Unstable Motion of Free Spar Buoys in Waves 



In the plane (H , T ) the instability region is located above 



the curve defined by ( III-3.5 ) .As an example , figure n° 31 gives 



the ranee of H and T in the North Atlantic . Figure n° 32 gives the 



v v 



region of rolling for type 1 1 buoy . 



In practice , relation (III-3. 5) does not allow us to study by 

 means of calculus only the effect of the buoy characteristics on the 

 presence of a rolling motion because Nejp' is not known theoretically 

 but only experimentally . 



IV - EXPERIMENTAL STUDY - 



4.1- Experimental apparatus and procedure - 



In order to verify the validity of the rolling criterion (III-3. 5) 

 we have performed experiments in irregular waves with a spectral 

 density given by the modified Pierson-Moskowitz formula . Only type 

 1 , 11 , 14 and 15 buoys have been tested in tankn° 2 of Bassin d'Es- 

 sais des Carenes . This tank is equipped for generating irregular 

 waves [24 J : any spectral density may be simulated by using a dri - 

 ving voltage . This driving voltage is obtained by running a pseudo - 

 random white noise through a linear filter so designed that the square 

 of its frequency response has the desired shape . Figures 3 3 and 34 

 show an example of a measured spectral density of waves and of re- 

 lative motion . 



The experiments were carried out in the manner discussed 



below . A driving voltage was selected , corresponding to a given 



value of T . Then the value of H was set by adjusting the gain of an 



v v 



amplifier located at the input of the generator of the Ward Leonard 



group . Unfortunately , during these experiments , the gain could be 



adjusted only by step . Consequently , the critical value of H (i. e. 



the value above which the model rolls) was not precisely determined . 



4.2- Results - 



Figures 32 and 35 to 37 show the results foftype 11 , 1 , 14 

 and 15 buoys . In these figures we can see the "theoretical curves" 

 which give the critical value of H versus T as given by equation 

 (III-3. 5) . As was said before , the number of experimental points 



are too small for the critical values of H to be well-defined . Yet it 



v 

 seems that there is no fundamental discordance between the theoreti- 

 cal curves and the experimental results . 



1067 



