1196 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



X2 = horizontal distance from B to 0, 



8 = vertical distance from A to 0, 



To = cable tension at 0. 



If the cable is being paid out with a slack e, then conservation of the 

 total cable length gives the equation 



Si -\- Sz — 



h 



sin a 



+ (1 -\- e)Vt + cable stretching. 



(95) 



Fig. 35 — Coordinate.s for the analysis of tension rise when a cable is com- 

 pletely suspended. 



It is assumed that there is no cable pulled from the bottom. The cable 

 stretching we evaluate as in the example of Section 3.6, viz., 



cable stretching = (*Si + *S2) 



EA 



This makes (95) read 



S,+S, = J^ + {\-\- e)Vl + (5i + S-^ ^ 

 sm a EA 



(96) 



To obtain further relations for the unknowns appearing in (96), we 

 assume that from the ship to point the cable configuration is a station- 

 ary one governed by the equations developed in Section 3.6, while from 

 points to A we assume that the cable configuration is a static catenary. 

 These assumptions yield the following relations: 



(a) 

 (b) 



