On the Stability of Racing Sailing Boats with Foils


Philippe DESTUYNDER,Caroline FABRE.On the Stability of Racing Sailing Boats with Foils[J].Chinese Annals of Mathematics B,2018,39(3):427~450
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Philippe DESTUYNDER; Caroline FABRE
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. \begin{figure}[h] \centering \includegraphics{fig.1.eps}\\[2mm] {\small Figure 1\ \ Principle of the flying boat with the AC45 of Oracle USA Team---TV snapshot.} \label{fig0} \end{figure}


Hydrodynamics of foils, Mathematical analysis, Stability


35C07, 65M15, 35M12, 65T60
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