Auto-Os dilations of Anchored Vessels 



with the increase in the flow velocity V Q and angle a Q . The am- 

 plitude of steady cyclic yaw is but slightly dependent on the flow para> 

 meters. On the contrary, the amplitude of lateral displacement of 

 the hawse-hole is substantially decreased with the increase of the 

 flow velocity. 



The increase in the flow velocity leads, all other things 

 being equal, to increasing angle /3 Q . In consequence, as is seen 

 from expression (25), the position of the vessel's equilibrium may 

 change from being instable in respect of yawing to a stable one, 

 which will involve complete ceasing of its oscillations due to yawing 

 and drifting. In the example given the oscillations of the electronic 

 model of an anchored vessel ceased at a flow velocity exceeding 

 0. 8 m/sec. 



It is obvious from equations (18) that period C of the 

 oscillations under consideration is mainly dependent on the depth 

 H at anchorage (Figure 6). At the same time there is a clearly 

 defined dependence of this period on wind velocity. The latter result, 

 however, needs to be explained additionally. 



In consequence of the ship's motions and wave action the 

 resistance to drift P -q 3 and yaw P a 2 must increase much like 

 the resistance of a ship moving in a seaway, which is not taken into 

 account by the set of equations (18). Additional resistance to drift 

 and yaw in a seaway brings about an appreciable reduction in drif- 

 ting velocity and, consequently, an increase in the period of auto- 

 oscillations of an anchored vessel, all other things being equal. 

 Hence, seaways may be considered as the cause of significant weake- 

 ning of the relationship between the period of yawing oscillations 

 and the velocity of wind. According to full-scale data, the period of 

 oscillations due to strong wind slightly differs from that when the 

 wind force is 3-4 (on Beaufort scale). 



10. Ways to eliminate the auto -oscillations of anchored vessels 



Solution of equations (18) indicates that the intensity of 

 auto-oscillations for the given depth at anchorage and wind velocity 

 may be in direct relation to the extent of instability of the ship's 

 equilibrium position. This latter is defined by the difference bet- 

 ween the right-hand sides of inequalities (25) and (2 6). In similar 

 anchorage conditions the left-hand side of these inequalities is sub- 

 stantially dependent upon the position of the hawse-hole along the 

 ship's length. The right-hand side of the inequalities is eventually 

 characterized by the initial (for /3 = 0) value of the positional 



1091 



