ABSTRACT 



A theoretical analysis of the variation in moorlng-cable 

 tension of ships anchored in deep water is presented. The 

 hydrodynamic forces produced by the ocean currents are neglected 

 in comparison with the elastic forces of the cable and based on 

 this assumption, the wave equation for longitudinal vibrations 

 is derived. The wave equation Is solved for two sets of boundary 

 conditions and the results are applied to three typical ship- 

 anchoring problems in deep water. 



INTRODUCTION 



There are an increasing number of applications where ships 

 must be anchored In deep wate,?. For example, cable -laying ship3 

 and radar picket ships are occasionally anchored in deep water. 

 In applications of this type usually the hydrodynamic forces 

 produced by ocean currents are small and may be neglected in 

 comparison with r.he effect of ship motion on the elastic forces 

 in the anchor cable. 



The purpose of this paper is to show tnat che wave equation 1 

 can be used to compute the mooring cable tension produced by ship 

 motion providing that certain simplifying assumptions can be made. 

 The equation for longitudinal /lbra tions-a_long the cable is derived 

 f.nd a solution Is presented for two sets of~~ boundary conditions. 

 Also, three numerical examples of ships anchored in deep water are 

 included. 



MATHEMATICAL FORMULATION OF PROBLEM 



An elastic cable In equilibrium subjected to known forces 

 at each end is considered. Both the normal and tangential com- 

 ponents of the hydrodynamic force are neglected. Tr.e weight 

 of the cable is included in the determination of the steady-state 

 tension at each end. Also, the sum of the elastic forces acting 

 on the cable is equated to the mass times the acceleration of 

 the cable. Then, in the analysis, the cable can be assumed to 

 lie in any arbitrary plane. Hence, consider a piece of cable 

 of length xy as shown by the sketch in Figure 1. 



References are listed on page 22, 



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