Kaplan 



Dg = drag due to wind acting on a buoy 



Dg, Lg, Mg = cur rent- induced drag, lift, and moment acting 

 on buoy 



T = cable tension {at buoy attachment point) 



4» = cable angle from horizontal (at same point) 



B(0,h) = buoyancy force 



W = total weight of buoy 



ig, Zg = horizontal and vertical distances respectively 

 from cable attachment to CG 



GZ(9,h) = hydrostatic righting arm 



Thus, for a given buoy configuration in a particular condition of sub- 

 mergence in a given current, Eq, (53) can be solved for 9, T and 

 ^; that is, the buoy trim equilibrium and the cable tension and angle 

 at the buoy. This result then becomes the initial condition for the 

 static equilibrium cable geometry calculation. 



When considering the problem of the dynamics of the complete 

 moored buoy system, separate considerations in the analysis are 

 given initially to the buoy and to the mooring system, with ultimate 

 combination (i.e. coupling) exhibited later. The motion of a buoy 

 in waves considers the buoy to be equivalent to some type of hull 

 form, and the restriction to planar motion results in analyzing only 

 three degrees of freedom which may be considered to be surge, 

 heave and pitch. The equations of motion of the buoy are formulated 

 in the same general way as for a surface ship, described previously. 

 The only possible additional Influence in the present case of the buoy 

 is to allow for the effect of a uniform surface current, which can be 

 included in the equations by interpreting the current as an equivalent 

 forward speed of the buoy hull through the water. However, for 

 simplicity here, this effect is deleted when analyzing the buoy wave 

 responses. 



For the case of a ship- form buoy hull the hydrodynamic 

 force derivation is similar to that shown previously for the moored 

 ship. The general equations of motion in the vertical plane for the 

 coupled motions of surge, heave and pitch can be represented in 

 a more specific form as 



a„x +a,2X +a,;e = X„ + X„ (54) 



1056 



