30 Airspeed Definitions & Airspeed Measurement

Introduction

Knowing how fast an aircraft travels through the air is critical to its piloting and engineering. The performance characteristics of an aircraft are generally presented in terms of its airspeed, as well as a function of its flight altitude (usually the density altitude) and in-flight weight. However, determining an aircraft’s airspeed must be done with great care, and the process requires a knowledge of aerodynamics and other engineering principles.

Pilots are usually concerned more about the indicated airspeed, or IAS, which is read off the airspeed indicator (ASI) in the cockpit. If the IAS can be corrected for mechanical and static pressure reading errors, then it is called the equivalent airspeed or EAS. This particular airspeed is significant because it measures the actual dynamic pressure acting on the aircraft. However, engineers are also concerned with the true airspeed or TAS of the aircraft through the air, which will, in general, not be the same as the IAS or the EAS. True airspeed, TAS, and ground speed (which include the effects of the winds) are also needed by pilots for navigation purposes. Therefore, to avoid confusion and potential misinterpretations of what is called “airspeed,” the proper basis of airspeed measurement and the various definitions of airspeed must be understood, as well as how such measurements are actually used in both engineering and aviation practice.

Objectives of this Lesson

  • Understand the aerodynamic principles associated with airspeed measurement.
  • Know the difference between indicated, equivalent, calibrated, and true airspeeds.
  • Be able to calculate the true airspeed of an aircraft.

Airspeed & Mach Number Regimes

When a flight vehicle’s performance is addressed, its “speed” capabilities are obviously critical. This means the speed through the air or airspeed and specifically the true airspeed of the aircraft relative to the air, or what is referred to in engineering terms as the quantity “V_{\infty}.” The achievable airspeed (or airspeed range) of a flight vehicle is best classified in terms of its corresponding flight Mach number, as shown in the figure below. Recall that the Mach number is the ratio of airspeed to the speed of sound, so the flight Mach number M_{\infty} at any altitude will be given by

(1)   \begin{equation*} M_{\infty} = \frac{V_{\infty}}{a_{\infty}} \end{equation*}

where V_{\infty} will be the true airspeed and a_{\infty} is the ambient speed of sound at that altitude and temperature.

When categorizing aerodynamic flows about a flight vehicle, its in-flight Mach number is one of the most useful.

The speed of sound depends on the outside air temperature T_{\infty} at any altitude, i.e.,

(2)   \begin{equation*} a_{\infty} = \sqrt{ \gamma R T_{\infty}} \end{equation*}

so for a given true airspeed the flight Mach number increases with increasing altitude in the atmosphere. Again, engineers would generally default to using the ISA model for any atmospheric properties needed for calculations unless instructed otherwise. The ISA has the advantage of standardizing measurements because it can be used as a universal basis for instrument calibration or another reference.

A flight vehicle classified as being low subsonic speed capable will cruise in the range up to M_{\infty} < 0.3 to 0.4, i.e., a predominantly incompressible flow region where the effects of compressibility about the vehicle are small and would be expected to have a minimal impact on any aspect of the vehicle’s performance. This range is where most general aviation aircraft, rotorcraft, and uncrewed aerial vehicles (UAVs) fly.

A flight vehicle that would be classified as a high subsonic vehicle will fly at Mach numbers up to M_{\infty} < 0.7 to 0.85, which is where many commercial airliners fly, and here compressibility effects would be expected to manifest in some form. In subsonic flow, the airloads are readily predictable but are somewhat more challenging to predict in transonic flow. Recall that the transonic region occurs approximately when M_{\infty} = 0.8 to 1.2, so most airliners begin to intrude into the transonic region of flight.

Vehicles capable of supersonic flight will fly from M_{\infty} = 1 up to as much as 5. This upper Mach number range is called hypersonic flight for M_{\infty} > 5. There are very few flight vehicles capable of sustained hypersonic flight, all of them are research vehicles. One of the most significant issues here, besides the efficient aerodynamic design of the aircraft itself, is developing a suitable engine that can operate in this high Mach number regime to power the aircraft. Exceptions naturally include space vehicles, which reach hypersonic conditions during re-entry into the Earth’s atmosphere.

Definitions of Airspeeds

So far, the term “V_{\infty}” has been used frequently, which has generally been termed as the aircraft’s true speed through the air, i.e., the true airspeed or TAS. However, when dealing with airplanes (and aircraft, in general), several different speeds may be used, and these must now be defined. For example, the aircraft’s speed over the ground differs from the true airspeed. The ground speed depends on the magnitude and direction of the winds in the air mass in the direction of flight. Also, the speed read by an airspeed indicator (see the figure below) is not the true speed of the aircraft, nor is it the ground speed. This may all sound confusing, and it is, which is why the various types of airspeeds that are used for aircraft must be understood.

It is best to understand precisely what an airspeed indicator (ASI) measures. An ASI, as shown in the figure below, is one of the most fundamental instruments used for flight, and the readings made by an ASI are used not only for piloting but for engineering purposes. An ASI is a pressure-measuring (pneumatic) instrument that responds to dynamic pressure q variations with a scale calibrated in speed units. The ASI is calibrated to read airspeed, usually in units of “knots” (kts), which means nautical miles per hour. Knots is a unit used universally in aviation, but some ASIs may be calibrated in km/h (kph) units.

An airspeed indicator or ASI, which is calibrated in units of speed but responds to dynamic or “ram” pressure. The pressure source is either a pitot-static probe or a separate pitot probe and a static vent.

Recall that dynamic pressure is the difference between the total or stagnation pressure p^* (sometimes also called the “ram” pressure) and the static pressure p, i.e., q = p^* - p_s. Sometimes a Pitot-static probe will be used to measure dynamic pressure, but other times a separate total pressure probe (which measures q^*) and a static pressure vent placed somewhere on the surface of the aircraft (which measures p_s) will be used. In either case, the measured pressure difference is the dynamic pressure, to which the ASI responds.

Consider flight at low Mach numbers where the flow can be assumed as incompressible. If the total (stagnation) pressure is denoted as p^* then the use of Bernoulli’s equation (which is valid for incompressible flow) gives that

(3)   \begin{equation*} p_s + \frac{1}{2} \rho V_{\infty}^2 = p^* \end{equation*}

Rearranging this latter equation gives the true airspeed (TAS), i.e.,

(4)   \begin{equation*} {\rm TAS} = V_{\infty} = \sqrt{ \frac{p^* - p_s}{2 \rho}} = \sqrt{ \frac{\Delta p}{2 \rho_0} \frac{1}{\sigma} } \end{equation*}

which is exact if the density of the air \rho is known as well as the measured value of \Delta p.

Of course, this latter equation is hardly convenient to use even to find TAS even if p^* and p_s are known because \rho depends on both pressure altitude and temperature. Not only that, there must be a speed scale on the ASI that is associated with any given \Delta p, which means that a formal calibration is needed against some reference. It will also be apparent that the scale needed on the ASI will be non-linear because of the relationship between the value of static pressure and square of the airspeed (or dynamic pressure) as formalized by the Bernoulli equation.

To resolve these apparent dilemmas, the airspeed measurement on the ASI is referenced to mean sea level (MSL) density conditions by calibrating the speed scale based on the assumption that \rho = \rho_0, the corresponding measured airspeed then being known as the equivalent airspeed or EAS, i.e.,

(5)   \begin{equation*} {\rm EAS} = \sqrt{ \frac{p^* - p_s }{2 \rho_0} } = \sqrt{ \frac{\Delta p}{2 \rho_0}} \end{equation*}

The true airspeed is then obtained from calculation by using

(6)   \begin{equation*} {\rm TAS} = \frac{{\rm EAS}}{\sqrt{\rho/\rho_0}} = \frac{{\rm EAS}}{\sqrt{\sigma}} \end{equation*}

which requires the value of \sigma to be evaluated. To find \sigma first requires a measurement of pressure altitude and outside air temperature, and then using the equations of the ISA model.

The critical thing to remember is that TAS is not a directly measurable quantity and requires measurement of EAS followed by a calculation using the value of \sigma to obtain TAS. Nevertheless, measuring the EAS on the ASI is very convenient from a piloting perspective because the actual dynamic pressure (to which the aircraft responds aerodynamically) is related to EAS. However, it does not solve the problem that engineers generally require TAS, for which a calculation is always needed. Notice that the EAS and TAS will only be equal if the aircraft is flying at MSL and that the EAS measurement is entirely error-free, the latter being an issue that must now be considered.

Why is Airspeed Measured in Knots?

The “knot” or “knots” is a unit of speed equal to one nautical mile per hour. It is equivalent to 1.15078 mph or 1.852 km/h or 0.514 m/s. The knot’s standard symbol is “kn” but the use of “kt” or “kts” is also common, especially in aviation. The symbol “kt” is the specific form recommended by the ICAO. The term knot or knots originally derives from pre-19th century nautical use when sailors would estimate the speed of a ship by counting the number of knots in the line that was unspooled from a reel in a specific time.

Measurement of Total & Static Pressures

The “error-free” issue in airspeed measurement mentioned previously requires further elaboration because the preceding arguments are predicated on two major points:

  1. The total and static pressure can both be measured accurately.
  2. The ASI can be adequately calibrated against a suitable reference in terms of units of speed.

One source of error is called the Static Position Error or SPE (discussed later), which is the error in measuring the local static pressure on the outside of the aircraft relative to the actual static pressure at that altitude and airspeed. If the IAS reading is corrected for the SPE and mechanical errors, the resulting speed is called the calibrated airspeed or CAS. If the SPE and mechanical instrument errors are small, it is sufficient to state that IAS = CAS = EAS. However, it must be appreciated that, in general, the IAS differs from the EAS and the TAS.

For many piloting purposes, the SPE and mechanical errors are usually small enough (perhaps a couple of kts) that they can be ignored. Nevertheless, the correction is always included (by FAA regulations) in the aircraft’s flight manual. In the case of a modern airliner, the correction is included in the electronic flight control system as a software correction to airspeed. However, for engineering purposes, all such errors must be accurately accounted for in all aircraft performance analyses.

While sometimes a pitot-static probe is used to measure dynamic pressure, in practice, it is found that it can be measured somewhat more accurately by using a separate pitot probe and static vent, as shown in the schematic below. There may be more than one static vent, which is for redundancy. The pitot probe is set off from the aircraft’s surface into the flow; these pitot probes may be mounted on an airplane’s nose or, in some cases, under the wing. The total pressure is connected to the airspeed indicator (ASI), with the static pressures being connected to the altimeter and vertical speed indicator. A heating element is used on the Pitot probe to prevent icing and give false pressure readings.

Typical pitot-static system on an airplane, which provides the reference pressures needed for the airspeed indicator as well as other pneumatic instruments. Notice in this case the use of a pitot probe to measure total pressure and a separate static vent (usually located somewhere on the side of the fuselage) to measure the reference static pressure.

Total Pressure

The total (ram) pressure can be measured without much error because the probe points directly into the airflow, and the resulting pressure is relatively high compared to the static pressure. The only exception might be in cases where the aircraft is significantly yawed with respect to the oncoming airstream, although this would not be a common flight condition. An example of a total pressure probe placed on the nose of an airplane is shown in the photograph below.

Pitot probe mounted on the right-side of the nose of an airplane.

Static Pressure

The static pressure is always more challenging to measure accurately because its value is relatively smaller and measured on the airplane’s outer surface, usually at a location where the local static pressure is close to the ambient static pressure. However, there can be no point on the surface where the local static pressure exactly equals the static pressure in the free-stream flow. Therefore, the static pressure measurement available to the ASI is always in error to a lesser or greater degree, called static position error or SPE.

Static vents on the side of the nose of an airplane. Notice the multiple separate vents, which is for redundancy in the event that one or more vents becomes blocked.

Static Position Error (SPE)

The effects of SPE must always be measured and, in most cases, corrected for engineering and piloting. This process is conducted using a formal calibration process during flight testing with the specific make and model airplane. Measurements of the true static pressure are compared to the local static pressure measured at the pressure tap(s) on the outside of the aircraft. As shown in the figure below, there are a few points on the outside of the aircraft where the local static pressure is equal to the true static pressure in which the aircraft is flying. The static pressure port on a prototype airplane is usually re-positioned after flight tests such that it is ultimately located where the SPE is minimized as much as possible. However, the SPE will never be precisely zero.

There are several options at which to place a static pressure port to minimize the SPE, although even then the SPE will vary somewhat with airspeed and altitude.

In the SPE calibration process, which is performed during flight testing, the true static pressure is measured well behind the aircraft using a trailing cone apparatus, as shown in the photograph below. The SPE will vary somewhat at different airspeeds and altitudes, so the SPE must be mapped out over the entire operating envelope of the aircraft. Usually, the SPE is highest at lower airspeeds and lower at higher speeds and also at higher altitudes. The process must also be conducted with the aircraft in the “clean” configuration (i.e., flaps and landing gear retracted) as well as in the “dirty” configuration (i.e., with flaps and landing gear down, such as for landing). The results will then apply to all production aircraft of the exact same make and model. The results, by regulation, are always included in the aircraft’s flight manual and perhaps the flight control system software.

The trailing cone method is used to calibrate the pitot-static system on an aircraft to account for static position error.

Mechanical Error

The mechanical error in the ASI can be obtained in a laboratory setting using a calibration against a reference ASI, which results in a standard mechanical error calibration chart (or table), as shown in the example below. Each calibration will apply to a specific ASI, and a new calibration will be needed if the ASI is replaced. The errors are usually small enough to be unimportant for piloting purposes, but they should be included in any data reduction process for engineering work.

Airspeed Measurement at Higher Mach Numbers

The issue of airspeed measurement in higher-speed flight where compressibility issues manifest must also be addressed. In this case, using the Bernoulli equation would not be appropriate. In practice, compressibility effects on airspeed measurement are negligible below about 10,000 feet and 200 knots; at higher altitudes, the lower air temperatures decrease the speed of sound, thereby increasing Mach numbers.

Remember that airspeed values on the ASI are  referenced to MSL density conditions by calibrating the speed scale based on the assumption that \rho = \rho_0, so corresponding equivalent airspeed or EAS is then

(7)   \begin{equation*} {\rm EAS} = \sqrt{ \frac{p^* - p }{2 \rho_0} } = \sqrt{ \frac{\Delta p}{2 \rho_0}} \end{equation*}

The true airspeed is then

(8)   \begin{equation*} {\rm TAS} = \frac{{\rm EAS}}{\sqrt{\rho/\rho_0}} = \frac{{\rm EAS}}{\sqrt{\sigma}} \end{equation*}

the value of \sigma being obtained measurements of pressure altitude and outside air temperature.

For subsonic Mach numbers above 0.3, then the total and static pressures can be related using the isentropic thermodynamic relationships. In this case

(9)   \begin{equation*} \frac{p^*}{p_s} = \left[ 1 + \frac{\gamma - 1}{2} M^2 \right]^{\gamma/(\gamma -1)} \end{equation*}

which can be used to solve for the Mach number, M, i.e.,

(10)   \begin{equation*} M = \sqrt{\left( \frac{2}{\gamma - 1} \right) \left[ \left( \frac{p^*}{p_s} \right)^{\gamma/(\gamma -1)} - 1 \right] } \end{equation*}

so basically the Pitot system now gives a measurement of Mach number.

Not only does the total pressure and static pressure need to be measured in higher speed flight, but the total temperature must be measured too, from which airspeed can again be obtained by calculation. The airspeed is then given by

(11)   \begin{equation*} V = a M = \frac{a_0^2 M^2}{1 + \displaystyle{\frac{\gamma-1}{2} } M^2} \end{equation*}

but this calculation requires either the value of the static speed of sound a or the stagnation speed of sound a_0. To this end, the stagnation temperature of total air temperature (TAT) or T_0 is usually measured during flight so that

(12)   \begin{equation*} a_0 = \sqrt{ \gamma R T_0} \end{equation*}

from which the EAS and the TAS can then be determined.

For supersonic Mach numbers, a bow shock wave forms ahead of the Pitot probe, further complicating the airspeed measurement issue. However, appropriate equations can be used across a shock wave to find the relationship between the total pressure after the shock, the static pressure, and the Mach number, the resulting equation being called the Rayleigh pitot tube formula.

Summary: Airspeed Definitions

The following definitions of airspeeds in aviation may be encountered:

1. TAS is referred to as “True airspeed,” which is the true speed of an aircraft through the air relative to an undisturbed air mass. In engineering work, this is V_{\infty}.

2. IAS is referred to as “Indicated airspeed,” which is the actual speed shown on an airspeed indicator or ASI. In general, IAS is not the same as TAS because the ASI is calibrated based on MSL conditions, i.e., \rho = \rho_0.

3. CAS is “Calibrated airspeed,” which is the indicated airspeed corrected for errors such as static position error (i.e., the error in the measurement of true static pressure on the aircraft) and any instrument errors.

4. EAS is referred to as “Equivalent airspeed,” which corresponds to the dynamic pressure at the same true airspeed. For an error-free ASI, then the indicated airspeed would be equal to the equivalent airspeed. However, the true airspeed needs to be determined by calculating the air density at that altitude.

Summary & Closure

Airspeed measurement is straightforward using a pitot-static system, but precisely what airspeed is being used must be understood and carefully qualified, e.g., it is equivalent airspeed, calibrated airspeed, or true airspeed. Engineers usually require a measurement of the aircraft’s true airspeed, which must be obtained indirectly by measurement and calculation. True airspeed is not a direct measurement. Pilots, however, require the equivalent airspeed (to which the aircraft responds aerodynamically) as well as the true airspeed (for navigation). Static position errors and mechanical errors in airspeeds measurement must also be addressed. Remember also that the ASI is calibrated based on mean sea-level (MSL) density, i.e., the calibration is performed by assuming that \rho = \rho_0. For higher subsonic and supersonic airspeeds, the compressibility effects will affect the total and static pressure measured by the Pitot probe so appropriate corrections (based on isentropic flow relations) are needed to determine the Mach number and true airspeed.

5-Question Self-Assessment Quickquiz

For Further Thought or Discussion
  • An airplane is flying at 10,000 ft with an indicated airspeed of 200 kts. What is its true airspeed? Hint: Assume no SPE and an error-free airspeed indicator.
  • Why does a pilot need both the indicated airspeed and the ground speed?
  • If an aircraft is found to have a large SPE, what might be the consequences? For the pilot? For engineering analysis?
  • Research the effects of compressibility on airspeed measurement. What happens to the reading from a pitot probe when an aircraft exceeds the speed of sound?

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