stability of an airplane

The aircraft's response to disturbance is associated with the inherent degree of stability built in by the designer, in each of the three axes; and eventuating without any reaction from the pilot. Another condition affecting flight is the aircraft's state of trim or equilibrium where the net sum of all forces equals zero. Some aircraft can be trimmed by the pilot to fly 'hands off' for straight and level flight, for climb or for descent. If the trim is wrong, and perhaps it flies with one wing low, inherent stability will maintain that wing-low attitude and not restore the aircraft to a wings-level attitude. It is desirable that longitudinal trim doesn't change significantly with alterations in power, nor does directional trim change significantly with alterations in airspeed.

An aircraft's stability is expressed in relation to each axis: lateral stability stability in roll, directional stability stability in yaw and longitudinal stability stability in pitch. The latter is the most important stability characteristic. Lateral and directional stability are inter-dependent.

Degrees of stability

An aircraft will have differing degrees of stability around each axis; here are a few examples:

  • A totally stable aircraft will return, more or less immediately, to its trimmed state without pilot intervention; however such an aircraft is rare and undesirable. We usually want an aircraft just to be reasonably stable so it is easy to fly: if it is too stable they tend to be sluggish in manoeuvring and heavy on the controls. If it tends toward instability the pilot has to continually watch the aircraft's attitude and make the restoring inputs, which becomes tiring, particularly when flying by instruments. Some forms of instability make an aircraft unpleasant to fly in bumpy weather.

     

  • The normally or positively stable aircraft, when disturbed from its trimmed flight state will without pilot intervention commence an initial movement back towards the trimmed flight state but over-run it, then start a series of diminishing damping oscillations about the original flight state. This damping process is usually referred to as dynamic stability and the initial movement back towards the flight state is called static stability. The magnitude of the oscillation and the time taken for the oscillations to completely damp out is another aspect of stability. Unfortunately a statically stable aircraft can be dynamically unstable in that plane i.e. the oscillations do not damp out.

     

  • The neutrally dynamically stable aircraft will continue oscillating after disturbance but the magnitude of those oscillations will neither diminish nor increase. If these were oscillations in pitch the aircraft will just continue 'porpoising' if there were no other disturbances and the pilot did not intervene.

     

  • The negatively stable or fully unstable aircraft may be statically unstable and never attempt to return towards the trimmed state. Or it can be statically stable but dynamically unstable, where it will continue oscillating after disturbance with the magnitude of those oscillations getting larger and larger. Significant instability is an undesirable characteristic, except where an extremely manoeuvrable aircraft is needed and the instability can be continually corrected by on-board 'fly-by-wire' computers rather than the pilot for example, a supersonic air superiority fighter. The best piston-engined WW2 day fighters were generally designed to be just stable longitudinally, neutrally stable laterally and positively stable directionally.

Longitudinal stability

Longitudinal stability is associated with the restoration of aoa to the trimmed aoa after a disturbance changes it.

Angle of incidence

Angle of incidence is a term which is sometimes confusingly used as being synonymous with wing angle of attack, however the former cannot be altered in flight. Angle of incidence, usually just expressed as incidence, is within the province of the aircraft designer who calculates the wing aoa to be employed in the main role for which the aircraft is being designed, probably the aoa in performance cruise mode. The designer might then plan the fuselage wing mounting so that the fuselage is aligned to produce the least drag when the wing is flying at the cruise aoa. Wings which incorporate washout will have differing angles of incidence at the wing root and at the outer section.

A notional horizontal datum line is drawn longitudinally through the fuselage and the angle between that fuselage reference line (FRL) and the wing chord line is the angle of incidence. Incidence should be viewed as the mounting angle of the fuselage rather than the mounting angle of the wings.

Incidence may also be called the 'rigger's incidence' or some similar expression carried over from the earlier days of aviation.

Longitudinal dihedral

An angle of incidence is also calculated for the horizontal stabiliser with reference to the FRL and the angular difference between wing and stabiliser angles is called the longitudinal dihedral, although it is probably more correct to say that the longitudinal dihedral is the angular difference between the two surfaces at their zero lift aoa. Incidentally the angle of the line of thrust is also expressed relative to the FRL.

It is the longitudinal dihedral, combined with the horizontal stabiliser area and moment arm, which provides the restoring moment to return aoa to the trimmed state. However bear in mind that the moment arm, which supplies the restoring leverage and thus the stability, is affected by the cg position and if the cg lies outside its limits the aircraft will be longitudinally unstable.

When flying with level wings, at a particular weight, each aoa is associated with a particular IAS. We might as well take advantage of that by arranging the longitudinal dihedral so that the built-in state of trim produces a particular indicated airspeed.

Directional stability

Directional stability is associated with the realigning of the longitudinal axis with the flight path (the angle of zero slip) after a disturbance causes the aircraft to yaw out of alignment and produce slip; remember yaw is a rotation about the normal (vertical) axis. The restoring moment the static stability provided by the fin is the product of the fin area and the moment arm and the moment arm leverage will vary according to the cg position the aircraft's balance.

The area required for the fin has some dependency on the net sum of all the restoring moments associated with the aircraft fuselage and undercarriage side surfaces fore (negative moments) and aft (positive moments) of the cg. Some aircraft have ventral or dorsal fins added to increase their directional stability.

The areas of side surface above and below the cg also affect other aspects of stability.

The similar term 'weathercocking' refers to the action of an aircraft, moving on the ground, attempting to swing into wind. It is brought about by the pressure of the wind on the rear keel surfaces, fin and rudder causing the aeroplane to pivot about one or both of its main wheels. It is usually more apparent in tailwheel aircraft because of the longer moment arm between the fin and the main wheels: although if a nosewheel aircraft is 'wheelbarrowing' with much of the weight on the nose wheel, then there will be a very long moment arm between the nose wheel pivot point and the fin.

Lateral stability

Lateral stability refers to roll stability about the longitudinal axis and ailerons provide the means whereby the aircraft is rolled in the lateral plane. However, unlike the longitudinal and normal planes where the horizontal and vertical stabilisers provide the restoring moments necessary for pitch and yaw stability, no similar restoring moment device exists in the lateral plane.

But let's imagine that some atmospheric disturbance has prompted the aircraft to roll to the left, thus the left wingtip will be moving forward and down, the right wingtip will be moving forward and up. Now think about the aoa for each wing the wing that is moving down will be meeting a relative airflow coming from forward and below and consequently has a greater aoa than the rising wing. A greater aoa, with the same airspeed, means more lift generated on the downgoing side and thus the left wing will stop going further down or perhaps even rise and return to a wings level state. This damping of the roll is known as lateral damping.

So roll stability, except at or very close to the stall, is intrinsic to practically all single-engined light aircraft. (When the aircraft is flying close to the stall the aoa of the downgoing wing could exceed the critical aoa and thus stall, which will exacerbate the wing drop and might lead to an incipient spin condition.

But, and there always seems to be a 'but', when the aircraft is banked other forces come into play and affect the process. If you re-examine the turn forces diagram in the manoeuvring forces module you will see that when an aircraft is banked the lift vector has a substantial sideways component, in fact for bank angles above 45 that sideways force is greater than weight. So we can say that any time the aircraft is banked, with the rudder and elevators in the neutral position, an additional force will initiate a movement in the direction of bank i.e. creating a slip. The aircraft's directional stability will then yaw the nose to negate the slip and the yaw initiates a turn, which will continue as long as the same bank angle is maintained.

There are several design features that stop that slip and level the wings thus promoting lateral stability, for instance placing the wing as high as possible above the cg promotes 'pendulum' stability; the feature usually employed with low wing monoplanes is wing dihedral, where the wings are tilted up from the wing root a few degrees. Another design method is anhedral where the wings are angled down from the wing root, but it is unlikely to be used in light aircraft.

Spiral instability

An aircraft with positive spiral stability tends to roll out of a turn by itself if the controls are centred. Some light aircraft with little or no wing dihedral and a large fin tend to have strong static directional stability but are not so stable laterally. If a sideslip is introduced by turbulence and left to their own devices such aircraft will gradually start to bank and turn, with increasing slip and hence increasing turn rate and rapid increase in height loss. The condition is spiral instability and the process is spiral divergence which, if allowed to continue and given sufficient height, will turn into a high speed spiral dive. Neutral spiral stability is the usual aim of the designer.

It is evident that directional stability and lateral stability are coupled and to produce a balanced turn, i.e. with no slip or skid, the aileron, rudder and elevator control movements and pressures must be balanced and co-ordinated.