DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 



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vt-- 



«^fe^^^^^^^^^^^^s:^^^^^^mlj^^^^^^^^^^ 



g^i^^^^ 



p' 



Fig. 7 — Illustration of vertical cable sinking rates. 



On the other hand, consider the intersection of the cable configuration 

 with a vertical line (Fig. 7). In the time t, as the ship sails a distance 

 Vt, the intersection moves from .4 to A' , a distance Vt tan a. Hence the 

 cable configuration in this sense sinks vertically at the rate V tan a, 

 and the time 6 for the configuration to reach bottom in a depth h is 

 Q = h/V tan a. One may be interested in how long it takes after the ship 

 has passed over an ocean bottom anomaly P' (Fig. 7) for the cable con- 

 figuration to reach the anomaly. This is just the time 6. 



Hence, the vertical sinking rates Vc sin a and V tan a can both be of 

 interest. At the usual ship speeds, sin a ^ tan a ^^ a ^^ Us/V. Further 

 Vc normally differs little from V. Hence, both these rates are indeed 

 normally approximately equal to Us . 



3.5 General Solution of the Stationary Two-Dimensional Model 



Assume that each cable element is traveling along the stationary cable 

 configuration with the constant speed Vc . Starting at the ocean bottom 

 let s be the arc length along the stationary configuration. We define s to 

 be positive in the direction opposite to the direction of travel of the cable 

 elements. So, as Fig. 8 indicates, in laying, positive s is directed from the 

 ocean bottom toward the ship, while in recovery the situation is reversed. 

 We let 6 be the angle between the positive s direction and the direction 

 of the ship velocity. 



RECOVERY 



LAYING 



^^^^^m^^mm^^^^. 



^^^^^^^m^p^^^^^^^c^^^^^^^^m 



Fig. 8 — Definition of coordinates for the two-dimensional stationary model. 



