Extraction of Dominant Parameters and Proposal of Simplified Formula for Ship Motion in Waves

Abstract

In this study, the authors proposed explicit formulae of the surge, heave, and pitch motion of ship in regular waves expressed as the explicit function of principal hull-form parameters and extracted dominant hull-form parameters of those for simple estimation of the wave loads for the ship structural design. In order to develop the estimation formulae which have enough accuracy and wide range of applicability, the theoretical approach was adopted based on the linear seakeeping theory. In the process of deriving formulae, the equations of motion were simplified based on the relationship of the fluid forces that cancel out each other and the approximation that the ship speed is slow. For both surge and pitch motion, 1-DOF model, in which interaction effects were ignored, was applicable and the dominant parameters were successfully extracted. On contrast, heave motion in head sea was significantly affected by pitch motion especially for full loading conditions. Although the mechanism of interaction effect and the factor were clarified, it was difficult to express simple form and extract dominant parameters. However, in beam sea, the heave motion can be expressed as the 1-DOF model, and the dominant parameter was extracted straightforwardly. By using the extracted dominant parameters, the approximated formulae of peak value of the response amplitude operators of the vertical motion were proposed. It was confirmed that the proposed formulae have enough accuracy regardless of ship size and ship type through validation compared with numerical calculation by using actual hull-forms of 77 ships × 2 loading conditions.