Observations by crew of high-speed planing boats and sea trial tests have indicated that high-speed planing hulls suffer poor longitudinal and transverse instabilities, and boat may experience unfavorable motions due to any small environmental excitation. In this regard, dynamic motions of planing boats have been investigated over the last thirty years, during which innovative linear and nonlinear methods have been developed .In these studies, different method s have been developed by various authors to determine forces and moments acting on the hull. However, majority of investigators have focused on vertical motions of planning boats in waves (such as Zarnick [1978], Hicks and Troesch [1994] etc.) and few researchers have only attempted to model motions in transverse and horizontal planes including sway, yaw and roll motions. Furthermore, most of researches dealing with transverse and horizontal planning motions, were experimentally conducted (such as Judge [2010], Morabito et al [2014] etc). There exist only few articles, in which mathematical models for transverse motion have been developed. Therefore, it is needed to develop as implemathematical models for prediction of transverse motions of planing boats for use in conceptual design phase. During the last five years, there has been an increased interesting study of transverse motions, and in the current paper, an attempt has been made for a mathematical study of roll motion of planning hulls.

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