Wave drag of slender star-shaped bodies at moderate supersonic flight velocities (Q1082955)

The wave drag of star-shaped bodies at moderate supersonic flight velocities is discussed using an expression for slender sharp-pointed bodies that leads to a two-dimensional boundary value problem. The main equation describing the wave drag is taken over from the quoted literature. Polar coordinates are introduced as well as an approximate potential function which is connected to an other function by the Cauchy- Riemann conditions. Some transformations are carried out, especially a conformal mapping of the interior of the unit disk onto the exterior of the n-ray star. A Dirichlet problem is formulated for a complex potential, a term of which can be expressed by means of a Poisson integral, which however diverges at a certain point. Differentiation and the use of the Lagrangian formula finally leads to the solution of the Dirichlet problem mentioned above. There occur infinite sums which contain Euler's psi function and Euler's constant. It is shown, that the several terms of the wave drag expression either belong to an axisymmetric part or to a nonaxisymmetric one. The physical meaning of the solution parameters is discussed in detail. For instance the wave drag depends on the number of rays and on their shape. Best results within the family of star-shaped bodies discussed gives a five-point start with thin rays.