With the help of an existing tune-domain simulation program which is also applicable to semi-submersibles some aspects concerning the dynamic positioning (DP) performance of such vessels are investigated. To this end the basic assumptions underlying the program are discussed first, including an account of environmental forces and propulsive forces. After showing some correlations results obtained from monohulls the program is applied to a specific semisubmersible and a number of aspects which are important for the DP performance such as control coefficients, wind feed forward and phase lags originating from different sources, are covered. Finally a simple criterion for the extra power necessary to counter dynamic effects will be compared with results obtained with the tune domain simulation program, as well as with measurements.


The current trends in offshore operations have led to the increased use of dynamically positioned structures. Examples include the recently ordered 9000 tons semi-submersible crane vessel and the SWOPS-tanker, as well as the growing number of work-over vessels, diving support vessels and cable-laying vessels.

In the design stage questions as to the thruster arrangement, amount of power to be installed and maximum position deviations have to be answered For the operation of such vessels it is important to know the vessels response to wind, waves and current and the forces which the thrusters will exert on the ship. Ideally this information will be fully implemented in the on-board control mechanism to increase the efficiency and safety of the operations.

One tool to provide answers to the above questions is a time-domain simulation program which includes all environmental forces, thruster forces (including possible interactions)and a control mechanism.

In ref. (1) such an approach has been attempted and simulation results are shown for a partly loaded 200 kDWT tanker. These results showed for instance the influence of phase-lag and thruster/thruster interaction on the DP capabilities For that purpose the MARIN program MOORSIM had been extended to include a thruster module

By this means, first order and second order motions can be calculated enabling also the analysis of wave feed forward systems as well as low pass filters used in DP systems

However, to obtain a program which can be installed on small computer systems, which admits large yaw motions (course-tracking) and which requires only limited input, it was decided to develop a simulation program containing only low-frequency motions.

For the simulations the three horizontal equations of motion are solved in the time-domain: (The Formula is available in full paper)

Here mkj are assumed to be frequency independent. Considerations of symmetry lead to m21 = m31 = m12 = m13 = 0 Here directions 1, 2 and 3 denote respectively surge, sway and yaw.

The values of the other added inertia coefficients are dependent on the hull shape and principal particulars. To avoid the necessity of performing model tests regression formulae obtained by Clarke et al2 have been used. A correction for the difference between the positions of the center of gravity and amidships is applied.

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