Auto-Oscillations of Anchored Vessels 



— < ( — > Cr ^ 



the auto-oscillations of the anchored vessel are eliminated. Even 

 so, this conclusion based on the analysis of small perturbation 

 stability quite satisfactorily characterizes motion in general. 



The test results shown in Figure 9 (a) and (b) for an 

 electronic model of an anchored vessel t"^ s = 0. 068, — r— = 5. 0) 

 give an idea of the effect the longitudinal arrangement of the hawse- 

 hole has on the intensity of yaw and drift. The dashed lines in the 

 region of unstable equilibrium represent the curves of yaw ampli- 

 tudes against abscissa t ^ hh . During the tests no auto-oscillat- 

 ions were observed at ( y ] values beyond the left ends of these 

 curves. The solid lines indicate the j3 Q and Y^q parameters 

 for the ship's equilibrium position. These relationships were cal- 

 culated from static equilibrium equations (see section 8) ; the 

 results obtained from equations (18) are illustrated by points on 

 the solid lines. 



It is obvious that the results presented are in good 

 agreement with the boundary of auto-oscillations region determined 

 by calculation from formula (29). Setting *? hh ~ ^ * or t ^ le critic- 

 al abscissa of the hawse-hole the following formula can be obtained 



, *hh x 3 C o 



jt\ cr^t^(^ + ^- < 30 > 



o s 



arj 



In contrast, for eliminating the auto -oscillations of the anchored 

 vessel by shifting the hawse-hole aft it is desirable that the centre 

 of aerodynamic pressure (CP) should be shifted forward. 



Really, in the position of ship's equilibrium the line of 

 aerodynamic action coincides with the anchor chain horizontal 

 projection and passes through the hawse-hole. Hence, no auto- 

 oscillations are present if the following inequalities are met simul- 

 taneously : 



*hh < J cr , «» <«cr < 31) 



1093 



