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Tacking—a maneuver used to sail a boat against the wind, changing direction in a zig-zag fashion—is one of the most difficult but necessary sailing maneuvers. While tacking is common, the movement of the sails and wind forces during the turn are not well understood.

A new study by New York University and University of Michigan mathematicians addresses these matters head-on.

It offers a detailed characterization of how sails behave during a wide range of tacking motions and with an array of sail types. Its findings serve as both a framework for improved sail designs and a pathway for making today's autonomous sailboats—vital in oceanographic research—more efficient and reliable when changing direction in unpredictable wind conditions.

"Tacking is more than just a turn," explains Christiana Mavroyiakoumou, an instructor at NYU's Courant Institute of Mathematical Sciences and the lead author of the paper, which in the journal ÌÇÐÄÊÓƵical Review Fluids.

"It is a high-stakes maneuver where sail performance can make or break a race or a sailing journey in general. By uncovering what determines a successful flip and how long it takes, this research gives sailors and engineers a new resource for mastering the wind."

"There has been a lot of work on optimizing the shapes of the sails and hulls of sailboats, but much remains to be understood about fluid-structure interactions during unsteady maneuvers," adds University of Michigan Professor Silas Alben, who authored the paper with Mavroyiakoumou. "The tacking maneuver is one important example where simplified modeling can help us understand the basic physics."

The researchers studied the dynamics of sail movement during a tacking maneuver: when the sail angle of attack, or angle between the wind and a sail's chord line, is reversed in order to sail upwind. In successful tacking, the sail flips around to adopt its mirror-image shape while in unsuccessful tacking the sail remains stuck in a state close to its initial shape.

The researchers used a combination of mathematical modeling and numerical simulations to better understand how sails interact with the background wind during tacking, which was modeled by examining how a sail moves in the wind and how the wind changes in response. Overall, their computations revealed the following:

• Three factors play the biggest roles in whether the flip happens at all: a sail's stiffness (or, conversely, ability to extend), its tension prior to encountering wind, and final sail angle in relation to the wind. More specifically, a less flexible and, thus, less curved—or deflected—sail whose tension prior to encountering the wind is high and which is angled at 20 degrees to the wind after tacking is most likely to result in successful tacking.
• The sail's mass and the speed and acceleration of the turn mostly affect how fast the flipping happens.
• Slack sails are harder to flip during tacking.

The researchers add that, beyond competitive sailing, this research could potentially benefit automated sailing vehicles under different wind conditions.