# Stability

The word stability [from Middle English stabletee; stabilite, from Old French stabilité; from Latin root of stabilitas (“firmness, steadfastness”), from stabilis (“steadfast, firm”)] has several meanings based on context and scope.

## Definitions

• (physics) (architecture) (technology) (engineering) ability of a physical system to resist external forces and stresses;
• (chemistry) property of a chemical system to remain unchanged;
• (politics) (economics) economic or political situation characterized by continuous slight fluctuations around a given level;
• (mathematics) lack of alteration of a dynamic system;
• (figurative sense) is the existential inner solidity, the ability to face multiple situations, places, people with courage and without weakness.

## Metrology

In metrology, stability represents a static characteristic of a measuring instrument and the ability of an instrument to retain its performance throughout is specified operating life. The stability of a measurement is its ability to maintain a constant value.

The variations of the read value can be discontinuous, with random directions and amplitudes, or even slow, continuous and monodirectional (commonly called drifts). The causes of these variations can be different, for example: poor quality of instrumentation, presence of environmental disturbances, real variations of the measurand, etc..

Normally in the metrological field we refer to three types of stability:

2. measurement stability (over time);
3. instrumentation stability.

### Reading stability of a measurement

Reading stability is the ability of a measurement to maintain (during the survey) the read value within the resolution limits of the instrument. This concept overlaps with that of measurement repeatability.

During the reading of a measurement, especially with high-resolution instruments, it is common to find that the read value varies from instant to instant.

If the variations are discontinuous, with random directions and amplitudes, you can look for possible sources of disturbance to try to eliminate or reduce them; but if this is not possible or not successful, you will be forced to revise the resolution of the measurement or to take into account the presence of a repeatability error.

If the variations indicate a drift, one can look for a possible influence quantity to stabilize, otherwise, even in this case, one is forced to take into account a repeatability error dictated by the drift of the read value.

In some cases, if the drift has sufficiently stable characteristics, it is possible to take repeatable measurements by checking the influence quantity; for example, if a dynamometer drifts constantly following the application of a load, it is possible to obtain repeatable measurements by reading the load always after a precise period of time from its application. It should be noted, however, that most of the instrumentation needs a certain period of set-up, before taking a measurement, following the power on or the application of the measurand, in some cases it is kept permanently on in an environment with controlled temperature and humidity.

### Measurement stability over time

It is common to call measurement stability the ability of a measurement to remain of constant value over a long period of time. Such considerations arise from monitoring a measurand observed over time (sometimes for years).

For these types of measurements, the quality of the instrumentation used must be taken care of in advance, in order to ensure that the variations read over time are properly referable to the observed measurand.

Normally two types of phenomena emerge from these measurements:

1. drifts linked to some effect that varies the characteristics of the measurand over time. For example, in the case of measurements on a tool, the mechanical wear it undergoes during its use may show up as a continuous variation of some dimensional parameter.
2. sudden changes in the characteristics of the measurand due to accidental causes. For example, in the case of strain gauge measurements on a bridge girder, sudden changes in the measured stress may indicate the failure of a part of the structure.

### Stability of measuring instrumentation

The stability of a measuring instrument is its ability to maintain constant metrological characteristics.

An ideal instrument, once made, should maintain its characteristics constant. In reality, due to internal causes (e.g. deterioration and consumption of components, defects in manufacturing) or external (e.g. change of environmental conditions, misuse), the instrument varies its metrological characteristics in a more or less significant way.

In practice, one never speaks of “instrumental stability” in a generic sense, but one always refers to variations dictated by some influence quantity. Therefore, the concept of stability overlaps with the concept of instrument reproducibility.

Commonly, when we talk about the “stability” of an instrument, without specifying anything else, we mean the stability of its characteristics in the long run (also known as time drift). However, when we refer to the stability of an instrument when another quantity changes, it is necessary to specify which quantity we are referring to.

Among the most significant influencing quantities is ambient temperature (hence temperature stability). Among the specifications of the instrumentation it is common to find information related to the thermal drift of the same. This information is important in determining the portion of the measurement uncertainty associated with the change in ambient temperature.

### Zero stability

Zero stability is defined as the ability of an instrument to return to the zero reading after the input signal or measurand comes back to the zero value and other variations due to temperature, pressure, vibrations, magnetic effect, etc., have been eliminated.

## Construction engineering

The stability of a structure is a fundamental requirement because it must not undergo deformations over time that are incompatible with its equilibrium. The stability is checked both during the calculation phase and after the completion of the work by means of tests that are different according to the structure and that constitute the verification of stability.

Elastic stability is that of an elastic body, which, removed from its equilibrium configuration by the action of external forces, tends spontaneously to return to it as soon as the perturbing action ceases.

In the case of elements with a very small section compared to the other dimensions, such as slender rods or thin plates, stability assumes a relevant importance as it coincides with the resistance itself. In fact, since these elements are stressed only according to their axis or surface, they require an accurate control of the working load which, if it exceeded the critical load, would cause sudden bending and buckling which, growing rapidly, would lead to a configuration that would no longer be stable, becoming of minimum resistance.

The achievement of the stability of a building, i.e. of a rigid body as a whole, consists in eliminating the danger of displacements that are inadmissible for the structure as a whole (when we want to consider the integrity of the structure and of its component parts, it is more appropriate to speak of resistance), a problem generally always referable to an accurate study of the ground and to a correct foundation of the construction: in fact, there are essentially two possible instabilities, by rotation and by translation.

For example, when a tall and very exposed building is hit by a strong wind thrust, if it is not well anchored, it can topple over even without disconnecting; or when it rests on a ground with non-uniform resistance, this, with differentiated settlements, leads it to rotate. In the case of a building constructed on steeply sloping ground, the construction, instead, tends to slide due to its own weight, due to slippage of the foundations and/or the layer of soil adhering to them on an underlying layer.

## Meteorology

Atmospheric stability essentially depends on the differences in value between verticaladiabatic gradient and thermal gradient, that is, between the increasing or decreasing temperature variation of a descending or ascending air mass, and the vertical temperature variation outside the moving mass.

• If the two gradients have the same value, it is said that the atmosphere is in indifferent equilibrium: each moving air mass will always be at the same temperature of the surrounding air at the same altitude;
• if the thermal gradient is less than the adiabatic variation, the condition of stability is realized: an air mass that rises will meet less cold air and being then heavier than the surrounding air will tend to descend to re-establish the equilibrium;
• if, instead, the thermal gradient is greater than the adiabatic one, the air that rises will meet a colder environment and will continue to rise being lighter: in this case a condition of instability is realized because the initial displacement tends to be maintained.

These considerations are valid for both unsaturated and saturated air; for the latter, the heat of condensation, decreasing the adiabatic variation, increases the differences in value between the two gradients and exalts the instability conditions.

## Aeronautics

The stability characteristics that are sought to be ensured to aircraft relate primarily to the stability of the balance of the aircraft itself with respect to its rotations around a trio of barycentric axes, which, where possible, should dampen through a series of oscillations of decreasing amplitude or, more rarely, with aperiodic behavior (dynamic stability).

A prerequisite for dynamic stability is, usually, adequate static stability, which can be assessed through the ratio between the pullback moments, which tend to bring the aircraft back to the attitude from which it accidentally deviated, and the magnitude of the deviations from the initial attitude, measured through the aircraft rotations with respect to the previously specified axes. While it is relatively simple to ensure a satisfactory static stability in most cases, the problem of dynamic stability is much more complex, not only because of the importance of the inertial characteristics of the aircraft (often variable within considerable limits), but also because the achievement of adequate damping is often linked to the existence of corresponding dissipative forces, such as the aerodynamic resistance of the aircraft.

In order to avoid having to impose on the aircraft the burden of high aerodynamic resistance, as well as to avoid compromising its manoeuvrability by obtaining stability characteristics that are too marked, today the use of artificial stabilisation systems is increasingly widespread, These systems are made up of sensors for detecting aircraft motion perturbations, systems that amplify the signals they provide and actuators that, controlled by the aforementioned devices, act on the aircraft’s steering surfaces to restore its accidentally disturbed balance.

Correct stability characteristics are essential to ensure that the aircraft has satisfactory controllability. In the case of an airplane, for example, the requirements of static stability with the controls locked, i.e., with the various control surfaces held at assigned angles, coincide with those for which changes in aircraft attitude require proper movement of the corresponding control elements (e.g., a reduction in incidence is obtained by forward movement of the stick, or the handwheel, and vice versa).

On the other hand, imposing on an aircraft the correct amount of static stability when the controls are free (i.e. the control surfaces can rotate freely) is equivalent to making the movements of the corresponding control elements require the pilot to exert forces on them that are directed in accordance with these movements. Finally, the existence of appropriate stability of maneuvering allows the pilot to appreciate, through the amplitude of control excursions and the magnitude of piloting efforts exerted on them, the greater or lesser violence of the evolutions performed, characterized by the load factor imposed on the aircraft.

## Navy

In the case of a ship, transversal stability is very important, that is stability for inclinations around a longitudinal axis: in the case of an immersed body, in fact, stability depends on the reciprocal positions of the barycentre and the thrust center: it is assured if the first is always above the second. Important is the stability test, i.e. the one performed in a perfectly calm stretch of water by artificially impressing transversal oscillations to a ship for the study of its behavior and the determination of some parameters.

The stability of platform, that is the attitude of a ship to oscillate limitedly in wavy sea, can be obtained with appropriate forms of hull, with opportune values of the metacentric height and with devices to dampen the oscillations (stabilizers); the stability of route is, instead, the attitude of a floating in movement to maintain the route also in presence of actions tending to make it change.