifting, rolling, and pitching wings and for wings in nonuniform downwash fields. Correspondence is also established between the build-up of circulation with time of a wing starting impulsively from rest and the build-up of lift of the same wing moving in the reverse direction into a sharp-edged gust.
The compressive buckling stress of outstanding flanges reinforced by bulbs was computed by the strain-energy method for flanges having 10 shapes and a range of lengths. The results were checked for some cases by computations based on a differential-quation method. The edge of the flange opposite the bulb was considered clamped, and the loaded ends were considered simply supported.