The Influence of Mooring Line Damping on the Prediction of Low-Frequency Vessel Motions at Sea
Authors: Matsumoto K. 
Published: October 2008

ABSTRACT
In some recent OTC papers (Refs. 2 through 4) the importance of mooring line damping on low-frequency surge motions on the moored vessel at sea was demonstrated. In the present paper the contribution of mooring line damping is compared with the other surge damping contributions, viscous damping and wave drift damping on the hull. For this purpose surge decay tests are performed with the model of ship-type floating production system in horizontal mooring and catenary mooring in still water, and also with horizontal mooring in regular waves. Measured dampings are compared with theoretical estimations. The results show that the main contribution to low-frequency surge damping is due to mooring system.
For the prediction of low-frequency surge motions in irregular waves time domain simulation calculations are performed with and without mooring line damping. Their results are also compared with experimental results. Their comparisons show a good prediction accuracy of the present theoretical procedure, and also show that the mooring line damping can not be neglected for the prediction of low-frequency surge motions on the moored vessel at sea.

1. INTRODUCTION
A characteristic feature of moored offshore structures is their slow oscillatory motions at resonant frequencies. They take place at much lower frequency than the frequency range of the wave spectrum. They are excited mainly by second order wave force. In surge direction, these low frequency motions are often dominating in comparison with the first order motions occurring at wave frequencies, and they are correspondingly very important to the prediction of peak off-sets of the vessel, of peak loads in the mooring lines, to the riser design requirements. etc.
First order vessel motions at sea can today be accurately calculated by theoretical methods. Second order motions (low-frequency motions at resonance) are still more uncertain. Since these low-frequency motions are the results of low-damped systems at resonance, their amplitudes are very dependent on the system damping. This system damping, however, has not so far be calculated on a purely theoretical basis. The accurate prediction of system damping, therefore, becomes very important in the prediction of low-frequency vessel surge motions.
Main contributions to the damping for low-frequency surge motion of moored vessel arise mainly fromdrag and friction damping on the vesselwave drift dampingdrag forces on mooring lines.
Other dampings such as due to wind force or friction between mooring line and sea bed are not dealt with in this paper.
Among the above contributions to the total low-frequency surge damping, the first item has so far been determined by experiments in many cases. Huse and Matsumoto (Ref. l) presented a procedure for estimation of viscous surge damping on smooth ship-shaped hulls by applying the theory for skin friction on oscillatory flat plate and a concept of the form factor in oscillatory flow.
The second item, wave drift damping, has been treated by many researchers theoretically as well as experimentally.
The mooring line damping (item 3) has been customarily neglected as a contribution to the total surge damping.