Refinement of Norrbin Model via Correlations between Dimensionless Cross-Flow Coefficient and Hydrodynamic Derivatives

Abstract

To develop a simplified and highly accurate ship motion model, this study thoroughly investigated the relationship between the dimensionless cross-flow coefficient and the four hydrodynamic derivatives of the Norrbin model. Eight different types of ships were simulated to explore the impact of dimensionless cross-flow coefficients and individual hydrodynamic derivatives on the ship’s turning circle. A set of precise formulas is proposed to depict the interplay between these variables. The simulation outcomes indicate that the average deviation in the agreement between the turning circles produced by adjusting the dimensionless cross-flow coefficient and those predicted by modifying the four hydrodynamic derivatives was only 2.70%. Furthermore, the similarities between the two circles and the sea trail were significantly higher at 91.45% and 92.87% compared with the original Norrbin model’s accuracy of 78.12%. Adjusting the dimensionless cross-flow coefficients enabled the rapid identification of a curve that closely mirrored the sea trail. This research aimed to improve the accuracy of the Norrbin model and resolve issues related to determining the magnification of the hydrodynamic derivatives, laying a robust foundation for subsequent studies and applications in relevant domains.

Keywords

• ship-turning circle
• Norrbin model
• dimensionless cross-flow coefficient
• hydrodynamic derivatives