In the last ten years computer simulation programs for SPM moored vessels have been developed by several authors. At present the application of such programs, if at all, is limited to some preliminary calculations in the very early design stage. The reasons for the reluctance to apply such computation methods in the more final stage of the design is clearly due to the failure of reliable input data and uncertainties concerning the procedures to describe the governing physical phenomena more accurately.

In this paper experimental and theoretical results for the input and the methodologies involved in simulations of the behaviour of and the mooring forces induced by a large tanker moored in wind, irregular waves and current will be presented.


A vessel moored in the open sea can perform high and low frequency motions. The low frequency oscillations can be an important problem. The large horizontal excursions that occur can cause large forces in the mooring system.

As is schematically indicated in Fig. 1, in the computation procedure distinction can be made in a low frequency and a high frequency part of the equations of motion of a moored vessel. Nowadays reasonably reliable computations can be carried out concerning the high frequency input for the equations of motion. For the low frequency part, however, uncertainties exist concerning the input of the hydrodynamic reaction forces and the wave drift force excitation in current. Since, in general, an SPM system is a weakly damped system, reasonance peaks in the modes of motions in the horizontal plane can often be clearly distinguished. Therefore in order to predict the motion responses correctly, attention must be paid not only to the excitation but also to the damping.

In this paper results will be presented on input data and computation procedures in order to clarify the mentioned uncertain terms in the equations of motion of the low frequency part.

In order to obtain the low frequency hydrodynamic damping an extensive model test program has been carried out. .A review of the experiments is shown in Fig. 2. Some results will be given in this paper. To show the computation procedures examples for 1-DOF and 3-DOF will be highlighted.

For the 1-DOF of a linearly moored 200 kDWT tanker the following computation procedures will be dealt with:

  • wave drift force and wave drift damping in still water;

  • wave drift force and wave drift damping in current;

  • viscous surge damping in still water and in current;

  • solution of the equations of motion in the frequency domain.

For the 3-DOF case a formulation of the coupled equations of motion for tanker motions in the horizontal plane (in still water and in a current field) has been experimentally determined. In the past descriptions of the equations of motion for the low frequency tanker motions in the horizontal plane have been given by many authors, ref. [1] through [11].

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