1154 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1957 

 IV. EFFECTS OF SHIP MOTIONS 



4.1 Tensions Caused hy Ship Motions 



111 the basic stationary model a perfectly calm sea is postulated. 

 However, in reality, wave action gives rise to a random motion of the 

 ship which in turn induces variations in cable tensions around those cor- 

 responding to the basic model. 



To analyze this effect, we assume that the mean forward velocity of 

 the ship and the mean pay-out or haul-in rate are constant and that the 

 mean tension at the ship and the mean direction of the cable as it enters 

 water are those given by the stationary model. In a reference frame mov- 

 ing with the mean velocity, we resolve the ship displacement into a 

 longitudinal component Po (Fig. 17) along the mean or stationary direc- 

 tion and a transverse component Qo perpendicular to the stationary di- 

 rection. 



Fig. 17 — Longitudinal and transverse components Po and Qo of the ship 

 displacement. 



Intuitively, one might e.xpect the tensions caused by the transverse 

 displacement Qo to be negligible compared to those caused by the longi- 

 tudinal displacement Po . An analysis we have carried through in fact 

 yields this conclusion. Because of its complexity and length, this analysis 

 and the model upon which it is based are given in Appendix D. The re- 

 sults for the case of harmonic variation of Qo with time indicate, at least 

 for cable No. 2, that the tension associated with the transverse com- 

 ponent Qo is indeed negligible for all except ship motions so extreme as to 

 rarely occur. 



In addition, this analysis indicates that for the transverse disturbance 

 Qo , the amplitude of the responding transverse cable motion decreases 

 exponentially after the cable enters the water because of the damping 

 action of the water drag forces. The "half-life" distance for cable No. 2, 

 that is, the distance along the cable at which the amplitude of a harmonic 

 transverse motion is damped to one-half its surface value, is plotted in 

 Fig. 18 as a function of the period of the motion for various depths h and 

 ship velocities V. The striking feature of these figures is the rapidity of 

 this damping. The analysis thus shows for cable No. 2 that the effect of 

 a transverse disturbance penetrates only a short distance into the water. 



