Page 82 - Introduction to Naval Architecture

FLOTATION AND STABILITY 69

Even with centreline bulkheads and shifting boards spaces will
appear at the top of the cargo as it settles down. To help fill these spaces
feeders are fitted to provide a head of grain which will feed into the
empty spaces. Hold feeders are usually formed by trunking in part of
the hatch in the 'tween decks above. Feeder capacity must be 2 per cent
of the volume of the space it feeds. Precautions such as those outlined
above permit grain cargoes to be carried with a high degree of
safety.

DYNAMICAL STABILITY
So far stability has been considered as a static problem. In reality it is a
dynamic one. One step in the dynamic examination of stability is to
study what is known as a ship's dynamical stability. The work done in
heeling a ship through an angle d<p will be given by the product of the
displacement, GZ at the instantaneous angle and d<p. Thus the area
under the GZ curve, up to a given angle, is proportional to the energy
needed to heel it to that angle. It is a measure of the energy it can
absorb from wind and waves without heeling too far. This energy is
solely potential energy because the ship is assumed to be heeled slowly.
In practice a ship can have kinetic energy of roll due to the action of
wind and waves. This is considered in the next section.

Example 4.4
Using the tabulated values of GZ from the previous example,
determine the dynamical stability of the vessel at 60°
inclination.

Solution
The dynamical stability is given by:

This integral can be evaluated, as in Table 4.3, using Simpson's
1,4,1 rule and the ordinate heights from Table 4.2,

The area under the curve to 60°

Dynamical stability