Editing Equivalent airspeed

{{short description|Airspeed corrected for the compressibility of air at high speeds}}
{{Refimprove|date=January 2009}}

In [[aviation]], '''equivalent airspeed''' ('''EAS''') is [[calibrated airspeed]] (CAS) corrected for the [[compressibility]] of air at a non-trivial [[Mach number]].  It is also the [[airspeed]] at sea level in the [[International Standard Atmosphere]] at which the [[dynamic pressure]] is the same as the dynamic pressure at the [[true airspeed]] (TAS) and altitude at which the aircraft is flying.<ref>Clancy, L.J. (1975), ''Aerodynamics'', Section 3.8, Pitman Publishing Limited, London. {{ISBN|0-273-01120-0}}</ref><ref>Anderson, John D. (2007), ''Fundamentals of Aerodynamics'', p.215 (4th edition), McGraw-Hill, New York USA. {{ISBN|978-0-07-295046-5}}</ref> In low-speed flight, it is the speed which would be shown by an [[airspeed indicator]] with zero error.<ref>Houghton, E.L. and Carpenter, P.W. (1993), ''Aerodynamics for Engineering Students'', Section 2.3.3, Butterworth-Heinemann, Oxford UK. {{ISBN|0-340-54847-9}}</ref> It is useful for predicting aircraft handling, aerodynamic loads, stalling etc.

<math display=block>\mathrm{EAS} = \mathrm{TAS} \times \sqrt{\frac{\rho}{\rho_0}}</math>

where {{mvar|&rho;}} is actual [[air density]] and {{math|''&rho;''{{sub|0}}}} is standard [[air density|sea level density]] (1.225&nbsp;kg/m<sup>3</sup> or 0.00237 slug/ft<sup>3</sup>).

{{math|EAS}} is a function of [[dynamic pressure]]:

<math display=block>\mathrm{EAS} = \sqrt{\frac{2q}{\rho_0}}</math>

where {{mvar|q}} is the dynamic pressure <math>q = \tfrac12\, \rho\, v^{2}.</math>

EAS can also be obtained from the aircraft [[Mach number]] and [[static pressure]].

<math display=block>\mathrm{EAS} ={a_0} M \sqrt{P\over P_0}</math>

where {{math|''a''{{sub|0}}}} is {{cvt|1225|km/h|kn|sigfig=5}} (the standard speed of sound at 15&nbsp;°C), {{mvar|M}} is the Mach number, {{mvar|P}} is static pressure, and {{math|''P''{{sub|0}}}} is standard sea level pressure (1013.25 hPa).

Combining the above with the expression for Mach number gives EAS as a function of [[impact pressure]] and static pressure (valid for subsonic flow):

<math display=block>\mathrm{EAS} = a_0 \sqrt{ \frac{5P}{P_0} \left[\left( \frac{q_c}P + 1 \right)^\frac{2}{7} - 1 \right]}</math>

where {{mvar|q{{sub|c}}}} is [[impact pressure]].

At standard sea level, EAS is the same as [[calibrated airspeed]] (CAS) and [[true airspeed]] (TAS). At any other altitude, EAS may be obtained from CAS by correcting for compressibility error.

The following simplified formula allows calculation of CAS from EAS:

<math display=block>\mathrm{CAS} = {\mathrm{EAS} \times \left[ 1 + \frac{1}{8}(1 - \delta)M^2 + \frac{3}{640}(1 - 10\delta + 9\delta^2)M^4 \right]}</math>

where the pressure ratio <math>\delta = \tfrac{P}{P_0}, </math> and {{math|CAS, EAS}} are airspeeds and can be measured in knots, km/h, mph or any other appropriate unit.

The above formula is accurate within 1% up to Mach 1.2 and useful with acceptable error up to Mach 1.5. The 4th order Mach term can be neglected for speeds below Mach 0.85.

== See also ==
{{div col|colwidth=23em}}
* [[Acronyms and abbreviations in avionics]]
* [[International Civil Aviation Organization#Use of the International System of Units|ICAO recommendations on use of the International System of Units]]
* [[Calibrated airspeed]]
* [[Flight instruments]]
* [[Global Positioning System]]
* [[Indicated airspeed]]
* [[Position error]]
* [[True airspeed]]
{{div col end}}

==References==
{{Reflist}}

===Bibliography===
* Anderson, John D. (2007), ''Fundamentals of Aerodynamics'', Section 3.4 (4th edition), McGraw-Hill, New York USA. {{ISBN|978-0-07-295046-5}}
* Gracey, William (1980), [http://apps.dtic.mil/dtic/tr/fulltext/u2/a280006.pdf "Measurement of Aircraft Speed and Altitude"] {{Webarchive|url=https://web.archive.org/web/20210926222531/https://apps.dtic.mil/dtic/tr/fulltext/u2/a280006.pdf |date=2021-09-26 }} (11 MB), NASA Reference Publication 1046.

==External links==
* [https://www.fxsolver.com/browse/formulas/Equivalent+airspeed Equivalent airspeed calculator]

[[Category:Airspeed]]