Dynamics and Kinematics of the Laying 

 and Recovery of Submarine Cable 



By E. E. ZAJAC 



(Manuscript received June 5, 1957) 



This paper is an attempt to formulate a comprehensive theory with which 

 the forces and motions of a submarine cable can be determined in typical 

 laying and recovery situations. In addition to the fundamental case of a 

 cable being laid or recovered with a ship sailing on a perfectly calm sea over 

 a horizontal bottom, the effects of ship motion, varying bottom depth, ocean 

 cross currents, and the problem of cable laying control are considered. Most 

 of the results reduce to simple formulas and graphs. Their application is 

 illustrated by examples. 



TABLE OF CONTENTS 



Page 



I. Introduction H'^^ 



II. Basic Assumptions H"^"^ 



III. Two-Dimensional Stationary Model 113-1 



3.1 General 1134 



3.2 Normal Drag Force and the Cable Angle a 1135 



3.3 Tangential Drag Force 1139 



3.4 Sinking Velocities and Their Relationship to Drag Forces 1141 



3.5 General Solution of the Stationary Two-Dimensional Model 1143 



3.6 Approximate Solution for Cable Laying 1146 



3.7 Approximate Solution for Cable Recovery 1149 



3.8 Shea's Alternative Recovery Procedure 1153 



IV. Effects of Ship Motions 1154 



4.1 Tensions Caused by Ship Motions 1154 



V. Deviations from a Horizontal Bottom 1158 



5.1 Kinematics of Laying Over a Bottom of Varying Depth 1158 



5.2 Time-Wise Variation of the Mean Tension in Laying Over a Bottom 



of Varying Depth 1161 



5.3 Residual Suspensions 1163 



VI. Cable Laying Control 1165 



6.1 General 1165 



6.2 Accuracy of the Piano Wire Technique 1166 



VII. Three-Dimensional Stationary Model 1169 



7.1 General 1169 



7.2 Perturbation Solution for a Uniform Cross-Ciu-rent 1172 



Appendix A. Discussion of the Two-Dimensional Stationary Configuration 



for Zero Bottom Tension 1175 



Appendix B. Computation of the Transverse Drag Coefficient and the Hydro- 

 dynamic Constant of a Smooth Cable from Published Data 1177 



1129 



