Groundschool – Theory of Flight
Airspeed
and the properties of air
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Groundschool – Theory of Flight |
Airspeed
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Atmospheric density — a function of pressure and temperature — decreases with increasing height. It affects the generation of lift and aircraft performance, as does the angle of attack at which the aircraft is flown. In normal, unaccelerated flight, there is a relationship between airspeed and angle of attack. So, in light aircraft, the airspeed indicator instrument — which measures dynamic pressure — 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 performance airspeeds, and of critical airspeeds, is defined.
2.1 The atmospheric pressure gradientThe 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. |
2.2 Atmospheric densityThe average density of dry air in mid-latitude, 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* = air density kg/m³ P = static air pressure in hectopascals R = the gas constant = 2.87 T = air temperature in kelvins [K] = °C + 273 *r is the Greek letter rho, pronounced 'row', as in 'row your boat'.
By restating the equation of state as: P = RrT , it can be seen that if density remains constant; pressure increases if temperature increases. |
2.3 The ICAO International Standard AtmosphereThe 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:
It can be seen that (from sea level to 10 000 feet) air density decreases by about 33 grams/m³ per 1000 feet. Also, not immediately apparent from the ISA table, is that the pressure lapse rate (the rate of change with height) is exponential. It starts at about one hPa drop per 28 feet height increase, then slowing to 31 feet per hPa at 6000 feet (averaging 30 feet height increase per hPa drop up to 6500 feet), 36 feet per hPa at 10 000 feet, 50 feet at 20 000 feet and so on. However, the following provides a useful rule of thumb:
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2.4 Bernoulli's principle and the continuity equationDaniel Bernoulli (1700-1782) was a Swiss mathematician who propounded the principle that for a given parcel of freely flowing fluid, the sum of gravitational potential energy, kinetic energy and static pressure energy always remains constant.For aerodynamic purposes we can ignore the gravitational potential energy. Dynamic pressure = ½rv² and kinetic energy = ½mv² where m = mass. Air density is mass per unit volume; i.e. kg/m³ so dynamic pressure is the kinetic energy per unit volume. Static pressure is internal kinetic energy per unit volume, or pressure potential energy. So for our purposes (in a parcel of freely flowing air) Bernoulli's principle can be reduced to: ½rv² [dynamic pressure] + P [static pressure] = constant The statement 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 statement then indicates that, in a free stream flow, if speed [v] increases static pressure [P] must decrease to maintain constant mechanical energy per unit volume; 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 (transferred to the skin) due to the skin friction. (Incidently Daniel Bernoulli's father Johann [born 1667] was the mathematician who first adopted the symbol 'g' for the acceleration due to gravity.) Stagnation pressureAnother aspect of Bernoulli's principle 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 application of the principle is apparent in the air speed indicator, as demonstrated below.Stagnation pressure is the basis of the ram-air parachute wing used in sport parachutes, paragliders and powered parachutes, see 'The ram-air parachute wing'. Also aircraft fuel-tank vents rely on stagnation pressure to prevent inflight siphoning of fuel from the tank. Continuity equationThere is another principle of aerodynamic interest to us — the fluid flow continuity equation — which states that, in a steadily moving airstream, the product of density, cross sectional area [s] and speed 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 principles 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. |
2.5 Measuring airspeedThe dynamic pressure of the airflow, in N/m², is represented by the expression ½rV², where:
*Note: a lower case v is the symbol for speed in physics while an upper case V is generally the symbol for the free stream speed in aerodynamics, which is why I have used the lower case v in section 2.4 but an upper case V in this section and most of this flight theory guide.) 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 or ram-air 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. Although the dial is calibrated and marked to indicate airspeed in knots or mph rather than hPa, it is still basically a simple pressure gauge and an imperfect airspeed gauge. 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. The indicated airspeed is not the actual aircraft speed through the air, 'V' in the equations. A bit confusing — but brace yourself, for it gets worse!
Note that the dynamic pressure at 1250 N/m², or 12.5 hPa, 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 'V' in the equations is the true airspeed [TAS] — the free stream speed or the air distance flown over time. We know that the ASI dial is calibrated assuming a fixed air density of 1.225 kg/m³ [ro ], so a perfect ASI will only indicate the real airspeed (the true airspeed) when the actual environment density is 1.225 kg/m³; that could only occur when the aircraft is operating at low altitude.
From this we can deduce that a perfect ASI will generally underread. The IAS will always be less than the TAS, except in very cold conditions at 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% less than the ISA value for each 3 °C that the temperature is above the ISA value. |
2.6 Indicated airspeedSo, you might ask, what's the point of an ASI that really is indicating just dynamic pressure, and is unlikely to indicate your real 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. CAS was once known as rectified airspeed [RAS]. *The reason why CAS does not always correlate to aoa in level flight is that when inertia and random displacement forces — atmospheric turbulence — come into play, aoa may change momentarily without a noticeable change in CAS. (Note: there are means of audibly conveying the angle of attack to the pilot. The simplest is a stall warning horn operated by a basic two-position vane switch incorporated in the leading edge of the wing and switched on by the airflow pressing the vane up if the aoa comes close to the stalling aoa. There are other airstream direction detectors (ADDs) that provide a range of warning tones in the pilot's headset.) An ASI is an imperfect mechanical instrument which is subject to instrument errors; the poorer the quality of the instrument the greater the instrument error; the permissable limit for a certified ASI is ±one knot. The associated pitot/static and tubing system is also prone to pressure sensing errors due to the positioning (and design) of the pitot head — and/or the static air vent — relative to the airstream. That relative airflow changes as aoa changes and when sideslipping. CAS is the airspeed after you have applied corrections to the IAS for those instrument errors plus position 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 under-reading by 10 knots or so — particularly at high aoa or when the pilot is maintaining a significant sideslipping manoeuvre. Below is an airspeed correction card for a particular aircraft in balanced level 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.
Converting CAS to TASTAS = CAS × √(ro / r)Using our example, from section 2.5, of the Jabiru cruising at 88 knots IAS at 6500 feet, where the air density is 1.0 kg/m²: TAS= 88 × √(1.225 / 1.0) = 88 × 1.107 = 97 knots We need TAS for navigation and as the density lapse rate just about follows a straight line below 10 000 feet – there is a simple mental calculation to determine TAS from CAS.
The 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 speeds for normal operations. 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, Vne, that should never be exceeded 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
Electronic ASIElectronic 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. |
2.7 Measuring vertical airspeedThe vertical airspeed 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 variometerIn soaring flight, paraglider, hang glider, sailplane and power-assisted sailplane 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 soaring.For more information on varios and their uses see the article 'Basic sailplane instruments. The article only refers to fixed installation varios but very light-weight hand-held varios are available for hang glider/paraglider pilots. |
2.8 Stalling airspeeds
The torque stallFor 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 weightIf 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.
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:
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 and manoeuvring 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 'Wind shear and turbulence" tutorial. |
2.9 V-speedsIt is important to have a simple, easily understood and universally 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 — applicable to single-engine aircraft — with alternatives and definitions are shown below. These are relevant to recreational and sport aircraft including low momentum ultralight aircraft, and might appear in flight manuals, pilot's operating handbooks and even sales literature but those indicated with open bulleting º are probably only applicable to a few very light aircraft types. There are two classes of airspeed codes. One is the structural design speeds (specified in national airworthiness requirements) used in determining the airframe and control surfaces strength requirements for type certification. Such speeds include the term 'design' in their description. The other class are the designer recommended operating speeds. 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.
Cruise speedsA cruising aircraft is normally flying at a moderate, fuel efficient speed and maintaining the appropriate cruising altitude. The Australian Civil Aviation Regulations hold this definition:"cruise phase of flight" means the part of an aircraft's flight: (a) that starts when the aircraft reaches its first planned cruise level, ... and (b) that ends when the aircraft reaches the point at which the aircraft first starts its descent for the purpose of landing; and includes flight level changes made during that part of the flight. • 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].  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, in this case, indicates a Vbr that is about 15 knots greater than Vmd. This is the same principle used by sailplane 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 utilises 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 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. Many minimum ultralights are unable to comply with the FAR Part 23 design requirement for a minimum design cruising speed. For most light aircraft, Vc is synonymous with Vno. FAR 23 Appendix A provides simplified design load criteria and allows designers of many conventional single-engine monoplanes weighing less than 2700 kg to take advantage of the simplification. That same appendix is generally duplicated in the design regulations of most other countries. One advantage is that it is not necessary to specify Vno; instead, Vc is designated in the flight manual as the maximum structural cruise speed (i.e. Vno = Vc) and that Vc may be set at 90% of Vh. 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.
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2.10 The design manoeuvring flight envelopeThe structural design manoeuvring flight envelope of a recreational aircraft has been 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' refer to flap and spoiler extensions, undercarriage position and the gross weight. The flight envelope is only relevant for an aircraft within the required weight and balance conditions.The boundary of the envelope is formed by combinations of the applicable load limit factors and airspeeds. It is a two-dimensional model that has airspeed along the horizontal axis and flight load factors expressed in 'g' accelerations along the vertical. The loads are those parallel to the aircraft's normal axis, i.e. perpendicular to the longitudinal axis — the aerodynamic loads in the aircraft's pitching plane. The symbol 'n' is used to identify loads in the airworthiness regulations. The parameters for a light aircraft usually are the limiting critical airspeeds — Vs, Va, Vno, Vne, Vd and the certificated limit load factors. There are other flight limitations which are not displayed in the flight envelope diagram, e.g. an angle of bank limitation of 60° for some aircraft categories. For weight-shift aircraft in particular, there are also pitch limitations; — e.g. 45° nose up or nose down from the horizontal. The manufacturers of high performance non-recreational aircraft would also provide other charts, altitude performance or turning performance for example. The V-n [or V-g] diagram below is a simplified representation of a few aspects of the manoeuvring flight envelope for an LSA category aircraft at MTOW and low altitudes. An airspeed scale would normally be displayed along the horizontal axis and the load factors (in units of 'g') along the vertical axis between the certificated load limits for light sport aircraft of +4g to –2g. This diagram does not refect any flaps extended conditions. The positive and negative 'aircraft normal force coefficient curves'* are for the aircraft as a whole but can be assumed to approximate the accelerated stall speeds at loads of Vs1g × Öload factor. (*Normal force: pilots consider the aerodynamic force acting on the aircraft in terms of lift and drag, lift being perpendicular to the relative free-stream airflow and drag being parallel with it. Aerodynamicists may also consider the total aerodynamic force in terms of a 'normal force' which is parallel to the aircraft's normal axis and an 'axial force' which is parallel to the longitudinal axis. The symbol for the aircraft normal force coefficient is Cna. At low angles of attack the vectors drawn to represent the L/D and the normal/axial forces would be close but diverge as aoa increases) The stall speed at a 4g load limit factor would be Vs1g × Ö4 = Vs1g × 2, thus if the Vs1 stall speed was 45 knots then the stall speed where the positive curve intersects the 4g load limit factor line is 90 knots, i.e. that speed is the lowest possible speed at which the pilot can pull maximum g, i.e. 4g. That corner of the envelope is usually the position of Va — the design manoeuvring speed. You can see from the curve that at the Va airspeed the aircraft will stall when the wing loading exceeds 4g. Sustained flight is not possible in the white region to the left of the accelerated stall curves because the wings will be stalled. (Note: the light blue area between +1g and –1g is the realm of reduced gravity, or microgravity. NASA and other organisations use C135 and DC-9 aircraft flying a parabolic trajectory to produce reduced or near-zero gravity conditions, for the aircraft occupants, for periods of 20–30 seconds. A light aircraft can be flown in the white area for a brief period by 'unloading' the wings — 'bunting'.) Except for turbulence loads the negative flight envelope below the 0g line mainly relates to aerobatic aircraft though, for such aircraft, the outline of the flight envelope would include more corners.
(Note: in section 2.8 we determined that a 60° banked level turn doubled the normal wing load. With Vs1 at 45 knots and Va 90 knots then visualise a horizontal line from the 2g point; the interception with the curve will equate with about 60 knots. So that would be the lowest possible speed for a 60° banked level turn.) The white areas above and below the envelope represent structural loads beyond the positive and negative limit loads. Flight loads caused by control misuse and/or atmospheric turbulence that exceed +4g or –2g may cause temporary pilot incapacitation (greyout/blackout/redout) and airframe damage. Flight loads 50% greater than +4g or –2g (i.e. +6g or –3g) are likely to cause airframe breakup. In the aircraft design process the design maximum dive speed Vd is a calculated speed, but in the flight test stage the aircraft may be tested up to a speed where it still demonstrates no flutter, or other, problems. This is the flight-demonstrated dive speed Vdf which is lower than the design Vd but, possibly, it could be equal to it. The speed which a pilot must not exceed is Vne, and that is required to be no more than 90% of Vd or the flight-demonstrated dive speed. At the very high speed of Vne the aircraft is flying at a very small angle of attack, deriving most of the aerodynamic force from its velocity. If the pilot — or turbulence — suddenly increases the aoa the consequent increase in the lift coefficient CL (amplified by the aircraft's inertia momentarily maintaining the original flight path) could place an extreme load on the airframe, enough to break it. See 'Wind shear and turbulence'. For more information concerning the risks of flight at excessive speed read 'Don't fly real fast!' in the 'Decreasing your exposure to risk' tutorial. The maximum airspeed allowed is Vne, but full and rapid control applications are restricted to speeds at or below Va. Vno is the maximum structural cruise speed or 'normal operating limit' for flight in light to medium turbulence. Above the Vno/Vc speed flight should only be conducted cautiously and in smooth air. So, the aircraft can be flown in the dark green area without limits on (smooth) control use and it can be operated within the light green area in light to moderate turbulence, but it should not be operated in the tan area except in a reasonably smooth atmosphere. If it is inadvertently operated in the white area — i.e. outside the certificated load limits, or at velocities greater than Vne — 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 aerodynamic forces. The faster the aircraft is moving, the greater the gust-induced load. FAR Part 23 has requirements for designers to consider unexpected gust loads. The resulting gust envelope is often represented as the flight manoeuvring envelope with overlaid gust lines. 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 most light aircraft because, for such aircraft, 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. The same applies to the use of flaps. 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 'Don't 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
• Absolute temperature is expressed in kelvins [K], one K equals 1 °C. The base temperature is zero kelvin — equivalent to minus 273 °C — so 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. In addition if the airflow is not squarely aligned with the entry of the pitot head there will be a reduction in the indicated airspeed which increases as aoa increases. 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 or no reading. Position error corrections plus the instrument error corrections for the system 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 use the EAS term — rather than IAS or CAS — assuming an ASI, that has no errors caused by mechanical, position, aoa or compressibility effects, would display the ISA standard condition sea-level true airspeed, which is equivalent to the dynamic pressure in the instrument at any altitude. For more information see 'Notes: compressibility of airflow and Mach number'. • 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) (or) 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 |
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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 © 2000–2012 John Brandon [contact information]
