1138 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 



mal component of water velocit3^ For small values of the incidence 

 angle a 



cos a ;^ 1, 



sin a 7^ a, 



and (6) is approximately 



2w 



1/2 



cos a 



V-UfT-K9' 



(10) 



where ao is the approximate value of a. The quantity {2w/CDpdy is a 

 constant for a given cable. It brings together all the cable parameters 

 which influence the magnitude of the incidence angle a. If the angle a 

 for a given speed is determined accurately, as can be done in a towing 

 test or with a sextant during over-the-stern laying, this cjuantity is easily 

 computed. Because of its importance, we shall call it the hydrodynamic 

 constant of the cable and denote it by H, namely, 



» = (e&)" 



By virtue of (7) and (8) we may write 



a,y = H. (9) 



The constant H rather than the drag coefficient Cd ^^^ll be used from this 

 point on. 



When the approximate relationship (9) is not valid, a can be obtained 

 by solving (6). This gives 



where V is in knots and H in radian-knots. In terms of ao we obtain in J 

 turn 



cos a = /</ 1 + 7 «u'* "~ 9 «u^- (11) 



This relationship is shown in Fig. 4, where the incidence angle a is plotted 

 as a function of the approximate incidence angle ao . It is seen that for 

 a < 20° the difference between ao and a is negligible. 



Physicall}^ a as given by (10) is the angle the cable assumes in the 

 straight-line shape for the ^'elocity V. However, in addition, (10) show> 

 that a can be thought of as a dimensionless parameter which embodies 



i 



