Page 63 - Introduction to Naval Architecture

50 FLOTATION AND STABILITY

Similarly the vertical moment of volume shift is:

From the figure it will be seen that:

This is called the wall-sided formula. It is often reasonably accurate for
full forms up to angles as large as 10°. It will not apply if the deck edge
is immersed or the bilge emerges. It can be regarded as a refinement of
the simple expression GZ = GM sin <p.

Influence on stability of a freely hanging weight
Consider a weight w suspended freely from a point h above its centroid.
When the ship heels slowly the weight moves transversely and takes up
a new position, again vertically below the suspension point. As far as the
ship is concerned the weight seems to be located at the suspension
point. Compared to the situation with the weight fixed, the ship's
centre of gravity will be effectively reduced by GGi where:

This can be regarded as a loss of metacentric height of GGj.
Weights free to move in this way should be avoided but this is not
always possible. For instance, when a weight is being lifted by a
shipboard crane, as soon as the weight is lifted clear of the deck or
quayside its effect on stability is as though it were at the crane head.
The result is a rise in G which, if the weight is sufficiently large, could
cause a stability problem. This is important to the design of heavy lift
ships.