GerassimoVj Pershitz and Rakkmanin 



aerodynamic derivative coefficient (9) : 



c/ = C V { 6 + 6 ) , (27) 



ma o o s 



i. e. by the lengthwise position of the centre of sail area. Figure 7 

 gives an indication of the relationship between the intensity of yawing 

 and the extent of instability of the' ship's equilibrium position. The 

 intensity of yawing is characterized in this figure by the relative 

 amplitude = £ j ffi versus the derivative C ma . Here /3 m = 

 dimensional amplitude fo yaw, mo = dimensional amplitude of 

 yaw for the vessel with -^- = 5. 0, 6 Q - 0. 068. The curve of 

 ^mo a g a i ns t the anchorage depth is presented in Figure 8. 



Thus the elimination of the wind-induced auto-oscillations 

 of an anchored vessel may be brought about if stability of its equi- 

 librium position is ensured. This latter can be ensured, as evidenc- 

 ed by the analysis of condition (25), by shifting aft both the centre 

 of sail area and the hawse-hole. This same condition, along with 

 (2 6), gives the quantitative value of the required shifting of the 

 above points. 



When the hawse-hole is located near the forward perpen- 

 dicular, the auto-oscillations of the anchored vessel subjected to 

 wind may be eliminated at the cost of shifting the centre of sail area 

 well aft. As angle j8 Q = corresponds in this case to the ship's 

 equilibrium position, and the „ ° ,. ratio is rather large, so the 

 stability of equilibrium position, as follows from inequality (26), 

 can practically be ensured if the right-hand side of this inequality 

 is close to zero or negative. This will be the case if 



6 S < - 0,25 (28) 



So considerable a shifting of the centre of sail area, however, 

 adversely affects the controllability of the vessel in wind. 



The shifting of the hawse-hole aft of the forward perpen- 

 dicular must be greater than that where the ship's equilibrium is 

 possible with the value of & different from zero. As the angle 

 increases, the instability of equilibrium position decreases, 

 and at a certain value of ( y ) q t the position becomes stable, 

 viz. inequality (2 5) is satisfied. Thus, with 



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