Towards a New Mathematical Model for Investigating Course Stability and Maneuvering Motions of Sailing Yachts

Abstract

In order to create capability for analyzing course instabilities of sailing yachts in waves, the authors are at an advanced stage of development of a mathematical model comprised of two major components: an aerodynamic, focused on the calculation of the forces on the sails, taking into account the variation of their shape under wind flow; and a hydrodynamic one, handling the motion of the hull with its appendages in water. Regarding the first part, sails provide the aerodynamic force necessary for propulsion. But being very thin, they have their shape adapted according to the locally developing pressures. Thus, the flying shape of a sail in real sailing conditions differs from its design shape and it is basically unknown. The authors have tackled the fluid-structure interaction problem of the sails using a 3d approach where the aerodynamic component of the model involves the application of the steady form of the Lifting Surface Theory, in order to obtain the force and moment coefficients, while the deformed shape of each sail is obtained using a relatively simple Shell Finite Element formulation. The hydrodynamic part consists of modeling hull reaction, hydrostatic and wave forces. A Potential Flow Boundary Element Method is used to calculate the Side Forces and Added Mass of the hull and its appendages. The Side Forces are then incorporated into an approximation method to calculate Hull Reaction terms. The calculation of resistance is performed using a formulation available in the literature. The wave excitation is limited to the calculation of Froude - Krylov forces.