Page 69 - Introduction to Naval Architecture

56 FLOTATION AND STABILITY

Usually a ship has a small trim by the stern as it enters dock and as
the water is pumped out it first sits on the blocks at the after end. As the
water level drops further the trim reduces until the keel touches the
blocks over its entire length. It is then that the force on the sternframe,
or after cut-up, will be greatest. This is usually the point of most critical
stability as at that point it becomes possible to set side shores in place
to support the ship.
Suppose the force at the time of touching along the length is w, and
that it acts a distance ~x aft of the centre of flotation. Then, if t is the
change of trim since entering dock:

The value of w can be found using the value of MCT read from the
hydrostatics. This MCT value should be that appropriate to the actual
waterline at the instant concerned and the density of water. As the
mean draught will itself be dependent upon w an approximate value
can be found using the mean draught on entering dock followed by a
second calculation when this value of w has been used to calculate a
new mean draught. Referring now to Figure 4.19, the righting moment
acting on the ship, assuming a very small heel, is:

Should the expression inside the brackets become negative the ship will
be unstable and may tip over.

Example 4.2

Just before entering drydock a ship of 5000 tonnes mass floats at
draughts of 2.7m forward and 4.2m aft. The length between
perpendiculars is 150m and the water has a density of 1025kg/
3
m . Assuming the blocks are horizontal and the hydrostatic data
given are constant over the variation in draught involved, find the
force on the heel of the sternframe, which is at the after
perpendicular, when the ship is just about to settle on the
dockblocks, and the metacentric height at that instant.