A perturbation procedure is developed for the two-dimensional motion produced by a long ship in heave when the draft is assumed small. The procedure reduces the shallow draft problem to a series of problems for a "raft" of zero draft. A considerable simplification in the method of integral equations is found to occur. For the first approximation, that is, a raft of finite width, the integral equations are solved numerically to determine pressure, virtual mass and damping. The problem of heave of a circular disk of zero draft is treated by the same methods so that an evaluation of strip theory in this special case is possible.

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