DYNAMICS AND KINEMATICS OF SUBMAKINE CABLE 



1173 



tan <p 



Yw sin |S 



Y - Y^ cos ,8 



(51) 



Associated with Y' we have a critical angle a which is given approxi- 

 mately by RIY' or exactly by (10) or (11). 



In terms of ip, a\ and a the analysis of Appendix F yields the following 

 values of d and e. 



d = h' { etna' 

 '(pciwa ( 



Aa 



2 COS^ a' 



e = h 



h — h' 



-(-:- 



/\2ctn2a' -1 



1 



1 - 



h 



t\ ctn^a' 



(a) 



, (b) 



(52) 



where Aa = a — a' is the difference of lower and upper stratum critical 

 angles, h' is the depth of the upper, cross-current stratum and h is the 

 total depth.* Curves from which d and e may be evaluated are given in 

 Figs. 28 and 29 in dimensionless form. To illustrate their application we 

 consider the following. 



12 



10 



^ he- 



0.1 



0.2 



0.3 

 h'/h 



0.4 



0.5 



0.6 



Fig. 28 — Distance the laid cable is offset from the ship's path. 



* In Api)endix F the equation of the space curve formed by the cable in the 

 upper stratum is also given. 



