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Groundschool – Theory of Flight

Safety: flight at excessive speed


Revision 17a — page content was last changed 20 March 2014
  
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The following notes apply chiefly to three-axis aeroplanes and sailplanes that have been tested and received type certification from a national airworthiness authority. Owner-designed and built aircraft do not go through the certification process; the builder would generally just rely on simple static load tests to partly prove the wing structure only. Also no full flight testing program would be undertaken by a professional test pilot to determine the safe flight envelope and to identify deficiencies. However, the principles apply even if there is no properly established flight envelope data.

The theme common to all problems encountered when moving at very high speed is that there is no warning, and no time to do anything about it! The term 'excessive speed' is entirely relative. In a low-momentum aircraft it might be 70 knots. In an aircraft that cruises at 100 knots, excessive speed may be less than 140 knots.

The only safe procedure is not to push the high-speed end of that aircraft's envelope at any height, however control actuating system deficiencies may produce dangerous aerodynamic reactions at normal speeds.

There is a companion document 'Don't fly real fast' in the 'Decreasing your exposure to risk' guide that includes and expands some of the following material — and should be read.


      Content


13.1 Airframe strength and elasticity

Aircraft structures are designed to be as light as possible with some degree of structural flexibility while still providing adequate strength for the aircraft's operational category. To receive type certification, the design of a general aviation or recreational aircraft must conform with certain standards — among which are the in-flight structural load minimums — for the category in which the aircraft may be operated.

In FAR Part 23, a recognised world standard for light aircraft certification, the minimum load factors that an aircraft at maximum take-off weight [MTOW] must be designed to withstand are:
  • +3.8g to –1.5g (or –1.9g) for the normal operational category (which would include most factory-built recreational aircraft).
  • +4.4g to –1.8g (or –2.2g) for the utility category (which includes most GA, and perhaps some RA, training aircraft).
  • +6g to –3g for the acrobatic (i.e. aerobatic) category.
  • +4g to –2g for the Light Sport Aircraft category manufactured in compliance with ASTM F2245-07 standard specification for design and performance of a Light Sport Airplane.
  • Sailplanes and powered sailplanes are generally certificated in the utility or acrobatic categories of the European Joint Airworthiness Requirements JAR-22, which is the world standard for sailplanes; aerobatic sailplanes have limit loads of +7g and -5g.
For more information see 'Limiting loads and ultimate loads'. There is an increasing risk of failure when exceeding the minimum load factors, and each instance of excessive loading will compound the failure risk. We use load factors in terms of g for convenience, but what we are also considering is total aerodynamic loading — remember that dynamic pressure increases with the square of the velocity; i.e. dynamic pressure = ½rV².

Note:       1. Uncertificated minimum ultralight aircraft, even with their low wing loading of perhaps 12 kg/m², can be overstressed readily just by flying at maximum level speed and increasing g in a pull-up (positive g) or a push-over (negative g).

      2. Many aircraft are type certificated in both normal and utility category, and some are certificated in those plus the acrobatic category. In this case, the MTOW and cg limits are not fixed values, but vary according to the flight operating category. See the table in weight/cg position limitations.

Weight and balance
There are fixed limits to the payload an individual aircraft may carry safely. The payload must be distributed so that the aircraft's balance — the position of the aircraft's centre of gravity — is maintained within calculated limits. In addition, there is a maximum safe operating weight permitted by the aircraft designer. However, for many recreational aircraft, the MTOW will be limited by national legislation, which has nothing to do with aeronautical engineering.

The aircraft's weight and balance very much affect control and stability at high speeds. Excess weight reduces the designed structural load limits, while cg positions outside the designated fore and aft limits may enhance unfavourable reactions to aerodynamic loads, affect stability, reduce controllability, or delay (or prevent) recovery from unusual or high-speed situations.
Aeroelastic effects
Elasticity is a property of certain materials that enables them to return to their original dimensions after an applied stress has been removed, see the notes on 'stress and strain' in the 'Builders guide to safe aircraft materials'.

Elastic structures have a natural frequency of vibration and all aircraft structures exhibit some degree of elasticity; that is, they distort or deform a little, changing shape — flexing, elongating, compressing, bending and/or twisting — under applied aerodynamic loads; each type of distortion produces a particular mode of vibration. Transient structural distortions also contribute to a change in the aerodynamic forces, so the distortions and forces are mutually dependent. This is particularly so with the wings and tailplane. Wings have a low frequency bending mode of vibration where the tips flex up and down (i.e. flap) relative to the wing root, under changing flight loads — in turbulence for example. The degree of oscillation or flapping is more pronounced with high aspect ratio wings. While bending upward the wing adds a vertical velocity* to its forward velocity — the true airspeed — which results in a decreasing angle of attack (aoa) reducing the lift of the up-moving portion of the wing and thus causing an aerodynamic damping of the flapping oscillation. Similarly a downward bending motion results in an increasing aoa, increasing the lift of the down-moving wing and again causing an aerodynamic damping of the flapping oscillation.

*A similar resultant velocity concept to a vertical gust encounter.

Wings also exhibit a higher frequency torsional mode of vibration where they twist about the wing's elastic axis as the centre of pressure moves chordwise and consequently produces a spanwise variation in the aoa and changes the lift force and its distribution. If the centre of pressure moves forward it can then again increase the wing twist, aoa and lift, developing a non-stable situation. Twisting and bending distortions result in independent oscillations or vibrations and alter the effectiveness of lifting surfaces, though structural and inertial forces provide a natural positive damping that normally keeps vibratory energy in check.

The elastic axis is defined as the line along the span of the wing where no torsion occurs when a loading is applied to the wing. A lifting force centred aft of the elastic axis will tend to twist the outer wing leading edge down, reducing aoa and thus aerodynamic force. A lifting force centred forward of the elastic axis will tend to twist the leading edge up, increasing the aoa and the aerodynamic force. The wing aerodynamic centre is usually designed to be close to or behind the elastic axis; if the aerodynamic centre is forward of the elastic axis then wing twist will increase aoa leading to the non-stable situation described in the preceding paragraph.

The degree of torsional distortion is dependent on (1) the area of wing surface affected, (2) the distance between the aerodynamic centre and the elastic axis plus (3) the torsional stiffness (rigidity) of the surface. The torsional stiffness designed into the wing resists twisting, and structures usually revert to the normal status when the load is normalised. Aeroelasticity may lead to some problems at high speed, but reducing elasticity means increasing rigidity, which perhaps involves an unwarranted increase in structural weight. So, aircraft structural engineering must be a compromise between rigidity and elasticity.

[ The next section in the airmanship and safety sequence is the following section Aerodynamic reactions to control system deficiencies or to flight at excessive speed ]





13.2 Aerodynamic reactions to flight at excessive speed

Flutter
Wing structures are akin to a very-low-frequency tuning fork extending from the fuselage. When a tuning fork is tapped, the fork vibrates at a particular frequency; the stiffer the structure, the higher its natural frequency. The natural frequency of a wing or tailplane structure may apply another limiting airspeed to flight operations related to a self-exciting interaction between elastic, aerodynamic and inertia forces that result in 'flutter' of control surfaces and the structure to which the surface is attached.

For example, when the airflow around a wing, tailplane or control surface is disturbed (by aerodynamic reactions, turbulence or pilot inputs) the structure's elastic reactions – twisting and bending – may combine as an oscillation or vibration of the structure that will quickly damp itself out at normal cruise speeds because of the structure's resistance. It is possible that the oscillation does not damp out but is sustained at a constant amplitude (perhaps felt in the airframe as a low-frequency buzz) that is not, in itself, dangerous but may contribute to structural fatigue. At some higher airspeed — the critical flutter speed, where the oscillations are in phase with the natural frequency of the structure — the oscillations will not damp out but will become resonant, rapidly increasing in amplitude. (Pushing a child on a swing is an example of phase relationships and amplification.) This flight resonance – flutter – is very dangerous, and unless airspeed is very quickly reduced, the increasing aerodynamic forces will cause control surface (or even wing) separation within a very few seconds.

In 1966 NASA recorded a 24-second video of an in-flight flutter test on a Piper PA30 Twin Comanche demonstrating how rapidly stabilator oscillations increase in amplitude; Google 'NASA flutter video'.

The following is an extract from an article by William P. Rodden which appeared in the McGraw-Hill Dictionary of Science and Technology; it provides a succinct description of flutter:

"Flutter (aeronautics) — An aeroelastic self-excited vibration with a sustained or divergent amplitude, which occurs when a structure is placed in a flow of sufficiently high velocity. Flutter is an instability that can be extremely violent. At low speeds, in the presence of an airstream, the vibration modes of an aircraft are stable; that is, if the aircraft is disturbed, the ensuing motion will be damped. At higher speeds, the effect of the airstream is to couple two or more vibration modes [e.g. bending plus twisting ... JB] such that the vibrating structure will extract energy from the airstream [JB's emphasis]. The coupled vibration modes will remain stable as long as the extracted energy is dissipated by the internal damping or friction of the structure. However a critical speed is reached when the extracted energy equals the amount of energy that the structure is capable of dissipating, and a neutrally stable vibration will persist. This is called the flutter speed. At a higher speed, the vibration amplitude will diverge, and a structural failure will result."


So, flutter is a vibrational instability that (if the structure is not sufficiently stiff) is generally related to the aerodynamic forces and thus the airspeed; but there are many flutter modes. Providing high torsional stiffness in an airframe structure — particularly a high aspect ratio wing — may incur weight penalties that are unacceptable for those aircraft whose MTOW is limited by national legislation, rather than normal design parameters.

Mass inertia and the status of the control actuation systems are also involved in flutter development. Consequently ailerons, elevator or stabilator and the rudder (in that order) should be considered for mass-balancing, i.e. their centre of gravity is made coincident with their hinge centre line. This limits the mass moment of inertia so that the control surface does not rotate about its hinge line when the main structure moves; e.g. when the wing bends upward the aileron does not rotate downward but maintains the same floating position relative to the wing. It may be acceptable for the control surface to be over-balanced; i.e. its cg is slightly forward of the hinge line but under-balancing may achieve little. Mass-balancing of the control surfaces, including the rudder, should prevent flutter of that control surface, but the possibility of, for example, wing flexing/twisting flutter might still exist.

Mass-balancing of ailerons might be accomplished by attaching moulded lead weight/s, or a lead-filled steel tube, within the nose of the control structure forward of the hinge centre line. As the moment arm, between that centre line and the centroid of the added weight, could be quite short the balance mass needed could be twice the mass of the unweighted control, so it is possible the end effect could be close to tripling the total weight of the aileron. Mass balancing of elevators might be achieved using a weight on an arm contained within the tail structure or within control horns, while a rudder might also be balanced by a weight within a control horn.

The friction within aircraft control surface actuating systems adds to the damping of control surface oscillations and this damping ability increases as the oscillation frequency increases. So, it is important that all parts of the control actuating systems are made as rigid and secure as possible and checked to ensure that rigidity is always maintained so that control surfaces cannot deflect without a corresponding movement in the cockpit control. The possibility of destructive flutter increases if any of the following conditions exist:
  • wear in control surface hinges, pulleys, fairleads or guides
  • lack of tension, wear or slop in actuating pushrods/cables/conduited push-pull cables/cranks/torque tubes/turnbuckles
  • safetying wire improperly installed
  • faulty trim tabs.
Also water or ice inside control surfaces or absorbed within a foam core; mud outside; additional surface coatings applied after mass balancing; tail buffeting caused by unsteady airflow related to, for example, alterations to the engine exhaust system; or other system anomalies that alter structural reactions also play a role in flutter development. Also see AC43.13-1B Chapter 7 'Aircraft hardware, control cables, and turnbuckles'.

This is an extract from an RA-Aus accident investigation report:

"(Witnesses) observed the aircraft in a steep dive at what appeared to be full power. The port wing appeared to detach from the aircraft ...

The wing that tore away from the fuselage had the attach points intact but had pulled the mountings out of the top of the cockpit. This action would have released the door, which landed close to the wing. The wings were intact but the ailerons were detached. There was no delamination of the fibreglass structure. The ailerons were not mass balanced.

The (prototype) aircraft was a conventional design being a high wing, monoplane of composite construction. While the fuselage was a proven design the pilot /builder had designed his own wing including the aerofoil section. The workmanship was excellent and there is no evidence of any lack of structural integrity.

The eyewitnesses reported seeing a sort of 'shimmying' from the aircraft. It is believed that this shimmying was aileron flutter which led to the detaching of both ailerons. This same flutter condition would account for the massive forces required to detach the wing from the aircraft in the manner that occurred. Flutter could have been triggered by the wing aerofoil design combined with the manoeuvre the pilot was conducting or from the aileron control design ...

The aircraft suffered a massive inflight structural failure almost certainly caused by severe aileron flutter and the aircraft speed in the dive. Any flutter would have been exacerbated by the lack of mass balancing."
Vne — the standard limiting airspeed
If an aircraft is operated within its specified flight envelope, observing the limiting accelerations and control movements, and maintaining airspeed commensurate with atmospheric conditions, then the only possibilities of in-flight structural failure relate to:
  • improper modification, repair or repainting of the structure
  • control actuating system deficiencies
  • cumulative strain, or minor damages, in ageing aircraft
  • failure to comply with the requirements of airworthiness notices and directives
  • poor care and maintenance of the airframe.
Flight at airspeeds outside the envelope (or at inappropriate speeds in turbulent conditions, or when applying inappropriate control loads at high speed) is high risk and can lead to airframe failure. Vne is the IAS, specified by the designer, which should never be intentionally exceeded in a descent or other manoeuvre. For a fuller description of Vne and how it is calculated see 'How fast is too fast?' in the 'Decreasing your exposure to risk' tutorial.
Wing divergence
Wing divergence refers to a state where — at very low angles of attack and high speed (when the nose-down pitching moment is already very high) — pressure centres develop, which push the front portion of the wing downward and the rear portion upward. This aerodynamic twisting action on the wing structure — while the rest of the aircraft is following the flight path — further decreases the aoa and compounds the problem. The action finally exceeds the capability of the wing/strut structure to resist the torsional stress, and causes the wing to separate from the airframe with no warning. This could be induced if turbulence is encountered at high speed.
Control reversal
As airspeed increases, control surfaces become increasingly more effective. They reach a limiting airspeed where the aerodynamic force generated by the ailerons, for example, may be sufficient to twist the wing itself. At best, this results in control nullification; at worst, it results in control reversal. For example, if the pilot initiates a roll to the left, the downgoing right aileron will twist the right wing, reducing its aoa and resulting in loss of lift and a roll to the right, probably with asymmetric structural loads. All of which would make life difficult when attempting to roll the wings level during recovery from a high-speed dive.

Many of the uncertified minimum ultralights, and perhaps some of the certificated aircraft, have low torsional wing rigidity. This will not only make the ailerons increasingly ineffective with speed (and prone to flutter), but will also place very low limits on Vne and g loads. Vne may be so low that it can be achieved readily in a shallow descent at 75% power.
Effect of wing washout
Wings incorporating geometric washout have a significantly lower aoa towards the wing tips. At high speed when the wing is flying at low aoa, there are high aerodynamic loads over the wings. However, the outer sections could well be flying at a negative aoa and the reversed load in that area will bend the wingtips down, possibly leading to outer spar fracture. See the accident technical report below.
Vertical gust shear and gust loads
The effective aoa of an aircraft encountering an atmospheric gust with a significant vertical component (updrafts, thermals, downdrafts, microbursts, macrobursts and lee waves) will be increased momentarily if the air movement is upward relative to the aircraft's flight path, or decreased momentarily if the air movement is downward. Thus, an updraft will increase CL and lift, increasing the aerodynamic loading and lead to an upwards acceleration of the aircraft. The magnitude of the acceleration is determined largely by the change in aoa, the aircraft speed (the higher the speed, the greater is the g load), the design wing loading and the aspect ratio. The lower the design wing loading and/or the higher the aspect ratio, the greater is the change in load factor for a given increase in aoa and the easier it is to overstress the wings at high speed. The effects of shear and gust loads are expanded in the section on wind shear and turbulence.
Other effects
It is not just the preceding items that may be a problem at high speed. The maximum speed may be limited by the ability of the fuselage to withstand the bending moments caused by the loads on the tailplane necessary to counter the wing's substantial nose-down pitching moment at very low aoa, or the aoa changes due to vertical gust shear, or the extreme loads caused by a high speed pull-up. Applying rudder in a high speed pull-up applies twisting loads to the rear fuselage. Even a very small bird can cause severe damage in a high-speed bird-strike.

When nearing the zero-lift angle of attack in a high-speed descent, many cambered wings suddenly experience a strong nose-down pitching moment and the aircraft will 'tuck under' rapidly; this will certainly make the pilot wish she/he was somewhere else. The symmetrical aerofoil wings often used in aerobatic aircraft don't have this problem. Also, the possibility of a runaway propeller in a high-speed dive is always there for those aircraft with a constant-speed propeller governor or perhaps an in-flight adjustable system.

The following is a condensed version of an Australian Transport Safety Bureau Technical Analysis Occurrence Report. Note: the Coroner's findings in relation to the fatal accident near Atherton does not support any view that the accident was caused by pilot mishandling; rather, the Coroner's "preference is towards port side wing tip separation as a consequence of the un-airworthy state of the aircraft ..."

"An Airborne Edge microlight aircraft impacted terrain during a 2005 flight to Atherton, in Far North Queensland. The pilot, the sole occupant of the aircraft, was fatally injured. In 2006 a similar Airborne Edge aircraft impacted terrain at Cessnock, New South Wales, also fatally injuring the pilot, the sole occupant of the aircraft.

In both instances, RA-Aus initiated safety investigations to determine contributing factors to these accidents. During the course of these investigations, similarities in the structural failures of both aircraft were observed. In addition, a third accident involving an Airborne aircraft registered with HGFA with similar structural failure was identified. This accident had occurred in 1996 in Hexham, NSW.

In order to determine possible connections between all three accidents, ATSB was asked to conduct technical examination and analysis on recovered parts from the Atherton and Cessnock accidents, to assist the RA-Aus investigation. Information regarding the 1996 accident was taken from coronial findings.

In all three accidents, the failure of the main wingspars had occurred near the wingtip. Qualitative analysis of the structural design and loading of the part during this safety investigation and the examination of the coronial findings from the Hexham accident, revealed that all main wingspars had failed under negative G loading. Such loading was likely if the aircraft entered or encountered flight conditions outside the manufacturer's specified flight envelope. Examination of material characteristics of the failed wingspars did not show evidence of material deficiencies that could have contributed to these accidents.

The manufacturer's operating handbook prohibited all aerobatic manoeuvres including whipstalls, stalled spiral descents and negative G manoeuvres. The manual specified that the nose of the aircraft should not be pitched up or down more than 45 degrees, that the front support tube of the microlight and the pilot's chest limit the fore and aft movement of the control bar, and that the aircraft should not exceed a bank angle of 60 degrees.

Review of photographs of the Airborne Edge, indicate that the wing adopts a degree of twist while in flight. Twist will effect the load distribution by shifting some of the lift from the tips inboard (i.e. more lift is generated in the middle of the wing). Given the structural restraint of the tip struts and battens located at the tip of the trailing edge of the wing, the aerofoil at the wing tip must adjust and try to align with the relative airflow. This results in a smaller amount of lift generated near the wing tips due to a reduced angle of attack to the relative airflow."
(Or an aoa reduced below the zero lift aoa, i.e. reversed lift ... JB)

[ The next section in the airmanship and safety sequence is the following section Recovery from flight at excessive speed ]





13.3 Recovery from flight at excessive speed

Generally, excessive speed can only build up in a dive, although just a shallow dive can build speed — and rate of descent — quite quickly. The table below is a calculation of the rate of descent after a few seconds at dive angles of 10°, 30° and 45° for a moderately slippery light aircraft.

Dive angleAirspeed (knots)Rate of descent (fpm)
10° 100 1700
30° 150 7500
45° 180 12 500


Recovery from an inadvertent venture into the realm of flight near, or even beyond, Vne is quite straight-forward, but requires pilot thought and restraint in initiating recovery procedures, particularly so if the aircraft is turning whilst diving. Considerable height loss will occur during recovery, so the restraint is required when terra firma is rapidly expanding in the windscreen.
  1. Halt the buildup in airspeed by closing the throttle.

  2. Unload the wings to some extent by moving the control column to the neutral position or just aft of it. Keep the slip ball and the ailerons centred — the twisting action of excess rudder at very high airspeed may strain the tailplane and rear fuselage.

  3. Gently roll off any bank while using coordinated rudder; this will ensure the total lift vector is roughly vertically aligned. Maintain the control column position at neutral or slightly aft to avoid any asymmetric loading arising from simultaneous application of aileron and elevator at high speed.

  4. When the wings are level, start easing back on the control column until you are pulling the maximum load factor for the aircraft : +3.8g or +4.4g, perhaps less for some ultralights. Do not pull back so harshly that the aircraft enters a high-speed stall. Hold the applied loading near the maximum until the aircraft's nose nears the horizon, then level off. The aircraft will have sufficient momentum to reach this position before opening the throttle.

    If you have ample height at the commencement of recovery, then there is no need to pull such high g — particularly if the atmosphere is bumpy when gust loads, added to the high manoeuvring g, may prove excessive. In aircraft not certified for aerobatics, it is best to wait until airspeed is less than Va before pulling g — if circumstances permit.

A problem with this procedure is that most light aircraft do not have an accelerometer [g-meter] fitted, so it is difficult to judge the g being pulled. However, if properly executed 60° steep turns are practised, then some idea of the 2g load on your own physiology can be gained. At the higher end of acceleration the average fit person will probably start feeling the symptoms of greyout by 4g.

[ The next section in the airmanship and safety sequence is the following section Recovery from a spiral dive ]





13.4 Recovery from a spiral dive

In a well-developed spiral dive, the lift being generated by the wings (and thus the aerodynamic loading) to provide the centripetal force for the high-speed diving turn, is very high, and much of it is directed inward. The aircraft is near the extremes of its design flight envelope, with very high aerodynamic loading and very high speed, well above Va. The pilot must be very careful in the recovery from such a dive, or damaging structural loads will be imposed. If rearward stick force is applied to pull the nose up while the aircraft is turning, the result will be a tightening of the turn and further lowering of the nose, thus dramatically increasing the applied loading or possibly prompting a very punishing high-speed stall. Also aileron to level the wings must be applied with restraint, the aileron on the lower wing will increase the aerodynamic force on the portion of wing ahead of it and move the centre of force further towards that wingtip, so increasing the moment of force at the spar root. The downgoing aileron is also applying a twisting force to the outer wing structure. Sudden or excessive aileron deflection at airspeeds well above Va could well lead to outer wing or full wing separation.

Control reversal could also be a factor, see 'High-speed control reversal: will it always roll in the direction you want?'

The recommended procedure — for a fixed undercarriage aircraft without propeller pitch control — is:
  • Reduce power.
  • Carefully centralise controls: the forward movement of the control column will partially unload the wings.
  • Smoothly level the wings with aileron while the rudder and elevators are held in the neutral position. As the wings become level with the aircraft still diving at high speed, much of the lift that was providing the centripetal force will now be directed vertically (relative to the horizon); and if up elevator is applied, the aircraft may start a high g pitch-up — even into a half loop.
  • Thus to prevent this, the pilot must hold the elevators in the neutral position while rolling level or even applying further FORWARD stick pressure — before applying aileron — to reduce aoa; but not below the zero-lift aoa, i.e. the load factor must remain positive. At high speed, the stick force required will be high, but the position of the elevator trim should not be altered. Also it is probably not wise to apply two controls simultaneously at very high speeds because of the consequent asymmetric airframe loading.


Read this Australian Transport Safety Authority analysis of an inflight breakup most likely caused by excessive control force during spiral dive recovery.

The theme common to all problems encountered when moving at very high speed is that there is no warning and little time to do anything about it! The only safe procedure is not to push the high-speed end of the envelope at any height: make gentle, smooth control movements and avoid asymmetric flight loads and never put yourself in the position where you may encounter non-visual flight conditions at low levels.

[ The next section in the airmanship and safety sequence describes 'Risk management' ]





13.5 Notes: compressibility of airflow and Mach number

These notes have little value for the recreational aviator, but are included for interest.
  • Except for a slight EAS correction to IAS/CAS, and the possible propeller effects, the compressibility/elasticity of airflow (i.e. the density change resulting from pressure disturbances) does not have any significant airframe aerodynamic effects for aircraft operating at speeds below 200 knots TAS and altitudes below 10 000 feet. Pressure disturbances, or waves, propagate through the atmosphere in all directions, at the speed of sound.

  • Mach 1.0 is the notation for the speed of sound. For aerodynamic purposes airflow speeds are classified within five ranges:
    Hypersonic flow — airflows greater than Mach 5.0
    Supersonic flow — airflows between Mach 1.5 and Mach 5.0
    Transonic flow — airflows between Mach 0.8 and Mach 1.5
    Subsonic flow — airflows between Mach 0.3 and Mach 0.8
    Incompressible flow — airflows below Mach 0.3

    The term 'incompressible flow' doesn't mean that air is incompressible; it just indicates that at flow speeds below Mach 0.3 (30% of the speed of sound or about 200 knots TAS), local density variations within the flow — due to compressibility — are insignificant; so aerodynamicists can assume constant density within the flow.

  • At subsonic velocities, significant density changes may occur in the airflow around wings, which will produce flow separation and a turbulent wake — wave drag. The associated drag coefficient builds rapidly at airspeeds above Mach 0.75 then reduces as Mach 1.0 is exceeded.

  • The speed of sound in the atmosphere varies with air temperature. The Mach number is the measure of an aircraft's TAS in relation to the ambient speed of sound. For example, Mach 0.6 indicates that the aircraft's true airspeed is 60% of the speed of sound.

  • The speed of sound is proportional to the square root of the absolute temperature. In the ISA, Mach 1.0 at sea level = 663 knots, and temperature at sea level = 15 °C [288 K]. Thus, if the temperature = −36 °C (237 K) then the ambient Mach 1.0 = 663 × √237/√288 = 601 knots. Thus, Mach 0.60 at 15 °C would be 398 knots TAS, while Mach 0.60 at −36 °C would decrease to 360 knots TAS. Below the tropopause — the speed of sound decreases as altitude increases.

  • A machmeter is an instrument that measures and compares the speed of the aircraft and the speed of sound, using the outside air temperature. It adjusts for actual air density but is still subject to the same position errors as the ASI. The machmeter is usually incorporated within an ASI; the numeric Mach appears in a small window within the ASI dial.

  • You may see references to design diving speed presented as 'Vd/Md' which indicates the speed may be expressed as IAS or Mach number. Other reference airspeeds are presented in similar fashion.


For interest, the following table is the maximum permissable speed/altitude for a late 1940s/early 1950s piston-engined naval fighter — the Seafire 47:

Altitude feetMax. IAS knotsMach no.Approx. TAS
Sea level – 10 0004550.78505
10 000 – 15 0004100.78495
15 000 – 20 0003750.78485
20 000 – 25 0003400.78472
25 000 – 30 0003000.78459
30 000 – 35 0002700.78448
35 000 +2400.78432


Subsonic jet transport aircraft are designed to cruise close to their maximum allowable speed — Vmo/Mmo. Vmo is the limiting indicated airspeed and Mmo is the limiting Mach number. Mmo is probably between Mach 0.80 and Mach 0.85. In normal operations the limiting airspeed is Vmo, up to a change-over pressure altitude (perhaps around 25 000 feet). Above this altitude Mmo becomes the limiting speed value because of compressibility problem restraints.

Vmo could be shown as a fixed red line on the ASI (or 'Mach/Airspeed Indicator') but, because the speed of sound decreases as altitude increases, Mmo can't be represented by a fixed marking on the indicator. So, a moving red-and-white striped pointer, the 'barber pole', shows the limiting Vmo/Mmo varying with altitude. It shows the IAS corresponding to the lower of Vmo or Mmo for the current altitude. For further explanation read this Boeing flight operations review document.


The next module in this Flight Theory Guide discusses loss of control in low level turns.


Groundschool – Flight Theory Guide modules

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

| 3. Altitude & altimeters | 4. Aerofoils & wings | 5. Engine & propeller | 6. Tailplane surfaces |

| 7. Stability | 8. Control | 9. Weight & balance | 10. Weight shift control | 11. Take-off considerations |

| 12. Circuit & landing | [13. Safety: flight at excessive speed] | 14. Safety: control loss in turns |


Supplementary documents

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



Copyright © 2004 — 2014 John Brandon     [contact information]