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Heat-transfer data from four wind-tunnel experiments and two free-flight experiments with turbulent boundary layers have been examined to see whether or not they are well represented by the Reynolds analogy or a modification thereof. The heat-transfer results are put into the form of dimensionless Stanton numbers based on fluid properties at the outer edge of the boundary layer and are compared with skin-friction coefficients for the same Mach numbers and wall to free-stream temperature ratios as obtained from an interpolation of the existing skin-friction data. The effective Reynolds number is taken to be the length Reynolds number measured from the effective turbulent origin, a position which differs importantly from the leading edge of the test surface in some cases.
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The external wave drag of bodies of revolution moving at supersonic speeds can be expressed either in terms of the geometry of the body, or in terms of the body-simulating axial source distribution. For purposes of deriving optimum bodies under various given condtions, it is found that the second of the methods mentioned is the more tractable. By use of a quasi-cylindrical theory, that is, the boundary conditions are applied on the surface of a cylinder rather than on the body itself, the variational problems of the optimum bodies having prescribed volume or caliber are solved. The streamwise variations of cross-section area and drags of the bodies are exhibited, and some numerical results are given. The solutions are found to depend upon a single parameter involving Mach number and radius-lenght ration of the given cylinder. Variation of this parameter from zero to infinity gives the spectrum of optimum bodies with the given condition from the slender-body result of the two-dimensional. The numerical results show that for increasing values of the parameter, the optimum shapes quickly approach the two-dimensional.
The method has been applied to various types of configurations in several wind-tunnel investigations conducted by the National Advisory Committee for Aeronautics at Mach numbers up to 4, and in all cases the calculated roughness height caused premature boundary-layer transition for the range of test conditions.