1148 THE BELL SYSTEM TECHNICAL JOUKNAL, SEPTEMBER 1U57 



U- 



vt — 4 >!<- Lcos a. J 



X A 



t: 



Fig. 11 — Cable geometry at a time I after the onset of negative slack. 



For cable No. 2 a ship speed of six knots corresponds to a = 11.7 de- 

 grees. By Fig. 10, this corresponds to X — k = 1.4 X 10~^ Also w = 

 0.705 lbs/ft by Table I. We get therefore 



n = wh + 3000 



Thus, according to this calculation the tension in this example rises at 

 the extremely rapid rate of 8000 Ibs/min. We note also that the rate of 

 tension rise is here independent of the depth h. 



In the model which has been postulated, the cable is inextensible; that 

 is, it is assumed not to stretch under load. Because the difference between 

 the lengths of AOC and the sum of the hnear segments AD and DC (Fig. 

 11) is small, one might suspect that the effect of cable extensibility in 

 the present example is important. We can account for this effect in a 

 crude way by assuming that the curve AOC has an additional length cor- 

 responding to the stretching caused by the load To acting over the length 

 L. For a cable made of a single material, the stretching would be TqL/EA, 

 where E is the Young's modulus of the material and A is the cross-sec- 

 tional area of the cable. In analogy to this we denote the extensile rigidity 

 of the cable by EA, using the bar to indicate that EA is actually a single 

 number obtained directly by measuring the extension of a length of cable 

 loaded in tension. With this notation (25) becomes 



L + 1^(1 - 6); + =^ = S + Vt - (X - L cos a), 



KA 



and repeating the previous computation we find 



w 



wh + r 



wh 



EA sin a 



-\- X - K 



V8I. 



It is to be noted that in this computation, unlike the inextensible case, 

 the rate of tension rise depends on the depth h. 



