An analysis is presented for the steady state configuration of an extensible cable system moored in the presence of a current profile that varies both in magnitude and direction with depth. A description is given of the FORTRAN IV computer program based on the above analysis. The program allows for the presence of an arbitrary number of different cable segments and intermediate bodies. Using this computer program, some numerical results are presented for a cable system with fixed parameters moored in the presence of various current profiles with a single variation of magnitude with depth, but with different variations of direction with depth. These results show that, contrary to statements in the moored cable literature, the planar current profile need not be a conservative design case from the standpoint of the cable scope required.
The study of the behavior of cable systems has been an area o£ active interest for the past 50 years. The earlier cable studies usually consider the two-dimensional steady-state problem. In these studies, dynamic motions are neglected, and the cable is restricted to lie entirely in the plane formed by the vertical and the constant direction of the relative fluid flow. More recent studies have considereddynamic motions of the cable and/or allowed the cable to lie in all three directions. Casarella and Parsons1 have written an excellent survey of the various cable studies.
The three-dimensional steady-state equation for a cable have been derived by a number of authors, including Zajac, 2 Gay3 Schneider and Nickels, 4 Schram5 and Reid6. The principal differences among the various analyses lie in the modeling of the extensibility of the cable, the nature of the hydrodynamic forces acting on the cable, and the method of derivation. Of the above authors, Gay, Schneider and Nickels, and Schram have programmed their analyses for solution on electronic computers. Gay and Schram considered the case of an inextensible cable in a uniform stream subjected to locally coplanar hydrodynamic normal and tangential forces acting in the plane formed by the direction of the uniform stream and the cable segment, and hydrodynamic lift forces perpendicular to this plane. It is the presence of these lift forces, which act on faired and stranded cables, that cause the cable to lie in all three directions. Schneider and Nickels considered the case of an elastic cable subjected to locally coplanar hydrodynamic forces. Their study does not specify the manner in which the magnitude and direction of the current profile varies with depth. Casarella and Parsons1 interpret their study as solving the problem of a moored cable system in which the forces acting on the surface buoy have a component perpendicular to the plane of the planar current.
The present study investigates the effect of a current profile that varies both in magnitude and direction with depth on the configuration of moored cable systems. The cable is taken to be extensible bare cable, for which the hydrodynamic forces are locally of the coplanar type.