Findings provide 'a new resource for mastering the wind' and have potential engineering applications for automated boats and vehicles
Study: Sail dynamics during tacking maneuvers (DOI: 10.1103/37xg-vcff)
A maneuver called tacking that's 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 from the University of Michigan and New York University mathematicians addresses these matters head-on.
"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," said Silas Alben, a U-M professor and author of the paper. "The tacking maneuver is one important example where simplified modeling can help us understand the basic physics."
The study, supported by the U.S. National Science Foundation, 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," said Christiana Mavroyiakoumou, an instructor at NYU's Courant Institute of Mathematical Sciences and the lead author of the paper, which appears in the journal Physical Review Fluids.
"It is a high-stakes maneuver where sail performance can make or break a race or a sailing journey in general," said Mavroyiakoumou, who earned her doctorate at U-M. "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."
The researchers add that, beyond competitive sailing, this research could potentially benefit automated sailing vehicles under different wind conditions.
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.
