Motions of small boats moored in standing waves

Abstract

This study was conducted to determine the dynamic characteristics of small boats moored with non-linear-elastic lines in an asymmetrical manner. The motions being considered are surge motions where the moored boat is allowed to move either in the direction of the bow or the stern, but not in other coordinate directions. An analytical model is proposed where the small boat is simulated by a block-body which is moored asymmetrically to a fixed dock. A method is developed from which the non-linear restoring forces and the dynamic response of the boat in surge can be obtained. The restoring force which is associated with the boat displacement is defined by the material, condition, and dimensions of the lines and the mooring geometry. From those results, an approximation to the restoring force is made so that a closed solution to the problem is possible. The periods of free oscillation determined by this method are compared to the results of some experiments conducted on a 26-foot boat with a displaced weight of approximately 7000 lbs. The experiments were performed using this small boat moored under different conditions: all lines taut, 4 inches slack in all lines, and 8 inches slack in all lines. These results compared favorably with the analytical results. The response of seven small boats of various displaced weights were determined analytically to evaluate the range of important wave periods for this sample. The mooring dimensions of these boats were measured in situ and the theoretical approach developed was applied. The results indicate, for the samples considered, that the important range of periods of forced oscillation for excessive motions of these boats in surge was less than 10 secs. If stiff mooring systems had been employed for all of these boats the important wave period range for these motions could probably be reduced further. Due to the different mooring systems used, the response curves for some of the small boats were highly asymmetrical indicating the possibility of much greater motions in one direction than in another under the action of a periodic symmetrical force. A limited series of experiments were conducted to determine the effect of the proximity of flotation chambers which are used on some floating slips on the response of the moored boat. It was found that these chambers, as simulated in the laboratory, did not have a significant effect on the dynamic characteristics of the moored boat. However, they did act as floating breakwaters thereby reducing the transmitted wave energy.

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