Energy analysis of ship motion in waves and a novel method for predicting wave added resistance

Energy analysis of ship motion in waves is carried out, and a novel method to predict the corresponding wave added resistance is proposed in this paper. First, a semi-analytical three-dimensional translating and pulsating source method that accounts for steady wave effects is employed to solve the first-order radiation and diffraction hydrodynamic problems. The work expressions of various forces in the ship motion equation, i.e., the different energy components, are derived based on the principle of energy conservation. Based on the derived formulas, a numerical program is developed to validate the first-order hydrodynamic results and investigate the energy conversion relationships of ship motion in waves. It is found that the incident wave energy is dissipated by the ship in the form of radiated and diffracted waves, while the inertial and restoring forces have no impact on energy conversion. Furthermore, the wave-induced resistance of ships sailing in waves is divided into the steady wave-induced resistance in calm water and the unsteady radiated wave-induced and diffracted wave-induced resistance. The mean value of this unsteady wave-induced resistance is equal to the wave added resistance. Accordingly, a novel method for predicting wave added resistance is proposed, which comprehensively incorporates both radiation and diffraction effects. For short waves, an empirical formula is employed to compensate for the insufficient consideration of viscous and nonlinear effects, and the smooth transition of the wave added resistance response function in the full wavelength range is achieved by analyzing its generation mechanism.