Trajectory simulation of a ship and a submarine (using linear and non-linear hydrodynamic derivatives) using MATLAB

Abstract

Predicting a vessel's maneuvering behavior during the early design stages is of utmost importance. Usually, model testing is undertaken to estimate the hydrodynamic derivatives. However, during the early design stages, model testing may not be feasible, and one needs to depend on analytical or semi-empirical methods to predict their values. This study aims to develop a code for simulating the trajectory of a ship/submarine. The hydrodynamic derivatives can either be directly inputted or, in the absence of the hydrodynamic derivatives, especially during initial phases of design, the same is computed using the empirical formulas available in the open domain. A comprehensive study has been undertaken on the empirical formulae available in the open domain for predicting the hydrodynamic coefficients of ships, especially the non-linear terms. For computing the submarine hydrodynamic derivatives, the same has been calculated, considering the submarine to be a purely axisymmetric body having an ellipsoidal shape of the same length and diameter as the submarine. Trajectory simulations of the vehicle motion are obtained by solving the equation of motions utilizing the robust coding environment of MATLAB. For integrating the differential equations, Euler's method is used. The accuracy of the program results varied from 0.1% to 3%. It is hoped that the study carried out would be beneficial to naval architects involved in ship/submarine design studies.