When operating large ships in water depths only slightly greater than the draft, as super tankers at near-shore terminals, it is necessary to know precisely how much clearance is required for safety. Recent developments in hydrodynamics are applied to determine the motions of a ship due to waves and current with draft to depth ratio approaching unity. A computer program written for this purpose is outlined. Computed motions are compared favorably with experimental data.


Operation of super tankers introduces a note of urgency into the calculation of ship motions in shallow water. The term "shallow water" is relative; in this case, it is meant to imply depths only slightly greater than the draft of the vessel. Considering the largest super tankers afloat today, we can include depths as great as 100 feet within this definition of shallow water. Since few harbors even approach 100 feet in depth, these vessels will encounter shallow water in exposed locations far from shore. Here, seas may be severe and vessel motions become important not only for the traditional reasons but also with respect to safe bottom clearance.

The incentive for this study was provided by SEADOCK, INC. The intended location of the SEADOCK terminal off the coast of Texas is in gradually shoaling water; hence, the length of the pipelines will vary greatly with small changes in water depth. It is important, therefore, to determine with precision the depth of water required to accommodate super tankers with safe and minimum under-keel clearance.

The principal factors affecting under-keel clearance are heave, pitch, and roll motions in waves and squat or trim due to currents or the ship's own velocity through the water. The wave-induced motions of ships in shallow water have been treated by Tuck 1970 (1) and Tuck and Taylor 1970 (2), Kim 1969 (3), Hooft 1974 (4), Monacella 1966 (5), and others. The present work is based primarily on the first of these sources. The squat due to ship or current velocity is based upon the work of Hooft 1974 (4), Tuck 1974 (5), and other references.

This paper presents the results of motion clearance for tankers ranging in size from 200,000 to 550,000 deadweight tons. Water depth, sea state, and direction of seas are treated as independent variables. Calculations and data are also given for squat due to longitudinal and transverse flow past the vessels.

A comparison with model basin data is presented to lend validity to the results. The effect of the proximity of the bottom is illustrated by a comparison of motions calculated with respect to unrestricted depth and those calculated by the method given here in.

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