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Stable flotation If a body is designed to float, it must do so in a stable fashion. This means that if the body suffers an angular displacement, it will automatically return to the original (correct) position. To appreciate how a floating body may exhibit this self-righting property, it must be realized that (with the exception of circular sections) the angular displacement of a body causes a lateral displacement in the position of B. Consider, for example, the pontoon of rectangular section shown in Figure 1.11 (a). For upright flotation, the pressure distribution across the base is uniform. The centre of buoyancy lies on the vertical centreline. Since the pontoon is upright, the weight, W, must also be acting along the vertical centreline. If the vessel now rotates about its longitudinal axis (,heels over') through angle e (Fig. l.1lb), the pressure distribution on the base becomes non-uniform, although still linear. This is, therefore, similar to the other pressure distribution patterns which have been examined. The shift from a uniform distribution (with the vessel upright) to a non-uniform distribution necessarily implies a corresponding shift in the position of the line of action of the resultant force. The buoyancy force now acts through B' rather than through the original centre of buoyancy B. If a vertical line (representing the buoyancy force) is drawn through B', it intercepts the centreline of the vesse~ point M, which is called the 'metacentre'. Using trigonometry, the distance BB' may be found:

+ freeboard

centre of gravi ty /'" centre of buoyancy

plan

vertical component (FtI )

H

y

/ uniform pressure distribution on base

(a) Pontoon in upright position

p = pg (Y + y) = pg ( Y + a sin 6)

(b) Pontoon heeling through angle 6 (c) Pressure distribution on pontoon base

Figure 1.11 Flotation of pontoon.