On the unsteady motion of two-dimensional sails

An equation is derived to describe the motion of a two-dimensional inextens ible sail at a small, time-dependent, angle of incidence to a uniform two-d imensional flow. The equation derived is a singular partial integro-differe ntial equation, which in the steady case reduces to the sail equation of Vo elz. A number of limiting versions of the equation are derived and analysed for cases where the relative mass of the sail is large or small. For gener al unsteady sail motions the governing equation must be solved numerically. A scheme is proposed that employs Chebyshev polynomials to approximate the position of the sail; ordinary differential equations are derived to deter mine the relevant Chebyshev coefficients and a number of examples are illus trated and discussed. It is found that in some cases where the angle of att ack changes sign the tension may become large; in these instances the under lying physical assumptions of the model may be violated.