c = velocity of sound in the cable 



M = virtual mass of the load 



Cq = drag coefficient appropriate to the load 



A = projected area of the load in the direction of motion 



L = length of cable 



p = density of sea water 



The difficulty in obtaining an exact solution to Equation 1 subject to the 

 boundary conditions. Equations 2 and 3, arises from the nonlinear term | Su/St' |(Su/St') 

 in Equation 2. This difficulty is avoided in the A. D. Little report^ by an approxi- 

 mation which is described in Appendix A. 



Defining a normalized displacement amplitude U' equal to U divided by I U ] 

 and noting that U] is the value of U' at the load, a solution for U' as a function of 

 x' is given by 



U' = Uj cosoj'y' + CsinuJ'y' 



where C is a complex constant and 



y' = 1 - x' 



CO' 



u;L 

 c 



Hence the maximum value of the dynamic stress in the cable is given by 



(!■ f = (co')^(u;)^[l + tan<p(tan'I'+sec*)] 

 max I 



/here (UJ)^ = 



cos^ (u)' + <p) 



2 . 2 2 



2^ sin cp sin u)' 



1 + 



jS^ sin^uj' sin^2(p 



4 

 cos (oj'+cp) 



l1/2 



- 1 



60' 77 



arc tan — , ^ (D ^-r- 

 M 2 



^ = arc tan y ^^ (U ') tan<p - cot 2(p , 



2 2 



(5) 



(6a) 

 (6b) 



(7) 



(8) 



(9) 

 (10) 



