Page 60 - Introduction to Naval Architecture

FLOTATION AND STABILITY 47

overestimate the volume. It is reasonable to assume the deflected
profile of the ship is parabolic, so that the deflection at any point
2
distant xfrom amidships is d[l - (2x/L) ], and hence:

where b is the waterline breadth.
Unless an expression is available for b in terms of x this cannot be
integrated mathematically. It can be evaluated by approximate integra-
tion using the ordinates for the waterline.

Longitudinal position of the centre of gravity
Suppose a ship is floating in equilibrium at a waterline W 0Lo as in
Figure 4.13 with the centre of gravity distant x from amidships, a
distance yet to be determined. The centre of buoyancy B 0 must be
directly beneath G. Now assume the ship brought to a waterline Wj LI
parallel to those used for the hydrostatics, which cuts off the correct

Figure 4.13

displacement. The position of the centre of buoyancy will be at B 1?
distant y from amidships, a distance that can be read from the
hydrostatics for waterline Wj L^. It follows that if t was the trim, relative
to Wj L! , when the ship was at W 0Lo:

giving the longitudinal centre of gravity.

Direct determination of displacement and position ofG
The methods described above for finding the displacement and
longitudinal position of G are usually sufficiently accurate when the trim