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Groundschool – Theory of Flight

and the properties of air

Rev. 83 — page content was last changed
October 10, 2007
[small additions to V-speeds text]

Module content

Atmospheric density, which decreases with height, affects lift generation and aircraft performance; as does the angle of attack at which the aircraft is flown. In unaccelerated flight there is a relationship between airspeed and angle of attack so, in light aircraft, the airspeed indicator instrument acts as a very limited angle of attack indicator. From this comes the need to establish a safe aircraft flight envelope within which a range of critical and best performance airspeeds are defined.

2.1 The atmospheric pressure gradient

The random molecular activity or internal kinetic energy within a parcel of air is known as the static pressure and is proportional to the absolute temperature. (Absolute temperature is expressed in kelvin units [K]. One K equals one °C and zero degrees in the Celsius scale is equivalent to 273 K.)

When in contact with an object (an aircraft wing for example) the static pressure exerts a force on that object at right angles to all the exposed non-porous surfaces; measured in newtons per square metre [pascals] of surface. Air pressure is usually reported as hectopascals [hPa] for meteorological purposes: one hectopascal equals 100 N/m² [or one millibar].

Atmospheric pressure reflects the average density ( i.e. mass per cubic metre), and thus the weight, of the column of air above a given level; so the pressure at a point on the earth’s surface must be greater than the pressure at any height above it, in that column. An increase in surface pressure denotes an increase in mass, not thickness, of the column of air above the surface point. Similarly a decrease in surface pressure denotes a decrease in the mass. The air throughout the column is compressed by the weight of the atmosphere above it, thus the density of a column of air is greatest at the surface and decreases with altitude.

However a warmer air column will be thicker, i.e. extend further upwards, than a cooler air column with the same surface pressure; thus a particular pressure level will be at a higher elevation in the warmer column. Which means that the level in the atmosphere at which any particular pressure occurs is also dependent on the temperature (or thickness) of the air column.

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2.2 Atmospheric density

The average density of dry air in temperate climates is about 1.225 kg/m³ at mean sea level, decreasing with altitude.

There are several gas laws which relate the temperature, pressure, density and volume of air. However the equation most pertinent to aeronautical needs is the equation of state:

   r = P/RT    where:
  r (the Greek letter rho) = air density, expressed in SI units as kg/m³
  P = the static air pressure in hectopascals
  R = the gas constant = 2.87
  T = the air temperature in Kelvin units = °C + 273

We can calculate the ISA standard sea level air density, knowing that standard sea level pressure = 1013 hPa and temperature = 15 °C or 288 K

  i.e. Air density = 1013 / (2.87 × 288) = 1.225 kg/m³

However if the air temperature happened to be 30 °C or 303 K at the same pressure then density would = 1013 / (2.87 × 303) = 1.165 kg/m³ or a 5% reduction.

By restating the equation of state: P = RrT it can be seen that if density remains constant, pressure increases if temperature increases.

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2.3 The ICAO International Standard Atmosphere

   The International Civil Aviation Organisation's International Standard Atmosphere [ ISA ] provides a fixed standard atmospheric model used for many purposes among which are the uniform assessment of aircraft performance and the calibration of some aircraft instruments. The model is akin to the average condition in mid-latitudes but contains the following assumptions:
  • dry air is assumed throughout the atmosphere
  • the mean sea level pressure = 1013.25 hPa
  • the msl temperature = 15 °C [288 K]
  • the tropopause is at 36 090 feet [11 km] and the pressure at the tropopause = 226.3 hPa
  • the temperature lapse rate to 36 090 feet = 6.5 °C per km or nearly 2 °C per 1000 feet
  • the temperature between 36 090 and 65 600 feet [20 km] remains constant at –56.5 °C.
The table below shows a few values derived from the ISA. Those pressure levels noted with a flight level designator are standard pressure levels used for aviation weather purposes, particularly thickness charts.

PressureFlight levelTemperatureAir densityAltitude
hPa °C kg/m³feet
1013   15 1.225 msl
1000   14.3 1.212 364
950   11.5 1.163 1773
900   8.6 1.113 3243
850 A050 5.5 1.063 4781
800   2.3 1.012 6394
750   -1.0 0.960 8091
700 A100 -4.6 0.908 9882
650   -8.3 0.855 11 780
600 FL140 -12.3 0.802 13 801
550   -16.6 0.747 15 962
500 FL185 -21.2 0.692 18 289
450   -26.2 0.635 20 812
400 FL235 -31.7 0.577 23 574
350   -37.7 0.518 26 631
300 FL300 -44.5 0.457 30 065
250 FL340 -52.3 0.395 33 999
200 FL385 -56.5 0.322 38 662
150 FL445 -56.5 0.241 44 647
100   -56.5 0.161 53 083

   Not immediately apparent from the ISA table is that the pressure lapse rate starts at about one hPa per 28 feet, averaging around one hPa per 30 feet up to the 850 hPa level, then slowing to 40 feet per hPa at the 650 hPa level, 50 feet at the 450 hPa level, 75 feet at the 300 hPa level and so on, however, this provides a useful rule of thumb:

Rule of Thumb #1

    "An altitude change of 30 feet per hPa can be assumed for operations below 10 000 feet."

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2.4 Bernoulli's principle and the continuity equation

Daniell Bernoulli (1700-1782) was a Swiss mathematician who propounded the principle that for a given parcel of freely flowing fluid the sum of kinetic energy, gravitational potential energy and static pressure energy always remains constant. For aerodynamic purposes the gravitational potential energy can be ignored; kinetic energy = ½ m V² where m = mass and density [r] is mass per unit volume thus dynamic pressure is kinetic energy per unit volume and static pressure, as explained above, is internal kinetic energy per unit volume, so Bernoulli's principle can be reduced to:

      ½ r V² [dynamic pressure] + P [static pressure] = constant

The equation doesn't take viscosity, heat transfer or compressibility effects into account but for operations below 10 000 feet and airflow velocities below 250 knots compressibility effects [see below] can be ignored – thus no change in flow density [r] is assumed.

The equation then indicates that, in a free stream flow, if speed [ V ] increases static pressure [ P ] must decrease to maintain constant energy; and the converse — if speed decreases static pressure must increase. Or, turning it around, a free stream airflow will accelerate in a favourable pressure gradient and decelerate in an adverse pressure gradient.

[A favourable pressure gradient is one where static pressure decreases with distance downstream, an adverse pressure gradient is one where it increases with distance downstream.]

Bernoulli's doesn't apply in boundary layer flow because the viscosity effects introduce loss of mechanical and thermal energy due to the skin friction.

Another aspect to the equation is that the constant is the stagnation pressure – the pressure energy needed to halt the airflow – thus it can be written ½ r V² + P = stagnation pressure and the stagnation pressure is the highest pressure in the system. This aspect of Bernoulli's is used in the air speed indicator, as demonstrated below.

Stagnation pressure is also the basis of the parachute wing. Those wings consist of an upper and lower fabric surface enclosing individual front opening cells. In a moving air stream the cells are at stagnation pressure – the highest – and thus form the semi-rigid wing shape which provides the high manoeuvrability of such parachutes.
Continuity equation
There is another equation of aerodynamic interest to us – the continuity equation which states that, in a steadily moving airstream, the product of density, velocity and cross sectional area [S] must always be a constant:

r × S × V = constant

If there is no change in density within the flow [which is the norm in the airspeed range of light aircraft, see compressibility effects below] then we can state that:

S × V = constant.

Thus if air flows into a smaller cross section area speed must increase to maintain the constant and Bernoulli states that if speed increases static pressure must decrease; so the velocity of a constricted airstream increases and its static pressure decreases. Note that the S term is used both for cross sectional area and wing surface area.

Both these equations are related to the conservation laws; Bernoulli's to the conservation of energy, the continuity equation to the conservation of mass. We will examine these properties of air further in the aerofoils and wings module.

The venturi effect — used in carburettors, the total energy variometer and the airframe mounted venturi that provides suction for some flight instruments — is an application of the principles above.

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2.5 Measuring airspeed

   The dynamic pressure of the air flow, in newtons/m², is represented by the expression ½ r V², where:
  • r is the density of the air, in kg/m³ and
  • V² is the aircraft (or free airstream) speed, in metres per second, squared.
   and we can deduce that the speed of the airstream is related to air density and dynamic pressure.

We can measure the dynamic pressure with a simple mechanical pressure gauge. Imagine a 6 mm internal diameter aluminium tube positioned under the wing of the moving aircraft, outside the slipstream, so that the open end points forward into undisturbed air flow and the other end of the tube terminates within a spring loaded, flexible capsule – similar to that in an aneroid barometer – thus the capsule halts the airflow within the tube.

   The back pressure, applied by the capsule to halt the flow, must be equal to the stagnation pressure. The capsule is contained within a casing which, in turn, is connected to a static vent supplying the casing with the ambient atmospheric pressure: or, in a lower quality system, the casing may just be open to the atmospheric pressure within the fuselage.

   So if we have stagnation or impact pressure, which is dynamic plus static pressure, within the capsule and static pressure surrounding it, the capsule will expand or contract to reflect the changes in dynamic pressure at the mouth of the tube. (The system is a "pitot tube" devised by Henri Pitot (1695-1771): during World War 1 the air speed indicating instruments themselves were called 'pitots'). The capsule movement is mechanically or electrically linked to rotate a pointer on a dial which has been calibrated to indicate airspeed, but, as the instrument cannot determine the density component of the dynamic pressure, the calibration assumes a constant air density of 1.225 kg/m³. This cockpit instrument is then an airspeed indicator or ASI and it displays the indicated airspeed or IAS based on ISA conditions. A bit confusing – but take heart for it gets worse!

   We can calculate the dynamic pressure for the Jabiru using the scenario in section 1.4 for calculating CL, i.e cruising at 6500 feet, airspeed 97 knots or 50 m/s, air density 1.0 kg/m³. The ISA atmospheric pressure at 6500 feet is about 800 hPa.

   •   static pressure = 800 hPa
   •   dynamic pressure = ½rV² = ½ × 1.0 × 50 × 50 = 1250 N/m² = 12.5 hPa

Note that the dynamic pressure at 1250 N/m² is less than 2% of the static pressure, but applying that dynamic pressure over the 8 m² of wing area and the lift coefficient of 0.4, i.e 1250 × 8 × 0.4, still gives the lift force of 4000 newtons that we calculated in section 1.4 of the basic forces module.

   The airspeed we have been discussing to this point is the true airspeed or TAS – air distance flown over time. We know that the ASI is calibrated assuming a fixed air density of 1.225 kg/m³ so an accurate ASI will only indicate the true airspeed when the actual environment density is 1.225 kg/m³; that is when the aircraft is operating close to sea level.

What will be the IAS in our example above?

IAS = V / square root (1.225 / r)

     = 97 / square root (1.225 / 1.0)    = 97 / 1.1    = 88 knots.

From this we can deduce that an accurate ASI will generally under-read. That is the IAS will always be less than the TAS, except in cold conditions at very low altitude, where the air density may be greater than 1.225 kg/m³. For instance, using the equation of state above, if temperature was –3 °C and pressure 1030 hPa, the density would be 1.33 kg/m³.
Density is about 1% greater than ISA for each 3 °C that temperature is below ISA.

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2.6 Indicated airspeed

So, you might ask, what's the point of an ASI that really is indicating just dynamic pressure and usually doesn't indicate your airspeed – air distance flown over time – accurately? Well admittedly it does mean a little more calculation to be done in navigation, but there are very significant advantages with an instrument that displays IAS, rather than TAS.

This will be covered in the aerofoils and lift module, but the sum of it is that, generally, for all angles of attack in unaccelerated flight at a particular weight, there is a corresponding IAS (though it does get a bit fuzzy near CLmax), so that, in the absence of an angle of attack instrument, the ASI can generally* be regarded as an indication of angle of attack if the lift being produced matches aircraft mass. Also all the performance parameters ( the "numbers") for an aircraft – best rate of climb, best angle of climb, best glide angle etc – require it to be flown at a particular aoa, for that weight, and thus a particular IAS. Or more accurately a particular calibrated airspeed or CAS and that particular CAS does not change with altitude, as TAS does, only with weight.

(*The reason why CAS does not always co-relate to aoa is that when inertia and random displacement forces – atmospheric turbulence – come into play, aoa may change momentarily without a change in CAS.)

We will use CAS in these notes from here on, rather than IAS, just remember that it is IAS after you have applied corrections for the position and instrument errors occurring at that aoa in that particular aircraft. The measured corrections should be stated on a card placed near the ASI. You should also be aware that position errors may be quite significant, possibly 10 knots or so – particularly at high aoa or when the aircraft is slipping.

Below is an airspeed correction table for a particular aircraft – in balanced flight i.e. not slipping or skidding. The normal cruise speed for this aircraft is around 95 knots. You can see that in this particular installation the ASI significantly underreads at low speeds and overreads at high speeds.

IAS knots42526169738796104113122130
CAS knots49576471738694102110117125

We do need TAS for navigation and there is a simple mental calculation to determine it from CAS.

Rule of Thumb #2

    "To convert CAS to TAS multiply the (density) altitude, in 1000s of feet, by a factor of about 1.5 to get the percentage increase to apply."

    e.g. CAS = 88 knots at 6500 feet = 6.5 x 1.5 = 10% = 97 knots. The factor increases with altitude reaching about 2 at 30 000 feet.

Compressibility effects
As mentioned above the compressibility of air within the pitot tube has little effect on the accuracy of the ASI reading for aircraft operating below 10 000 feet and 200 knots: at an airspeed of 200 knots compressibility will cause CAS to over-read by only 0.5 knots or so. However, for aircraft operating at high speed or high altitude, compressibility will cause the ASI to over-read and there is a need to correct CAS using a compressibility correction chart. The correction value is deducted from CAS to give the compressibility corrected CAS – otherwise known as equivalent air speed or EAS.

For most medium speed aircraft it is probable that the compressibility correction value has been built into the IAS – CAS airspeed correction table and anyway EAS has no practical application for recreational pilots.

For more information see the notes on compressibility of air flow.

The airspeed indicator
airspeed indicator     You will note the green and white peripheral arcs, and other colour marks, on the face of this instrument. These are standard markings some of which should appear on the face of every light aircraft ASI as they display the speed constraints applicable to the aircraft operations.

The white arc indicates the flaps operating range starting, at the lower end, from the indicated airspeed, Vso [55 knots], at which the aircraft will stall in the landing configuration with flaps fully extended, and with the throttle closed. The top end of the white arc indicates the maximum speed, Vfe [108 knots], at which the aircraft's flaps can be extended, or remain extended, without causing strain. The bottom end of the green arc indicates the stalling speed of the aircraft, Vs1 [62 knots], with flaps (and landing gear if applicable) up, throttle closed and wing loading = 1g. The top end of the green arc indicates the maximum structural cruise speed, Vno [173 knots]. The green arc in itself indicates the designed range of cruising speeds for the aircraft. The yellow arc indicates a speed range in which the aircraft may be flown, but with caution and only in smooth atmospheric conditions. The red line at the top end of the yellow arc indicates the speed that should never be exceeded, Vne, because of risk of structural damage.

The other red mark at 70 knots, and the blue mark at 88 knots, are of no interest: these markings would only appear on a twin engine aircraft ASI and relate to operations with one engine shut down.

A properly functioning ASI responds rapidly to pressure changes i.e. there is no instrument lag. A slow response put down to instrument lag is most likely solely due to the inertia of the aircraft – when attitude in pitch is changed an aircraft takes a little time to accelerate/decelerate to the appropriate airspeed.

Airspeed summary
  • True airspeed [TAS] = V in the dynamic pressure and other expressions = air distance flown over time.

  • Indicated airspeed [IAS] = airspeed displayed on the cockpit airspeed indicator [ASI] – based on a fixed air density of 1.225 kg/m³. The ASI only indicates true airspeed when ambient atmospheric density is actually 1.225 kg/m³ and the system error corrections are made.

  • Calibrated airspeed [CAS] = IAS adjusted (mentally from a printed table) for known system errors occurring within the normal speed range.

  • Equivalent airspeed [EAS] = CAS adjusted (mentally from a chart) for air compressibility effects occurring at both high dynamic pressures and low static pressures. There is no practical application for recreational pilots but note that aerodynamicists tend to use the EAS term – rather than IAS or CAS – presuming a 'perfect' ASI (i.e. an instrument that has no errors caused by mechanical, position, aoa or compressibility effects) would display the standard sea level airspeed [TAS] which is equivalent to the dynamic pressure in the instrument at any altitude.
Electronic ASI
Electronic flight instrument systems [EFIS] use solid state electronic componentry as sensors plus software to display flight data on a single screen. In such systems the static and dynamic pressures are fed to pressure transducers which sense and convert pressures to voltages which the electronic circuitry converts to an airspeed display. See the liquid crystal primary flight display of the Dynon D10A light aircraft EFIS. Note that the EFIS has an outside air temperature probe and, with static pressure, the software can calculate air density and thus display TAS when needed.

Electronic ASIs are also available as single panel instruments or possibly combined with an altimeter function. Note that the electronic systems are still subject to much the same errors as a mechanical system and the IAS has to be corrected for CAS unless there is a means for incorporating some form of compensating table into the software.

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2.7 Measuring vertical airspeed

The vertical airspeed indicator
 vertical speed indicator     In flight it is important to the pilot to know the rate at which the aircraft may be climbing or descending. A simple vertical speed indicator – VSI – is a pressure gauge that measures the rate of pressure change as an aircraft is climbing or descending. There are two pressure inputs, both from the static vent system; one to each side of a flexible diaphragm or capsule. On the open side there is a normal input which reflects the static pressure change as it occurs. On the closed side the input/output is via a fine capillary tube which slows the equalising pressure change – and also the response time of the instrument. The resultant deflection of the diaphragm is magnified via a geared mechanical linkage to a dial pointer which indicates whether the aircraft is maintaining altitude (in which case the pressure on both sides of the diaphragm is equal), climbing or descending and the rate, usually graduated in feet [×100] of altitude per minute. Some form of vibration damping and thermal change compensation is included within the VSI and ASI instruments.
The variometer
In free flight glider pilots are totally reliant on finding sources of atmospheric uplift to gain the gravitational potential energy enabling the aircraft to stay airborne for sufficient time to complete the flight plan. A variometer (usually condensed to vario) is a specialised vertical speed indicator which enables the pilot to derive the vertical speed of the parcel of air in which the aircraft is flying. Variometers are also fitted to ultralight motor gliders and other powered aircraft which have some soaring capability.

For more information on varios and their uses see the article "Basic sailplane instruments".

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2.8 Stalling airspeeds

The normal stall
    One of the first questions a pilot might ask, when converting to a new aircraft type, is "What's the stall speed?" The reason for the enquiry is that usually, but not written in stone, the approach speed chosen for landing is 1.3 to 1.5 times Vso – the minimum steady flight speed in the landing configuration, below which speed the aircraft will stall or at which speed the aircraft will stall if any manoeuvring [i.e. turning] is attempted.

    Perhaps from a pilot's point of view a stall is "the point following deceleration at which the pilot ceases to have full control over the aeroplane". In aerodynamic terms the 'stall' is the sudden wide-spread separation of the boundary layer from the upper wing surface, that occurs when the wing exceeds a particular angle of attack – for light aircraft, without high-lift devices, usually around 15° or 16° although minimum aircraft with single surface fabric wings may have a stall aoa 2 or 3 degrees lower. This critical angle of attack has no relationship either with the aircraft attitude relative to the horizon or the airspeed – it can readily be reached in a high speed dive – but it does have a direct relationship with elevator position and thus the control column position. In non-inverted flight an aircraft cannot be stalled unless the control column is moved well into the rearward portion of its travel.

    The separation starts at the wing trailing edge, generally near the wing root for roughly rectangular wings (and particularly for wings with "washout"), spreading forward and outward over the upper surface until there is a significant detachment of boundary layer flow over the upper surface. There is probably little change to the under surface boundary layer flow. Between the two remnant boundary or shear layers a thick turbulent wake will attach to the wing and be dragged along by the aircraft. The reaction to the acceleration and energising of that wake is a sudden deceleration of the aircraft accompanied by a large increase in the nose-down pitching moment plus some lift loss. The initial wake turbulence [ or burbles] near the wing root will affect flow over the tailplane and may provide a few warning buffets felt in the controls [also referred to as burbles or nibbles] and thus warning of an impending stall. There also may be 'oil-canning' noises from pressure changes on metal skinned fuselages or wings as the thin metal flexes in response to pressure changes but, on the other hand, there may be no pre-stall warning whatsoever.

The next comments are specifically aimed at stalls induced:
    •   when flying straight and level at slower speeds
    •   or in a low speed descent – such as the approach to landing
    •   or in a climb – such as the initial climb after take-off
    •   or in a go-around following an aborted landing approach.

The last two circumstances are sometimes referred to as full power stalls or 'departure stalls'. In non-turbulent atmospheric conditions and if the aircraft is in balance all of the circumstances above can only induce a stall if the control column position is placed in, trimmed into or allowed to move into, the last half of its rearward travel. Many aircraft are designed so that the control column must be at or near the limit of its rearward travel to reach the stalling aoa. [The rearward travel range commences from the neutral position, as does the forward travel range.]

    Because of the airflow turbulence, and increasing induced drag as the critical aoa is nearing, total drag is increasing and the aircraft is slowing as it approaches CL max. The rapid reduction in airspeed after passing the critical aoa means the wing is now unable to provide sufficient lift to totally balance weight and, in a normal stall, the aircraft starts to sink. The (possibly pronounced) nose-down pitch will occur even though the control column is near its rearward travel limit. However some aircraft may not assume that nose down attitude but just sink (mush down) at quite a high rate and at an extreme angle of attack. Because of the nose-up attitude the high descent rate may not be apparent unless the aircraft is close to the ground.

The aircraft is instantly recovered from the stall just by smoothly reducing the aoa so that it is below the critical aoa, i.e. easing the control column forward and generally no further than the neutral position. If one wing stalls before the other that wing will drop in which case the control column must be firmly moved sufficiently forward that the dropping wing is unstalled, the wings levelled with aileron, then sufficient rudder is applied to stop further yaw. An increase in speed (by increasing power or holding a lower nose attitude for several seconds) is also needed so that a safe flight speed is quickly achieved without wasting altitude and the aircraft returned to the intended flight path. See standard recovery procedure for all stall types.

If the stall recovery control movement is both excessive and abrupt the result could be an aoa movement below the zero lift aoa in which case there will be a reversed lift force on the wings hindering recovery. Weight shift controlled trikes do not react well to negative g, if excessive the wing spars may buckle at an outer position.

Many aircraft are designed so that the nose will drop at the stall but the aircraft will self-recover (i.e. without pilot intervention) in a stable descent or with some oscillations which, if the control column is still held back, will result in another stall. Some aircraft may be designed so that the wing is usually not able to reach the stalling angle but the aircraft will enter a stable 'mushing' descent. A normal stall is the type occurring when the wing loading is close to normal i.e. near 1g.

    The cg position will also affect the manner of stall, if the cg is at the extreme forward limit some aircraft may not fully stall, just 'mush' down. If it is too far aft the stall aoa can be reached with a much reduced rearward movement of the control column. Another factor affecting the manner of stall is the use of power. Generally when flying slowly the longitudinal axis of the aircraft is pitched up, relative to the flight path, consequently the thrust vector will include a vertical component, a lifting force, and the amount of lifting force provided depends on the amount of thrust. Also, for aircraft with the propeller mounted in front of the wings, the energy in the slipstream tube in slow flight increases the velocity of the airstream over part of the wing (depending also on the mounting of the wing in relation to the thrust centre-line) and reduces the aoa of that part. Thus the completely stalled wing may occur at a lower speed, depending on the amount of power in use but when it comes the stall will be much more pronounced, possibly with a fast-acting wing drop. There are other complications because of the slipstream also affecting parasite and induced drag.

In very smooth air competent pilots can maintain level flight at Vs, but once speed drops below Vs, i.e. the aircraft stalls, a competent pilot can usually keep the wings level, reduce the angle of attack, not lose significant height and continue doing that in a series of level flight stalls and recoveries – more or less but not in all aircraft.

    Some pilots, in suitable aircraft and atmospheric conditions, prefer to land that aircraft by approaching at 1.3 to 1.5 times normal stall speed – Vso – and, in the flare with the throttle closed, holding the aircraft just above the surface; preventing it touching down by smoothly increasing CL as drag decreases V², thus maintaining constant lift – until CLmax is reached, when the aircraft will then gently sink the short distance onto the runway.

[ The next section in the airmanship and safety sequence is the follow-on section "The accelerated stall" ]

The accelerated stall
    It is misleading to talk about stalling speed without further definition. The stall occurs at a particular aoa not a particular speed. The speed – Vs – below which the stall will occur depends on the wing loading. If the aircraft reaches the critical aoa under a load higher than 1g the stalling speed will be higher than the normal 1g stall speed, at that mass. This latter stall is called an accelerated stall and is usually more pronounced than a normal stall. Remember that the wing loading normally increases in a turn (as we saw in section 1.10 where we calculated that, in a 45° banked turn, the wing loading was 1.41 times normal) thus when turning the stalling speed is higher than normal and the pilot must ensure that a reasonable airspeed margin above the accelerated stall speed is maintained throughout the turn. See the table below.

But be aware that the airspeed at which an accelerated stall in a turn occurs is only indirectly associated with the angle of bank, it is directly brought about by the increase in wing loading. Indeed it is possible to have the aircraft banked at 60° with a stall speed less than Vs1 if the wings are 'unloaded'; slight forward pressure on the control column and the aircraft allowed to sink, produces a load less than 1g, maybe 0.9g, with a stall speed less than Vs1, even though the aircraft is steeply banked. However once the 'unloaded' condition ceases the possibility of an accelerated stall immediately returns, if the stalling angle of attack is reached either by rearward movement of the control column or a vertical wind gust momentarily changing the relative airflow.

    In section 1.10 we showed that wing loading or W/S = CL × ½rV² thus W/S at the stall must = CLmax × ½rV². But CLmax is a fixed value (for each flap setting) so that if W/S, at the stall, is greater than the normal loading, the only value on the right side that can increase, to match, is V².

    Which all indicates that the speed at which an accelerated stall occurs is proportional to the square root of the wing loading. If that wing loading is expressed relative to the normal load, e.g 2g , then the stall speed – Vs 2g – equals the square root of the load × normal 1g stall speed, e.g. square root of 2 = 1.41 × Vs.

    The aircraft's momentum may also contribute to an accelerated stall, particularly when the aircraft is diving at speed and the pilot applies a harsh rearward control column movement. This will have the initial effect of rotating the aircraft around its lateral axis while inertia maintains the aircraft on its existing flight path for half a second or so; thus the aoa may exceed the stalling aoa [even though the control column has not been pulled back to the normal stall position] with a consequent, and rather violent, high speed stall.

    An accelerated stall can also be produced when:
    •   the control column is jerked back whilst the aircraft is climbing or in level flight, see the flick roll
    •  an aircraft in level cruising flight encounters a strong vertical gust [see manoeuvring speed below]
    •  any other abrupt flight path change, applying acceleration loads, is made
    •  an excessive bank angle, coupled with excessive control column back pressure, is applied during a level, climbing or descending turn.

[ The next section in the airmanship and safety sequence is the follow-on section "Wing loading in a turn" ]

Wing loading in a turn
    The table below shows the increase in stall speed at various bank angles in correctly executed level turns. The wing loading [W/S] increase or 'g' = 1/cosine of the bank angle and the Vs multiplier = the square root of the W/S increase. The table shows that once you reach bank angles of 30° or more the aircraft stall speed increases rapidly; 7% increase at 30°, 19% at 45° and 41% at 60°.

Thus level turns involving bank angles exceeding 20 – 30° should not be made at low levels, including take-off and landing operations, even so the airspeed should be increased to allow an appropriate safety margin – for gentle turns a safe speed near the ground is 1.5 × Vs.

The stall speed in a turn = Vsturn = Vs × Vs multiplier. A minimum turning speed at height might be 1.2 × Vsturn,   for example if Vs is 50 knots and the bank angle is 45° then Vsturn is 50 × 1.19 = 60 knots and the minimum safe turning speed at height is 1.2 × 60 = 72 knots or about 1.45 × Vs.

Bank angleCosineW/S increase [g]Vs multiplier
10° 0.98 1.02 1.01 [+1%]
20° 0.94 1.06 1.03 [+3%]
30° 0.87 1.15 1.07 [+7%]
40° 0.77 1.30 1.14 [+14%]
45° 0.71 1.41 1.19 [+19%]
50° 0.64 1.56 1.25 [+25%]
54° 0.59 1.7 1.3 [+30%]
60° 0.50 2.00 1.41 [+41%]
70° 0.34 2.94 1.71 [+71%]
75° 0.25 4.00 2.00 [+100%]

Note that the 10° increase in the bank angle between 20° and 30° increases stall speed by four percentage points but the 10° increase in the bank angle between 50° and 60° increases stall speed by 16 percentage points [i.e. four times greater] while between 60° and 70° the stall speed is increased by 30 percentage points. Aircraft certificated in the normal category are limited to a turning angle of bank of not more than 60 degrees.

Note that at an approach speed of 1.3 times Vs the aircraft will stall if turning with 54° bank. The limits on climbing and descending turns is discussed in module 14 Safety: control loss in turns.

[ The next section in the airmanship and safety sequence is the section below "Critical speeds" ]

The torque stall
For high performance aircraft, with a very high power-to-weight ratio, the possibility of a torque stall exists. The most likely scenario is a sudden application of full power in a 'go-around' following an aborted landing, where the airspeed has been allowed to decay below the safety speed. The torque of the engine and inertia of the heavy propeller tends to twist the aircraft around the propeller shaft and the consequent roll may increase the aoa of the downgoing wing past the critical aoa. If that happens the wing loses lift, accelerating the roll and the aircraft loses height very rapidly. However torque stalls are probably not applicable to light aircraft; although the torque effect may influence the characteristics of a stall in a climbing turn.

Effect of weight
    If the aircraft is below its MTOW the wing loading will be less and the stall will occur at a lower speed than when at MTOW.

For example, if we refer to the Jabiru the wing area is 7.9 m², MTOW is 4200 N, Vso is 40 knots CAS and we can calculate that CL with flaps fully extended is 2.0.

We saw above that W/S at the stall = CL × ½rV².
We will rearrange that and say Vs² = (W/S) / (CLmax × ½r) and substituting the values, including 1.225 for density, we get the following –

Vs² = (4200/7.9) /(2.0 × 0.5 × 1.225) = 532/1.225 = 434 m/s and Vs = 20.8 m/s = 40 knots CAS

Now what will Vs be when the Jabiru is at the low weight of 3400 N? Well substituting that weight we get –
Vs² = (3400/7.9) /(2.0 × 0.5 × 1.225) = 430/1.225 = 351 m/s and Vs = 18.7 m/s = 36 knots CAS.

There are other, somewhat simpler ways to calculate the reduction in Vs corresponding to a reduction in weight but what we see above is that a reduction in weight of 800 N, or about 19%, occasions a reduction in Vs of 4 knots, or about 10%. This brings us to the mathematical rule of thumb that when two values are not that far apart in percentage terms, say up to 40%, their square roots are about half that distance apart in percentage terms and because aerodynamic pressure is proportional to V², there are many occasions where the square root of a value is relevant. Which allows a simple, but reasonably accurate, mental calculation:

Rule of Thumb #3

    "The percentage reduction in Vs is half the percentage reduction in weight."   

    i.e. If weight is reduced by 10% from MTOW then Vs will be reduced by 5%.

    and conversely, if weight is 10% over MTOW then Vs will be 5% higher.

Thus in the paragraph above, where we referred to unloading the wings with the aircraft banked at 60°, the reduction of weight from 1g down to 0.9g is 10% and so the unloaded stall speed would be about 95% of Vs1. You can also see the same relationship in the preceding table; for bank angles up to 45° the percentage increase in Vs is about half the percentage increase in W/S.

    It is appropriate to mention here that not only is the speed at which the stall occurs affected by aircraft weight/wing loading. Some of the other critical performance values are also achieved at a particular aoa, and the associated airspeeds are also changed by a change in weight. The same rule of thumb applies to them. These critical performance values (the "numbers") are: best rate of climb speed, best angle of climb speed, lowest power-off sink rate speed, best glide ratio speed, manoeuvring speed and design cruise speed.

    Another aspect we will look at in the aerofoils and wings module is the effect of flaps, but we will just state here that flaps provide an increased CL at all angles of attack consequently allowing a reduction in V², or the stalling speed. In some aircraft extending flaps also increases wing area thus W/S is reduced, a handy technique for high performance military aircraft, manoeuvring at maximum allowed wing loading – they can tighten the turn even further without breaking the aircraft.

    The final aspect of the stall is the effect of atmospheric turbulence on aoa and this affects 'manoeuvring speed'. We will look at it in the flight envelope section below.

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2.9 V-speeds

    It is important to have a simple, universally understood and accepted, identification method for the various airspeeds at which an aircraft may be operated but currently it's a bit messy and there is no complete, and universally recognised, airspeed designation system published by any regulatory authority.

Current nomenclatures are generally made up of 2 to 6 letters/numbers with the first being V. Some of these V-speed codes with alternates, and definitions, which may be relevant to light single engine aircraft, including ultralights, and which might appear in flight manuals, pilot's operating handbooks and even sales literature, are shown below. Please note those speeds indicated with open bulleting   º   are probably only applicable to a few very light aircraft types.

Please be aware that the various 'best' performance speeds mentioned below [rate of climb, angle of climb, cruising range, gliding range etc] merely indicate the midpoint in an airspeed range extending perhaps 1%—2% either side of that point. Also the performance speeds are very much affected by the horsepower of the particular engine fitted plus the type of propeller and its pitch setting. If there is no pilot's operating handbook for the particular airframe/engine/propeller configuration then the pilot must calculate the performance speeds by trial and measurement.

Critical limiting speeds
   •  Va – design manoeuvring speed. Sometimes referred to as the 'speed for maximum control deflection'. Design rules state that the minimum acceptable manoeuvring speed is a fixed calculation relative to Vs1 for all aircraft within the same category; for a normal category light aircraft (whose certificated vertical load limit factor is +3.8g) minimum Va = Ö3.8 Vs1 or 1.95 × Vs1. For a utility category light aircraft (whose certificated vertical load limit factor is +4.4g) minimum Va = Ö4.4 Vs1 or 2.1 × Vs1. Of course the aircraft designer may specify a Va speed which is greater than that minimum requirement.

It is unwise to make full or abrupt applications of any one primary flight control if you are flying at a speed greater than Va because at higher speeds it is easy to apply forces that could exceed the aircraft's structural limitations and particularly so if you apply more than one control e.g. apply lots of elevator and aileron together. Even when flying at or below Va it is unwise to make rapid control reversals.

Va is not marked on the ASI but there should be a placard indicating the MTOW manoeuvring speed on the instrument panel near the ASI; if not you can assume it's twice maximum weight Vs1 for non-aerobatic light aircraft.

Va decreases as the aircraft's weight decreases from MTOW because the effects of the aerodynamic forces become more pronounced as its weight decreases. Sometimes the aircraft's flight manual will specify the design manoeuvring speeds for weights below MTOW but it may be left to the pilot to calculate. Using rule of thumb #3 above the reduction in Va will be half the percentage reduction in aircraft weight; for example if, with only one person on board, weight is 16% below MTOW then Va is reduced by 8%. (Actually Va decreases with mass rather than weight, but that is splitting hairs a bit.)

If you look at the manoeuvring flight envelope for a particular aircraft type below you will note that Va is 94 knots. You can also see from the accelerated stall curve in the diagram that flying at speeds much below Va in turbulent conditions also enhances the possibility of stalls induced by vertical gusts – and also may reduce aileron and rudder effectiveness.

Misuse of controls in light aircraft can generate greater structural loads than those possibly encountered in turbulence so Va is also useful as a 'turbulent air operating speed' and most light aircraft operating handbooks recommend that airspeed be reduced to Va in turbulent conditions. When flying above this speed gust-induced loads can exceed the structural design limit, and gust loads in the high temperature conditions of the Australian tropical continental air mass can be extremely high. Va is the recommended indicated cruising speed (CAS) when flying in moderate turbulence – strong intermittent jolts. At this compromise speed the aircraft will generally produce an accelerated stall, and thus alleviate the aerodynamic force on the wings, if it encounters a vertical current imparting an acceleration sufficient to exceed the load limit factor.

If the aircraft designer has specified a manoeuvring speed which is greater than the minimum specified in the regulations then, when flying at Va and if a substantial nose-up pitching manoeuvre is applied, the aircraft may exceed the limit load factor before stalling. A maximum manoeuvring speed Vo might be established as an operating limitation being a selected speed that is not greater than Ö3.8 Vs1 for a normal category aircraft and is a speed where the aircraft will stall in a nose-up pitching manoeuvre before exceeding the structural load limits.

   º  Vb – the design speed for maximum gust intensity or the maximum gust penetration speed. Vb is developed by the designer as a recommended turbulence penetration speed for commercial passenger aircraft rather than using Va so that higher cruise speeds can be maintained and there is no danger of inadvertent stall. Stalling larger aircraft is not a good idea, not least because of height loss and possible excessive loads in the recovery.

   •  Vno – maximum structural cruise speed or 'normal operating limit', indicated by the top end of the ASI green arc. Flight above Vno should only be conducted cautiously and in smooth air. Vno must be equal to or greater than Vc (below) but in most light aircraft Vno and Vc are assumed synonymous. When cruising at, and below, Vno the aircraft should not be damaged by a 30 feet/second vertical gust – which is in the top end of the moderate turbulence scale of 20 – 35 feet/second vertical gusts.

   •  Vne – never exceed speed. The IAS which should never be intentionally exceeded in a dive or other manoeuvre – in smooth air. The red line at the top end of the ASI yellow arc. For light aircraft operating below 10 000 feet it can probably be assumed that Vne is a fixed IAS but if VNE varies with altitude FAR part 23.1545 (c) requires a means [a placard next to the ASI] to indicate to the pilot the appropriate limitations throughout the aircraft's operating altitude range. For further information read 'Safety: flight at excessive speed'.

   •  Vs1 (sometimes incorrectly shown as Vsi) – stalling speed, or the minimum steady flight speed, in a specified flight configuration. For a simple aircraft Vs1 is normally measured in erect level flight with flaps up, at MTOW and 1g wing loading, with engine idling following a gradual deceleration — accompanied by increasing control column rearward movement — to that minimum flight speed. The bottom end of the ASI green arc, but it may be documented as IAS or CAS; if the former the quoted stall speed is probably inaccurate. Vs1 decreases as the aircraft weight decreases from MTOW, which also means that if the pilot can reduce the wing loading below 1g – by an 'unloading' manoeuvre – Vs1 is decreased. Stalling speed under a 2g wing loading, for instance, might be referred to as Vs2g.

   •  Vso stalling speed, or the minimum steady flight speed, in the landing configuration of flaps down, engine at low or idle power as it would be just prior to touchdown. Measured using the same method as Vs1 but with the cg at the most extreme position allowed, usually the most forward position where backward movement of the control column may be limited. The bottom end of the ASI white arc, but it may be documented as IAS or CAS. Like Vs1, Vso decreases as the aircraft weight decreases from MTOW. The designation Vs is used as a general reference to either or both Vso and Vs1.

[ The next section in the airmanship and safety sequence is section 2.10 "Aircraft flight envelope" ]

Cruise speeds
     •  Vbr – best range or Vmd – minimum drag – the speed that provides maximum L/D by producing minimum drag and thus the best power to speed ratio. Might utilise about 55% power and is usually flown at the lowest altitude where the throttle is fully open to obtain that speed. Vbr/Vmd decreases as the aircraft weight decreases from MTOW. It's rather boring to fly at that speed, wind conditions have to be taken into account and the fuel saving may not be that significant compared to flying at a speed 10% faster. Also the engine manufacturer's operating recommendations should be followed, but mixture is usually leaned, and minimum rpm set if a constant speed propeller is fitted. Same basic airspeed range as Vy and Vbg [below].

power curve     However there is a difference in concept between Vbr and Vmd. Pilots of low powered aircraft are generally not interested in the best power to airspeed ratio in cruise; ground speed achieved per litre is far more significant, so in some conditions Vbr equals Vmd but in headwind conditions Vbr is increased. Look at the diagram from section 1.7 at left and note the pink line that has been drawn from the junction of the vertical and horizontal axes tangential to the power required curve. That line just touches the curve at a position corresponding to the minimum drag airspeed Vmd. Now imagine a 30 knot headwind and start the tangential line from a point along the horizontal axis that is equivalent to 30 knots; that [the blue line] will be tangent to the power required curve at a position corresponding to a higher speed — Vbr for a 30 knot headwind. The rule of thumb is to add half the head wind to the basic Vbr, which indicates in this case a Vbr that is about 15 knots greater than Vmd. This is the same principle used by glider pilots to establish their best penetration speed — see the speed polar curves for optimum glide speed in the "Coping with emergencies guide".

     •  Vbe – best endurance or Vmp – minimum power – the CAS which gives the greatest airborne time per litre (i.e. least fuel flow per hour and power is proportional to fuel flow) possibly around 80% of Vbr/Vmd, decreasing as the aircraft weight decreases from MTOW. Flight at lowest safe altitude provides best engine performance. Might utilise about 45% power at MTOW. It is the speed for minimum power required for level flight shown in the power required curve above.

Vbe is the speed that might be used when flying a search pattern allowing a proper area survey, or when waiting for ground fog to disperse, but it is possibly uncomfortable to fly for long periods at such a low speed. Also the very low power setting may be inconsistent with good engine handling practise. Carburettor icing may be aggravated. The Vmp designation and airspeed is synonymous with the power-off glide speed Vmp providing the best endurance [i.e. least rate of sink, see below] and in the same speed range as Vx — the best angle of climb airspeed.

   •  Vc – the design cruising speed or the optimum cruise speed – the latter being the speed giving the most velocity (i.e greatest distance/time) from a litre of fuel, usually utilising 75% power at MTOW and about 20%—30% greater than the maximum L/D speed – Vbr above. The speed and power required decrease as the aircraft weight decreases from MTOW. Refer rule of thumb #3.

For most light aircraft Vc is synonymous with Vno. For normal category aircraft FAR Part 23 specifies a minimum design cruising speed (in knots) = 33 Ö W/S. For this calculation the wing loading W/S is expressed in pounds per square foot. Alternatively Vc can be set at 90% of Vh — see next. Many minimum ultralights are unable to comply with the FAR part 23 design requirement for a minimum design cruising speed.

   º  Vh – the maximum level flight indicated speed (CAS) attainable at sea level utilising maximum continuous engine power which, for most engines, will be less than full throttle power, at sea level i.e. the aircraft's maximum continuous speed in level flight.

Take-off and landing speeds
   •  Vfe – maximum flaps extended speed. The top end of the ASI white arc. Flight with flaps extended, or extending flaps, above this speed may result in distortion of the flaps or the extension mechanism. Various Vfe speeds may be specified according to the available flap settings. Generally speaking the flight load limit factors are reduced by about 50 % when flaps are fully extended, for example for a normal category aircraft the Aircraft Flight Manual will probably note that load limit factor is reduced from 3.8g to 2g.

   º  Vle – retractable undercarriage aircraft – the maximum indicated speed at which the landing-gear can remain extended without risking gear door damage.

   º  Vlo – the maximum indicated speed at which the landing gear system can be operated. Vle and Vlo are unlikely to be applicable to most ultralights.

   º  Vlof – lift off indicated speed (CAS) – for normal take-off. About 10% above Vmu.

   •  Vmu – minimum unstick speed. An indicated speed (CAS) used in take-off conditions where it is advisable to lift off at the lowest possible airspeed to get the tyres off the surface (e.g. soft field or wet grass ) and safely fly in ground effect until a Vtoss is attained to allow climb away. Acceleration after lift-off at Vmu is slow, due to the drag at the high aoa, and should not be used as an obstacle clearance technique.

     •  Vref – the reference indicated (CAS) approach speed, usually about 1.3 to 1.5 times Vso plus 50% of the wind gust speed in excess of the mean wind speed. e.g. Vso = 30 knots, wind speed 10 knots gusting to 20 knots, Vref = 1.3 x 30 + 5 knots = 44 knots. Faster, heavier aircraft would tend towards the 1.3 times Vso end; lighter, slower aircraft would tend towards the 1.5 times Vso end. Normal landing procedure is to set up the approach so that an imaginary 15 metre [50 ft] high screen placed before the runway threshold is crossed at Vref and the airspeed is reduced to maybe 1.2 to 1.3 Vso – plus the gust allowance – when rounding out prior to touchdown. The ground distance from the screen to the touch-down point can be roughly estimated, using the 1-in-60 rule, from the approach slope. For example with a 6° slope – which is around the norm for most light aeroplanes – the distance will be 60/6 × 15 = 150 metres, to which must be added any float period plus the ground roll distance with normal braking, to give the total landing distance over the standard 15 m screen – in nil wind conditions.

   •  Vtoss – minimum take-off safety speed. An indicated speed (CAS) chosen to ensure that adequate control will still exist during initial climb after lift-off if power is lost or turbulence encountered. After lift-off the aircraft should be held down and not allowed to climb away until Vtoss is attained.

CAO101-28, the airworthiness certification requirements for commercially supplied amateur-built kit ultralights, states in part:-
"The take-off distance shall be established and shall be the distance required to reach a screen height of 50 feet from a standing start, with ... short,dry grass surface ... the aeroplane reaching the screen height at a take-off safety speed not less than 1.2 Vs1 ... take-off charts ... shall schedule distances established in accordance with the provisions of this paragraph, factored by 1.15." Sea level ISA and nil wind conditions are implied. CAO 95.55 has much the same wording but specifies 1.3 Vs1 as the take-off safety speed.

(Similarly CAO101-28 states that the landing distance stated will be that to come to a full stop from a screen height of 50 feet, with the screen being crossed at 1.3 Vso and the same conditions as specified for the take-off distance.)

However in normal take-off conditions Vtoss should be somewhere between 1.3 and 1.5 Vs1 with 'draggy' aircraft tending to the higher value. Should power be lost in the initial climb a draggy aircraft will lose airspeed very rapidly and take some time to regain it even though the pilot reacts quickly and pushes the control column forward.
Climb speeds
   •  Vx – indicated speed (CAS) providing best angle of climb for obstacle clearance i.e. to attain height over the shortest ground distance using maximum thrust available. Probably better described as the emergency climb speed — the initial climb speed used when there are obstructions off the end of a marginal airstrip or when climbing out of an obstructed valley. Vx decreases as the aircraft weight decreases from MTOW, refer rule of thumb 3 above, but the angle of attack is maintained at around 8º — 10º. It is the climb airspeed where the ratio of vertical speed to horizontal [ground] speed is the highest. Vx may be less than or equal to Vtoss. However be aware that the angle of climb will also depend on the low level wind conditions at the airfield. In a headwind the speed flown is reduced by around one quarter of the windspeed but increased in a tailwind by a similar amount. Also note that aoa during climb may be only 5 or 6 degrees below the critical aoa thus care must be taken not to induce a "departure stall", particularly in turbulent conditions. And remember that Vs1 increases in a turn so that the small safety gap between Vx and Vs1 will be eroded if a climbing turn is attempted; see 'Safety: loss of control in low level turns'.

Climbing at Vx should always be regarded as a short term emergency procedure and once clear of obstacles airspeed should be increased to Vy – or an appropriate enroute climb speed which latter although reducing the rate of climb has the benefit of reducing total sector time and may be beneficial to engine operation but, more importantly, provides a little more airspeed in hand should the engine falter or fail. The CAS for Vx increases with [density] altitude and is much the same airspeed as Vbe although engine cooling requirements might mandate something higher.

   •  Vy – indicated speed (CAS) for best rate of climb. i.e. To attain height in the shortest time using maximum power, or possibly maximum continuous climb power. Vy decreases as the aircraft weight decreases from MTOW, refer rule of thumb #3 above, but the angle of attack is maintained at around 6º—8º. After reaching a safe height airspeed may be increased to an appropriate enroute climb speed. The CAS for Vy decreases with [density] altitude, i.e. as TAS increases, and also is usually fairly close to the maximum L/D speed Vbr taking engine cooling flows into account. Vx and Vy converge as [density] altitude increases.
Power-off descent speeds
     •  Vbg – best power-off glide – the CAS that provides minimum drag thus maximum L/D, or glide ratio, consequently greatest still air glide range available from the potential energy of height. It is much the same basic airspeed as Vbr/Vmd and Vy though it may be a bit lower and decreases as the aircraft weight decreases from MTOW. However like Vbr wind direction and speed have to be taken into account before you can choose the Vbg speed when in a forced glide; for more information on the power-off glide speeds read the 'Know the best glide and minimum descent airspeeds' and 'Know the practical glide ratio and terrain footprint' sections in the "Coping with emergencies guide". In lower wind conditions Vbg is increased in a headwind by around one quarter of the windspeed but decreased in a tailwind by a similar amount. In higher wind conditions, say above 25 knots, the speed changes required would be around one half of the windspeed.

     º  Vmp – minimum power – the speed that results in the lowest rate of sink in a power-off glide, providing the longest duration of flight from the potential energy of height. The lowest rate of sink occurs at the minimum value of drag × velocity. Probably around 80-85% of Vbg, and may be a similar speed to Vbe and Vx.

Vbg for an average sailplane with a wing loading of 32 kg/m² could be 50 knots providing a glide ratio of 38 :1, while Vmp would be 41 knots providing a sink rate of 0.6 metres/sec or 120 feet/minute. If you want further explanation of sink rates etc [with excellent diagrams] read this article on glider performance airspeeds.

[Note: the term Vmd meaning minimum descent rather than minimum drag – is in common usage to designate the speed for lowest rate of sink in a power-off glide.]

Both Vbg distance and Vmp time are adversely affected by the extra drag of a windmilling propeller, which creates much more drag than a stopped (but unfeathered) propeller, following engine shut-down or failure. A windmilling propeller has a negative aoa and the "thrust" direction is reversed, in effect adding to drag. Much the same thing happens when simulating a glide at the specified Vbg/Vmp speed with the engine idling; the propeller drag will increase the rate of sink beyond that expected and perhaps leading to the erroneous conclusion that the best glide speeds in the handbook are understated.

[ The next section in the airmanship and safety sequence is section 11.2 Factors affecting safe take-off  performance ]

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2.10 Aircraft flight envelope

    The design flight envelope is not the cruise-to-stall ratio nor the range of airspeed between minimum and maximum, rather the flight envelope of an aircraft may be stated as "the parameters within which an aircraft can be safely operated, with average pilot ability, at varying density altitudes, airframe states, power outputs, wing loadings and atmospheric turbulence". Airframe states refers to flap extensions, undercarriage position and the weight. It is a dynamic two or three dimensional model which has airspeed along one axis, wing loading or 'g' along the second and perhaps density altitude along a third, and there are separate flight envelopes for each airframe state. The parameters for a light aircraft usually are the limiting critical airspeeds – Va, Vne, Vno, Vs1 and Vso; the certificated load limits and possibly an angle of bank limitation – e.g. 60°. For weight-shift aircraft particularly there are pitch limitations – e.g. 45° nose up or nose down from the horizontal. Most of the critical airspeeds vary with changes in static weight and in dynamic loading and an extreme cg position may place further limitations on the flight envelope.

The V-n [or V-g] diagram below is a simplified representation of a few aspects of the manoeuvring flight envelope for a 'utility category' aircraft, at MTOW, displaying airspeed along the horizontal axis and the wing loading along the vertical – in units of 'g' – between the usual certificated load limits for such aircraft of +4.4g to –1.8g. The curves represent the accelerated stall speeds of Vs1 × Ög, thus the stall speed with a 4.4g loading is 94 knots, which is usually Va, the design manoeuvring speed at maximum take-off weight. You can see from the curve that at 94 knots the aircraft will stall when the wing loading reaches 4.4g. The aircraft cannot be flown in the regions to the left of the accelerated stall curves because the wings will be stalled.

In section 2.8 above we determined that a 60° banked level turn doubled the normal wing load. If you visualise a horizontal line from the 2g point the interception with the curve will equate with about 65 knots Vs.

 V-n diagram

The maximum airspeed allowed is Vne but full and abrupt control applications are restricted to speeds at or below Va, so the aircraft can be flown in the green area without limits on control use and it can be operated with due care within the yellow area, but it should not be operated in the pink area. (Please note the green/yellow areas are not related to those green/yellow arcs that appear on the ASI.) If it is inadvertently operated in the red area i.e outside the certificated load limits, or at velocities greater than Vd, structural distortion then failure may result. The more load placed on the wings while the aircraft is operating in the red region the greater the possibility of structural failure. The potential exists to exceed both Vd and maximum load in the pullout from a spiral dive.

Vertical gusts impose loads on the wing structure by inducing rapid, but momentary, changes in aoa with consequent changes in the lift force. The faster the aircraft is moving the greater the gust induced load. FAR 23 has requirements for designers to consider unexpected gust loads. A gust envelope is often represented as an overlay to the V-n diagram, having the effect of diminishing the flight envelope. Vb is developed by the aircraft designer as a recommended turbulence penetration speed in severe turbulence, with varying vertical gust components – up to 50 feet/second considered for a light aircraft at cruise speed. However Vb is not specified for ultralights or, indeed, for most light aircraft because there is probably not much difference between Va and Vb.

The flight envelope is considerably reduced if asymmetric manoeuvring loads are applied to the airframe. Such loads might be applied by an aircraft yawing or rolling while recovering from a high speed descent.

There are other attributes that define the envelope – resistance to spin and spin recovery for example. Note that the term 'average pilot ability' doesn't imply that those who consider themselves 'above average' can push the envelope without losing control or stressing the airframe.

There is more information on the flight envelope in the safety brief document 'Fly real fast'.

[ The next section in the airmanship and safety sequence is section 8.6 "The stall/spin phenomenon" ]

The next module in this Flight Theory Guide discusses altitude and altimeters, but first read the notes below.

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Things that are handy to know

   •  ASI position error. The static vent is an opening, best placed at a position on the aircraft's fuselage (if such exists), where atmospheric static pressure is not influenced by the shape of the fuselage or other aerodynamic disturbances. (Some aircraft may be fitted with a static vent on each side of the fuselage to counter static pressure disturbances caused when the aircraft is slipping/skidding and/ or a switchable alternative static source within the cockpit). The opening is tube connected to the cockpit and supplies the ambient atmospheric pressure, or static pressure, to the three pressure sensing instruments – ASI, VSI and altimeter. The static vent is usually subject to some pressure disturbances at particular aircraft attitudes; as is the pitot tube, but probably to a lesser degree. These disturbances result in position error: for a wing mounted vent the ASI may under-read by 10 knots at stalling aoa. In a sideslip a single fuselage mounted static vent may be subject to dynamic pressure and ASI and VSI readings will consequently be completely misleading. Also the instrument movements will have inbuilt errors, usually occasioned by excessive friction. Obstructions in the tubes – water, wasp's nests – will cause misreadings.

Consequently position error corrections for the instruments should be noted in the Pilot's Operating Handbook and placarded on the instrument panel. The IAS corrected for instrument and position errors is called the calibrated airspeed or CAS. Either CAS or IAS may be the reference speed in the Pilot's Operating Handbook for aircraft operations, but if the position error corrections are not shown then the ASI system has not been assessed for accuracy. In some poor ASI installations, IAS may be 20% less than CAS at low speeds, but they are usually much the same at normal cruising speeds.

Regulations for type certificated aircraft require that the complete airspeed indicating system of pitot head, static vent, connecting tubes and instrument be tuned so that the IAS reading is within 3% of the true reading over the normal airspeed range from Vs to Vc. However you should suspect that any non-certificated ultralight ASI system will be inaccurate at all speeds and particularly so at high aoa. When comparing published stall speeds between different aircraft types it is wise to determine CAS, as published IAS stall speeds may be downright misleading.

   •   Checking validity of claimed stall speeds. There is a simple method to check the validity of published stall speeds. Practically all ultralight aeroplanes (and excepting those with single surface wings like the Wheeler Scout or weight shift aircraft) use simple, long proven, standard camber aerofoils to form the wings: the lift coefficient attainable at maximum aoa with such wings without flaps is about 1.2 or 1.3 for faster cruising aircraft to 1.5 or 1.6 for the slower, higher lift sections. If equipped with flaps over say half the trailing edge then CLmax might be increased by 0.5 when the flaps are extended to at least 35°. When other high-lift devices [for example full length leading edge slats/slots] are added to the wing then CLmax might increase 0.6. Thus a specialised short take-off and landing aircraft fitted with a high-lift aerofoil, full length leading edge slats and large extended flaps would have a CLmax of [at least] 1.6 + 0.5 + 0.6 = 2.7.

The lift equation at normal stall speed is:

  Lift = CLmax × ½rV² × S = weight

or re-arranged:

CLmax = weight / (½rV² × S)

We can use that equation to check the validity of stall speed claims if we know the maximum take-off weight [MTOW] and the wing area [S]. Let's say a supplier claims that an aircraft, lacking any high-lift devices, has a stall speed of 30 knots. The MTOW is 450 kg and the wing area is 12 m².

In the equation the weight must be expressed in newtons – so multiply kg × 10 = 4500 N; and the stall speed must be expressed in metres per second – so just halve the velocity in knots = 15 m/s: the air density used must be the ISA msl density = 1.225 kg/m³.

Thus CLmax = 4500 / (0.5 × 1.225 × 15 × 15 × 12) = 2.7

A lift coefficient of 2.7 is very much higher than that achievable without high-lift devices so you would conclude that the claimed stall speed is nonsense, a figure of 38 knots is probably closer to the mark.

   •  Conversely you can do a rough approximation of stall speeds using the following simplified formulae if you [1] know the wing loading in kilograms per square metre or in pounds per square foot and [2] can estimate CLmax with flaps stowed or fully extended.

Stall speed [knots] = 7.8 times square root (wing loading in kg/m² divided by CLmax)

Stall speed [knots] = 17.2 times square root (wing loading in lb/ft² divided by CLmax)

Using our previous example of a lightly loaded Jabiru with a mass of 340 kg [748 lb], wing area of 7.9 m² [85 ft²] thus wing loading = 43 kg/m² [8.8 lb/ft²] and estimating CLmax with flaps fully extended as 2.0 then:

estimated stall speed = 7.8 × square root (43/2) = 7.8 × 4.64 = 36 knots

or estimated stall speed = 17.2 × square root (8.8/2) = 17.2 × 2.1 = 36 knots


Stuff you don't need to know

   •  The tropopause marks the boundary between the two lower layers of the atmosphere – the troposphere, and above it, the stratosphere. The height of the tropopause varies daily, seasonally, and latitudinally; being at about 28 000 feet at the poles and perhaps 55 000 feet at the equator. The significant difference between the troposphere and the stratosphere is that air temperature decreases steadily with height in the former, but initially remains constant then increases steadily with height in the stratosphere, until the stratopause at about 50 km. The stratosphere contains very little water vapour and is much more stable than the troposphere. The ozone layer is within the stratosphere.

   •  Boyle’s law:- at a constant temperature the volume (V) of a given mass of gas is inversely proportional to the pressure (P) upon the gas. i.e. PV = constant.

   •  The pressure law:- at a constant volume the pressure is directly proportional to temperature (T) in Kelvin units.

   •  Charles’ law:- at a constant pressure gases expand by about 1/273 of their volume, at 273 K, for each one kelvin rise in temperature, i.e the volume of a given mass of gas at constant pressure is directly proportional to the absolute temperature.

   •  For one mole of gas the preceding laws are combined in the gas equation PV = RT where R = the gas constant = 2.87 when P is expressed in hectopascals. Ordinary gases do not behave exactly in accordance with the gas laws.

   •  The change in altitude for each one hPa change in pressure can be roughly calculated from the absolute temperature and the pressure at the level using the equation:=96T/P feet.

   •  The term 'burble' also refers to the atmospheric wake of an object. Skydivers refer to their wake as 'the burble' while the disturbed airflow and exhaust gases behind a fast-moving aircraft carrier was (probably still is) known to pilots as 'the burble'.

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 performance | 6. Tailplane surfaces |

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

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

Supplementary documents

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

Copyright © 2000–2007 John Brandon     [contact information]