Motora and Koyama 



where 



k^ = added mass coefficient, 



p = density of surrounding fluid, 



V = volume of a body, 



Zw = wave elevation, 



Nz = damping coefficient, 



g = acceleration of gravity, 



A = waterplane area, and 



y ^y i^y z a^^*© correction factors for the orbital motion of the wave. 



The first two terms correspond to the body-wave interaction, and the third term 

 corresponds to the Froude-Krylov buoyancy. The first term is also an inertia 

 term due to added mass effect. Factor 73 has been known as Smith Correction 

 Factor. 



If the wave elevation is of the form 



Zw = Zw e ^ '^ '^ 



where oj is the circular frequency, then 



Zw - - o;"^ Zw . 



Therefore, Eq. (1) is rewritten as 



^zw " -rik^/oVw^Zw + yjNzZw + y^p^KbK . (2) 



The inertia term is reverse in sign in relation to the buoyancy term and will in- 

 crease rapidly as the frequency '^ increases. In case of ordinary ship form how- 

 ever, the first term is not large enough to cancel the buoyancy term in a fre- 

 quency range of ordinary wave encounter. However, if the form of a body is 

 chosen so that the inertia term is large enough compared to the buoyancy term, 

 it will be possible to eliminate the heaving force in a relatively low frequency 

 range. 



According to Newman (5), heaving force is related to the damping coefficient 

 by the following formulas: 



Nz = ^Zvi (two-dimensional case) 



(3) 



f/'g'h- 



F, (0) de (three-dimensional case) 







384 



