Unstable Motion of Free Spar Buoys in Waves 



N = 



o 



N 



Y<P 



O 

 N 



<P<P 



O 



O 



II - EQUATION OF HEAVE MOTION - 



The equation (II- 1. 1 ) gives for heave 



2 



(II-2.1) (m + m ) -^-|+N -^ 

 zz Z zz at 



at 



+ Pg I dv = pi a dv 

 Jv J tt ozo 



+ mg 



then 



if the potential of on-coming waves is 

 g -k z Q 



(x , z , t) = — J . e sin (cr t - k x ) 



o o cr A v o 



- k z 



a = - kg f A e coscrt 



ozo & A 



Let S(z) be the area of transverse section at station z 

 pg/* dV= pg J S(z) dz =p gf S(z) dz + mg 



S (z) = S(o) 



with l(z) 



In type 1 buoy , S (z) is roughly : 

 z + h 



: 1 ( - z -hj) 



1 ( + z + h ) 



h and h define the form of upper part of the buoy as indicated on 

 the following figure 



1033 



