EXTREME TENSIONS IN OPEN-OCEAN TOWING

Statistics of extreme towline tensions encountered when one ship tows another in sea waves are determined by numerical simulation. For rare extremes, very long random simulations are required. As an example, to determine the tension that has a probability of 0.1% of being exceede d in one day of towing, simulation of several thousand days is require d. The simulations are based on solutions of the governing dynamical e quations driven by the sum of the first- and second-order wave forces applied to the tug and to the tow. Fast Fourier transforms are used to make the calculations computationally efficient. It is found that in severe sea states addition of the second-order wave forces can more th an double the tension extremes based on first-order wave forces alone. Good agreement is demonstrated between measured towline behavior at s ea and the behavior predicted by the dynamical towline equations. A to wline tension time history measured at sea, while only of 40 minutes' duration, does show good agreement between its largest tension and the statistical prediction for the tension with a 50% probability of exce edance for this time period under the prevailing conditions. The numer ical procedure developed herein are suitable for evaluation of towing system reliability and safety.