Mooring and Positioning of Vehicles in a Seaway 



Different effects as to the cable displacement directions occur for 

 the cables, at either the bow or the stern, for the influence of the 

 lateral motions, while the same direction of displacement (at either 

 bow or stern) occurs for the surge motion. The general expression 

 for the fluctuating cable force may be written as 



Fc = C X cos a ± ( y * •7~4') sin a 



where C is the effective spring constant for a single wire rope, 

 and particular values for each of the four cables are given in the 

 following, where a positive cable force is defined as that which pulls 

 on the restraining anchor support on the ocean floor. 



The expressions for the Individual cable forces (c,f. sketch 

 of mooring-line system) are listed below: 



Bow 



Stern 



F| = - Clx cos a + ( y +-^i|i) sin a port 



Fg = - C X cos a - (y +-^4') si^ '^ starboard 



F_ = Cx cos a - (y --^i^ijsina port 



F = C X cos a + ( y - ^4^ ) sin a starboard 



(21) 



(22) 



For the present case where the barge is moored with a = 60°, 

 L = 260 ft, the mooring system restoring constants are 



k^ = 1250 lb/ft 



ky = 3750 lb/ft (23) 



k^= 633,75 X 10^ Ib-ft/rad 



These values are the effective spring constants for surge, sway and 

 yaw, and as a result there also exist natural periods for these 

 motions in the case of moored ships. There still exist natural 

 periods of heave, pitch and roll, as in the case, of free ships, and 

 these natural periods are relatively unaffected in the present case. 

 The introduction of the existence of natural periods in surge, sway 

 and yaw (with possible large motions associated with resonances in 



1031 



