1130 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Appendix C. Some Approximate Solutions for Laying and Recovery 1180 



C.l Laying 1180 



C.2 Recovery 1183 



Appendix D. Analysis of the Effect of Ship Motion 1184 



D.l Formulation of the Differential Equations 1184 



D.2 Perturbation Equations 1187 



D.3 Solution of the Perturbation Equations 1189 



D.4 Transverse Response 1190 



D.5 Second-Order Longitudinal Response 1191 



D.6 Numerical Results 1194 



Appendix E. Tension Rise with Time for Suspended Cable 1195 



E.l Formulation of the Solution of the Problem 1195 



E.2 Nomograph for the Solution of Equation (99) 1198 



E.3 Numerical Example 1199 



Appendix F. The Three-Dimensional Stationary Model 1202 



F.l Derivation of the Differential Equations 1202 



F.2 Perturbation Solution for a Uniform Cross Current 1204 



Acknowledgments 1206 



References 1206 



Glossary of Symbols 



A Amplitude of harmonic ship motion 



Ci , C2 , C2 Longitudinal wave velocity; trans- 



verse wave velocity in air and water 



Cd , Cf Transverse and tangential drag co- 



efficients 



d Cable diameter, also distance be- 



hind the ship at which the cable 

 enters the lower stratum 



Dn , Dt Normal and tangential unit drag 



forces 



e Sidewise distance from the laid cable 



to the ship 



KA Extensile rigidity 



h Ocean depth 



h = ^ Dimensionless ocean depth 



EA 



H Hydrodynamic constant 



L Inchned cable length from surface to 



bottom, also from ship to surface 



AT^ Reynolds number 



p^ q Longitudinal and transverse devia- 



tional cable displacements 



Po ^ Qo Longitudinal and transverse ship 



displacements 



