Unstable Motion of Free Spar Buoys in Waves 



5,3- Type 1 Buoy - 



Figures 9- and 10 show that Newman's theory is not in 

 agreement with the experiment . At certain frequencies there exist a 

 double regime in the relative motion . For example at f = O. 286 Hz, 

 during the same experiment we obtained the values 4f = 1. 1 and 

 ■ f-f = 4. 7 simply by giving to the model a vertical impulsion at the 

 right time . The gain curve in s exhibits a slight resonance for 

 f = f q and a zone of unstability for f = 2 f q . For£<2 f ft but close to 

 2 f~the signal has the following shape 



s(t) 



Wien the frequency is exactly equal to 2 f^the recording of s (t) is 

 untractable , it is very irregular and corresponds to very large va - 

 lues of s (t) . 



The gain curve in © shows the existence of a frequency 

 interval in which the points are very scattered . In this zone pitching 

 varies with time in the same way as s (t) does . The frequency inter - 

 val coincides approximately with |fz , 2 f~l 



5.4 - Type 1 1 Buoy - 



The type llbuoy was chosen so that all conditions of 

 validity of the slender body theory be satisfied . In particular the 

 slenderness has a large value ( H/R = 19- 34 ) , and the upper part 

 out of water has a cylindrical circular shape as the rest of the buoy . 

 This upper part is quite high (h = 0.42 m. ) 



Figures 11, 12 and 13 show that Newman's theory is 

 rather well verified . However two discrepancies can be noted : for 

 f = 2 fQthe experimental points are well above the theoretical curve 

 (see in particular the gain in Z) . Furthermore it is difficult to check 

 experimentally the value of the gain at resonance which is very 

 sharp . At resonance , the gain depends chiefly on the damping coef- 

 ficient . The theoretical heave damping coefficient is 0,92 , while 

 that determined experimentally in calm water is 85 . It seems there- 

 fore that there is a large inaccuracy for the value of the heave dam - 



1021 



