Simplified estimation formula for frequency response function of roll motion of ship in waves

Abstract

This study proposes a simplified formula for estimating the frequency response function of ship roll motion expressed by the main hull-form parameters of a ship (length L, breadth B, draft d, block coefficient Cb, waterplane area coefficient Cw, height of center of gravity KG‾, and metacenter height GM‾). By taking a theoretical approach, starting from the equation for roll motion and approximating each fluid force component, the authors have developed a formula that is physically clear and simple, yet engineering accurate and extendible. For nonlinear effects, this study assumes the case where decay coefficients or Bertin's N-coefficient are given, and it considers the nonlinearities in the quadratic damping force by equivalently linearizing the force. For equivalent linearization, a convergence calculation is usually required, but in this study, it is replaced by an explicit formula. To validate the proposed equation, numerical calculations using the linear 3D-Green's function method program were performed for 154 actual merchant ships with a wide parameter range, and it was confirmed that the equation is applicable regardless of ship type and size.