IIGO THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



Fig. 20 — Kinematics of straight-line descent laying. 



In accordance with usual terminology we define the slack e as 



6 = (F. - V)/V. 



(31) i 



We shall think of the slack as being composed of two parts: a fill f, which 

 is the amount of slack required for the cable to cover the bottom, and an 

 excess, equal to e — /, which will normally be laid to provide a margin of 

 safety. Substituting Vc from (31) into (30) we get the expression for the 

 fill /. The result can be transformed to the form 



I 



/ 



tan - tan - = .^^^. 



(32) 



The quantities a, 13 and / are normally all small quantities and we may 

 make the approximations 



a a 

 tan-^-. 



tan 





/ 

 2+/ 



f 



For a, 13 < 30° and / < 0.06, the error in each of these approximations 

 is less than 3 per cent. Hence, with good accuracy we write (32) as 



f = ^ 

 J 2' 



(33) 



where a and jS are expressed in radians. Further, we have from (9) that 

 a in radians is very nearly a = H/V, where H is in radian knots. Sub- 

 stituting this expression into (33), we get for the fill 



