Theory of a Thin-Ring Airfoil in an Incompressible Inviscid Source Flow Field

Abstract

This analysis concerns itself with the loading calculation of a thin-ring airfoil symmetrically positioned in an unbounded spherical source flow field. A spherical source was used to replace the undisturbed, nonparallel, but axisymmetric, freestream. A ring vortex distribution was used to replace the thin-ring airfoil. The thin-airfoil theory not only limits the shape of the airfoil, but also applies only for a small angle σ, between the chord line and the relevant undisturbed source flow rays. With the latter restriction, the distance between the source origin and the midchord of the airfoil, roa of Fig. 2, is considered to be longer than the chord ca and the terms of 0 1roa/ca2 and higher-order terms were neglected in the analysis. The result of the analysis is a set of algebraic equations containing geometric parameters of the flow field. For a given geometry the strength of the ring vortex distribution can be calculated readily.