Page 48 - Introduction to Naval Architecture

FLOTATION AND STABILITY 35

STABILITY AT SMALL ANGLES

The concept of the stability of a floating body can be explained by
considering it to be inclined from the upright by an external force
which is then removed. In Figure 4.6 a ship floats originally at waterline
W 0L 0 and after rotating through a small angle at waterline WiL } .

Figure 4.6 Small angle stability

The inclination does not affect the position of G, the ship's centre of
gravity, provided no weights are free to move. The inclination does,
however, affect the underwater shape and the centre of buoyancy
moves from B 0 to B^ This is because a volume, v, repesented by
W 0O W t , has come out of the water and an equal volume, represented
by LoOLj, has been immersed.
If g e and gj are the centroids of the emerged and immersed wedges
and g egi = h, then:

where V is the total volume of the ship.
In general a ship will trim slightly when it is inclined at constant
displacement. For the present this is ignored but it means that strictly
B 0, BI , g e etc., are the projections of the actual points on to a transverse
plane.
The buoyancy acts upwards through E l and intersects the original
vertical at M. This point is termed the metacentre and for small