used to allow for relative motion between the vessels, the above are the most common. However, as the relative motion nears the limits of the winch, catenary, and hawser system capabilities, the towing arrangement will either become very stiff, with consequent large shock loads, or the winch will pay out more line than it can recover. In either case, the tug will be unable to continue towing.
To estimate required tug horsepower, it is assumed that a vessel has lost all power upwind of a lee shore, and that the tug would be required to tow the vessel head into the wind and waves or at least maintain position relative to the lee shore.
The calculations used in this study are based on published information relating to the behavior of tank vessels in various wind and sea conditions. A relatively simple procedure was used to analyze the size of tug required to tow various size tankers. This consisted of calculating the mean wind and wave forces on the tanker and tug and converting them into required bollard pull. This is a static analysis, not a dynamic analysis, and as such assumes that the towing system consisting of the towing winch, towline, and spring make adequate provision for relative motion between the two vessels. The calculation of the wind and wave forces is described below.
In analyzing the forces on a large ship in storm conditions, it is necessary to estimate the actual sea state in terms of significant wave height and period, because wave drift forces acting on a vessel increase as the wave height increases and usually decrease as the wave period increases. Figure I-13 provides data on sea states relative to wind speed for fully developed seas. A fully developed sea is one in which the wind has been blowing long enough and far enough for the waves to develop to their maximum extent. Footnote a to this table notes that this rarely occurs for winds in excess of 50 knots. As shown in the table, a minimum duration of 69 hours and a fetch of 1,420 nautical miles would be required for a sea to become fully developed in 50-knot winds.
For this study, wave height and period statistics were taken from Global Wave Statistics by British Maritime Technology Limited.4 This book provides wave height and period probability distributions worldwide. These probability distributions are tied to specific areas of the world and specific wind directions. These data allow us to calculate the joint probability of various wave heights occurring at the same time as onshore winds for different regions of the United States. Graphs of the calculated joint probability are attached (Figures I-2 through I-6).
Based on a range of typical sea states, the mean wave drift forces were estimated using OCMOTA,5 ship motion and wave force prediction program developed by the Maritime Research Institute of the Netherlands (MARIN) for the Oil Companies International Marine Forum (OCIMF). To ensure that the probable range of wave heights and periods were fully covered, two different average wave periods were used for each wave height. This was done since wave drift forces are sensitive to wave period. The curves of wave drift force presented (Figure I-7) represent the mean of these two conditions. It should be noted that the wave energy spectrum used was a Jonswap spectrum with a peak enhancement factor of 3.3. This is representative of a building storm. The wave drift forces on a ship in a building storm are normally much higher than in a fully developed sea of the same height because of the shorter mean wave periods. Wind forces were calculated based on Prediction of Wind and