Establishment of empirical formulae for hydrodynamic derivatives of submarine considering design parameters

The hydrodynamic derivatives are necessary for assessing the dynamic characteristics, such as dynamic stability and maneuverability which are crucial in evaluating navigation safety and operational efficiency. Hence, it is required to compute the hydrodynamic derivatives precisely. This study nominates the new empirical formulae for predicting the hydrodynamic derivatives of a submarine. The proposed empirical formulae are derived from hydrodynamic forces and moments which are measured using Computational Fluid Dynamic (CFD) approach. Because the BB2 generic submarine is designed with an appropriate geometry and outstanding features, especially directionally stability, so, it is designated to establish the empirical formulae. The design parameters that have a significant impact on the maneuverability of the BB2 submarine, such as the length-to-diameter ratio, sail position, and sail height, are altered to fit different types of submarines for various purposes. Then, hydrodynamic derivatives of each change factor of the design parameter are taken using the least square method and assessed in relationship with the design parameters through correlation analysis. The high correlation values determine the independent variables which are the design parameters to form the empirical formulae for each hydrodynamic derivative based on multiple regression analysis. The applicability of the established empirical formulae is confirmed by applying them to calculate the hydrodynamic derivatives of BB2 and 2000 tons submarines, and comparing the calculation with the available data. The high precision implies that the established empirical formulae can be used to predict the hydrodynamic derivatives of similar profile submarines to the BB2 and 2000 ton submarines, and they can be extended to submarines in general at the designing phase.