OSCILLATIONS OF SHIPS 



37 



As the displacement increases, the curve, to which the plane of flotation 

 is everywhere tangent, is known as the Curve of Flotation, and evidentl}' 

 in rolling the motion of the body is exactly the same as if an imaginary 

 curve of flotation fixed in the vessel were to roll on a fixed horizontal 

 surface. The position of the instantaneous axis of oscillation may then 

 be determined by noting that since the weight of the vessel and the 

 buoyancy, both vertical, are the only forces acting on the body, the C. G. 

 of the vessel must move vertically, if at all, so that the instantaneous 

 axis is in the horizontal line 

 through G (Fig. 20). Again 

 since the curve of flotation 

 rolls on a horizontal surface, 

 the instantaneous centre must 

 also be in the vertical through 

 the centre of flotation F, i.e., 

 the axis is at 0, the point of 

 intersection of G and F 0. 

 For small oscillations will 

 sensibly coincide with G. 



If k = radius of gyration of 

 a body of weight W about an 

 axis through its C. G., and if 



m = metacentric height for rolling displacements, the equation of 

 motion may be written 



FIG. 20. 



dt* ' 



or for small displacements 

 d*0 

 dt* 



Wti 



W m = 



I A; 2 

 from which we get T = 2 TT ^/ , the relation given above. 



Although a certain unknown mass of water will move along with the 

 vessel, increasing the inertia of the moving mass without increasing the 

 restoring couple and thus tending to increase the time of oscillation, yet 

 in practice very close agreement is found between the calculated and 

 experimental periods. 



E.g. In the Devastation, the calculated time was 7 sees.* 



experimental ,, 6*75 sees. 



* These are the times of a single oscillation. 



