DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 



1155 



340 



200 



LL 



LU 

 U 



z 



If) 

 a 



160 



120 



1 80 



< 



I 



40 



8 12 16 4 8 12 



PERIOD OF TRANSVERSE SHIP MOTION IN SECONDS 



16 



= 



(27) 



Fig. 18 — • Variation of half-life distance of cable No. 2 with the period of 

 ship motion. 



As far as cable tensions are concerned, the important ship displacement 

 then is the longitudinal component Po , directed along the stationary 

 direction of the cable. The analysis of Appendix D leads to the basic 

 one-dmiensional wave equation 



d ip 1 ^-p 



for the description of the longitudinal motion. In this equation p is the 

 tleviation in longitudinal displacement from the mean pay-out or haul-in 

 displacement, and the remaining symbols are defined as (Fig. 17) 



X = distance from the mean ship position along the stationary cable 



configuration, 

 t = time, 

 c\ = EAIpc . 



The additional tension Tp due to ship motion is in tiu'n given by 



dp 



ax 



(28) 



As in the example of Section 3.6, we ha\'e again assumed that bj^ using 



