Page 54 - Introduction to Naval Architecture

FLOTATION AND STABILITY 41

Figure 4.10 Trim changes

Trim
Suppose a ship, floating at waterline W 0Lo (Figure 4.10), is caused to
trim slightly, at constant displacement, to a new waterline WjLq
intersecting the original waterplane in a transverse axis through F.
The volumes of the immersed and emerged wedges must be equal so,
for small 0 :

where jf and y a are the waterplane half breadths at distances Xf and x^
from F,
This is the condition that F is the centroid of the waterplane and F is
known as the centre of flotation. For small trims at constant displacement
a ship trims about a transverse axis through the centre of flotation.
If a small weight is added to a ship it will sink and trim until the extra
buoyancy generated equals the weight and the centre of buoyancy of the
added buoyancy is vertically below the centre of gravity of the added
weight. If the weight is added in the vertical line of the centre of flotation
then the ship sinks bodily with no trim as the centre of buoyancy of the
added layer will be above the centroid of area of the waterplane.
Generalizing this a small weight placed anywhere along the length can
be regarded as being initially placed at F to cause sinkage and then
moved to its actual position, causing trim. In other words, it can be
regarded as a weight acting at F and a trimming moment about F.

Longitudinal stability
The principles involved are the same as those for transverse stability but
for longitudinal inclinations, the stability depends upon the distance