Influence of Surge on Extreme Roll Amplitudes

Interference of the wave-induced ship surge motion with roll dynamics has been studied. The surge motion has been included in a previously derived hydrodynamic roll prediction model in order to account for the ship speed variation due to the longitudinal incident wave pressure force. Depending on the position of the wave crest relatively to the ship, the ship will be slowed down when she meets the wave. In this paper attempts are made to accurately account for added resistance and additional thrust, applied in order to maintain the ship speed. The surge equilibrium equation has been longitudinally balanced in order to determine the added thrust term that would represent actions to maintain speed The resulting forward speed variation affects the frequency of encounter and the parametric roll resonant condition is directly influenced by this speed variation. The analysis procedure is demonstrated for an example containership sailing mainly in head sea condition and higher sea states. Sensitivity of the results to the added thrust model and vertical motion calculation is discussed.