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

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, r_oa of Fig. 2, is considered to be longer than the chord c_a and the terms of 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.