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

$$\backslash mathrm\{EAS\}\; =\; \backslash mathrm\{TAS\}\; \backslash times\; \backslash sqrt\{\backslash frac\{\backslash rho\}\{\backslash rho\_0\}\}$$

where {{mvar|ρ}} is actual air density and {{math|ρ{{sub|0}}}} is standard sea level density (1.225 kg/m³ or 0.00237 slug/ft³).

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

$$\backslash mathrm\{EAS\}\; =\; \backslash sqrt\{\backslash frac\{2q\}\{\backslash rho\_0\}\}$$

where {{mvar|q}} is the dynamic pressure $q\; =\; \backslash tfrac12\backslash ,\; \backslash rho\backslash ,\; v^\{2\}.$

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

$$\backslash mathrm\{EAS\}\; =\{a\_0\}\; M\; \backslash sqrt\{P\backslash over\; P\_0\}$$

where {{math|a{{sub|0}}}} is {{cvt|1225|km/h|kn|sigfig=5}} (the standard speed of sound at 15 °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):

$$\backslash mathrm\{EAS\}\; =\; a\_0\; \backslash sqrt\{\; \backslash frac\{5P\}\{P\_0\}\; \backslash left[\backslash left(\; \backslash frac\{q\_c\}P\; +\; 1\; \backslash right)^\backslash frac\{2\}\{7\}\; -\; 1\; \backslash right]\}$$

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:

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

where the pressure ratio $\backslash delta\; =\; \backslash tfrac\{P\}\{P\_0\},$ 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.