Mooring and Positioning of Vehicles in a Seaway 



|GM| is the difference between the distance between the CG and the 

 CB of the submerged portion of the buoy, and the nnetacentric radius 

 between the CB and the intersection of the displaced buoyancy vector 

 with the vertical axis. 



The metacentric radius is determined from the value of the 

 lateral displacement of the CB of the submerged section of the disc 

 cylinder. This is determined as the ratio of the moment of inertia 

 of the waterplane area about the buoy vertical centerline plane, to 

 the displaced volume. With this moment of inertia found to be 



4/ 2 



I A __j ...li-i- ii T..„ -r j.T-„ ^uoy volume given by irR c 



ading to a metacentric height | GM 



irR /4, and with the value of the buoy volume given by irR'^d', the 

 metacentric radius is R /4d', leadin 

 given by 



r2 , 

 GM = -^- BG (73) 



4d 



where |BG| is the verticeil distance between the CB and CG of 

 the buoy. 



Similarly, values for added mass and added inertia for the 

 disc-shaped buoy can be found from the work of [ 13] , based on con- 

 sidering this hull as a shallow draft vessel. In that case the total 

 added mass in the vertical direction is given by 



I 



A^gdx = pR^My (74) 



where the value of My is given in [ 13] . Similarly, the added pitch 

 inertia term is represented by 



I 



A^^x^ dx = pR'i* (75) 



where the value of \\ is given in [ 13] . These values are weakly 

 frequency dependent for the range of significant wave lengths of 

 concern in the buoy problem, and an appropriate approximate 

 constant value can be used. The damping coefficients for heave and 

 pitch are represented, respectively, by 



and 



^25 



^38 



= \ N^ dx = pR^wNy (76) 



= \ N^^ dx = pR^coH^ (77) 



1061 



