4 



Ry/ 



t6 



Ry 



dr 



o V T„ / 



[la] 



r^o Ry-1 



= dr, 



[3a] 



For minimum T, dT must vanish. Hence from Equations [la], [3a], and [3] 



Ry r r 



t6v 



~a7 



[5: 



77 _T 



dr 



[5a: 



This equation may be used to determine the value of 4> that obtains 

 at the optimum configuration. From Equation [3] the appropriate value of T Q 

 may then be found; thence T, s, and x can be calculated from [1 ] , [2], and 

 [4]. 



The designer is usually interested in the optimum conditions for 

 high-speed operation. If the speed of towing is sufficiently high so that the 

 weight of the cable can be neglected, the functions r, a , tj , and 4 may be tak- 

 en as those given in TMB Report C-122, Appendix I, p. 27, i.e., 



t = 1 + f csc0; f = 

 a = cot <j> 



[6] 

 [7] 

 t) = In cot ■?■ [8] 



f = CSC0- 1 [9] 



where F is the drag per unit length of the cable when the cable is parallel 

 to the stream. Equation [5a] then becomes 



4. <t> 1 + f CSC^ , 4. ^0 



ln cot 2 " f cot 6 = ln cot — 



[5b] 



