DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 



1139 



a. 

 O 



20 



40 60 80 



OCn IN DEGREES 



100 



120 



Fig. 4 — Variation of a with ao . 



both the hydrodyiiamic properties of the cable and the ship speed. Thus, 

 even when the configuration is not a straight fine, we shall find it con- 

 venient to express results as a function of the single parameter a, rather 

 than as a function of the two parameters H and T'. For this reason, 

 following Pode, ^' ^■' we call a the critical angle. 



3.3 Tangential Drag Force 



Over the range of velocities encountered m laying and recovery the 

 I drag coefficient Cd in equation (6) is essentially constant. However, the 



corresponding coefficient for the skin friction force associated Avith Vt , 

 I the component of flow along the cable, is not constant. For the cable of 



smooth exterior (cable No. 1), the expression 



Dt = Cf^pV^ir d, 



(12) 



with Cf = 0.0o5/{Nr) ' , was found to give good agreement with the 

 experimental data, as is shown by Fig. 5. Here Dt is the skin friction or 

 tangential drag force per miit length; Vt is the relative velocity of the 

 water \\ith respect to a cable element gi\'en for straight-line lajdng by 



Vt = Vc — V cos a, 



(13) 



where Vc is the cable pay-out rate; p is the mass density of water; and 

 Nr is the Reynolds number defined as Nr = Vi L/v, where v is the kine- 

 matic viscosity of water. The data of Fig. 5 are for 100 foot lengths of 

 cable towed in fresh water at a temperature of 60°F. 



