# Equivalent Airspeed

In der Luftfahrt unterscheidet man verschiedene Fluggeschwindigkeiten:

Equivalent airspeed (EAS) is defined as the speed at sea level that would produce the same incompressible dynamic pressure as the true airspeed at the altitude at which the vehicle is flying. An aircraft in forward flight is subject to the effects of compressiblity. Likewise, the calibrated airspeed is a function of the compressible impact pressure. EAS, on the other hand, is a measure of airspeed that is a function of incompressible dynamic pressure. Structural analysis is often in terms of incompressible dynamic pressure, so that equivalent airspeed is a useful speed for structural testing. At sea level, standard day, calibrated airspeed and equivalent airspeed are equal (or equivalent), but only at that condition. For the performance engineer, there is no practical reason to use equivalent airspeed for anything. However, structural analysis is often performed in terms of equivalent airspeed (since it is a direct function of the incompressible dynamic pressure), so the performance engineer needs to be able to convert Ve to parameters that are more useful.: [1]

Let q represent the dynamic pressure 1/2 ·ρ · v2 = 1/2 · ρ0 · ve2.

Then the relationship between the pressure difference ptps sensed by a pitot-static system and the dynamic pressure is given by:

(ptp)/q = vi2/ve2 = 1 + 1/4 · M2 + (2γ)/24 · M4 + (2γ)·(32·γ)/192 · M6 + ...

Where
M is the Mach number,
v is the true airspeed,
ve is the equivalent airspeed,
γ is the ratio of the specific heats of air and
ρ is the air density.

The ratio of the specific heats, γ is 1.4 in air. Substituting this value gives:

$\frac{p_\mathrm{t} \, - \, p}{q} = \frac{V_i^2}{V_\mathrm{e}^2} = 1 + \frac{1}{4} M^2 + \frac{1}{40} M^4 + \frac{1}{1600} M^6 +...$

(This section needs editing due to confusion between V (TAS) and Vi (CAS) and ambiguity regarding ASI calibration - incompressible flow equation above or compressible flow equation under calibrated airspeed? If the ASI is calibrated to the CAS calibration equation which (for subsonic speeds) eliminates compressibility error at standard sea level then the compressibility correction above is not valid. See also link to equivalent airspeed)

This approximation is valid up to about Mach 2.3.

Source: Aerodynamics of a Compressible Fluid. Liepmann and Puckett 1947. Publishers John Wiley & Sons Inc.

The difference between calibrated airspeed and equivalent airspeed is negligible at low Mach numbers rising to 3 % at Mach 0,5 and 13 % at Mach 1 depending on altitude.

The significance of equivalent airspeed is that at Mach numbers below the onset of wave drag, all of the aerodynamic forces and moments on an aircraft scale with the square of the equivalent airspeed. The equivalent airspeed is closely related to the Indicated airspeed speed shown by the airspeed indicator. Thus, the handling and 'feel' of an aircraft, and the aerodynamic loads upon it, at a given equivalent airspeed, are very nearly constant and equal to those at SL, ISA irrespective of the actual flight conditions.

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