1136 THE BELL SYSTEM 



TECHNICAL JOUUXAL, SEPTEMBER 1957 



50 



45 



01 40 



UJ 



LU 



cc 



^ 35 

 Q 



30 



25 



20 



< 



O 16 



CC 



U 10 



2 3 4 5 6 7 8 



TOWING VELOCITY IN 'KNOTS 



10 



Fig. 2 — Experimental and theoretical variation of critical angle with towing j 



velocity for cable No. 1. ! 



i 



where D^^ is the normal drag force per unit length, Co is the so-called 

 drag coefficient, p is the mass density of the fluid, and d is the diameter 

 of the cable. For the straight-line configuration, the vector diagram in 

 Fig. 1 shows that 



Vn = V sin a. 

 Substitution of (5) and (4) into (1) yields in turn 



CDpV'd . 2 



w cos a = sni a. 



(5) 



(6) 



Eciuation (6) suggests how the value of the drag coefficient Co can be 

 obtained experimentally. By towing a length of cable in water at a con- 

 stant velocity, one can establish the straight-line configuration. The 

 angle a can then be measured as a function of velocity, from which Cd 

 can be computed by (6). 



Figs. 2 and 3 show the results of such tests together with plots of (6) 

 for the indicated values of Co ■ These results are taken from an analysis 

 by A. G. Norem of experimental data obtained by H. N. Upthegro^•e, 

 J. J. Gilbert, and P. A. Yeisley. The properties of these cables are listed 

 in Table I.* To eliminate end effects different lengths of cable were towed, 



* Cable No. 2 is very similar to present type D transatlantic telephone cable. 

 For engineering calculations, type D can be considered the same as cable No. 2. 



