Page 55 - Introduction to Naval Architecture

42 FLOTATION AND STABILITY

between the centre of gravity and the longitudinal metacentre. In this
case the distance between the centre of buoyancy and the longitudinal
metacentre will be governed by the second moment of area of the
waterplane about a transverse axis passing through its centroid. For
normal ship forms this quantity is many times the value for the second
moment of area about the centreline. Since J5M L is obtained by
dividing by the same volume of displacement as for transverse stability,
it will be large compared with jBM T and often commensurate with the
length of the ship. It is thus virtually impossible for an undamaged
conventional ship to be unstable when inclined about a transverse
axis.

KM L = KB + BM L = KB + 7 L/V

where / L is the second moment of the waterplane area about a
transverse axis through its centroid, the centre of flotation.
If the ship in Figure 4.10 is trimmed by moving a weight, w, from its
initial position to a new position h forward, the trimming moment will
be wh. This will cause the centre of gravity of the ship to move from G
to Gj and the ship will trim causing B to move to Bj such that:

GGi = wh/W

and Bj is vertically below G }
The trim is the difference in draughts forward and aft. The change
in trim angle can be taken as the change in that difference divided by
the longitudinal distance between the points at which the draughts are
measured. From Figure 4.10:

from which:

This is the moment that causes a trim t, so the moment to cause unit
change of trim is:

WGM L/L
This moment to change trim, MCT, one unit is a convenient figure to quote
to show how easy a ship is to trim. The value in SI units would be 'moment
to change trim one metre'. This can be quite a large quantity and it might
be preferred to work with the 'moment to change trim one centimetre'