EAS

[sierra910]

my instructor once asked me.. what is equivalent airspeed(EAS) equivalent to? i did not know the answer and later he did explain, but I just cannot recollect it..can somebody help me out?
thanks

[QJB]

Taken from aerodynamics for naval aviators: "The equivalent airspeed (EAS) is the flight speed in the standard sea level air mass which would produce the same free stream dynamic pressure as the actual flight condition".

The standard airspeed indicator is calibrated to account for compressibility effects at sea level in the standard atmosphere. However when ambient conditions are different from standard sea level additional corrections have to be made to calibrated airspeed in order to determine the actual dynamic pressure acting on the aircraft.

[lasseb]

To the best of my knowledge, the ASI is not calibrated to take compressibility into account.
This is the reason we have EAS. in the first place.
When dealing with ASI keep in mind it is just a simple pressure gauge. Someone just put knots on the scale in stead of pressure..Simply speaking the ASI will measure the pressure difference between total and static pressure and it cannot deal with compressed air, and some idiot labelled the scale with knots in stead of pascal..
The next problem is then if you fly fast or high the air gets compressed in the pitot tube and all pressure measures goes down the drain.
In order to figure out what dynamic pressure the plane is actually subject to EAS was "invented". If we could measure the pressure the plane was subject to in the flying high/fast scenario, we could convert that pressure into a true airspeed equivalent..So we measure the pressure At some altitude. We then imagine that we where flying at sea level on a standard day and figure out what speed we had to fly to get the same pressure. This speed is EAS. If the pressure in the pitot tube was incompressible, TAS. and EAS would always be equal.

[selfin]

To the best of my knowledge, the ASI is not calibrated to take compressibility into account. This is the reason we have EAS. in the first place.

ASIs have been designed to take account of compressibility since the 1930s. Equivalent airspeed has absolutely nothing to do with compressibility. EAS is exactly as QLB has pointed out: a value, expressed in units of speed, associated to a dynamic pressure. The lynchpin in understanding why it has nothing to do with compressibility lies in acknowledging that dynamic pressure assumes the fluid is incompressible.

If the pressure in the pitot tube was incompressible, TAS and EAS would always be equal.

EAS = TAS * sqrt(rho/rho_0), contains the variable rho (air density) whose variation with altitude leads to a divergence between TAS and EAS. (rho_0 is ISA MSL rho).

There are plenty of rigorous treatments of this topic (John D Anderson, Liepmann & Roshko, etc). W. Aiken's 1946 NACA Report 837 is freely available at Cranfield's NACA mirror at this URL: Standard nomenclature for airspeeds with tables and charts for use in calculation of airspeed

[FlyingStone]

Originally Posted by selfin

ASIs have been designed to take account of compressibility since the 1930s.

So, assuming zero position and instrument error, the airspeed indicator is showing us EAS even in "high"-speed environment (M > 0.4)? Why even mention it then, if IAS = EAS (assuming IAS = CAS)? Not being an expert on the subject matter, but I hardly doubt that's the truth...

EAS is actually very important, because airspeed indicators get dynamic pressure by substracting static pressure (static port) from total pressure (pitot tube). But this is done under assumption that air is incompressible, which is a lie of course, since every fluid is compressible, it's just the compressibility factor that is different between fluids. In high airspeed environment (beyond spamcan range, around M = 0.3 and upwards) the compressibility effect becomes noticeable, since the air flowing into the pitot tube is compressed and thus the sensed total pressure is higher than it actually is, so the sensed dynamic pressure will be higher, thus the indicated airspeed (IAS) will be higher as well. The effect of compressibility is even worse in high altitude environment, since the density of air is lower and the compressibility factor of air increases.

[lasseb]

Equivalent airspeed has absolutely nothing to do with compressibility

Well.. Yes and no. Looking strictly at EAS it deals with non compressible fluids. But as pilots we do not have a EAS gauge. We have a CAS gauge that is flawed due to air getting compressed (and a whole lot of other issues)

Since we have no correct CAS, we cannot obtain the correct TAS when air starts getting compressed. So the formula EAS=TAS*xxxx cannot be used as TAS/CAS is flawed from the beginning.
So if we need to actually know the forces on the airplane from an engineering point of view we need EAS, as this puts the pressure in the non-compressed "domain".

Regarding the design of ASI's, I have no practical experience, but theoretical knowledge books for pilots states that : "The ASI is calibrated to the ideal incompressible flow formula. Because of this a subtractive compressibility factor correction has to be applied"

[selfin]

[...] assuming zero position and instrument error, the airspeed indicator is showing us EAS even in "high"-speed environment (M > 0.4)?

The ASI reading, neglecting imperfections, only agrees with EAS when the ambient pressure and density are at the ISA MSL values.

[...] airspeed indicators get dynamic pressure by substracting static pressure (static port) from total pressure (pitot tube).

This is not true. The indicator uses something other than dynamic pressure. There are a number of available solutions to Euler's equation of which only one is the (incompressible) Bernoulli equation. The (incompressible) Bernoulli equation imposes the condition that density must be held constant along a streamline. While this condition will not be observed in a real physical process, the Bernoulli solution is still adequate until roughly Mach 0.3. Nevertheless, modern airspeed indicators are not designed to make use of the (incompressible) Bernoulli equation.

Among the several other available solutions to Euler's equation is one which has been variously described in the literature as the Saint-Venant equation, or the compressible Bernoulli equation, or airspeed indicator calibration law. This solution does take account of the variation in density along a streamline and is valid up to and including Mach 1. An extended version of the solution, called the Rayleigh Supersonic Pitot equation, exists for > Mach 1, valid up to roughly Mach 3 or 4. A further solution exists for the low hypersonic regime taking account of quantum mechanical effects once vibrational modes become excited. And so forth.

A problem arises if the term "dynamic pressure" is intended to refer to the difference between static and total pressures because the total pressure predicted depends on which solution to Euler's equation is chosen. NACA addressed the nomenclature on this point in the 1940s (c.f. aforementioned report) by introducing the term "impact pressure" (symbol: q_c) to mean the difference between the pressures with the total pressure determined by considering an isentropic process to account for density variation along a streamline. Some authors refer to "impact pressure" as "compressible dynamic pressure." In summary, airspeed indicators make use of neither the (incompressible) Bernoulli equation nor dynamic pressure.

"The ASI is calibrated to the ideal incompressible flow formula. Because of this a subtractive compressibility factor correction has to be applied"

Which textbook states this?