Novel Method for Predicting Linear Velocity Derivative in Modern Ship Hulls and Its Validation Using a Low-Speed Maneuvering Simulator

Ship maneuvering prediction relies on hydrodynamic derivatives, traditionally obtained through empirical formulations based on hulls built decades ago. A comparison with experimental data revealed a notable discrepancy, particularly for the linear sway velocity derivative (YV′), where these regression models inadequately capture the behavior of modern hulls. To overcome this limitation, a novel approach is proposed, in which 690 virtual static drift tests were conducted across a systematic series of 115 modern hull forms, parametrically generated in the Grasshopper platform and thus benchmarked against seven vessels. This extensive numerical dataset enabled the development of an updated regression formulation for YV′, which was grounded in key geometric parameters and incorporated specific terms related to the bow and stern shapes. The results obtained by the CFD-based method were compared with those obtained experimentally, confirming the high fidelity of this approach, yielding a maximum relative error of only 4.7% for the sway linear velocity derivative. Crucially, when this proposed empirical formula was integrated into a mathematical model (MM-TPN) to predict a ship’s trajectory, it demonstrated substantial improvement by reducing the absolute relative error in standard maneuvers from 23% to 10% compared with traditional methods used to describe the YV′. Furthermore, an extensive discussion regarding the regression model was conducted, leading to the establishment of the drift angle threshold that invalidates the linear theory (set at 10∘ for blunt hulls and 8∘ for slender hulls). A comprehensive three-step validation process, encompassing the V&V of the virtual static drift tests, validation of the derived maneuvering coefficient, and validation through standard maneuvers employing the novel approach proposed here, was fully executed.