Equivalent airspeed: Definition from Answers.com

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In low-speed flight, equivalent airspeed (EAS) is the speed which would be shown by an airspeed indicator with zero error.^[1] It is the airspeed at sea level which represents the same dynamic pressure as that flying at the true airspeed (TAS) at altitude.^[2]^[3] It is useful for predicting aircraft handling, aerodynamic loads, stalling etc.

$EAS = TAS \times \sqrt{\frac{actual\ air\ density}{standard\ air\ density}}$

Where: standard air density is 1.225 kg/m³ -or- 0.00237 slugs/ft³.

EAS can also be obtained from the aircraft mach number and static air pressure.

$EAS ={a_{sl}} M_a \sqrt{P\over P_{sl}}$

Where: ${a_{sl}}\,$ is the standard speed of sound at 15 °C (661.47 knots)

$M_a\,$ is Mach number,

$P\,$ is static air pressure,

$P_{sl}\,$ is standard sea level pressure (1013.25 hPa)

Combining the above with the expression for Mach number as a function of impact and static pressures gives, for subsonic compresible flow:

$EAS={a_{sl}}\sqrt{{5P\over P_{sl}}[(\frac{q_c}{P}+1)^\frac{2}{7}-1]}$

Where: ${q_c}\,$ is impact pressure

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

Relevant for engineering purposes is the relationship between indicated airspeed and true airspeed (or Mach number) for common altitudes and airspeeds. In engineering it is useful to have a formula that is reasonably accurate and can be used with values provided in International Standard Atmosphere as function of altitude. While for subsonic speeds up to Mach 0.6 the compressibility can be neglected and IAS/CAS can be obtained from TAS using density correction, it must be incorporated above these speeds for accurate results.

For speeds below Mach 1 a simplified formula can be used that allows quick calculation of IAS/CAS from TAS and vice versa can be used that needs the air density ratio σ and the pressure ratio δ.

$IAS={EAS\times[1+\frac{1}{8}(1-\delta)Mach^{2}+\frac{3}{640}(1-10\delta+9\delta^{2})Mach^{4}]}$

$IAS={TAS\times\sqrt{\sigma}\times[1+\frac{1}{8}(1-\delta)Mach^{2}+\frac{3}{640}(1-10\delta+9\delta^{2})Mach^{4}]}$

Density ratio: $\sigma=\frac{\rho}{\rho_{0}}$

Pressure ratio: $\delta=\frac{p}{p_{0}}$

$Mach\,$ being the Mach number

$IAS\,$ & $TAS\,$ the airspeeds in either knots, km/h, mph or any other appropriate unit

$\rho\,$ & $\rho_{0}\,$ the air density at current altitude and at sea level, respectively.

$p\,$ & $p_{0}\,$ the air pressure at current altitude and at sea level, respectively.

Above formula is accurate within 1% up to Mach 1.2 and useful with acceptable error up to Mach 1.5. It shouldn't be used beyond that. The 4th order Mach term can be neglected for speeds below Mach 0.85. No Mach number correction should be used below Mach 0.6.

Notes

^ 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
^ Clancy, L.J. (1975), Aerodynamics, Section 3.8, Pitman Publishing Limited, London. ISBN 0 273 01120 0
^ Anderson, John D. (2007), Fundamentals of Aerodynamics, p.215 (4th edition), McGraw-Hill, New York USA. ISBN 978-0-07-295046-5

References

Anderson, John D. (2007), Fundamentals of Aerodynamics, Section 3.4 (4th edition), McGraw-Hill, New York USA. ISBN 978-0-07-295046-5

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Equivalent airspeed

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