The berthing ship problem

Abstract

In this report a mathematical model is formulated which is sufficiently accurate to describe quantitatively and qualitatively the behaviour of a ship berthing to a structure equipped with fenders as well as to determine the response of the fenders themselves. In order to achieve this a set of equations is drawn up by which the (coupled) transient motions - in six degrees of freedom - of shiplike bodies can be described adequately. To this end use is made of the so-called 'impulse response function' - technique, which has as the restriction that the shipfluid system is supposed to be linear. This approach enables the inclusion of external forces of arbitrary nature; the fluid reactive forces are taken into account by means of the hydrodynamic coefficients which are ipcorporated in the impulse response functions representing the properties of the linear ship-fluid system. The influences of a restricted water depth and of a (quay-)wall parallel to the ship can be taken into account. The 'impulse response function'-technique is applied to the case of a ship with a box-like shape in order to avoid coupling between the respective ship motions. This is, however, not an essential simplification. Since berthing manoeuvres and the ship-fender interactions take place mainly in the horizontal plane, only the sway and yaw motions are considered; the effect of a forward speed is not included. For the case of shallow water with a horizontal bottom and relatively large horizontal dimensions the respective impulse response functions for the sway and yaw motion are calculated from experiments and/or theory. Using the 'impulse response function'-technique a mathematical model is presented describing both the behaviour of the schematized ship berthing to a structure equipped with one undamped, (non-)linear fender and the behaviour of the fender itself. 'Centric' as well as 'eccentric impacts' are considered. An extensive experimental verification was carried out by means of model tests on shallow water with relatively large horizontal dimensions. Two water depths were regarded. The same situations as investigated experimentally were simulated numerically by means of the mathematical model, using thereby the impulse response functions calculated. The results of calculations and model tests show a very good agreement.