Interaction between a pair of two-dimensional sails for the case of smoothly attached flow

Abstract

Linearized thin-wing theory is applied to the problem of the flow of an inviscid, incompressible fluid past a pair of two-dimensional sails (flexible airfoils of zero thickness) which interact with one another. Attention is confined to the case where the flow is smoothly attached at the leading edge of each of the two sails. The results in general confirm expectations regarding sail behaviour obtained by intuitive reasoning, and should be of value to the theoretically minded sailor The analysis is complicated by the fact that the shapes of the sails depend on the load distribution and vice versa; it leads to a pair of coupled integro-differential equations, which cannot be solved by conventional techniques. Each sail is represented by its properties at a series of N points along its chord, thereby converting the two ‘critical equations’ to matrix form. The result is an eigenvalue problem involving 2 N equations, 2 N unknowns, and two eigenvalues. This is solved by the use of an iterative technique, successive approximations being obtained alternately from each of the two matrix equations.