r I a? coAe'^^ sin (kag cos 9- - cot) -^^ [ R^ + (z- - ^f] ^ dt, 



The latter is effectively a diffraction potential; it is part of the singularity- 

 potential which offsets the normal velocity component of the incident wave 

 on the spar. These results can also be regarded as a special case of a 

 general body, accelerating in a time'- varying (but spatially constant) in- 

 finite field of fluid. It follows from consideration of the forces, both in 

 the fixed and moving coordinate systems,^ that the hydrodynamic force 

 on the body is the added mass times the relative acceleration plus the 

 displaced mass of fluid times the spatial acceleration of the (undisturbed) 

 fluid. For a circular cylindrical section, the added mass and the dis- 

 placed mass are equal, and the above relation for the x-component of the 

 force on the spar follows immediately. 



The z-component of force. Equation [14c], consists of three parts: 



(a) [pgSQJ ; 



(b) [- pg(zQ + aa.Q sin 9- - p a^ cos 9-) S(9)] ; 



(c) pgA sin (kaQ cos 9- - wt) [kTg - S(9)] . 



Part (a) is just the hydrostatic force. Part (b) is the decrease in buoyancy 

 which occurs w^hen the spar is raised an amount (zq + a slq sin 9 ■ — p ag cos 9- ). 

 Part (c) is the integral over the undisturbed spar surface of the vertical 

 pressure force due to the incident wave alone. This is easily seen by 

 noting that 



kTf,-S(9) = - f e^^i' -^ dz.' 

 and, thus, that Part (c) is equal to 



r kz' ds r 



[-pgAe 1 sin(kaQCOs9--cot)] dz-' = I Pq cos (n, z) dS 



14 



