stability

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stability is the ability of a ship to return to an upright position after being heeled by an external force, such as a weight being placed aboard or by rough sea conditions. If a ship is inclined at an angle and then naturally returns to the upright, it is known as being stable. Should the ship wish to continue moving from the upright and is heading for capsize, then it is described as unstable.

It is normal for ships to have their centre of gravity higher than the centre of buoyancy (see Fig. 1) creating what appears on first sight to be an unstable situation. However, as can be seen (Fig. 2), the centre of buoyancy travels away from the centre line as the ship is heeled, producing a restoring force.

In Fig. 2 the distance G–M is known as the metacentric height and is a measure of the stiffness, or stability, of a ship. The larger the metacentric height of a ship, the greater the stability. On the down side, very large metacentric heights produce violent rolling motions. So passenger ship operators, in particular, must find a suitable compromise which keeps their ships safe yet creates a slow rolling movement which neither upsets fare-paying passengers, nor damages fragile cargo. To assist in keeping the ship from excessive rolling, fin stabilizers are often fitted.

Naval architects (see naval architecture) calculate the metacentric height of every ship in all conditions, from being in ballast through to part and fully laden. As the safety of the ship is a statutory obligation it is important that the metacentric height be confirmed at full scale. For this reason an inclining experiment is carried out when the ship is afloat in still conditions. The stability can be calculated from the angle of heel adopted by the ship when a known weight is moved across the deck an exact amount.

During a ship's lifetime, it acquires additional topside weight through coats of paint, loose stores, etc. The ship's managers and officers must keep aware of this, and it is recommended that further inclining experiments be carried out every few years.

Fred M. Walker

stability A multidiscipline term with a variety of (related) meanings. In numerical analysis it is used with what appears to be a bewildering array of possible prefixes. There are, however, two important basic usages.

Given a well-defined numerical procedure it is important that roundoff errors do not seriously influence the accuracy of the results. This is referred to as numerical stability and depends on the error-propagation properties of the procedure.

Discretization methods for the solution of integral and differential equations are based on a subdivision of the region in which the solution is required. Stability here means that perturbations in the data (initial or boundary conditions) have a bounded effect on the solution obtained (ignoring roundoff error) for a given subdivision. The existence of a uniform bound on this effect over all sufficiently fine subdivisions is a necessary condition for the convergence of the method as the subdivision is refined.

In the solution of ordinary differential equations much of the stability theory has been developed in the study of stiff systems of equations. Of great importance to this development was the concept of A-stability introduced by Dahlquist in 1963. A method is A-stable if it produces bounded solutions for the test problem y′ = qy, y(0) = 1 Re(q) < 0

for all stepsizes. The trapezoidal rule (see ordinary differential equations) is an example of an A-stable method. Much of the later theory has investigated similar properties for more general test problems.

stability
1. Atmospheric condition in which air that is forced to rise tends to return to its pre-existing position in the absence of the uplifting force. If the adiabatic lapse rate of uplifted air is greater than the environmental lapse rate, then the vertically displaced air will become colder than the surrounding air and as its density increases it will tend to sink back. See also INSTABILITY.

2. In engineering, the resistance of a structure to collapse or sliding, dependent upon the shearing strength of the material.

3. In geochemistry, the state of equilibrium towards which a system will move from any other state under the same conditions.

4. In thermodynamics, the condition when a slight disturbance of temperature, pressure, or composition does not result in the appearance of a new phase.

stability An atmospheric condition in which air that is forced to rise tends to return to its pre-existing level in the absence of the uplifting force. If the adiabatic lapse rate of uplifted air is greater than the environmental lapse rate, the vertically displaced air will become colder than the surrounding air and as its density increases it will tend to sink back. Compare instability.

stability. Part of the commitment made by monks and nuns following the Rule of St Benedict. It is variously interpreted as meaning staying in one place, staying with one community, or perseverance in the monastic life.

sta·bil·i·ty / stəˈbilitē/ • n. the state of being stable: there are fears for the political stability of the area.

stability see equilibrium .

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