DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 

 8 



7 

 6 

 5 



1141 



Q 



2 3 4 5 6 7 8 



TOWING VELOCITY IN KNOTS 



10 



Fig. 6 — Experimental values of the tangential drag force for cable No. 2 

 compared with those obtained by equation (15). 



The ratio of Dr to the tangential component of the cable weight force 

 is given by Dt/w sin a. Ecjuations (14) and (15) indicate that even for 

 small values of a. of the order of twelve degrees, Dt/w sin a is of the order 

 of 6 per cent for relative tangential velocities Vt of 1.0 feet/sec. In many- 

 situations V t will be less than this value, and we can neglect Dt compared 

 to w sin a. As we shall see later, this approximation greatly simplifies 

 the differential equations of the two-dimensional stationary model. 



Historically, the question of the variation of Dt with Vt is of some 

 interest. In one of the early papers of 1858 Longridge and Brooks as- 

 sumed a velocity squared dependence. In 1875, W. Siemens attacked 

 this assumption stating that Dt actually varied linearly with Vt . There 

 ensued a debate in which many bitter words but few experimental data 

 were displayed.^ In view of our present knowledge that the skin friction 

 force, even in the simplest case of flow past a smooth plate, is the result 

 of complicated boundary layer phenomenon, the existence of this con- 

 fusion is not surprising. 



3.4 Sinking Velocities and Their Relationship to Drag Forces 



The studies of submarine cable forces in 1857 and 1858 preceded 

 modern fluid mechanics by many years. To characterize the hydrody- 

 namic forces acting on cal)le the eai-l}^ in\'estigators used sinLi'ng or 

 \settling \'elocities rather than the more recently conceived drag coeffici- 

 'ents. The transverse sinking velocity Us was deflned as the terminal ve- 

 locity attained by a straight, horizontal length of cable sinking in water. 



