This paper discusses different damping mechanisms in the ow frequency horizontal motion of a floating production unit and evaluates, numerically, the relative importance of each one of them for two classes of structures: a ship with a turret and a semi-submersible platform. For the ship the damping is very small and the most critical situation, both with respect to the offset and the tension on the mooring line, occurs when the ocean current is zero; in this case the "wave drift damping" is the most important damping mechanism although the influence of the viscous dissipation on the mooring lines thends to increase with the water depth. For the semi-submersible, where the drag on the columns is large, the worst situation occurs for the maximum ocean current and the slow motion is small, since the damping is very large then.
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