36 THE BELL SYSTEM TECHNICAL JOTJRNAL, JANUARY 1957 



age which other repeater elements such as connecting tapes between 

 compartments could safely hold without danger of breakdown or corona 

 noise; initial power potential and possible need for increasing dc cable 

 current later in life to combat repeater aging; allowance for repair re- 

 peaters; and a reasonable allowance for increased power potential to 

 offset adverse earth potential. 



Let R = dc resistance of center conductor (ohms/nautical mile) 

 L = length of one cable* (nautical miles) 

 Erep = voltage drop across one repeater at current I 

 / = ultimate (maximum) line current (amperes) 

 N = ultimate number of submerged repeaters, in terms of 



equivalent regular repeaters 

 n = allowance for repair repeaters, in terms of number of 



regular submerged repeaters using up same voltage drop. 

 Em = maximum voltage to ground at shore-end repeaters at 



end of life, and in absence of earth potential. 

 S = spacing of working regular repeaters (nautical miles) 



Then for the ultimate condition 



2E^ = LIR - 2SIR + NErep (1) 



in which the term 2SIR accounts for the sum of the cable voltage drops 

 on the two shore-end cable sections; the sum of their lengths is assumed, 

 for simplicity, to equal 2S. This equation also neglects a small allow- 

 ance (less than 0.6 volt per mile) for the voltage drop in cable added to 

 the system during repair operations. Also 



S(N - n + 1) = L (2) 



because the repeater spacing is determined by the number of working 

 regular repeaters. From (1) and (2), 



2Em = LIR + NErep " 2LIR/(N - n -|- 1) (3) 



The allowance n for repair repeaters was determined after studies of 

 cable fault records of transoceanic telegraph cables, including average 

 number of faults per year and proportion of faults occurring in shallow 

 water. If the fault occurs in shallow water — as is true in most casesf 

 • — • the net length of cable added to the system and the resulting attenua- 

 tion increase, are small. Several shallow-water faults might be permis- 



* The length of a cable is greater than the length of the route because of the 

 need to pay out slack. The slack allowance, which averages 5 per cent in deep 

 water on this route, helps to assure that tlie cable follows the contour of the 

 bottom. 



t Because of trawler activity, ship anchors and icebergs. 



