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# Math for Sailing

In 2001 Ernesto Bertarelli, the leader of the Alinghi team, contacted the Ecole Polytechnique Fédérale de Lausanne (EPFL) asking for a scientific advisor for the critical parts of the project, namely the materials for the hull and the fluid dynamics for the design of the boat. The EPFL research groups cooperated with the design team of Alinghi in order to help them design the optimal boat and test its performance. We will describe the contributions of the math group to the optimization of the design of Alinghi using advanced computational fluid dynamics (CFD) techniques. This design could not have been completed were if not for the advances in mathematics and computational algorithms created for this specific project.

 The design process can be represented as a loop which involves sailing experience and mathematical skills. New concepts are tested and improved by means of numerical simulations, to get the best compromise between performance and the constraints imposed by the racing rules. Enlarge. (Image courtesy of CMCS (Chair of Modeling and Scientific Computing-EPFL-Lausanne))

An America’s Cup yacht is a very sophisticated system that should work optimally in a wide range of sailing conditions. The different components (above and below the water surface) of a sailing yacht interact in several complicated ways, and the design of the yacht must consider this complexity as a whole. The development of suitable experimental and numerical tools, which can describe the system as accurately as possible is required in order to achieve an optimal configuration.

The goal in creating a sailboat design for competition is to find shapes of the boat, its appendages (like the keel), the bulb and the winglets, and its sails so that the sailboat moves with greatest speed and is more easily maneuverable in a variety of wind and wave conditions. Historically these designs were created by master craftsmen who made their choices based on experience and agreed on rules of thumb. In the 1990’s engineers started employing “simple” models to estimate basic quantities of physical relevance (such as the drag on the hull) prior to construction of the boat.

Recent advances allowed mathematicians to work with boat designers and sailors to create more realistic mathematical models for how a sailboat handles in different marine conditions. The solutions to these models are difficult to find, even numerically, for three reasons. First, the equations are not standard (they involve the coupling of different submodels) and a complete theory that guarantees the existence and uniqueness of the solutions is not yet available. Second, the equations are so complicated that finding accurate solutions numerically, even on a modern supercomputer, can take a long time. Third, solutions should simultaneously optimize boat performance in many different conditions (wind speed, boat direction relative to wind direction, wave height and direction, etc).

Mathematicians were essential because they set up the theoretical basis for solving the model equations, developed new numerical algorithms to solve the model equations more quickly (so that the equations modeling a given design could be solved under many different marine conditions), and determined strategies for deciding which of two different designs give generally better results over a variety of weather conditions.