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This report presents a method for the determination of axially-symmetric shapes with a given base area that are optimum with respect to wave drag in supersonic flow and which have finite nose angles. Use has been made of the exact non-linear differential equations for supersonic flow together with the shock equations. The computed results indicate that the optimum bodies with a finite nose angle have a lower drag than those with cusped noses. This would make their practical application of a certain significance. A number of such shapes have been presented in this report.