1140 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



From (12) we find 



0.14n 



Dt = 



0.055 v-''Vt 



1.86 



L 



0.14 



TT 



d. 



(14) 



This expression indicates that Dt for smooth cable depends on the in- 

 clined length of the cable as well as the relative tangential velocity Vt . 

 The form of (13) suggests that the flow tangential to a smooth cable is 

 similar to flow past a smooth plate. In such flow a turbulant boundary 

 layer develops which grows in thickness with distance from the leading 

 edge, resulting in a length dependence of the type shown by (14). Since 

 Fig. 5 refers to 100 foot cable lengths, (13) is probably not accurate for 

 the magnitudes of L occurring in deep-sea laying, and should be used 

 only to obtain the order of magnitude of C/ . 



Q 



Z 5 



in 





012345678 

 TOWING VELOCITY IN KNOTS 



10 



Fig. 5 — Experimental values of the tangential drag force for cable No. 1 

 compared with those obtained by equation (12). 



For the cable with conventional jute outer covering, (cable No. 2); 

 it was found that 



Z)^ = 0.01 Yl-'"' (15) 



fits the experimental data obtained by towing test (Fig. 6). Whereas Ie 

 (15) the constant 0.055 is dimensionless, the constant 0.01 in this equa- 

 tion has the dimensions necessary to give Dy in units of pounds per foo* 

 when Y i is in feet per second. We note that for this cable Dt is inde-< 

 pendent of the length of the cable. 



