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Groundschool – Theory of Flight


Revision 13 — page content was last changed 21 March 2013

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This module examines how an aircraft responds to changes in relative airflow, initiated by atmospheric turbulence, by unintentional pilot input or by other disturbances, including power changes. The subject is complex and only a simplified overview is presented here.

Earlier it was stated that an aeroplane has six degrees of freedom of movement — three rotational (hence 'three-axis') and three translational. It is important to grasp that the translational movements are not rotations about the cg but bodily movements sideways (slipping) or vertically (rising/sinking). Rising/sinking or mushing are associated with aerodynamics and stability, and climbing/descending are associated with power in that they are forward velocities angled up or down.


7.1 Concepts of stability and trim

The aircraft's response to disturbance is associated with the inherent degree of stability; i.e. self-correction built in by the designer — in each of the three axes — that eventuates without any pilot action. Another condition affecting flight is the aircraft's state of trim — or equilibrium where the net sum of all forces equals zero, i.e. the aerodynamic forces are balanced and the aircraft maintains a steady flight condition when cruising, climbing or descending. Some aircraft can be trimmed by the pilot to fly 'hands off' for straight and level flight, for climb or for descent. But very light aeroplanes generally have to rely on the state of trim built in by the designer and adjusted by the rigger, although most have a rather basic elevator trim device, but no rudder or aileron trim facility. If natural trim is poor — and perhaps it flies with one wing low — inherent stability may maintain equilibrium with that wing-low attitude and not restore the aircraft to a proper wings-level attitude. In which case, the pilot has to maintain a slight but constant control column deflection to hold the wings level, which can be quite annoying.

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 stabilitystability in roll, directional stabilitystability in yaw and longitudinal stabilitystability in pitch. The latter is the most important stability characteristic. Lateral and directional stability have some inter-dependence.
Degrees of stability
An aircraft will have differing degrees of stability about each axis; here are a few examples:
  • When disturbed 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 a sport and recreational aircraft just to be reasonably stable so it is comfortable to fly. If overly stable they tend to be sluggish in manoeuvring and heavy on the controls; i.e. significant control force is required to make it deviate from its trimmed state. 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 a bumpy atmosphere.

  • The normally stable 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 overrun it, then start a series of diminishing damping oscillations about the original flight state. This damping process is usually referred to as dynamic stability (or the tendency over time) 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, and if there were no other disturbances and the pilot did not intervene, the aircraft would just continue 'porpoising'.

  • 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 WWII day fighters were generally designed to be just stable longitudinally, neutrally stable laterally and positively stable directionally.

7.2 Longitudinal stability

Longitudinal stability is associated with the restoration of aoa to the trimmed aoa after a disturbance changes it; i.e. if a disturbance pushes the nose up the tailplane will counter with a nose-down pitching moment. In section 6.2 we discussed the provision of a tailplane to act as a horizontal (longitudinal) stabiliser. Before we go any further we need to look at another structural aspect of the airframe.
Angle of incidence
Angle of incidence is a term that is sometimes mistakenly used as synonymous with wing angle of attack; however, the former cannot be altered in flight except in weight-shift control aircraft (hang gliders and trikes). 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-to-wing mounting so that the fuselage is aligned to produce the least drag when the wing is flying at the cruise aoa. Wings that 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 — see 'Stuff you don't need to know'.

Incidence may also be called the 'rigger's incidence' or some similar expression carried over from the earlier days of aviation. For ultralight aircraft, incidence is something that should be checked at regular inspections by a qualified person.
Longitudinal dihedral
An angle of incidence is also calculated for the horizontal stabiliser with reference to the FRL. 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. The angle of the line of thrust is also expressed relative to the FRL.

Positive longitudinal dihedral — where the wing incidence is greater than that of the stabiliser — will help control a stall by ensuring that, if the aircraft approaches a stall, the wing will stall before the tail, giving the tail a chance to drop the nose. The tailplane of most very light 3-axis control aeroplanes is mounted in a position where the wing downwash may effect the angle of attack of the tailplane and that downwash angle increases as the wing angle of attack increases.

It is the horizontal stabiliser area and moment arm that 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. If the cg lies outside its limits, the aircraft will be longitudinally unstable.

We learned in section 2.6 that 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. In some ultralights a designer/rigger might pick Vbg — best power-off glide speed — as the natural airspeed so that, lacking pilot input, the aircraft will naturally attempt to adjust its aoa to the Vbg aoa, whether power is on or off.
Oscillating motions
It is possible that an aircraft, properly trimmed for continuing level flight, may develop a 'phugoid' motion if affected by a sharp disturbance. A phugoid cycle is a pitch increase followed by a pitch decrease without any discernible aoa change, i.e. a short climb during which speed decreases and the nose drops into a short descent during which speed increases and the cycle starts again. The aircraft is trading kinetic energy for an increase in the potential energy of height, using the latter to return to the trimmed airspeed in the descent; the cycle time for one oscillation in a very light aircraft might be 20 seconds or so. The oscillating motion issometimes described as 'porpoising'.

If the pilot doesn't intervene and the aircraft is phugoid stable the phugoid cycles will damp out after a few diminishing oscillations. If the aircraft is phugoid unstable the oscillations will diverge and the pilot must intervene.

The longitudinal dihedral and the tail moment arm affect phugoid stability.

7.3 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. In section 6.3 we discussed the provision of a fin to act as a directional stabiliser. The restoring moment — the static stability — provided by the fin is the product of the fin area and the moment arm. 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. For instance, the Breezy has, except for the pilot's body, very little lateral moment ahead of the cg because of the open frame fuselage; thus a small fin provides all the moment necessary for directional stability. But if the pilot and passenger were enclosed in a cockpit or pod, with a much greater side surface, then the negative moments would be greater and consequently the fin area would have to be greater. If the pilot removes his/her feet from the rudder pedals the rudder, will 'float', aligning itself with the relative airflow and thereby reducing the restoring moment of the fin.

The directional stability of very light aircraft with a lot of forward keel area — such as those with a cockpit pod and a 'boom' in place of a rear fuselage — may be 'conditional'; i.e. it is sensitive both to the position of the cg within its normal range and to the amount of sideslip. This is because the negative lateral forces of the pod are very much greater than the positive lateral forces of the boom and fin. Thus, beyond a certain angle of slip the moments change, positive stability is changed to neutral stability and yaw becomes locked in. It might also be associated with the fin stalling at high sideslip angles.

The most noticeable symptom to the pilot is aerodynamic rudder overbalance (or 'rudder force reversal' or 'rudder lock') — where the rudder moves to full deflection without any additional pilot input, or doesn't return to the neutral position when the rudder pedal pressure is released, or the pedal force has to be reversed as sideslip angle is increased. It may require significant opposite rudder input, and probably an increase in airspeed, to return to the normal state.

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

The 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, which cause 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 nosewheel, then there will be a dangerously long moment arm between the nose wheel pivot point and the fin.

7.4 Lateral stability

Lateral stability refers to roll stability about the longitudinal axis; in section 4.10 we established that 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, and 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 a little, although pilot action is usually needed to get back to a wings level state. This damping of the roll is known as lateral damping.

So roll stability, except when 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. See the stall/spin phenomenon.)

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. We know from the section 7.3 that 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 the slip and level the wings, thus promoting lateral stability. For instance, placing the wing as high as possible above the cg increases so-called 'pendular stability', (The stability due to the high wing is not really pendulum stability such as that applicable to powered parachutes.) Wing dihedral* is usually employed with low-wing monoplanes (and to a lesser degree of tilt with high wings), where the wings are tilted up from the wing root a few degrees. A swept-back wing format is used with trikes. 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, although the powered parachute wing utilises an anhedral arc for stability.

(*'Dihedral' is a mathematical term denoting the angle between two intersecting planes.)

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 slip is introduced by turbulence or by the pilot, such aircraft — left to their own devices — will gradually start to bank and turn — with increasing slip and nose drop — and hence increasing turn rate and rapid increase in height loss. Neutral spiral stability is the usual aim of the designer. The turning process starts slowly in aircraft with slight spiral instability but leads to spiral divergence which, if allowed to continue and given sufficient height, will accelerate into a high-speed spiral dive. This often occurs when a pilot without an instrument flight rating strays into cloud where all visual cues are lost. In that condition it is known as the 'graveyard spiral'.

Inadvertent entry into a fatal spiral dive, leading to inflight breakup, can happen even with experienced IFR pilots, see this Australian Transport Safety Bureau report.

It is evident that directional stability and lateral stability are coupled (i.e. rotation about one axis prompts rotation about the other) 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 coordinated.

Dutch roll
Induced motion in the lateral plane generally brings about a coupled motion in the directional plane, and vice versa. Dutch roll is a phenomenon in level flight where a disturbance causes a combined yaw and roll followed by a return to the level flight condition then a yaw and roll to the other side: the oscillations continuing until damped out. In a very light aircraft the time for each cycle might be 5 to 10 seconds. The motion is quite uncomfortable, viewed from the cockpit the wingtips complete a circular motion against the horizon as does the nose. Pilot intervention is by use of rudder.

7.5 Trim and thrust

We have covered above the reaction of the aircraft to changes in relative airflow whether induced by the pilot or minor atmospheric turbulence. We know from sections 1.8 and 1.9 that if an aircraft is properly trimmed for cruise flight and we increase thrust then it will climb; and if we reduce thrust it will descend. But how this eventuates is not at all straightforward. The reaction to changing power, without the pilot touching the control column, depends on whether the cg is above, below or inline with the line of thrust; in the Breezy, the cg is below the thrust line. The thrust line is best located so that it passes close to the vertical cg position to minimise the initial pitching moments associated with power changes.

The placement of the horizontal and vertical stabilisers, in relation to the propeller slipstream and to the wing downwash, affects flight performance and particularly flight at slow speeds — because then the total air velocity within the slipstream tube is nearly double that outside the tube; also the slipstream is rotating, and will thus impart a sideways moment to the fuselage and vertical stabiliser. Effects on individual aircraft types vary according to the designer's inbuilt compensations: for example, if the horizontal stabiliser operates in the wing root downwash airflow, then when the wing root stalls and the downwash becomes turbulent the stabiliser might undergo an abrupt change in aoa (and thus in its stability restoring moment). Or if the horizontal stabiliser operates substantially outside the downwash but if it is in the path of the turbulent flow from the stalled wing, it will then lose part of its aerodynamic force.

If a modification is made to that design, even a seemingly minor change, the consequential effect on stability may be quite surprising. To illustrate the point, I suggest you read an "airworthiness report regarding (among other factors contributing to general stability problems) a small change made in relocating the exhaust manifold of a Thruster that, at a particular aoa, promoted turbulent flow over the upper wing surface, which then extended to the horizontal stabiliser, and reduced the stabilising moment imparted by that surface.

The next module in this Flight Theory Guide deals with aspects of aircraft control.

Stuff you don't need to know
  • The term 'decalage' (French = gap or shift forward/back) relates to the difference in the angles of incidence of the upper and lower mainplanes of a biplane. Decalage is now occasionally used as synonymous with longitudinal dihedral.

  • The angle of incidence has some effect on the pilot's view over the nose. A very few naval aircraft designs have included 'variable incidence wings' where the angle of incidence could be changed by the pilot during flight, within a range of say 2–15°, using electric motors. Such aircraft included leading edge slats as a high-lift device.The idea was to take full advantage of the high maximum CL and consequent low speed, during the landing approach, without having the fuselage cocked up at a high angle blocking the view. As aoa increased and the aircraft slowed, the pilot wound the fuselage down, so that it remained more or less level during the approach and thus provided a better view of the flight deck! Variable incidence wings were also used with one of the post-WWII Supermarine amphibian designs.

Groundschool – Flight Theory Guide modules

| Flight theory contents | 1. Basic forces | 1b. Manoeuvring forces | 2. Airspeed & air properties |

| 3. Altitude & altimeters | 4. Aerofoils & wings | 5. Engine & propeller performance | 6. Tail assembly surfaces |

| [7. Stability] | 8. Control | 9. Weight & balance | 10. Weight-shift control |

| 11. Take-off considerations | 12. Circuit & landing | 13. Flight at excessive speed |

Supplementary documents

| Operations at non-controlled airfields | Safety during take-off & landing |

Copyright © 2000-2012 John Brandon     [contact information]

Page edited 2008 by RA-Aus member Dave Gardiner www.redlettuce.com.au