A hybrid empirical–analytical model for predicting the roll motion of prismatic planing hulls

Abstract

During the last 5 years, there have been some major advances in roll motion modeling of planing boats. In this article, previous studies have been reviewed, and an attempt has been made to propose a relatively straightforward method for computing roll motion coefficients and thus predicting the roll response of a planing vessel in calm water on a straight path with constant speed. The proposed method has been developed by modifying, combining, and using previous empirical and analytical methods. Roll restoring moment is determined by implementing an asymmetric parameter in previous relations of lift of planing hulls. Also, an empirical method is proposed for computing righting arm of this moment. Roll damping is computed using previous relations related to damping of lift force and considering the asymmetrical effects. Roll added mass is obtained by utilizing an analytical approach for the roll of a flat plate. However, an effective half-wetted beam computed by asymmetrical effects has been proposed for this purpose. Finally, it has been suggested that current hypothesis be used for time-domain simulation. Validity of the proposed method is evaluated by comparing the obtained righting moment, response amplitude operator, and roll hydrodynamic coefficients against previously published experimental data. This comparison confirms that the proposed method has relatively good accuracy against experimental results. Using the current method, the influence of Froude beam number on roll hydrodynamic coefficients and roll responses has been investigated. It is observed that increase in Froude beam number results in a decrease in roll added mass and an increase in the roll damping. It has also been concluded that for larger load coefficients, the roll hydrodynamic coefficients are larger. Results associated with roll response indicate that an increase in Froude beam number would yield an increase in the amplitude of the response. However, an increase in load coefficient results in a decrease in the response.