Mooring and Positioning of Vehiales in a Seaway 



In analyzing the mooring forces and moments, the barge is 

 assumed to be moored by a conventional line and anchor system, 

 with both bow and stern moorings. However, for application to 

 deep-sea conditions with depths of the order of 1000 fathoms, a 

 certain particular mooring scheme is utilized. This scheme 

 utilized a long-wire rope for each mooring leg assenably (12,000 ft 

 in length), which is supported in the water by a series of submerged 

 spherical buoys. The buoyancy of these buoys keeps the rope taut 

 along its entire length, thereby not allowing it to assume the usual 

 catenary shape. With this arrangement, an initial tension is applied 

 along each mooring let, and any changes in mooring forces on the 

 ship (and therefore also in the cables) occur as a result of elastic 

 forces resulting from ship displacements. A layout drawing of such 

 a system is shown in [ 4] , which has direct applicability to ships of 

 the same general displacement as the construction barge presently 

 studied. 



The displacements having greatest influence on the moorings 

 are in the horizontal plane, and these are surge, sway and yaw. 

 Since the mooring lines are fairly taut and are under an initial 

 tvsnsion, the elastic restoring effects may be taken to be fairly 

 linear, i.e. the restoring force is proportional to the displacement. 

 The proportionality factor for an effective displacement along a 

 single mooring cable is found from a knowledge of the modulus of 

 elasticity of the cable material. For the present case of i-inch 

 diameter bridge strand wire rope, which is 12,000 ft long, has a 

 cross section area of 0. 595 in , and an assumed modulus of 

 25 X lO^lb/in^, the effective spring constant for a single wire rope 

 is found to be C = 1250 lb/ft. This linear result only holds below 

 the yield point of 60,000 lb of static force (in a single cable), but it 

 is anticipated that the maximum deflection necessary for attaining 

 this force (viz. 48 ft) will not be experienced in the present case. , 



For the purposes of analysis, the barge is assumed to be 

 moored in an arrangement similar to that shown in the following 

 sketch of the mooring plan, A longitudinal displacement of the barge 



along X, denoted as Ax, leads to an effective displacement along a 

 single cable given by Ax cos a, where a is defined in the sketch 

 above. The force in a single cable is then C Ax cos a. The longi- 



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