Page 61 - Introduction to Naval Architecture

48 FLOTATION AND STABILITY

is small. To obtain more accurate results and for larger trims the Bonjean
curves can be used. If the end draughts, distance L apart, are observed
then the draught at any particular section can be calculated, since:

where x is the distance from where T a is measured.
These draughts can be corrected for hog or sag if necessary. The
calculated draughts at each section can be set up on the Bonjean curves
and the immersed areas read off. The immersed volume and position of
the centre of buoyancy can be found by approximate integration. For
equilibrium, the centre of gravity and centre of buoyancy must be in the
same vertical line and the position of the centre of gravity follows. Using
the density of water in which the ship is floating, the displacement can be
determined.

Heel due to moving weight
In Figure 4.14 a ship is shown upright and at rest in still water. If a small
weight wis shifted transversely through a distance h, the centre of gravity
of the ship, originally at G, moves to Gj such that GGj = wh/W. The ship
will heel through an angle <p causing the centre of buoyancy to move to
B! vertically below Gj to restore equilibrium. It will be seen that:

This applies whilst the angle of inclination remains small enough for M
to be regarded as a fixed point.

Figure 4,14 Moving weight