Dern 



a completely free model showed that for certain types of buoy , the 

 motions of the model are three-dimensional : the model oscillates 

 not only around the y-axis (pitching) but also around the x-axis 

 (rolling) . The top of the model describes then a 8-shaped curve , 

 and the rolling motion has a period equal to twice that of the waves : 



Tr = 2 Tw 



This rolling has the following properties 



- it is stable in amplitude , 



- this amplitude is considerable (larger than the corresponding 

 pitching amplitudes) 



- rolling occurs but for certain wave frequencies f = 1 / Tw 



- the wave amplitude has an important effect on the occurence and 

 amplitude of rolling . 



Figure 7 presents the rolling and pitching behavior of 

 type 1 buoy . 



The following remarks can be made : 



- for a given wave amplitude the rolling occurs only if the wave frequen- 

 cy lies between two values , one close to fz , the other close to 



2f e 



- for a given wave frequency , rolling takes place only if the wave 

 amplitude is sufficiently small . Furthermore for certain amplitu - 

 des either rolling occurs or it does not . 



- for a given wave amplitude the ratio 6 /f. varies irregularly 



-A. .A. 



with the wave frequency when the model is rolling . One of the rea- 

 sons of this phenomenon is the following : when there is rolling the 

 top of the model describes a 8-shaped curved but this trajectory is 

 not stable with time , the eight rotates slightly on itself while un - 

 dergoing deformation . The figure below clearly shows that this 

 modification has little effect on the measurement of rolling but has 

 much effect on that of pitching . 



1016 



