DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1133 



However, a present-day submerged-repeater transoceanic cable is a 

 delicate and expensive transmission system. Reducing the amount of 

 cable deposited by as little as one per cent can result in a substantial 

 saving in the first cost of such a system. Its repair is a costly operation 

 requiring the sustenance of an ocean ship and its crew. Therefore, it is 

 important to lay the cable without wasteful excess and with minimum 

 chances for failure after laying. Further, it is important that repair, if 

 necessary, be as efficient as possible. To accomplish these things, an un- 

 derstanding of the djaiamics and kinematics of cable laying and recovery 

 is essential. 



The purpose of this paper is to provide some of this understanding in 

 as straightforward a way as possible. To this end concepts and results 

 are stressed in the main part of the paper, mathematical details being 

 given in the appendices. Moreover, we hope to show that the results of 

 the analysis can pro^'ide a numerical basis for decision making in many 

 of the laying and recovery operations. Most of these results can be ex- 

 pressed in the form of simple formulas and graphs. Several numerical 

 examples are included to illustrate concretely how the results can be 

 applied in practice. 



The general plan of the paper is to proceed from simple to more re- 

 fined models of the laying and recovery processes. Thus, we discuss first 

 what we have called the two-dimensional stationary model. This model is 

 appropriate for laying and recovery on or from a perfectly flat bottom 

 while sailing on a perfectly still sea. As a preliminary to this discussion, 

 we consider in some detail the hydrodynamic behavior of typical deep 

 sea submarine cable. We then take up the effects of the ship motions 

 which are induced by wave action and the effects of a bottom of ^-arying 

 depth. These considerations are followed by a short discussion of the 

 problem of controlling the cable pay-out properly during laymg and the 

 associated problem of the accuracy of the present taut wire method of 

 determining ship speed. Finally, we consider the three-dimensional sta- 

 tionary model and the effects of ocean cross currents. 



II. BASIC ASSUMPTIONS 



Our analyses, like most analyses of physical problems, are based on 

 idealizations or mathematical models of the actual phj^sical system. The 

 extent of validity of these models must be ultimately determined by ex- 

 periment and experience. However we shall tr}' to give the reader an 

 idea of when they are clearly applicable and when they are not. 



All of the models we consider contain two basic idealizations, namely, 



(1) No bending stiffness in cable, i.e., it is a perfecth^ flexible string, 



(2) The average forward speed of the ship is constant. 



