DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 



1151 



where Ts is the tension factor defined by 7",. = T^/wh and y is given by 

 (23). Equation (26) is plotted in Fig. 12 in the form of Ts versus a for 

 various surface incidence angles as (Fig. 8). It is seen that the recovery 

 tensions are in fact considerably higher than the laying tension of approx- 

 imately wh. 



To illustrate the smallness of the error of neglecting the tangential 

 drag force in this computation, we have plotted the approximate and 

 exact curves of Ts versus ship velocity for cable No. 2 in Fig. 13. The 

 dotted curves have been computed from (26), while the solid curves have 

 been obtained by substituting Dt from (15) into (19) of the general solu- 

 tion and integrating numerically.* (The curve labeled Shea's recovery 

 method is discussed in the next section.) 



The distance along the cable S and the horizontal distance X from the 

 touchdown point to the ship cannot be expressed in a simple form as in 

 the case of laying. However, they can be obtained by numerical integra- 

 tion from (20). The results of this computation for Dt = are shown 

 in Figs. 14 and 15. 



How Figs. 12, 14 and 15 can be used is illustrated in the following ex- 

 ample. 



* The standard form of Simpson's rule was used for all the numerical integra- 

 tions mentioned in the paper. In each case the interval of integration was chosen 

 fine enough to obtain at least three significant figure accuracy. 



h 



10 



20 



30 



40 



50 60 



OC IN DEGREES 



70 



80 



90 



Fig. 14 — Variation of the horizontal distance to the touchdown point during 

 recovery with the critical angle. 



