Devn 



The following paragraph is devoted to the study of 

 pitching and vertical motions performed under these particular 

 experimental conditions . 



5,2- Presentation of results - 



The experimental results are presented under the 

 form of "gain curve" . In other words the following ratios are given : 



- pitching A/f A in degree per meter 



- relative motion £*A. / ^ A 



- heaving Z A / f A 



In principle these ratios should be independant of f , 



and each one of them should be equal to the modulus of the transfer ' 

 function computed from Newman's theory . Together with these 

 experimental gain curves , we also give the modulus of this transfer 

 function (denoted "J.N.Newman" in the figures) and in some cases 

 a curve denoted "second order" on the figures . This last curve was 

 obtained by modeling the dynamic system of the buoy (Input : wave 

 force , output : motion) by a second order differential system . 



Wave force I I motion (6, s or Z ) 



The wave force acting on the buoy was determined 

 theoretically from the hypothesis of Froude-Krilov (the expression 

 of these forces are given in section II) . 



For example , the transfer function of the second 

 order system is for pitching : 



GfMf) 



HjapUif) = mg (r+a) + ( 27rif jz (lyy+ Jyy) + 2rr if N («) 



G ft _(f) is obtained from the expression of the wave force . The cons- 

 tant coefficients in the denominator were experimentally determined 

 (damping test in calm water) . 



1020 



