Dern 



ping coefficient . The same result exists for the pitch damping 

 coefficient . 



5.5- Type n° 12 - 



In order to confirm the results obtain with the type 1 

 buoy , we tested a buoy model with the same dynamic characteris - 

 tics as type 11 , but with a conical upper part . This buoy model , 

 denoted type 12 , was tested for various wave amplitudes in order 

 to check the linearity hypothesis . The results of the experiments 

 are given in figures 14 , 15 and 16 , which show that Newman's li - 

 near theory is , here again , not valid . It can be noticed in particu- 

 lar that there is a jump in the gains in s and Z . The results obtai - 

 ned for f = 2 fg show that the three gains are not independent of the 

 wave amplitude . When f is close to but less than 2 f q , two regimes 

 of motion are possible , in particular for the relative motion s and 

 the heaving Z . These two regimes are characterized first by the 

 value of the gain , second by the frequency of the oscillations . For 

 small gain this frequency is equal to that of the waves , for larger 

 gains it is half the wave frequency . In both regimes the oscillations 

 are approximatively sinusoidal , except for pitching when the regi - 

 me corresponds to the higher gain . Furthermore , for the large 

 gain the model is periodically submerged by the waves . 



VI - CONCLUSION TO THE EXPERIMENTAL STUDY - 



The heave damping of a spar buoy being very weak , 

 when such a buoy is submitted to a wave train of frequency equal to 

 the buoy natural heaving frequency , it then performs motions of 

 large amplitude . Under these conditions if the upper part of the buoy, 

 normally out of the water , does not have a constant sectional area 

 non-linearities appear which modify completely the frequency res - 

 ponse of the buoy . In particular a phenomenon of double regime for 

 the vertical displacements appears . Discrepancies also occur for 

 frequencies close to but less than twice the natural pitching frequency. 



Thus J.N.Newman's linear theory for heaving motion 

 is not valid unless the upper part of these buoys , which is out of the 

 water in calm water , be of constant sectional area on a sufficient, 

 length . The conditions of validity of J.N.Newman's theory for pit - 

 ching and rolling motions are more complicated as we shall see in 

 Section II . 



1022 



