DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 



1135 



W COS a = Dn , (1) 



while the summation in the tangential direction gives for Ts , the ten- 

 sion at the ship, 



1\ = wL sin a - DtL. (2) 



Here iv is the weight per unit length of immersed cable, a is the cable's 

 angle of incidence, Dn and Dt are the normal and tangential drag forces 

 per unit length respectively, and L is the inclined length of the cable. 

 For most submarine cable used currently the force DtL is negligible 

 and we arrive at 



wL sin a = wh, 



(3) 



where h is the ocean depth at the cable touchdown point. Hence, during 

 slack laying the cable tension at the ship is very nearly equal to the 

 weight in water of a length of cable equal to the ocean depth. 



Fig. 1 — Forces acting on a cable in normal laying. 



The straight-line solution is the simplest and probably the most im- 

 portant result to be obtained from the stationary two-dimensional model. 

 We shall derive results for other important situations from this model 

 also. As a preliminary, we study first, however, the nature of the normal 

 and tangential drag forces D^ and Dt . 



.3.2 Normal Drag Force and the Cable Angle a 



The resistance at sufficiently slow speeds to the flow of a fluid around 

 an immersed body varies as the square of the fluid velocity. This relation- 

 ship is usually written as* 



(4) 



Jy.\ — Co ^: — , 



2 



* For towed stranded wire experimental verification of this relationship is 

 reported in Reference 11. 



