Prediction method for the effective wave slope function based on the natural roll period

The effective wave slope function is a concept employed to estimate the roll moment due to the action of the waves. In the present paper, the effective wave slope function calculated using semi-empirical formulas and simplified methods, as implemented in the Second Generation Intact Stability Criteria, and by the 3D potential method software Hydrostar®, is shown for a database of eight yachts. A regression providing the effective wave slope at the ship natural roll frequency is derived. The method requires as an input the natural roll period, which may be quickly estimated based on the main dimension and loading condition of the ship. The method is implemented in 1-DOF nonlinear time domain simulation in beam sea. The obtained RMS of roll motion is validated against experimental data of a 50-meters long yacht tested at University of Naples Federico II. The obtained results are comparable to the ones by more accurate methods that account for the entire hull geometry, such as 3D potential method and IMO’ standard methodology.