Added resistance in waves

Added resistance in waves is the mean increase in a ship’s resistance, above the calm-water value, caused by wave-induced motions, wave reflection, and wave diffraction at the hull. It is a second-order quantity proportional to the square of wave amplitude, so in irregular seas it is obtained by integrating a quadratic transfer function against the wave spectrum: R_aw = 2 times the integral of (R_aw/zeta_a squared) times S(omega) d-omega. Computed by radiated-energy (Maruo, Gerritsma-Beukelman) or near-field pressure-integration methods, it drives the speed loss and added power demand used in weather-routing and in the IMO minimum-propulsion-power assessment.