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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.

In the current paper we are extending our earlier work on the assessment of a ship’s tendency to capsize due to broaching-to in a stochastic seaway. Capturing, in a probabilistic context, interferences between different phenomena occurring during ship operation in extreme seas is a challenging task. Estimates of statistical correlations are deduced between high-run events, broaching-to and capsize. A phenomenological approach is adopted in this study for the classification of the targeted motions. Large scale simulations and a direct counting scheme are applied on the basis of a 4 degrees of freedom (4DOF) mathematical model for the coupled surge–sway–yaw–roll (and rudder) motions. Comparison with the results obtained from a previously used 3DOF model for the same scenarios is carried out in order to investigate the effect of roll on high-run’s correlation with broaching-to. Additionally, sensitivity studies are carried out in order to examine the effect of the commanded heading angle, the rudder control gains and the threshold values defining excessive (unsafe) motions. The concurrence level of the three processes considered here is found to be significantly affected by the examined parameters. The paper includes a short review of effective methods for identifying ship high-runs in following/quartering seas.