On the Stability of Racing Sailing Boats with Foils

Abstract

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 main 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 numerical examples 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.

Keywords

Hydrodynamics of foils / Mathematical analysis / Stability

References

[1] Bellman R.. Dynamic Programming, 1957, Princeton: Princeton University Press

[2] Cea J.. Optimisation, 1968, Dunod, Paris: Théorie et Algorithmes

[3] Ciarlet P.-G.. Introduction à l’analyse numérique et à l’optimisation, 1985, Paris: Masson

[4] Destuynder Ph.. Introduction à l’aéroélasticité et à l’aéroacoustique, 2007, Paris-Londres: Hermès-Lavoisier

[5] Destuynder Ph.. Analyse et contrôle des équations différentielles, 2010, Paris-Londres: Hermès-Lavoisier

[6] Destuynder Ph., Ribereau M. T.. Nonlinear dynamics of test models in wind tunnels. Eur. J. Mech. A/Solids, 1996, 15(1): 91-136

[7] Dowell E. H., Curtiss H. C., Scanlan R. H., Sisto F.. A Modern Course in Aeroelasticity, Mechanics: Dynamical Systems, 1989, Dordrecht: Kluwer Academic Publishers Group

[8] Ducoin A., Young Y.-L.. Hydroelastic response and stability of a hydrofoil in viscous flow. Journal of Fluids and Structures, 2013, 38: 40-57

[9] Fung Y. C.. An introduction to the theory of aeroelasticity, 1955, New York: John Wiley and Sons

[10] Lions J. L.. Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, 1988