| Home | Contact us | About  us | Learning to fly | Flight training facilities | Site map & search |

Recreational Aviation Australia Inc home page

Groundschool – Theory of Flight

and the properties of air

Revision 85 — page content was last changed October 28, 2008; consequent to editing by RA-Aus member Dave Gardiner www.redlettuce.com.au

Module content

Atmospheric density, which decreases with increasing height, affects the generation of lift 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.

Static pressure exerts a force on an object (for example, an aircraft wing) at right angles to all the exposed non-porous surfaces, and is 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 of air. 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 increasing 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. This 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. Meteorological offices produce 'thickness charts' for aviation use.

Back to top

2.2 Atmospheric density

The average density of dry air in temperate climates is about 1.225 kg/m³ at mean sea level; the density decreases with increasing altitude.

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

   r = P/RT    where:
  r (the Greek letter rho) = air density kg/m³
  P = static air pressure in hectopascals
  R = the gas constant = 2.87
  T = 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

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

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

Back to top

2.3 The ICAO International Standard Atmosphere

   The International Civil Aviation Organisation's [ICAO] International Standard Atmosphere [ISA] provides a fixed standard atmospheric model that is 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 [msl] 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 850 hPa, then slowing to 40 feet per hPa at 650 hPa, 50 feet at 450 hPa, 75 feet at 300 hPa 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."

Back to top

2.4 Bernoulli's principle and the continuity equation

Daniel 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. (Incidently his father was the mathematician who first adopted the symbol 'g' for the acceleration due to gravity). For aerodynamic purposes, the gravitational potential energy can be ignored. Kinetic energy = ½mv² 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.

Note: a lower case v is the symbol for speed in physics while an upper case V is generally the symbol for airspeed in aerodynamics.

So, Bernoulli's principle can be reduced to:
      ½r [dynamic pressure] + P [static pressure] = constant

The equation doesn't take into account viscosity, heat transfer or compressibility effects, but for operations below 10 000 feet and airflow velocities below 250 knots, compressibility effects 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.

Bernoulli's principle 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 of the equation is that the constant is the stagnation pressure — the pressure energy needed to halt the airflow — thus it can be written ½rv² + P = stagnation pressure; the stagnation pressure is the highest pressure in the system. This aspect of Bernoulli's principle 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 that 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) then we can state that:

s × v = constant

Thus, if air flows into a smaller cross-sectional area speed must increase to maintain the constant. Bernoulli's principle states that if speed increases, static pressure must decrease; so the velocity of a constricted airstream increases and its static pressure decreases.

Both the above equations are related to the conservation laws; Bernoulli's principle to the conservation of energy, and 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 stated above.

Back to top

2.5 Measuring airspeed

   The dynamic pressure of the airflow, in N/m², is represented by the expression ½rV², where:
  • r is the density of the air [kg/m³]
  • V² is the aircraft (or free airstream) speed [m/s²]
   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 a moving aircraft, outside the slipstream, so that the open end points forward into undisturbed airflow and the other end of the tube terminates within a spring-loaded, flexible capsule — similar to that in an aneroid barometer — thus the capsule stops the airflow within the tube.

The back pressure, applied by the capsule to stop the airflow, must be equal to the stagnation pressure. The capsule is contained within a casing which, in turn, is connected to a static vent that supplies 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 pressure 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 I, the airspeed indicating instruments themselves were called 'pitots'.) The capsule movement is mechanically or electrically linked to rotate a pointer on a dial that has been calibrated to indicate airspeed. Because 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 [ASI] and it displays the indicated airspeed [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, and 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 the 'Lift' section.

The airspeed we have been discussing to this point is the true airspeed [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 underread. 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 was 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.

Back to top

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 wings' module. Generally, for all angles of attack in unaccelerated flight at a particular weight, there is a corresponding IAS; though the relationship between aoa and IAS does get a bit fuzzy near CLmax. So, 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 [CAS] and that particular CAS does not change with altitude (as TAS does), but changes only with weight.

(*The reason why CAS does not always correlate 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 CAS is the airspeed after you have applied corrections to the IAS 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. In this particular installation the ASI significantly underreads at low speeds and overreads at high speeds.

IAS knots42526169738796104113122130
CAS knots49576471738694102110117125

We 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 increasing altitude, reaching about 2 at 30 000 feet.

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 1g load factor. The top end of the green arc indicates the maximum structural cruise speed, Vno [173 knots]. The green arc 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 for single-engine aircraft; these markings 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 because there is no instrument lag. A slow response attributed to instrument lag is most likely only 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 equation 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.
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 that the electronic circuitry converts to an airspeed display. See the liquid crystal primary flight display of the Dynon D10A light aircraft EFIS. 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. 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.

Back to top

2.7 Measuring vertical airspeed

The vertical airspeed indicator
 vertical speed indicator     In flight it is important for a 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 that reflects the static pressure change as it occurs. On the closed side the input/output is a fine capillary tube that 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 that enables the aircraft to stay airborne for sufficient time to complete the flight plan. A variometer (usually abbreviated to vario) is a specialised vertical speed indicator that enables a 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 that have some soaring capability.

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

Back to top

2.8 Stalling airspeeds

The normal stall
    One of the first questions a pilot might consider, when converting to a new aircraft type, is "What's the stall speed?" The reason for considering this is that usually, but not always, 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 is attempted.

    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, this is usually around 15–16° although minimum aircraft with single-surface fabric wings may have a stall aoa 2 or 3° lower. This critical angle of attack has no relationship with either 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.

The separation of the boundary layer starts at the wing trailing edge, generally near the wing root for approximately 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 loss of lift. The initial wake turbulence ('burbles') near the wing root will affect flow over the tailplane and may provide a few warning buffets ('nibbles') felt in the controls, and thus warning of an impending stall. There also may be 'oil-canning' noises from pressure changes on metal-skinned fuselages and wings as the thin metal flexes in response to pressure changes. 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
    •   in a low speed descent — such as the approach to landing
    •   in a climb — such as the initial climb after take-off
    •   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 aoa is increasing, total drag increases and the aircraft slows 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 rate of descent may not be apparent unless the aircraft is close to the ground.

The aircraft is instantly recovered from the stall 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 to unstall the dropping wing, the wings levelled with aileron, then sufficient rudder applied to stop further yaw. An increase in speed is also needed (by increasing power or holding a lower nose attitude for several seconds) so that a safe flight speed is achieved quickly without wasting altitude and the aircraft is returned to the intended flight path. See standard recovery procedure for all stall types.

If the control column movement for stall recovery 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 which hinders recovery. Weight-shift controlled trikes do not react well to negative g; if this is 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 semi-stable mushing descent — which sounds fine but can be disastrous if the pilot doesn't notice when close to the surface. A normal stall occurs when the load factor 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 smaller 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. When it occurs, the stall will be much more pronounced, possibly with a fast-acting wing drop. There are other complications because the slipstream also affects parasite drag and induced drag.

Many pilots, in suitable aircraft and atmospheric conditions, prefer to land by approaching at 1.3 to 1.5 times normal stall speed — Vso — and, after flaring 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. At which point, the aircraft can no longer be 'held-off' and it gently sinks the short distance onto the runway; touching down in a nose-high attitude.

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

The acceleration or 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 load factor. 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 acceleration stall or accelerated stall and is usually more pronounced than a normal stall. The load factor normally increases in a turn, as we saw in section 1.10 where we calculated that, in a 45° banked turn, the load factor was 1.41 times normal. Thus, when turning, the stalling speed is higher than normal and the pilot must maintain a reasonable airspeed margin above that accelerated stall speed throughout the turn. See the table below.

Be aware that the airspeed at which an acceleration stall in a turn occurs is only indirectly associated with the angle of bank, it is directly brought about by the increase in load factor. 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 0.8g — with a stall speed less than Vs1, even though the aircraft is steeply banked. However, once the 'unloaded' condition ceases — if the stalling angle of attack has been passed (either by the rearward movement of the control column or a gust momentarily changes the relative airflow) — the probability of a stall returns immediately.

    The speed at which an accelerated stall occurs is proportional to the square root of the load factor. (In the lift equation the airspeed is squared.) If that load factor is expressed relative to the normal load, e.g. 2g, then the stall speed at that load factor — Vs 2g — equals the square root of the load factor × 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 about its lateral axis while inertia momentarily maintains the aircraft on its existing flight path; 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 acceleration 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
    •  an abrupt flight path change, which applies acceleration loads, is made
    •  an excessive bank angle, coupled with excessive control column back pressure, is applied during a level, climbing or descending turn.

Note: The US Federal Aviation Regulations Section 23.203 standards define accelerated stalls somewhat differently from the above, referring to 'turning flight stalls' and 'accelerated turning stalls'.
"Turning flight and accelerated turning stalls must be demonstrated in tests as follows:
(a) Establish and maintain a coordinated turn in a 30 degree bank. Reduce speed by steadily and progressively tightening the turn with the elevator until the airplane is stalled. The rate of speed reduction must be constant, and--
(1) For a turning flight stall, may not exceed one knot per second; and
(2) For an accelerated turning stall, be 3 to 5 knots per second with steadily increasing normal acceleration*."
* 'Normal acceleration' refers to acceleration parallel to the aircraft's normal axis.

[ The next section in the airmanship and safety sequence is the follow-on section 'Load factor in a turn' ]

Load factor in a turn
The table below shows the increase in stall speed at various bank angles in correctly executed level turns. The load factor or 'g' = 1/cosine of the bank angle and the Vs multiplier = the square root of the load factor. 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 angleCosineLoad factor [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 4%. But the 10° increase in the bank angle between 50° and 60° increases stall speed by 16%; i.e. four times greater, while between 60° and 70° the stall speed is increased by 30%. Aircraft certificated in the normal category are limited to a turning angle of bank of not more than 60°.

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

[The next section in the airmanship and safety sequence is the section '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, which accelerates 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 operating wing loading will be less than the design W/S and the stall will occur at a lower speed than that marked on the ASI.

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 in the section 'The acceleration or accelerated stall' that W/S at the stall = CL × ½rV².
We will rearrange that and say Vs² = (W/S) / (CLmax × ½r). Substituting the values, including 1.225 for density, we get:

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 with no passenger on board 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%, reduces Vs by 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; and because aerodynamic pressure is proportional to V², there are many occasions where the square root of a value is relevant. This 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 — one of several reasons to avoid overloading an aircraft. (There is further discussion on weight control throughout these notes.)

Thus in the section 'The acceleration or accelerated stall' above, where we referred to unloading the wings with the aircraft banked at 60°, the load reduction from 1g down to 0.8g is 20% so the unloaded stall speed would be about 90% 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 it is not only aircraft weight/wing loading that affects the stall speed. 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 and 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 'Aircraft flight envelope' section below.

Back to top

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 two to six letters/numbers, with the first being V. Some of these V-speed codes with alternatives, and definitions are shown below. These may be relevant to light single-engine aircraft including ultralights, and might appear in flight manuals, pilot's operating handbooks and even sales literature. 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. This is 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 that 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 up 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. 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 that imparts an acceleration sufficient to exceed the load limit factor.

If the aircraft designer has specified a manoeuvring speed that 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, which is 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 in section 'Cruise speeds'), 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, which is the IAS which should never be intentionally exceeded in a dive or other manoeuvre — in smooth air. It is indicated by 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, then 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 'Don't fly real fast'.

   •  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 level flight with flaps up, at MTOW and 1g wing loading, with engine idling following a gradual deceleration [one knot per second] — accompanied by increasing rearward movement of the control column — to that minimum flight speed. It is indicated by the bottom end of the ASI green arc, but it may be documented as IAS or CAS; if it's 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 and engine at low or idle power as it would be just prior to touchdown. This is 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. It is indicated by 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, is the speed that provides maximum L/D by producing minimum drag and thus the best power-to-speed ratio. This speed 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. Vbr/Vmd has the same basic airspeed range as Vy and Vbg [below].

power curveThere 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, in this case, indicates 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, is the CAS that gives the greatest airborne time per litre (i.e. least fuel flow per hour and, of course, power is proportional to fuel flow), possibly around 80% of Vbr/Vmd, and decreases 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, as shown in the power required curve above.

Vbe/Vmp is the speed that might be used when flying a search pattern to allow 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 practice. Carburettor icing may be aggravated. The Vmp designation and speed is also used as a power-off glide speed, providing the best endurance — least rate of sink — in the glide; see 'Power-off descent speeds' below. Vbe/Vmp is 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 that gives the most velocity (i.e. greatest distance/time) from a litre of fuel, usually utilisies 75% power at MTOW and is about 20–30% greater than the maximum L/D speed — Vbr. The speed and power required both decrease as the aircraft weight decreases from MTOW. Refer to Rule of Thumb #3 in section 2.8 'Stalling airspeeds'.

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 ÖW/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. For most engines maximum continuous engine power at sea level will be less than full throttle power.

Take-off and landing speeds
   •  Vfe — maximum flaps extended speed. It is indicated by 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 — for 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 — the lift-off indicated speed for normal take-off. Vlof is about 10% above Vmu.

   •  Vmu — minimum unstick speed. This is an indicated speed 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-out. 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 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 m. To this 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. This is an indicated speed 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, an airworthiness certification requirement 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 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.)

In normal take-off conditions Vtoss should be somewhere between 1.3 and 1.5 times Vs1 with 'draggy' aircraft tending to the higher value. If power is 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. See 'Engine failure after take-off'.
Climb speeds
   •  Vx — indicated speed provides best angle of climb for obstacle clearance; i.e. to attain height over the shortest ground distance using maximum thrust available. This is 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 8–10º. 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 this speed is increased in a tailwind by a similar amount. Also note that aoa during climb may be only 5 or 6° 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 any appropriate 'enroute climb speed'. The latter reduces the rate of climb but has the benefit of reducing total sector time. This may be beneficial to engine operation but, more importantly, provides a little more airspeed in hand should the engine falter or fail. The airspeed for Vx increases with (density) altitude and is much the same airspeed as Vbe, although engine cooling needs might require a higher airspeed.

   •  Vy — indicated speed for best rate of climb. This speed is used 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 to Rule of Thumb #3 above), but the angle of attack is maintained at around 6–8º. 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 This is the airspeed that provides minimum drag thus maximum L/D, or glide ratio, and thus the greatest still air glide range 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 is 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. This is the speed that results in the lowest rate of sink in a power-off glide, and provides the longest duration of flight from the potential energy of height. The lowest rate of sink occurs at the minimum value of drag × velocity. It is 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 m/s 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 can happen 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 lead 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']

back to top

2.10 Aircraft flight envelope

The design 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". (The flight envelope is not the cruise-to-stall ratio, nor the range of airspeed between minimum and maximum airspeed.) 'Airframe states' refer to flap extensions, undercarriage position and the weight. It is a dynamic two-or-three dimensional model that 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 in particular, 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. This displays 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 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 the wings are loaded 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, and this has 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.

back to top

Things that are handy to know

   •  Absolute temperature is expressed in kelvins [K]. One K equals 1 °C and 0 °C is equivalent to 273 K.

   •  In a free stream airflow, a favourable pressure gradient is one where static pressure decreases with distance downstream. An adverse pressure gradient is one where static pressure increases with distance downstream.

ASI position error. The static vent is an opening, best placed at a position on the aircraft's fuselage, 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 counteract static pressure disturbances caused when the aircraft is slipping/skidding, and/or a switchable alternative static source within the cockpit.) The opening is a 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 underread 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 caused by excessive friction. Obstructions in the tubes — such as water or wasp's nests — will cause misreadings.

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 [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.

   •   Compressibility effects. 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 overread by only 0.5 knots or so. However, for aircraft operating at high speed or high altitude, compressibility will cause the ASI to overread significantly, so 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 airspeed [EAS].

For most medium-speed aircraft, it is probable that the compressibility correction value has been built into the IAS–CAS airspeed correction table.

There is no practical application for recreational pilots, but aerodynamicists tend to use the EAS term — rather than IAS or CAS — assuming 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 true airspeed, which is equivalent to the dynamic pressure in the instrument at any altitude.

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

   •   Checking validity of claimed stall speeds. There is a simple method to check the validity of published stall speeds. Practically all very light aircraft (except 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, and 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 × square root (wing loading in kg/m² divided by CLmax)

Stall speed [knots] = 17.2 × 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 — it is 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 troposphere, 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 kelvins.

   •  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 (and 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]