Kaplan 



leading to total hydrostatic restoring vertical force and pitch moment 

 given by 



y^B*de • z +pgy''"*' 



Zf, = - Pg\ B'^de • z +pg^ B'^l d^ • e, (12) 



and 



'^b . rC, 



M^ = pgj B e de • z - pg \ B^^e de • e . (is) 



In the case of roll motion, the hydrostatic restoring effect is given 

 by 



K^ = - pgV|GM|^ = - W|GM|^, (14) 



where V is the displaced volume, | GM | is the metacentric height, 

 and W = pgV is the ship displacement. 



The exciting forces and moments due to waves are obtained as 

 the sum of ternas due to buoyancy ctlterations as the waves progress 

 past the ship hull, together with hydrodynamic terms of inertia! 

 and damping. The buoyancy effect for the vertical force is repre- 

 sented by 



pgB*Ti(e,t) (15) 



at each section, and these contributions are combined to determine 

 the total forces and moments due to waves. The analysis includes 

 an allowance for the waves to be propagating at an oblique heading 

 with respect to the ship, and a further allowance for the influence of 

 the non-slenderness of the ship is also included. A correction factor, 

 relating the beam to the wave length and the heading, is included for 

 this purpose since the shipforms considered for mooring application 

 are often not very slender. Details of the evaluation of wave forces 

 and moments by these methods are presented in [ 6] . 



Before discussing the mooring forces and moments, informa- 

 tion on the characteristics of the vessel studied in this investigation 

 is given below. The particular vessel for which the equations are 

 formulated and solutions carried out is the CUSS I, which was the 

 vessel used in the preliminary Mohole drilling operation. This ship 

 is considered representative of the class of construction type barges 

 which will be utilized for deep-sea construction operations. A 

 diagram of the barge, together with its mooring and load-lowering 

 lines, is shown in Fig, 1. A summary of the numerical values of the 

 parameters characterizing the moored-barge system is presented 

 in Table 1. 



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