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A general discussion of applying these formulas to the numerical solution of partial differential equations is made. An illustrative problem with function value given on a circular boundary is solved by both relaxation and matrix methods. Similar applications to compressible flow past isolated and cascade airfoils, through turbomachines, and temperature and stress distribution is cooled turbine blades is indicated.
An investigation was made in the Langley gust tunnel of a 60 degree sweptback-wing model to determine its response to gusts. On the basis of results, a simplified method of analysis, which uses a slope of the lift curve derived by the cosine law and which uses strip theory to estimate the penetration effect, appears to be applicable for the prediction of gust loads on wings swept as much as 60 degrees.
Includes the Committee's Technical reports no. 1-1058, reprinted in v. 1-37.

Report

United States. Office of Scientific Research and Development

Published: 1963

Total Pages: 1522


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An analytical method is presented for obtaining turbulent temperature recovery factors for a thermally insulated surface in supersonic flow. The method is an extension of Squire's analysis for incompressible flow. The boundary layer velocity profile is represented by a power law and a similarity is postulated for squared-velocity the static-temperature-difference profiles.
Basic equations of Karman and Chien are solved by representing the shape of a torsion box by means of a Fourier series. Angles of twist, longitudinal stresses, and shear stresses are determined in terms of the series coefficients. The method is applied to the calculation of angles of twist and stresses in torsion boxes of rectangular, elliptical, and airfoil cross section. Results obtained for angles of twist and normal stresses are in good agreement with results of Karman and Chien except at sharp corners. Results obtained for shear stresses indicate the necessity for the use of large number of terms of the series for satisfactory accuracy.