Development of a mathematical model for analysis on ship collision dynamics

Abstract

This research work attempts to develop a model for ship to ship collision. The collision model is fundamentally divided into two segments namely, model for simulation before collision and model for simulation after collision. In the first part, mathematical formulations are derived for finding the possibility of a collision, determining the spatial location of collision and identification of the contact points on the ships. In the later part, a mathematical model is developed to study the kinetic energy losses, collision forces and dynamic responses with respect to different variables such as coefficient of restitution, ship speed, angle of attack, location of hitting, added mass for sway force and others. In the model, expressions for collision forces are derived based on changes in linear momentum. By incorporating the collision force into the equation of motion, which is a linear differential equation with constant coefficients, the dynamic responses are calculated for different collision scenarios. The study considered two different vessels of length 46 meter and 32 meter for conducting the simulations. Results obtained from the mathematical model suggest that collision forces can be reduced significantly by altering the considered variables; e.g. motion amplitudes can be reduced very significantly (as high as eighty five percent) by using materials with lower coefficient of restitution in the fenders and may save ships from capsizing in severe cases. Finally, a number of recommendations have been put forward and further investigations on such models are also proposed.