Quantitative and qualitative analyses of parametric roll for ship design and operational guidance

Abstract

This article presents a procedure for quantitatively analyzing the susceptibility of a ship to parametric roll for use in designing a ship against this phenomenon. Due to the nonergodic characteristics of parametric roll motion, numerous direct time-domain simulations are needed to obtain a stable long-term distribution of parametric rolls. To avoid such heavy computational demand and to accelerate numerical simulations, a 1-degree-of-freedom computational model for parametric roll prediction is developed for both regular- and irregular-wave excitations, adopting the approximated righting arm ([Formula: see text]) curve. In this model, the concept of transfer functions is introduced for the mean and the first harmonic component of metacentric height ([Formula: see text]), which is introduced to approximate [Formula: see text] fluctuation. The simulation results obtained by using this model are compared to those of a three-dimensional weakly nonlinear simulation program. The sensitivity of the simulation results to the initial value, time window, and number of simulations is investigated, and their proper values are proposed. Using the proposed model, the long-term predictions of parametric roll are carried out for typical post-Panamax container ships and a very large crude oil carrier by applying Monte Carlo simulation. Based on the simulation results, the susceptibility of each ship to parametric roll is evaluated, and the influence of still-water [Formula: see text] on the susceptibility is investigated. This study extends to the development of an operational guidance for the ship crew’s decision-support system, as one of countermeasures of a severe parametric roll. Particularly, a procedure for qualitatively developing an operational guidance is proposed. In this study, numerical simulations are carried out by using an impulse–response function approach. As an example model, a typical 10,000 TEU container ship is considered, and the results are discussed with respect to its operation.