speed vs mach at altitude

[MD83FO]

Hi.. was unable to find this punctual inquiry in the search.

on an A320 is it wrong to fly with reference to indicated speed rather than mach number above crossover altitude?
is the speed scale showing IAS at high altitude? or a compressibility corrected value. EAS.
Thanks.

[Pugilistic Animus]

Just use Mach as that limits above the cross over altitude...that's why they don't publish EAS...etc...because compressibility effects dominate at high altitudes over dynamic pressure effects...it still shows IAS...maybe CAS:)

[Rivet gun]

The speed tapes on current Airbus and Boeing aircraft are programmed to display CAS (instrument error is negligable and static source position error is automatically corrected for). However the compressibility error is deliberatly left in in order to make the speed tape read the same as would a traditional ASI. This is one of the reasons why indicated stall speed increases with altitude.

CAS exists only because of the limitations inherent in the mechanical ASI. An EFIS could just as easilly be programmed to display EAS which would be theoretically preferable.

If you want to know your EAS in flight, here's how. Print out the table below. The column labelled ESS is what might be called the "equivalent speed of sound" i.e the speed of sound expressed as EAS. Look up the ESS value for your flight level and then multiply this by your Mach number. This gives your EAS (in knots).

You will find that the EAS is always less than the CAS displayed on your speed tape. The difference is compressibility error. I have not bothered with the table below FL 100 because the compressibility error is small at lower altitudes.


Flight ESS
level

410 277.8
400 284.6
390 291.5
380 298.6
370 305.9
360 313.3
350 320.9
340 328.6
330 336.4
320 344.3
310 352.3
300 360.5
290 368.7
280 377.1
270 385.6
260 394.2
250 403.0
240 411.8
230 420.8
220 429.9
210 439.1
200 448.4
190 457.9
180 467.5
170 477.2
160 487.0
150 496.9
140 507.0
130 517.2
120 527.5
110 538.0
100 548.6

[CabinMaster]

You will find that the EAS is always less than the CAS displayed on your speed tape. The difference is compressibility error. I have not bothered with the table below FL 100 because the compressibility error is small at lower altitudes.

Let's rather say the Airbus is limited by its VMO at lower altitudes, so it cannot run into regions where compressibility is an issue. A faster aircraft would experience the same CAS/EAS disagree at M.78 at Sea Level as at higher altitude.

[Rivet gun]

Perhaps I need to explain compressibility error.

At sea level pressure altitude compressibility error is zero, i.e CAS = EAS. In theory this would be true even at Mach .9.

The reason is because the mechanical ASI is calibrated to account for the compressibility of the air at sea level. However the instrument does not know its own altitude. If you use the ASI at a higher altitude (for which it is not calibrated) then it will exhibit compressibility error.

Now a EFIS does know its own altitude. So a EFIS could display CAS or EAS depending on how it is programmed. Airbus and Boeing choose to display CAS.

[PBL]

Perhaps I need to explain compressibility error.


Yes, perhaps you do!

The difference between CAS and EAS is due to the density of the air through which you are flying. Air density is not a "compressibility effect", so I find it surprising that you are proposing to call it "compressibility error".

Below about Mach 0.3, s far as I known there are no (or few) compressibility effects worth noting for aerodynamicists*. Above Mach 0.3 (very roughly speaking), the "compressibility effects" consist (roughly speaking) of a correction factor which is an algebraic function of Mach number.

*Mad (Flt) Scientist has told of an airplane at which compressibility effects begin to be felt at about Mach 0.2.

PBL

[CabinMaster]

First, I was wrong on the sea level compressibility effect on IAS/CAS, "rivet gun" is right.
For CAS/IAS (I am putting these together as modern airliners usually have no mean to see the difference between them thanks to AD-computer) measurement is affected by by compressibility at Mach numbers above M0.7.

Here you find a formula for EAS-CAS conversion (scroll to bottom):
Equivalent airspeed - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Equivalent_airspeed)
When you insert a pressure ratio of "1" (Sea Level) the conversion factor becomes "1". As I wrote the formula in that article (I didn't develop it, I just spread the word), I am a bit sorry for my previous post.

[Rivet gun]

The difference between CAS and EAS is not a function of density. It is (as CabinMaster's formula shows) a function of static pressure and Mach number. The delta in the formula is pressure ratio, not density ratio.

Every pilot's text book I have come across refers to the difference between CAS and EAS as "compressibility error". I agree this is a misnomer, it might be better to call it something like "altitude error". The text books have to follow the terminology used in exams, so if we want to change terminology we will first have to convince the ATPL examiners ;)

To quote from Walt Blake in Boeing's Jet transport performance methods.

"This correction, although commonly called the compressibility correction, shouldn't be confused with going from incompressible to compressible flow equations. Recall that the airspeed equation is based on Bernoulli's equation for compressible flow. The correction is more truly a correction for the effect of altitude on displayed airspeed"

[PBL]

The difference between CAS and EAS is not a function of density. It is (as CabinMaster's formula shows) a function of static pressure and Mach number. The delta in the formula is pressure ratio, not density ratio.

Sorry, I was thinking of the difference between TAS and EAS.

Let me quote at length from John D. Anderson Jr's Introduction to Flight, one of the most ubiquitous textbooks on intro aerodynamics, with some change of symbolism from standard math to ASCII,

(Eqn 4.64) p0 = p + q This relation holds for incompressible flow only........
(Eqn 4.66) TAS = sqrt ( 2(p0 - p) / rho ). However, the measurement of atmospheric air density directly at the airplane's location is difficult. Therefore for practical reasons, the airspeed indicators on low-speed airplanes are calibrated by using the standard sea-level value of rho_s in [the equation]. This gives a value of velocity called the equivalent airspeed: (Eqn 4.67) EAS = sqrt( 2(p0 - p) / rho_s. The equivalent airspeed EAS differs slightly from TAS, the difference being the factor sqrt(rho / rho_s).

In the second quote, Anderson expressly introduces compressibility, talking about an F-16 flying at 300m/s at an altitude of 7km, a transonic speed.

EAS was introduced [in a previous section] for low-speed flight, where the flow is assumed to be incompressible. However, the concept of EAS has a broader meaning..... [F-16 example] Consider an airplane flying at some true airspeed at some altitude. Its equivalent airspeed at this condition is defined as the velocity at which it would have to fly at standard sea level to experience the same dynamic pressure. The equation for equivalent airspeed is straighforward ... It is EAS = TAS.sqrt(rho/rho_s).

That couldn't be clearer. Anderson does not introduce the notion of "calibrated airspeed", neither in this book nor in his Fundamentals of Aerodynamics.

Here are a couple of quotations from Shevell, Fundamentals of Flight, 1st edition.

The speed read on a perfect airspeed indicator with zero instrument error using a static source which records true ambient air pressure is called the calibrated airspeed, V_CAL. (Eqn 6.12) V_CAL .. = sqrt( 2(p_T - p0) / rho_s, where rho_s = sea-level standard density. When compressibility effects are negligible, the calibrated airspeed is identical to another defined airspeed known as the equivalent airspeed, V_E. V_CAL = V_E = V_0.sqrt(rho/rho_s) = V_0.sqrt(sigma), where sigma is the density ratio (= rho/rho_s). Note that V_0 is true airspeed....

p_T is the total pressure, as measured by a pitot tube. p is freestream pressure. p_T is p multiplied by an algebraic function of Mach number.

(Eqn 7.25) V_E = sqrt( (2/rho_s).(p_T - p).(1/(1+M^2/4+M^4/40+M^6/1600+....))). Eqn 7.25 differs from equation 6.12 for incompressible flow in the Mach number terms. The series in M is a Mach number correction applied to the scale of all airspeed indicators at sea level. At other altitudes, there are different values of Mach number corresponding to each value of V_E. The speed read by a perfect airspeed system (i.e., zero instrument and static error) with the Mach number correction based on a standard-day sea-level relationship between V_E and M is the calibrated airspeed, V_CAL. At sea level the Mach number correction is exact and V_CAL = V_E. At other altitudes, V_CAL = V_E + delta(V_C), where delta(V_C) is the difference between the true Mach number correction at the flight altitude and values based on sea level.

Shevell is somewhat misleading in that he implicitly suggests that Mach number versus AS correction is dependent on altitude, whereas of course it is dependent solely on temperature.

PBL

[Rivet gun]

I agree that Shevell is somewhat misleading, but not nescessarily for the reason you suggest. He first defines CAS for incompressible flow (where it is the same as EAS anyway) but he does not explicitly define CAS for compressible flow, other than to state CAS is the same as EAS at sea level.

The variables by which the different speeds are related are sometimes misunderstood.

Shevell correctly implies that the relation between CAS and EAS depends on pressure altitude and Mach number.

To summarise the others:

The relation between Mach number and TAS depends on static temperature

The relation between Mach number and EAS depends on statc pressure (i.e pressure altitude)

The relation between TAS and EAS depends on density

[PBL]

Shevell is somewhat misleading in that he implicitly suggests that Mach number versus AS correction is dependent on altitude, whereas of course it is dependent solely on temperature.
I agree that Shevell is somewhat misleading, but not nescessarily for the reason you suggest.

M = a.TAS and a=sqrt(gamma.R.T) so M = A.sqrt(T).TAS where A is constant. So M/TAS = A.sqrt(T).

I hope you are not disagreeing!

Shevell correctly implies that the relation between CAS and EAS depends on pressure altitude and Mach number.

First, pressure altitude??? Why make things complicated? Why not just freestream (=static) pressure?

EAS is an algebraic function of (stagnant pressure - freestream pressure), calculated by the pitot-static system, and speed-of-sound (usually denoted a). CAS is the same algebraic function, but where a is replaced by the constant a_s, the speed of sound at sea level in the ISA, so an algebraic function of (stagnant pressure - freestream pressure), measured by the pitot-staic system, alone.

As Anderson says, The static temperature in the air surrounding the airplane is difficult to measure. Therefore all high-speed (but subsonic) airspeed indicators are calibrated....assuming that [the speed of sound] is equal to the standard sea-level value a_s = 340.3 m/s.

The relation between Mach number and TAS depends on static temperature


And the relation between EAS and CAS also, as noted by Anderson and, derivatively, myself.


The relation between Mach number and EAS depends on statc pressure (i.e pressure altitude)

"i.e. pressure altitude"?? You prefer to think in terms of pressure altitude rather than in terms of static pressure? Every static port will disagree with you!

I would say that the relation between Mach number and EAS is as follows. TAS = M.a EAS = sqrt(rho/rho_s).TAS = sqrt(rho/rho_s).M.a = A.sqrt(rho).M.a where A is constant = B.sqrt(rho).M.sqrt(T) where B is constant and since p=rho.T.const, this is = C.M.sqrt(p). I would then say that the relation between Mach number and EAS is proportional to sqrt(p). More informative, no?


The relation between TAS and EAS depends on density

Specifically, proportional to sqrt(rho).

PBL

[Pugilistic Animus]

Just to add: a simple way to view this is to remember...that all disturbances propagate through the air, as a wave, the wave velocity is the sped of sound 'a'
however for slow moving objects that may have created the disturbance the wave moves far faster than the object that creates the disturbance therefore the effects of the wave which is a series of compressions and rarefactions, has no little or nil effect upon the object...however as the object speeds up it begins to 'catch-up' with the forward propagated disturbance and this leads to shock wave which disturbs lift on the airfoil and as the 'bow wave created becomes more and more severe-a loss of lift occurs and the overall center of pressure moves aft and creates a downward pitching moment....as a result of 'compressibility'..i.e all the air molecules scrunched up together...so for low altitudes...one references IAS because...dynamic pressure effects limits...i.e structural limits prevail...however, at higher altitudes stability problems created by shock-wave formation are more of a concern...hence why there's reference to M above a certain altitude...the crossover altitude....because at that speed/altitude combination the effects of compressibility will limit the airplane's performances long before structural issues will ever creep up---providing the ASI with a barber-pole makes the whole worry...obsolete though...:)

[Gi Dem Dub]

Brilliant explanation Pugilistic Animus. Thx for that.:ok:
A question is always worth being asked if it brings knowledge sharing... whoever asks it... pilot or simmer.... me thinks

[Rivet gun]

Originally posted by PBL
M = a.TAS and a=sqrt(gamma.R.T) so M = A.sqrt(T).TAS where A is constant. So M/TAS = A.sqrt(T).

I hope you are not disagreeing!

Wouldn't dream of it! But I did spot the deliberate mistakes.

[MD83FO]

thanks a lot for the input.

[Pugilistic Animus]

the Mach Meter does not use a Temperature input for it's readings...I just read more carefully:suspect:....all the 'gamma' stuff s because the compression is adiabatic so the adiabatic gas laws must by used to define impact pressure...that's all a simple solution to the diff eq. obtained by direct substitution:zzz::zzz::zzz:
§ 1.1 General definitions.

Calibrated airspeed means the indicated airspeed of an aircraft, corrected for position and instrument error. Calibrated airspeed is equal to true airspeed in standard atmosphere at sea level

Equivalent airspeed means the calibrated airspeed of an aircraft corrected for adiabatic compressible flow for the particular altitude. Equivalent airspeed is equal to calibrated airspeed in standard atmosphere at sea level.

True airspeed means the airspeed of an aircraft relative to undisturbed air. True airspeed is equal to equivalent airspeed multiplied by (ρ0/ρ)1/2.

Mach number means the ratio of true airspeed to the speed of sound.

No more and no less:ugh::ugh::ugh:
edit: this is complex:
zBs9gZQX7lQ&feature=related

[Pugilistic Animus]

Adios Ciao...because I'm a muppett:E