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On the Stability of Racing Sailing Boats with Foils

Chinese Annals of Mathematics,Series B 2018年第3期39卷 427-450页

作者： philippe destuynder Caroline FABRE Département d'ingénierie Mathématique Laboratoire M2N Conservatoire National des Arts et Métiers 292rue saint Martin75003 ParisFrance Laboratoire de Mathématiques d'Orsay Univ.Paris-SudCNRSUniversitéParis-Saclay 91405 OrsayFrance

The development of foils for racing boats has changed the strategy of sailing. Recently, the America＇s cup held in San Francisco, has been the theatre of a tragicomic history due to the foils. During the last round, the New-Zealand boat was winning by 8 to 1 against the defender USA. The winner is the first with 9 victories. USA team understood suddenly （may be） how to use the control of the pitching of the inain foils by adjusting the rake in order to stabilize the ship. And USA won by 9 victories against 8 to the challenger NZ. The goal in this paper is to point out few aspects which could be taken into account in order to improve this mysterious control law which is known as the key of the victory of the USA team. There are certainly many reasons and in particular the cleverness of the sailors and of all the engineering team behind this project. But it appears interesting to have a mathematical discussion, even if it is a partial one, on the mechanical behaviour of these extraordinary sailing boats. The nunlerical exanlples given here are not the true ones. They have just been invented in order to explain the theoretical developments concerning three points： The possibility of tacking on the foils for sailing upwind, the nature of foiling instabilities, if there are, when the boat is flying and the control laws.

关键词： Hydrodynamics of foils Mathematical analysis Stability

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