*Article* **Assessment of the Roll Derivatives of Different Surface Ships Based on Numerical Pure Roll Simulation**

**Thi Loan Mai 1, Anh Khoa Vo 1, Hyeon Kyu Yoon 2,\* and Dong Kyou Park 3,\***


**Abstract:** Among the 6 degrees of freedom (6-DoF), excessive roll motion is the most dangerous cause of ships capsizing. However, when analyzing the maneuverability of surface ships, the roll components have usually been ignored. It is widely known that the influence of roll moment becomes significant for surface ships with low GM (metacentric height) and high speed. This paper examines the pure roll test for several surface ships to assess the roll-related hydrodynamic derivatives of added mass and damping in maneuvering. The objective ships are the KRISO Container Ship (KCS), David Taylor Model Basin (DTMB), Office of Naval Research Tumblehome (ONRT), and Delft 372 catamaran, where the DTMB and ONRT ships are equipped with complementary bilge keels as damping devices and have a small GM, which the Delft 372 catamaran does not have. The flow during pure roll is analyzed by the Computational Fluid Dynamics (CFD) simulation method that allows the complex flow around ships to be captured, especially when the bilge keel and skeg are considered. The results indicate that the roll moment is greatest in the catamaran. Since the roll moments of the DTMB and ONRT are larger than that of the KCS, bilge keels and surface shape also contribute to increasing roll damping moment. In addition, a comparison of the damping derivatives due to roll rate with results obtained from another method indicates that CFD simulation is capable of accurately predicting the roll-related derivatives, which is difficult to perform by the experiment method.

**Keywords:** pure roll simulation; small metacentric height; surface ship; bilge keel; skeg; catamaran; roll-related derivatives; CFD
