115G THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



in (28) the limiting values of EA obtained by complete restraint to twist- 

 ing and no restraint to twisting during pulling, one can obtain bounds 

 on the actual displacements and tensions. 



The solution of (27) under arbitrary boundary conditions can be ob- 

 tained from standard textbooks. Probably it is most representative to 

 assume the cable is semi-infinite. That is, although damping of the cable 

 is normally so small that we neglect it in (27), we may assume, because 

 of the cable's great length, that the damping is sufficient to cause com- 

 plete decay of a disturbance initiated at the ship, and that such a dis- 

 turbance is not reflected from the ocean bottom. Under this condition 

 the additional tension Tp is given by 



T,= -VeApc^, (29) 



where P = Po + Pi with dPi/dt being in turn the increment in pay-out 

 rate or decrement in haul-in rate from the mean. For cable No. 2, Table I 

 (Section 3.2) indicates that 



\^EApc ^ 220 Ib/ft/sec (twist unrestrained), 



= 400 Ib/ft/sec (twist restrained). 



Two examples will make clear the application of (29). 



Example 1: Steady- Slate Laying or Recovery in a Regular Seaway. 



Assume that in a frame of reference traveling at the mean horizontal 

 ship velocity ship surging (to and fro forward motion) is zero and the 

 combined heave and pitch motion is normal to the ocean surface and is 

 given by 



W = Asin27r-. 



T 



If the period t is 6 seconds and the amplitude A is 15 feet find for cable 

 No. 2, 



a) (^p)max for laying at a constant pay-out rate and at a ship speed of 



6 knots, 

 ^'>) (7'p)max for recovery at a constant haul-in rate and with a surface 



incidence angle of 60°. 



In l)oth cases (a) and (b), the deviation Pi in pay-out or haul-in rate is 

 zero, hence P = Po = W sin a, , and (c?P/c?0,nax = (27r/r) .1 sin as . Since 



