Calculation of the added mass of circular cylinders in shallow water

The added mass of hull section shapes must be known, in order to carry out any studies of ship motions, which may be associated with either seakeeping or manoeuvring. Determination of the added mass in deep water can involve conformal mapping or surface singularity distributions. However, in shallow water the problem of determining the added mass is made more difficult by the proximity of the seabed. In this paper, three approaches to the problem of finding the added mass of semi-circular sections are explored. Although there is no known exact solution to this problem, the relationships given by the three methods are compared and the approximate nature of the solutions is examined. The first method is a series solution, which is taken here to include more terms than are normally given in the existing literature. The other two solutions are considered to be new, and so are given in some mathematical detail.