# Equivalent airspeed

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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.[1][2] In low-speed flight, it is the speed which would be shown by an airspeed indicator with zero error.[3] It is useful for predicting aircraft handling, aerodynamic loads, stalling etc.

${\displaystyle EAS=TAS\times {\sqrt {\frac {\rho }{\rho _{0}}}}}$

where:

${\displaystyle \rho \,}$ is actual air density.

${\displaystyle \rho _{0}\,}$ is standard sea level density (1.225 kg/m3 or 0.00237 slug/ft3).

EAS is a function of dynamic pressure.

${\displaystyle EAS={\sqrt {\frac {2q}{\rho _{0}}}}}$

where:

${\displaystyle {q}\,}$ is dynamic pressure ${\displaystyle q={\tfrac {1}{2}}\,\rho \,v^{2},}$

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

${\displaystyle EAS={a_{0}}M{\sqrt {P \over P_{0}}}}$

where:

${\displaystyle {a_{0}}\,}$ is the standard speed of sound at 15 °C (661.47 knots)

${\displaystyle M\,}$ is Mach number

${\displaystyle P\,}$ is static pressure

${\displaystyle P_{0}\,}$ 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):

${\displaystyle EAS={a_{0}}{\sqrt {{5P \over P_{0}}\left[\left({\frac {q_{c}}{P}}+1\right)^{\frac {2}{7}}-1\right]}}}$

where:

${\displaystyle {q_{c}}\,}$ 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:

${\displaystyle CAS={EAS\times \left[1+{\frac {1}{8}}(1-\delta )M^{2}+{\frac {3}{640}}(1-10\delta +9\delta ^{2})M^{4}\right]}}$

where:

pressure ratio: ${\displaystyle \delta ={\frac {P}{P_{0}}}}$

${\displaystyle CAS\,}$ and ${\displaystyle EAS\,}$ 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.

## Notes

1. ^ Clancy, L.J. (1975), Aerodynamics, Section 3.8, Pitman Publishing Limited, London. ISBN 0-273-01120-0
2. ^ Anderson, John D. (2007), Fundamentals of Aerodynamics, p.215 (4th edition), McGraw-Hill, New York USA. ISBN 978-0-07-295046-5
3. ^ 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

## References

• 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), "Measurement of Aircraft Speed and Altitude" (11 MB), NASA Reference Publication 1046.
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