1158 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



However, it is to be cautioned that these numbers are merely indicative 

 and might differ considerably from those which occur on a particular 

 cable ship. 



Example 2: Brake Seizure 



While laying cable No. 2 at six knots in a perfectly calm sea, a sudden 

 seizure of the brake occurs. What is the resulting initial rise in tension? 

 Because of the calm sea we have Po = 0. Therefore 



—- = Pi = —V cos as . 

 at 



With the value of T" = (3 knots and a corresponding «« of 11.7° (see Ex- 

 ample 1) we have dP/dt = 9.9 ft/sec and hence from (29) 



Tp = 2180 lbs (twist unrestrained), 



= 3970 lbs (twist restrained). 



These values of Tp pertain only to the transient values occurring while 

 the tension wave is being transmitted to the ocean bottom. If the seizure 

 in this case occurred at a depth of three thousand fathoms, the time of 

 transit to the ocean bottom would be only of the order of nine seconds. 

 After reaching bottom our initial assumption of no reflection from the 

 bottom w^ould be violated and (29) would no longer hold. In reality the 

 cable tension would continually increase at the ship and reversing ship 

 engines or some other action would be required to avoid rupture of the 

 cable. 



V. DEVIATIONS FROM A HORIZONTAL BOTTOM 



5.1 Kinematics of Laying Over a Bottom of Varying Depth 



Ocean bottom topography is not everywhere flat and horizontal as 

 postulated in the basic model. In the Mid-Atlantic ridge, for example, 

 there exist bottom slopes of thirty or forty degrees. In other places sub- 

 marine canyons with almost vertical sides have been found. Further- 

 more, where the bottom is steepest it is most likely to be rocky and 

 craggy since erosion tends to smooth out a sandy or muddy bottom. 

 Therefore, it is important to know how the cable should be paid out to 

 cover a bottom of varying depth. To help determine this, we extend 

 here the stationary model to the case of a non-horizontal bottom. 



In Section 3.1 we indicated that if the cable tension at the touchdown 

 point is zero the configuration according to the basic model is a straight 

 line, regardless of how the cable is paid out. If the cable is paid out with 



