A Conformal Mapping Suitable for Problems Involving Interaction Between Given Geometries and Known Far Fields.

A conformal transformation formula using Riemann-Stieltjes integrals is derived for use with problems involving the interaction between a given finite-sized geometry and a known far field. The derivative of this transformation is non-singular in the domain considered and tends to one at infinity. A formula is derived for transformation from the unit circle to the exterior of an arbitrarily given continuous curve with bounded variation. A special case of the transformation is very similar to that of Schwarz-Christoffel. Application to the generation of aerofoils gives some fairly flexible formulae of the finite product type. (Author)