DYNAMICS AND KINEMATICS OF SUBM.\IIINE CABLE 1149 



For conventional helically armored cable, one cannot define a single 

 extensile rigidity because of coupling between pulling and twisting. Thus, 

 how such a cable extends under tension depends on how it is restrained 

 from twisting at the ship and at the ocean bottom. Instead of trying to 

 determine these end restraints, we consider the limiting cases of no re- 

 straint and complete restraint to twisting. Data supplied by P. Yeisley 



indicate the values of EA for cable No. 2 in these conditions to be those 

 given in Table I (Section 3.2). If we take h = 6,000 and 12,000 feet, we 

 find with these values that 



h = 6000 feet: 



Ts = wh + 220 (Ib/min)/ (twist unrestrained), 



= wh -\- 640 (lb/min)i (twist restrained), 



h = 12,000 feet: 



Ts = wh + 120 (\h/mm)t (twist unrestrained), 



= wh -\- 360 (Ib/min)^ (twist restrained). 



Comparing with the inextensible computation, we see that the extensi- 

 bility markedly reduces the rate of tension build-up. Nevertheless, even 

 for the case of no restraint to twisting at a depth of 12,000 feet the rise 

 rate is a relatively high 120 Ib/min. Hence, at least over a rough bottom, 

 the tension would quickly indicate the onset of negative slack, although 

 the sensitivity of this indication would decrease with increasing depth. 



3.7 Approximate Solution for Cable Recovery 



Fig. 8 illustrates how cable is in present practice recovered from the 

 ocean bottom. The cable is in front of the ship as it is brought in over the 

 bow, and the ship pulls itself along the cable. In this process the cable 

 tends to guide or lead the ship directly over its resting place on the ocean 

 bottom. 



It is clear that during recovery by this procedure the tension at the 

 ocean bottom is not zero and the cable configuration is not a straight line. 

 Furthermore, in this situation the normal component of the water drag 

 force Da- pushes down on the cable instead of buoying it up as in the case 

 of laying. This in turn implies a higher tension at the ship during re- 

 covery than during lajang. 



If the tangential drag is neglected, the tension at the ship Ts during 

 recovery is given in dimensionless form by (see Appendix C) 



Ts - 1 



2 cos a + cos Us 

 tan a 



1 — cos a cos a. 



l/T 



(26) 



