Basic Naval Architecture by Philip A. Wilson
Author:Philip A. Wilson
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham
where m is called the Moment of Inertia of the body.
4.2 Application to Ships
In ship terms the work done by an external heeling moment (not constant, necessarily) is given by:
where initial heel angle and = final heel angle.
The potential energy stored against the righting moment is given by,
where
is the area under curve between and (measured in metres rads),
Fig. 18Definition of dynamical stability
As a matter of definition,
is called the DYNAMICAL STABILITY of the vessel at angle (see Fig. 18).
It is a measure of the ability of the vessel to absorb energy.
If at any stage in the heeling process the work done by an external heeling moment exceeds the energy stored due to dynamical stability the excess appears as kinetic energy of roll motion, unless it is dissipated by a damping mechanism, e.g. bilge keels or stabiliser fins, in addition to the damping originating from the surrounding water. Note that the work done by a heeling moment can also be expressed by dividing the heeling moment by the displacement to obtain a heeling lever, by analogy to the righting lever .
Thus,
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