Auto-Osaillations of Anchored Vessels 



P > = C° f Q Cos (3 , 



a£ 



P = C° — Q Sin , (7) 



ai7 ai? 2 



and the moment about the central vertical axis by 



M = C ^5JL Q A (8) 



a ma 2 



In the latter expression 



C a = C ( 6 + <?«, - -1/1. ")Sin (3 , (9) 



ma o 



o " "* " T7 



■where non-dimensional parameters <> and C are dependent on 

 the relative position of CA 



' = -7*" (10) 



s 



Z 



and defined by the generalized curve (Figure 3) plotted against the 

 data obtained from [2J and [3] . Irrespective of the CA position 

 coefficients C^ t and C° r\ may be considered as constant^ viz. , 



1 



C a £ = 0.14 and C^tj = 0.95-1.05 



5. Estimation of hydrodynamic forces 



The hydrodynamic force components, the longitudinal one 

 Ph£ and the normal P^™ , as well as the moment M^ originating 

 during rotation of the vessel may be estimated approximately from 

 the formulae 



F h, = C h„ (* *l + ^ \*»\ ) Sj t ■ <" 



1085 



