Page 146 - statbility for masters and mates

134 Ship Stability for Masters and Mates
Fig. 15.1
when on an even keel, the volume of the immersed wedge must be equal to the volume of the emerged wedge and F, the point about which the ship trims, is the centre of gravity of the water-plane area. The point F is called the `Centre of Flotation' or `Tipping Centre'.
A vessel with a rectangular water-plane has its centre of ¯otation on the centre line amidships but, on a ship, it may be a little forward or abaft amidships, depending upon the shape of the water-plane. In trim problems, unless stated otherwise, it is to be assumed that the centre of ¯otation is situated amidships.
Trimming moments are taken about the centre of ¯otation since this is the point about which rotation takes place.
The longitudinal metacentre (ML) is the point of intersection between the verticals through the longitudinal positions of the centres of buoyancy. The vertical distance between the centre of gravity and the longitudinal metacentre (GML) is called the longitudinal metacentric height.
BML is the height of the longitudinal metacentre above the centre of buoyancy and is found for any shape of vessel by the formula:
where
and
IL
BML IL V
the longitudinal second moment of the water-plane about the centre of flotation
V the vessel's volume of displacement