DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1157 



cable No. 2 has a hydrodynamic constant H of 70 degree-knots, we have 

 in case (a) 



as = 11.7 degrees and ( -y- ) =2.12 ft/sec. 



\ (It /max 



From (29) we get therefore 



(7'p)max = 466 lbs (twist unrestrained), 

 = 848 lbs (twist restrained). 

 In case (b) we have as = 60°, (rfP/(/Omax = 13.6 ft/sec, and hence 

 (Tp)inaK = 2,990 lbs (twist unrestrained), 

 = 5,430 lbs (twist restrained). 



During recovery by conventional methods the surface incidence angle 

 as is in general much larger than that which occurs during laying. The 

 above example points up that one can expect correspondingly larger 

 ship motion tensions during recovery than during laying in the same 

 sort of seas. Since the stationary tensions are also much larger during 

 recovery, recovery is the condition for which the strength of the cable 

 should be designed. 



In this example we have considered a regular seaway, something which 

 does not exist in nature. Recent work in the application of the theory of 

 stochastic processes to the study of ocean waves and ship dynamics 

 promises to develop into a realistic description of the behavior of ships 

 at sea.'^ When such a description becomes available, we shall be able to 

 obtain a better estimate of the magnitudes of ship motion tensions. 



As far as data presently available are concerned, the maximum storm 

 condition vertical velocity at the bow or stern recorded by the U.S.S. 

 San Francisco during her research voyage of 1934 was 22 feet/sec. 

 Since this ship was roughly the size of a cable ship such as the H.M.S. 

 Monarch, this figure might indicate the order of the maximum velocities 

 to be expected in cable practice. In terms of our example, for six knot 

 laying this vertical velocity would imply 



Tp = 980 lbs (twist unrestrained), 



= 1,780 lbs (twist restrained). 



For recovery at a surface incidence angle of 60°, it would imply in turn 



Tp = 4,200 lb (twist unrestrained), 



= 7,600 lb (twist restrained). 



