Fitt, A.D. and Lattimer, T.R.B.
(2000)
On the unsteady motion of two-dimensional sails.
*IMA Journal of Applied Mathematics*, 65 (2), 147-171.
(doi:10.1093/imamat/65.2.147).

## Abstract

An equation is derived to describe the motion of a two-dimensional inextensible sail at a small, time-dependent, angle of incidence to a uniform two-dimensional flow. The equation derived is a singular partial integro-differential equation, which in the steady case reduces to the sail equation of Voelz. 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 general 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 determine the relevant Chebyshev coefficients and a number of examples are illustrated and discussed. It is found that in some cases where the angle of attack changes sign the tension may become large; in these instances the underlying physical assumptions of the model may be violated.

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