Kaplan 



where the quantities Ny and Hj, are indicated as frequency-dependent 

 parameters in (77). 



For the surge degree of freedom the same expressions as for 

 the ship hull form for the coupling terms with pitch, and vice versa 

 for pitch with surge, are valid for the case of the disc-shaped buoy. 

 The damping due to surge also has the same expression, and can be 

 carried over to the present case of a disc-shaped buoy, with appro- 

 priate values of drag coefficient and reference area for the disc. 



The wave forces acting on the disc-shaped buoy are primarily 

 due to hydrostatic action and are evaluated on that basis. The verti- 

 cal wave force is expressed as 



• R 



where 



Z^=2pg\ f(x)ii{x,t) dx (78) 



f(x) = Vr^ - x^ (79) 



is the lateral offset of the buoy circular section axid T|(x,t) is the 

 wave height representation, as follows: 



•n(x,t) = a sin-r- (x cos P - Cy^t) 



'2ttx 

 = a s " 



in(£E£ - wt) (80) 



where the dependence on the heading angle P is deleted due to syna- 

 metry. The resulting expression for the vertical wave force is 



Z^ = - 4pgR a sin cot \ (i - cr cos \(r)d(r 



(81) 



'0 



/here tr = x/R and y = 2itR/\, leading to 



Z„ = - ZrrpgR^a • i^ sin cot (82) 



where J„( ) is a Bessel function. The pitch moment term due to 

 waves is given by 



.R 



M^= - 2pg \ xf(x)Ti(x,t) dt (83) 



1062 



