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Results offer ‘a new asset for mastering the wind’ with potential engineering implications for automated vessels and vehicles

A technique referred to as tacking, employed for sailing a boat upstream by altering direction in a zigzag pattern, is among the most challenging yet essential sailing maneuvers. Despite its prevalence, the behavior of the sails and wind forces during the transition remains poorly understood.

A recent investigation by mathematicians from the University of Michigan and New York University confronts these issues directly.

“Numerous studies have focused on optimizing the configurations of sails and hulls of sailboats, yet much is still to be learned regarding fluid-structure interactions during dynamic maneuvers,” remarked Silas Alben, a U-M professor and paper co-author. “The tacking maneuver serves as a notable instance where simplified modeling can enhance understanding of fundamental physics.”

This study, funded by the U.S. National Science Foundation, provides an exhaustive characterization of sail behavior across a broad spectrum of tacking motions and various sail designs. The results act as both a foundation for enhanced sail designs and a means of improving modern autonomous sailboats—crucial for oceanographic exploration—by making them more efficient and dependable in navigating unpredictable wind patterns.

“Tacking is more than just making a turn,” stated Christiana Mavroyiakoumou, an educator at NYU’s Courant Institute of Mathematical Sciences and the lead author of the paper published in the journal Physical Review Fluids.

“It represents a critical maneuver where the efficiency of the sail could determine the outcome of a race or an overall sailing endeavor,” said Mavroyiakoumou, who received her PhD from U-M. “By revealing what factors lead to a successful transition and the time required, this study equips sailors and engineers with a novel resource for mastering the wind.”

The researchers emphasize that, aside from competitive sailing, this investigation could also offer advantages for automated sailing vessels navigating varied wind conditions.

The team explored the dynamics of sail movement during the tacking procedure: changing the sail angle of attack, or the angle between the wind and the sail’s chord line, to navigate upwind. In effective tacking, the sail rotates to mirror its previous shape, while ineffective tacking sees the sail remaining in a state near its original configuration.

Employing both mathematical modeling and numerical simulations, the researchers aimed to deepen the understanding of how sails interact with the prevailing wind during tacking, which was analyzed by observing how a sail moves in the wind and how the wind responds. Overall, their computations indicated the following:

• Three key factors significantly influence whether the flip occurs: a sail’s rigidity (or, conversely, its ability to extend), its tension before engaging with the wind, and the final sail angle relative to the wind. More specifically, a stiffer and thus less curved—or deflected—sail with high pre-wind tension and angling at 20 degrees to the wind post-tacking has the highest likelihood of resulting in successful tacking.
• The sail’s weight and the speed and acceleration of the turn primarily affect how rapidly the flipping transpires.
• Loose sails are more challenging to flip during tacking.

Authored by James Devitt of New York University

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