A method is described for the mathematical simulation of the behaviour of a moored ship in waves. The method is based on the equations of motion in the time domain according to Cummins, while the hydrodynamic loads on the ship are obtained by means of the three dimensional source technique. Results of computations for a ship moored to a jetty are discussed and compared with experimental results.


Up till a few decades ago, the mooring of ships has been mainly a matter of practical experience. Ships were moored in harbours or sheltered areas only, where the external force are in general limited to the rather steady current and wind forces.@

With the development of the ocean industry and the advent of very large ships, which can only be accommodated in a few harbours with sufficient water depth, the need arose to moor ships in exposed areas. To this purpose special mooring facilities were designed to absorb the loads exerted by the environment on the moored ship. Nowadays a variety of mooring arrangements is in operation. @

Because of the short history and fast development of mooring in exposed areas, the design of terminals can not be based on empirism. On the other hand the problem is too complicated for an analytical treatment. There fore it is common practice to study the behaviour of a moored, ship by means of experiments with small scale models. Although model testing provides an effective tool to determine mooring forces and maximum motions of the moored ship for design purposes, this method inheres a few drawbacks. @

First, model tests are expensive and time consuming. The test set-up is complicated, it is essential that elasticity properties of mooring lines and fenders are simulated very carefully, and sophisticated facilities are needed to simulate the relevant environmental conditions. For this reason test programs are usually restricted to final design configurations and selected weather conditions which are assumed to be the most critical.@

Further, the fundamental insight gained from model tests on these complicated systems is limited. Only the resulting output is measured without learning much of the mechanism which causes this output. As an example the low frequency motion of a moored ship observed in tests in irregular waves may be mentioned. @

On a basis of model test results it is not possible to- conclude whether this motion is caused by second order effects in the wave loads, or by the fact that the elasticity properties of the mooring system are nonlinear. @

It is, therefore, highly desirable to dispose of a mathematical simulation method for the behaviour of a moored object. Such a method can help to increase the understanding of moored ship behaviour, and can be used as a tool in optimization studies in the early stages of design, prior to model testing.

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