A simplified modular approach for the prediction of the roll motion due to the combined action of wind and waves

In this work a combined analytical-numerical approach is proposed to address the problem of the ship roll motion under the combined action of wind and waves. Roll motion is modelled as a one-degree-of-freedom system non-linear in both damping and restoring. The approach is modular, allowing an easy update of the methodology on the basis of new research outcomes. Realistic environmental conditions regarding the effects of both wind and waves are taken into account and can be easily changed. The spatial correlation of wind gusts is taken into account by means of an 'aerodynamic admittance' function, whereas the moment due to waves is obtained from the sea slope spectrum using the concept of effective wave slope, leading to a 'hydrodynamic admittance' function. Both static and dynamic aspects of the problems are taken into account. The proposed analytical procedure, based on statistical linearization technique, allows approximate statistical averages of the roll motion, assumed to be Gaussian, to be obtained without necessarily resorting to time-consuming Monte Carlo simulations. On the basis of the results obtained, an estimation of the capsize probability can be carried out. It seems that the effect of wind gustiness could be considered very small when compared with the effects of waves and mean wind speed when the metacentric height is sufficiently large. Finally, the presented approach moves towards the concept of 'performance-based analysis', recently introduced at the International Maritime Organization as the basis for future developments of intact stability, in a clear and formal way.