## A slender-wing theory in potential flow

Chadwick, EA
2005,
'A slender-wing theory in potential flow'
, Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, **461** (2054)
, pp. 415-432.

**Official URL**: http://dx.doi.org/10.1098/rspa.2004.1295

## Abstract

Consider uniform, steady potential flow past a slender wing. By considering a horseshoe vortex in the limit as γ/Us → ∞, where γ is the circulation, U is the uniform stream velocity and s is the span, a model representing a vortex sheet is obtained from which the lift on the slender wing can be determined. (This is in contrast to the textbook approach of Batchelor and Katz & Plotkin, who discretize the vortex sheet with horseshoe vortices in the limit as γ/Us → ∞, but then relate the vortex strength to lift by using the two-dimensional limit γ/Us → 0. We shall argue that using these different limits in the same analysis is inconsistent and leads to an incorrect result.) The resulting potential term is shown to be the same as the potential term of the lift Oseenlet in Oseen flow. In the limit of high-Reynolds-number flow, only half the contribution to the lift integral comes from the potential-velocity part of the lift Oseenlet. The other half comes from the vortex-wake-velocity part of the lift Oseenlet. We therefore assume potential flow everywhere except at the vortex sheet, along which we allow a singular vortex-wake-velocity term of the lift Oseenlet. From this, a slender-wing theory is presented together with integral expressions for the lift and change in lift over the wing surface. Applications to slender bodies and large-aspect-ratio wings, in particular, the Lanchester-Prandtl lifting line, are then considered.

Item Type: | Article |
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Uncontrolled Keywords: | Potential flow, oseen flow, slender-body theory, slender-wing theory, manoeuvring |

Themes: | Subjects / Themes > Q Science > QA Mathematics Subjects outside of the University Themes |

Schools: | Schools > College of Science & Technology Schools > College of Science & Technology > School of Computing, Science and Engineering Schools > College of Science & Technology > School of Computing, Science and Engineering > Salford Innovation Research Centre (SIRC) |

Journal or Publication Title: | Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences |

Publisher: | The Royal Society |

Refereed: | Yes |

ISSN: | 13645021 |

Depositing User: | H Kenna |

Date Deposited: | 03 Sep 2007 14:54 |

Last Modified: | 29 Oct 2015 00:12 |

URI: | http://usir.salford.ac.uk/id/eprint/387 |

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