Journal of Ship Research, Vol. 63, No. 2, June 2019, pp. 94–107 http://dx.doi.org/10.5957/JOSR.09180078 Study on Roll Restoring Arm Variation Using a Three-Dimensional Hybrid Panel Method Shu Xia Bu,* Min Gu,* and Moustafa Abdel-Maksoud † *China Ship Scientific Research Center, National Key Laboratory of Science and Technology on Hydrodynamics, Wuxi, China † Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology, Hamburg, Germany Providing a reliable numerical tool for the prediction of parametric roll and pure loss of stability is a difficult task. It is acknowledged that the occurrence of these two failure modes is mainly attributed to the variation of roll restoring arm, which should be calculated accurately. This work studies exclusively the roll restoring arm variation numerically and experimentally. First, partially restrained experimental tests at dif- ferent constant heeling angles (up to 30°) are conducted to measure the variation of roll restoring arm in regular waves. Second, a numerical method for the calculation of roll restoring arm in waves taking radiation and diffraction moments into account is adopted. The calculation results are benchmarked against experimental model test data. Third, the characteristics of roll restoring arm variation and the effects of ra- diation and diffraction moments on roll restoring arm variation (GZ RD ) in head and following seas are investigated. Finally, the feasibility of GZ calculated by the integral of instantaneously average wetted surface is studied by comparing the results with that calculated by the integral of the fully instantaneously wetted surface. The research show that the GZ RD can be ignored in following seas. The GZ in head seas consists of two important harmonic components, and GZ RD is the main contribution of the second harmonic component. Therefore, GZ RD should be calculated with consideration of the instantaneous heeling angles and Froude number in head seas, especially for the prediction of large amplitude roll motion at high speed. Keywords: fully nonlinear boundary condition; radiation moment; diffraction moment; second-generation intact stability in IMO 1. Introduction Currently, the second-generation intact stability criteria are under development by the International Maritime Organization (IMO) (IMO SLF 53/WP.1-Add.1 2011; IMO SDC 3/WP.5 2016). Five different kinds of potentially dangerous dynamic stability failure modes in waves were proposed. Parametric roll and pure loss of stability are two of the stability failure modes that may lead to capsizing of a ship. According to the proposed drafts, a multilevel structure was adopted to make sure that numerical assessment procedures are only applied when the vulnerability to dynamical stability failures is beyond reasonable doubt. Assessment of the vulnerability criteria is normally based on simplified geometry characteristics or empirical formulas. However, direct stability assessment requires highly accurate prediction (Kobylinski 2012). Many efforts have been devoted to studying parametric roll and pure loss of stability (Umeda & Yamakoshi 1994; Bulian et al. 2003; France et al. 2003; Paulling 2006; Taguchi et al. 2006; Spanos & Papanikolaou 2007; Umeda et al. 2008; Shigunov et al. 2009; Sadat-Hosseini et al. 2010). These researches pointed out that roll restoring arm variation in waves is one of the main attributing factors of both failure modes. The restoring moment is susceptible to change when the wavelength is nearly equal to the ship length. The roll restoring moment will reduce if the amidship of a ship is located at a wave crest, and it will increase if the amidship of a ship is located at a wave trough, especially for ships with a large flared Manuscript received by SNAME headquarters December 10, 2018; accepted January 7, 2019. Corresponding author: Shu Xia Bu, bushuxia8@163.com 94 JUNE 2019 JOURNAL OF SHIP RESEARCH 0022-4502/19/6302-0094$00.00/0