Comment on "Statics and Dynamics of Anchoring Cables in Waves"

I Ref. 1, Goodman and Breslin determined the effect of hydrostatic pressure on an extensible cable in a heavy liquid by an integration of the fluid pressure on the cable surface. A different and more direct approach to this problem has been presented for the case of an inextensible cable, but, as will be seen in the following, the extensibility of the cable is easy to include. Let us first consider a segment of the cable of length ds. The total buoyance of the segment with "open ends" equals wb = pgA0ds and acts in the vertical z direction (see Fig. 1). Because of the assumption of an incompressible material, there will be no strain due to this pure hydrostatic pressure. Now, in order to compensate for the lack of pressure at the ends of the segment, we have to introduce axial tension as shown in Fig. 1. This axial tension introduces strain in the segment such that the area changes from A0 to A0/(l +e). Combination of the two end forces and the buoyant force wb results in a net buoyant force dFn, which acts in the center of gravity of the segment in a direction normal to the centerline and with the mangitude