Comparison Between Cubic and Quadratic Models of Hydrodynamic Derivatives to the Ship Course Stability Index

Abstract

The mathematical equations that describe the hydrodynamic forces on a ship's hull are important in understanding how a ship moves. These equations are based on specific values that vary depending on the type of ship. This research will focus on a mathematical model based on a polynomial model in order to investigate the differences between the 3rd order polynomial (cubic model) and the 2nd order polynomial (quadratic model). The course stability index is determined by utilizing linear hydrodynamic derivatives and examined to understand the distinctions between the characteristics of cubic and quadratic models. In this research, the measurement data of the hydrodynamic forces of 12 model vessels (total of 27 loading conditions) that had been conducted for turning tests and the zigzag tests in the past at Kyushu University were targeted. The  based 2nd order model and the  based 3rd order model are applied for re-analysis, and the results of a comparative study on the difference and approximation characteristics of the hydrodynamic force due to the difference of the adopted models are shown.

Keywords

• course stability index
• cubic model
• hydrodynamic derivatives
• ship manoeuvrability
• quadratic model