# Mach meter errors

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**Mach meter errors**

Here is a quote from an official FAA publication which can be downloaded here.

IFH-FAA-H-8083-15A.pdf - Windows Live SkyDrive

"Some older mechanical Machmeters not driven from

an air data computer use an altitude aneroid inside the

instrument that converts pitot-static pressure into Mach

number. These systems assume that the temperature at any

altitude is standard; therefore, the indicated Mach number is

inaccurate whenever the temperature deviates from standard.

These systems are called indicated Machmeters. Modern

electronic Machmeters use information from an air data

computer system to correct for temperature errors. These

systems display true Mach number."

Is this nonsense?

IFH-FAA-H-8083-15A.pdf - Windows Live SkyDrive

"Some older mechanical Machmeters not driven from

an air data computer use an altitude aneroid inside the

instrument that converts pitot-static pressure into Mach

number. These systems assume that the temperature at any

altitude is standard; therefore, the indicated Mach number is

inaccurate whenever the temperature deviates from standard.

These systems are called indicated Machmeters. Modern

electronic Machmeters use information from an air data

computer system to correct for temperature errors. These

systems display true Mach number."

Is this nonsense?

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Is this nonsense?

Very early B707's with the early KIFIS systems had rather large mach meter errors.

Later KIFIS systems had better accuracy, but nothing like the accuracy of much later (more modern) aircraft.

*KIFIS, Kollsman Integrated Flight Instrument System.

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This is no nonsense, although the error is probably not very big.

Mach is the ratio between TAS and the speed of sound. The speed of sound depends on the temperature: a = sqrt(1.4*287.05287*T) (T in Kelvin, a in m/s ).

Mach meters that rely on altitude measurements for temperature derive the temperature from the ICAO Standard Atmosphere (ISA). In ISA, temperature of the atmosphere at sea level is 288.15 K, or 15 °C, and cools down by 6.5° for every 1000 meter you go up. Above 11000m the temperature is assumed constant, at 216.65 K, or -56.5 °C.

The differences between the assumed ISA temperature and the actual temperature can be quite big, but are usually below 20° deviation.

Example:

An aircraft flying is 400 KTAS at 30.000 ft, the OAT is -55 °C.

-55° C = 218.15 K

The speed of sound is: sqrt(1.4*287.05287*218.15) = 296.1 m/s, or 575.6 KTAS

The mach number is: 400/575.6 = 0.695

According to ISA, the temperature would be:

30.000 ft = 9144 m

288.15-0.0065*9114m = 228.7 K or -44.4 °C

The speed of sound is: sqrt(1.4*287.05287*228.7) = 303.2 m/s or 589 KTAS

The mach number would read: 400/589 = 0.679.

So for a ±10 °C deviation at 30.000 ft you get a misreading of ± 2.4%

Cheers,

ATCast

Mach is the ratio between TAS and the speed of sound. The speed of sound depends on the temperature: a = sqrt(1.4*287.05287*T) (T in Kelvin, a in m/s ).

Mach meters that rely on altitude measurements for temperature derive the temperature from the ICAO Standard Atmosphere (ISA). In ISA, temperature of the atmosphere at sea level is 288.15 K, or 15 °C, and cools down by 6.5° for every 1000 meter you go up. Above 11000m the temperature is assumed constant, at 216.65 K, or -56.5 °C.

The differences between the assumed ISA temperature and the actual temperature can be quite big, but are usually below 20° deviation.

Example:

An aircraft flying is 400 KTAS at 30.000 ft, the OAT is -55 °C.

-55° C = 218.15 K

The speed of sound is: sqrt(1.4*287.05287*218.15) = 296.1 m/s, or 575.6 KTAS

The mach number is: 400/575.6 = 0.695

According to ISA, the temperature would be:

30.000 ft = 9144 m

288.15-0.0065*9114m = 228.7 K or -44.4 °C

The speed of sound is: sqrt(1.4*287.05287*228.7) = 303.2 m/s or 589 KTAS

The mach number would read: 400/589 = 0.679.

So for a ±10 °C deviation at 30.000 ft you get a misreading of ± 2.4%

Cheers,

ATCast

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To which part of the quote do you refer?

Checking my notes (prehistoric), and in very simple terms, Mach number (as measured by a machmeter) essentially compensates for temperature/density changes as they sit on both sides of the 'diaphragm' between the capsules ie if the air is warmer (less dense) then TAS needs to be higher to create the same dynamic pressure, which 'compensates' for the higher speed of sound in that air (although I have always been suspicious of the accuracy of this in a sort of luddite way). I believe the equation for Mach No does not in fact include temperature, but that bit of learning has long since vanished.

For ATCast - NB you refer to 'TAS' but remember the machmeter is using IAS, hence the 'automatic' compensation?

I therefore vote the whole quote as misleading, at best.

*"Modern electronic Machmeters use information from an air data**computer system to correct for temperature errors. These**systems display true Mach number."*is not strictly true as there are more errors than temperature.Checking my notes (prehistoric), and in very simple terms, Mach number (as measured by a machmeter) essentially compensates for temperature/density changes as they sit on both sides of the 'diaphragm' between the capsules ie if the air is warmer (less dense) then TAS needs to be higher to create the same dynamic pressure, which 'compensates' for the higher speed of sound in that air (although I have always been suspicious of the accuracy of this in a sort of luddite way). I believe the equation for Mach No does not in fact include temperature, but that bit of learning has long since vanished.

For ATCast - NB you refer to 'TAS' but remember the machmeter is using IAS, hence the 'automatic' compensation?

I therefore vote the whole quote as misleading, at best.

*EDIT after digging around in boxes....**Last edited by BOAC; 3rd Nov 2008 at 15:00.*

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Thanks for the replies,

I still think the quoted article is wrong to suggest that mach meter errors are caused by ISA temperature deviation. I suspect that the errors in early mach meters would be most likely caused by imperfectly compensated position errors (mostly in the static pressure).

A Mach meter, whether mechanical or EFIS, needs inputs of total pressure (pitot) and static pressure. I think temperature deviations will not affect the indicated mach number.

I still think the quoted article is wrong to suggest that mach meter errors are caused by ISA temperature deviation. I suspect that the errors in early mach meters would be most likely caused by imperfectly compensated position errors (mostly in the static pressure).

A Mach meter, whether mechanical or EFIS, needs inputs of total pressure (pitot) and static pressure. I think temperature deviations will not affect the indicated mach number.

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I think temperature deviations will not affect the indicated mach number.

The temperate is only needed to obtain the TAS

Regards,

ATCast

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Thanks everyone,

I also managed to find some relevent equations on the web. Like ATCast said, the Rayleigh equations are needed when there is a supersonic shock across the pitot tube.

For the subsonic case, the equations here would be appropriate.

Isentropic Flow Equations

Take equation 6, substitute the specific heat ratio = 1.4 and manipulate it to make M the subject. You then have the equation to program your air data computer to read Mach number given total and static pressure inputs. (OK I don't have an air data computer, but I can do a Excel spreadsheet simulation.)

Now to get TAS your computer also needs a TAT input (kelvins). Use equation 7 to derive SAT from TAT with the Mach number you already have. Then:

TAS= 661.5*M*sqrt(SAT/288.15)

I also managed to find some relevent equations on the web. Like ATCast said, the Rayleigh equations are needed when there is a supersonic shock across the pitot tube.

For the subsonic case, the equations here would be appropriate.

Isentropic Flow Equations

Take equation 6, substitute the specific heat ratio = 1.4 and manipulate it to make M the subject. You then have the equation to program your air data computer to read Mach number given total and static pressure inputs. (OK I don't have an air data computer, but I can do a Excel spreadsheet simulation.)

Now to get TAS your computer also needs a TAT input (kelvins). Use equation 7 to derive SAT from TAT with the Mach number you already have. Then:

TAS= 661.5*M*sqrt(SAT/288.15)

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Certainly have to grin at some of the new(er) folks in the industry and their ideas with regard to older jet transport models, and the limitations thereon.

You can plug all the mathematical data in you like, but the original posters quote, with regard to temperature effects and much older mach indicators are quite correct....of course, new(er) pilots simpy have no knowledge of this as they no doubt didn't fly any of these older aircraft.

You can plug all the mathematical data in you like, but the original posters quote, with regard to temperature effects and much older mach indicators are quite correct....of course, new(er) pilots simpy have no knowledge of this as they no doubt didn't fly any of these older aircraft.

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You can plug all the mathematical data in you like, but the original posters quote, with regard to temperature effects and much older mach indicators are quite correct....of course, new(er) pilots simpy have no knowledge of this as they no doubt didn't fly any of these older aircraft.

I know a captain in a 747 classic who's 25 years old. When I was his age, I was flying 40 year old equipment. The age of the pilot, and even the recency of the pilot, isn't really relevant to understanding "old" technology.

So far as mach number...mach being a function of temperature...temperature variation is relevant, and does apply.

Next we'll probably hear that if it's not an L1011, it's not really an airplane...

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**And.....**

Depending on the aircraft and the aircraft system, the indicated MACH may be slightly different from the true MACH. This, even though the

Mach is computed from the ADC, the TAS, etc.....

If you'll have a look at the AFM (FCOM, etc.) you may find a chart that

gives indicated MACH vs. true MACH....the difference being position errors, etc.

This becomes relevant when flying the constant MACH technique, e.g.

over the pond. On my aircraft, an indicated MACH of .80 is really a true MACH of about .787 or so. Over long distances, this is a consideration.

On my aircraft, indicated MACH is approximately equal to true MACH at around .71 or .72. Below that, true is slightly more than indicated...above that, true MACH is less....the difference becoming greater at higher MACH

numbers. For example, at MACH .86 indicated, true MACH is about .843 or thereabouts. (I don't have the actual graph in front of me at the moment.)

I'm not in agreement with 411A on all issues, but in many instances I do agree with him. In all cases, I enjoy the contributions he makes to PPrune.

Fly safe,

PantLoad

edited due to syntax and spelling....

Mach is computed from the ADC, the TAS, etc.....

If you'll have a look at the AFM (FCOM, etc.) you may find a chart that

gives indicated MACH vs. true MACH....the difference being position errors, etc.

This becomes relevant when flying the constant MACH technique, e.g.

over the pond. On my aircraft, an indicated MACH of .80 is really a true MACH of about .787 or so. Over long distances, this is a consideration.

On my aircraft, indicated MACH is approximately equal to true MACH at around .71 or .72. Below that, true is slightly more than indicated...above that, true MACH is less....the difference becoming greater at higher MACH

numbers. For example, at MACH .86 indicated, true MACH is about .843 or thereabouts. (I don't have the actual graph in front of me at the moment.)

I'm not in agreement with 411A on all issues, but in many instances I do agree with him. In all cases, I enjoy the contributions he makes to PPrune.

Fly safe,

PantLoad

edited due to syntax and spelling....

*Last edited by PantLoad; 4th Nov 2008 at 16:18.*

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The relation between Mach number and TAS is a function of temperature.

The relation between Mach number and total pressure / static pressure is NOT a function of temperature. Since a Mach meter works from inputs of total pressure and static pressure it is not theoretically subject to errors due to deviation of SAT from ISA.

This leaves open the question of why early Mach meters suffered from temperature errors. Maybe temperature errors were caused by expansion / contraction of the mechanical linkages. This would seem to be more related to cockpit temperature rather than ambient ISA deviation as the original quote implies. Also it does not explain why a modern air data computer would need to correct for temperature errors, assuming the pressure transducers (ADMs) dont have significant mechanical linkages.

The relation between Mach number and total pressure / static pressure is NOT a function of temperature. Since a Mach meter works from inputs of total pressure and static pressure it is not theoretically subject to errors due to deviation of SAT from ISA.

This leaves open the question of why early Mach meters suffered from temperature errors. Maybe temperature errors were caused by expansion / contraction of the mechanical linkages. This would seem to be more related to cockpit temperature rather than ambient ISA deviation as the original quote implies. Also it does not explain why a modern air data computer would need to correct for temperature errors, assuming the pressure transducers (ADMs) dont have significant mechanical linkages.

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Okay... I'll have a go, I guess...

The magic formula for Mach is:

Therefore, Mach is only a function of measured pressures (static pressure p and impact pressure qc) and.... gamma. Which is a constant 1.4 for air, if you assume that the air through which the aircraft is moving is calorically perfect (another assumption of the standard atmosphere). The above equation is actually derived from the compressible Bernoulli equation, which makes the assumption of isentropic flow, i.e. no entropy change or heat addition.

But, in reality, do those assumptions hold true? In reality, there would be heat transfer to/from the air flow, air is not really calorically perfect (but close enough) and the value of gamma is probably not constant for extremes of temperature, etc. etc.

So temperature does probably have an effect on the Mach reading, but I'm not sure, based on the above considerations, how big of an effect it is.

The magic formula for Mach is:

**M = {****(2/(****g****-1)) [ ( 1 + q****c****/p )****(****g****-1 )/****g****- 1 ] }****0.5**Therefore, Mach is only a function of measured pressures (static pressure p and impact pressure qc) and.... gamma. Which is a constant 1.4 for air, if you assume that the air through which the aircraft is moving is calorically perfect (another assumption of the standard atmosphere). The above equation is actually derived from the compressible Bernoulli equation, which makes the assumption of isentropic flow, i.e. no entropy change or heat addition.

But, in reality, do those assumptions hold true? In reality, there would be heat transfer to/from the air flow, air is not really calorically perfect (but close enough) and the value of gamma is probably not constant for extremes of temperature, etc. etc.

So temperature does probably have an effect on the Mach reading, but I'm not sure, based on the above considerations, how big of an effect it is.

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Thank you for the magic formula...

Will pass it along for the next Atlantic crossing, where we use the Mach technique separation.

I am sure Recife and Sal ATC will appreciate the formula too.

My last flight in 747 is on the 20 NOV... Will make a note for my Piper L-21.

We file for Mach .85... shall we file for Mach .8498678945031...?

xxx

Sorry to be dumb uneducated, low IQ pilot. Never got a "fATPL", you see... Just FAA certificates.

Happy contrails

Will pass it along for the next Atlantic crossing, where we use the Mach technique separation.

I am sure Recife and Sal ATC will appreciate the formula too.

My last flight in 747 is on the 20 NOV... Will make a note for my Piper L-21.

We file for Mach .85... shall we file for Mach .8498678945031...?

xxx

Sorry to be dumb uneducated, low IQ pilot. Never got a "fATPL", you see... Just FAA certificates.

Happy contrails

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Very old thread, I know, but I'm having real trouble with an ATPL Learning Objective in Instrumentation. For many years now, we've had the statement, "Explain why a Machmeter does not suffer from compressibility error." It's doing my head in, because I'm supposed to teach this to other people. I'm quite familiar with the workings of the Machmeter and understand that the density error in an ASI doesn't apply to the Machmeter, as the static capsule contained therein compensates for the change in density due to the change in altitude.

The problem I have is that the density also changes with speed. As the aircraft speeds up, the air compresses around the pitot tube, which would lead to an increase in dynamic pressure in an ASI. I cannot for the life of me understand how the Machmeter is able to detect this, unless it's somehow taken care of in the gearing or relationship between the ratio and ranging arms.

If anyone has an idea how this works, you would have my undying gratitude. I found the original reference but, other than a few lines about the temperature, nothing about compressibility.

The problem I have is that the density also changes with speed. As the aircraft speeds up, the air compresses around the pitot tube, which would lead to an increase in dynamic pressure in an ASI. I cannot for the life of me understand how the Machmeter is able to detect this, unless it's somehow taken care of in the gearing or relationship between the ratio and ranging arms.

If anyone has an idea how this works, you would have my undying gratitude. I found the original reference but, other than a few lines about the temperature, nothing about compressibility.

You can find them at https://ppubs.uspto.gov/pubwebapp/st...s/landing.html Look at Basic Search and type in the numbers or enter machmeter (which finds the first one) and maybe "mach meter" which is in the second one, which I found as a reference in the first one.

See https://en.wikipedia.org/wiki/Machmeter for the some of the math.