The University of Southampton
University of Southampton Institutional Repository

On the unsteady motion of two-dimensional sails

On the unsteady motion of two-dimensional sails
On the unsteady motion of two-dimensional sails
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.
0272-4960
147-171
Fitt, A.D.
51b348d7-b553-43ac-83f2-3adbea3d69ab
Lattimer, T.R.B.
dae29958-2dfc-4a4a-9ede-b30311e42e1a
Fitt, A.D.
51b348d7-b553-43ac-83f2-3adbea3d69ab
Lattimer, T.R.B.
dae29958-2dfc-4a4a-9ede-b30311e42e1a

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).

Record type: Article

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.

Full text not available from this repository.

More information

Published date: 2000

Identifiers

Local EPrints ID: 29123
URI: https://eprints.soton.ac.uk/id/eprint/29123
ISSN: 0272-4960
PURE UUID: 0c0b685e-ddab-4e36-88c3-b1a7fa9846ba

Catalogue record

Date deposited: 18 Jul 2006
Last modified: 17 Jul 2017 15:59

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×