Sail dynamics during tacking maneuvers

Abstract

We study the dynamics of sail membranes during a tacking maneuver, when the sail angle of attack is reversed in order to sail upwind. In successful tacking the sail flips to the mirror-image shape, while in unsuccessful tacking the sail remains stuck in a metastable state close to the initial shape. We investigate whether the sail flips, and if so, how long it takes and the subsequent dynamics, over a parameter space that describes the sail membrane properties and the kinematics of tacking. We find that the "steady" parameters -- stretching rigidity, pretension, and final angle of attack -- mostly determine whether a membrane flips or not. Flipping is more likely with larger values of the stretching rigidity, pretension, and final angle of attack. The dynamical parameters -- membrane mass density, concavity of angle-of-attack transition kinematics, and time-length of the tacking maneuver -- mainly affect how long flipping takes. With large membrane mass the membrane can maintain the momentum from the tacking motion long enough to reach the flipped state, but it may also take longer to converge to a steady shape. Concave-down angle-of-attack profiles and small tack times are generally associated with shorter flip times but a few exceptions exist, because these kinematics can also give a larger acceleration to the fluid-sail system that persists for longer times. We also investigate slack sails and find that they are more difficult to flip.