Development of Simplified Formula of Froude-Krylov Force of 6-DOFs Acting on Monohull Ship

Abstract

In this study, the authors have developed the simple and accurate formulae of the Froude-Krylov forces of 6-DOFs based on the linear theory, as a fundamental study to develop a closed formula of ship motion in waves. The proposed formulae have been developed by approximating the hull-form under waterline by the function uniquely determined by the principal particulars of the ship; length L, breadth B, draft d, block coefficient C_b, waterplane area coefficient C_w, midship section area coefficient C_m, height of center of gravity KG, longitudinal center of floatation LCF. Therefore, the proposed formulae are expressed as the explicit function determined by only principal particulars as well as the wave condition parameters. It was confirmed that the proposed formulae have high accuracy for all merchant ship types in any wave condition (wave angle and wave length) through validation compared with numerical calculation by using actual hull-forms of 77 ships × 2 conditions.