Relation between IAS and Mach number
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Relation between IAS and Mach number
This quote comes from the FAA's "Airplane Upset Recovery Training Aid" referring to Mach stability:
"This stability can be independent of airspeed if, for example, the airplane crosses a cold front. When the outside air temperature changes, the Mach number changes, even though the indicated airspeed may not change."
Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.
But then the source document was written by senior test pilots from Boeing and Airbus, so maybe I have got it wrong??
"This stability can be independent of airspeed if, for example, the airplane crosses a cold front. When the outside air temperature changes, the Mach number changes, even though the indicated airspeed may not change."
Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.
But then the source document was written by senior test pilots from Boeing and Airbus, so maybe I have got it wrong??
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Mach speed is affected by temperature. IAS is affected by altitude with constant mach. If you were above the trop and climbed 4,000 feet your IAS would decrease significantly but mach would be constant because temp would be constant. Say you cruise at .80.
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as a (bio)chemist I can't resist this,
Mach number depend on TAS which in turn depends on EAS (IAS corrected for compressibility and position error)
TAS=EAS/(sigma)^(1/2) and sigma is the ratio of densities this is the HTBJ part.
Now the partial pressures of the atmosphere add to give total pressure P (it's value can be determined from the the altitude, hypsometric formula of altimetry
) from the ideal gas law PV=nRT; n=moles of gas, R=gas constant 0.0831L*atm/mole*K.
n=mass/molar mass(MW) and rho or density =mass/volume
so I write PV=(m/Mm)RT; rearanging that I have PMm=rhoRT=dRT
so TAS depends on rho which depend on T and the two vary directly; actually with that equation you can relate mach no. to T or P or d=rho
Mach number depend on TAS which in turn depends on EAS (IAS corrected for compressibility and position error)
TAS=EAS/(sigma)^(1/2) and sigma is the ratio of densities this is the HTBJ part.
Now the partial pressures of the atmosphere add to give total pressure P (it's value can be determined from the the altitude, hypsometric formula of altimetry
) from the ideal gas law PV=nRT; n=moles of gas, R=gas constant 0.0831L*atm/mole*K.n=mass/molar mass(MW) and rho or density =mass/volume
so I write PV=(m/Mm)RT; rearanging that I have PMm=rhoRT=dRT
so TAS depends on rho which depend on T and the two vary directly; actually with that equation you can relate mach no. to T or P or d=rho
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Rivet Gun, I believe you are right, since you did say constant flight level. I don't believe these test pilots would be wrong, perhaps a misquote. Perhaps Bubbers and Rhov can specifically respond respond to your query, and state whether they agree with you or not. Of course, I have little formal qualifications, and have known to be completely wrong.
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It was difficult to know exactly what IAS would do flying a FL and flying into colder air because the mach would increase because of the colder air and the speed of sound would of course decrease but how much, if any, would this change the IAS? Also would the true altitude change? That is why I did the constant mach example. I don't want to get in to too much physics because then it is too hard to understand. Previous example proves that.
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Bubbers,I can't remember all the physics behind it but back in my 707 days cruising @ M.81 the formula used to X check or in case of Machmeter failure was:SAT+TAS=521(?) at any altitude.I'm pretty sure it was 521 but it was a while ago and it worked spot on every time.
Last edited by 30/30 Green Light; 18th May 2006 at 06:42.
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Mach is the ratio of an aircraft's True Airspeed (TAS) to the local speed of sound.
The local speed of sound is only dependent on temperature. Nothing else.
Therefore, it is conceivable that at a constant Mach one could cross a front and have a change to the TAS in order to maintain constanct Mach, which would require a change in IAS.
The colder the air mass, the higher the Mach number for a constant TAS
The warmer the air mass, the lower the Mach number for a constant TAS
I hope this helps... it's been a while!
The local speed of sound is only dependent on temperature. Nothing else.
Therefore, it is conceivable that at a constant Mach one could cross a front and have a change to the TAS in order to maintain constanct Mach, which would require a change in IAS.
The colder the air mass, the higher the Mach number for a constant TAS
The warmer the air mass, the lower the Mach number for a constant TAS
I hope this helps... it's been a while!
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Originally Posted by bubbers44
It was difficult to know exactly what IAS would do flying a FL and flying into colder air because the mach would increase because of the colder air and the speed of sound would of course decrease but how much, if any, would this change the IAS? Also would the true altitude change?
If pressure is not changed, flight level is not changed. But the density of air changes. Therefore the IAS changes at a constant TAS.
Right?
So, the same ought to apply at any higher FL... as the FL follows pressure, flying into colder air should increase IAS if the TAS is unchanged...
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Originally Posted by specialrider987
, which would require a change in IAS.
You are flying a constant flight level and the autothrottle holds a constant Mach number. You fly from a colder to a warmer air mass:
Going to the warmer air the local speed of sound increases, therefore TAS increases.
The warmer air is less dense, which affects the IAS / TAS ratio.
The laws of physics conspire such that these effects cancel each other and IAS remains constant.
Another way of looking at this is to consider the inputs required to an Air Data Computer (or traditional instruments).
To compute IAS (theoretically CAS if we correct for position error) requires only impact pressure (this is the pitot - static differential measured by the traditional "airspeed" capsule).
To compute Mach number requires both impact pressure and absolute static pressure (traditional "altitude" capsule).
So far we have both IAS and Mach number without any input of air temperature. Thus the relation between IAS and Mach number is independant of air temperature.
Now if we wish to compute Static Air Temperature (SAT) and TAS, we require also the Total Air Temperature (TAT) input.
Last edited by Rivet gun; 18th May 2006 at 10:06.
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Rivet Gun, guess I am the only one then that thinks you are correct. Seems the responses have all avoided your original question though. For the others who replied, here’s Rivet Gun’supposition from his original post,
“Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.”
The thread then departed to address other aspects, such as mach vs tas, EAS, compressibility, formulas…..
If Rivet is incorrect, then, will anyone go out on a limb and say what direction will the IAS (assuming no error correction/position error) or CAS will take if you fly at a constant mach and flight level and the air temperature gets colder?
Hawk
“Now I thought that at a constant flight level, the relationship between IAS and Mach number is independant of temperature. So if you maintain a constant flight level and constant IAS, you also fly a constant Mach number even if the air temperature changes.”
The thread then departed to address other aspects, such as mach vs tas, EAS, compressibility, formulas…..
If Rivet is incorrect, then, will anyone go out on a limb and say what direction will the IAS (assuming no error correction/position error) or CAS will take if you fly at a constant mach and flight level and the air temperature gets colder?
Hawk
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rivet gun
IAS corrected for Pressure = Calibrated
Calibrated corrected for Compressibility = Equivalent
EAS corrected for Density = TAS
it is conceivable in your example that the effects of P and C could cancel one another out on a particular aircraft on a particular day, leaving the IAS constant and the Mach number constant. This would have more to do with the compressibility effect of the aircraft being flown than the atmospheric factors.
The relationship above is universal, not aircraft dependent.
Cheers
IAS corrected for Pressure = Calibrated
Calibrated corrected for Compressibility = Equivalent
EAS corrected for Density = TAS
it is conceivable in your example that the effects of P and C could cancel one another out on a particular aircraft on a particular day, leaving the IAS constant and the Mach number constant. This would have more to do with the compressibility effect of the aircraft being flown than the atmospheric factors.
The relationship above is universal, not aircraft dependent.
Cheers
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SpecialRider, reference your quote
"it is conceivable in your example that the effects of P and C could cancel one another out on a particular aircraft on a particular day, leaving the IAS constant and the Mach number constant. This would have more to do with the compressibility effect of the aircraft being flown than the atmospheric factors"
I just don't see how your argument provides any answer to Rivet Gun's question. If by P you mean pressure, and by C you mean Compressibility correction, then I don't see why you think they "could cancel another out" has any bearing at all. Remember that P is a constant, a constant Flight level. And as per Rivet Gun's post, IAS is a constant, and if position/error correction are zero, then so is CAS. If pressure and calibrated airspeed are constants, then so is compressibility correction. So with all these being constants, good for all days and on all aircraft, I don't see why you say in your quote "on a particular aircraft on a particular day".
"it is conceivable in your example that the effects of P and C could cancel one another out on a particular aircraft on a particular day, leaving the IAS constant and the Mach number constant. This would have more to do with the compressibility effect of the aircraft being flown than the atmospheric factors"
I just don't see how your argument provides any answer to Rivet Gun's question. If by P you mean pressure, and by C you mean Compressibility correction, then I don't see why you think they "could cancel another out" has any bearing at all. Remember that P is a constant, a constant Flight level. And as per Rivet Gun's post, IAS is a constant, and if position/error correction are zero, then so is CAS. If pressure and calibrated airspeed are constants, then so is compressibility correction. So with all these being constants, good for all days and on all aircraft, I don't see why you say in your quote "on a particular aircraft on a particular day".
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Ultimately, the speed of sound in air depends on the air temperature only.
Therefore, you can have the speed of sound be different for the same density and pressure, as long as the temperature is different. Density and pressure determine flight level and TAS-to-IAS, so you'd be at the same FL, the same IAS, the same TAS, but a different Mach number.
In a single volume of gas, of course, I can't change JUST T and not p and V. But we're talking about a case of moving from one section of the atmosphere to another, so the gas law relationship doesn't have to hold.
So the original text is correct - if you pass a front such that there is a marked temperature change, you may find the relationship between Mach and IAS changes, even at a fixed FL, due to temperature changes.
In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure. Air is almost an ideal gas.
In a single volume of gas, of course, I can't change JUST T and not p and V. But we're talking about a case of moving from one section of the atmosphere to another, so the gas law relationship doesn't have to hold.
So the original text is correct - if you pass a front such that there is a marked temperature change, you may find the relationship between Mach and IAS changes, even at a fixed FL, due to temperature changes.
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Originally Posted by Mad (Flt) Scientist
Ultimately, the speed of sound in air depends on the air temperature only.
Therefore, you can have the speed of sound be different for the same density and pressure, as long as the temperature is different. Density and pressure determine flight level and TAS-to-IAS, so you'd be at the same FL, the same IAS, the same TAS, but a different Mach number.
In a single volume of gas, of course, I can't change JUST T and not p and V. But we're talking about a case of moving from one section of the atmosphere to another, so the gas law relationship doesn't have to hold.
Therefore, you can have the speed of sound be different for the same density and pressure, as long as the temperature is different. Density and pressure determine flight level and TAS-to-IAS, so you'd be at the same FL, the same IAS, the same TAS, but a different Mach number.
In a single volume of gas, of course, I can't change JUST T and not p and V. But we're talking about a case of moving from one section of the atmosphere to another, so the gas law relationship doesn't have to hold.
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Yep, that was nonsense.
The relationship between CAS, pressure altitude and Mach number is unique. So as long as you stay at the same pressure altitude CAS and Mach vary uniformly.
I'm not doing very well the last few days
The relationship between CAS, pressure altitude and Mach number is unique. So as long as you stay at the same pressure altitude CAS and Mach vary uniformly.I'm not doing very well the last few days
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Mad Scientist, are you then saying that if one maintains a given Flight Level, and given CAS, that should the aircraft then fly into an air mass that is now at a different temperature, the mach number does not change?
This was the crux of Rivet Gun's question, which seems to be still debated.
Thanks, Hawk
This was the crux of Rivet Gun's question, which seems to be still debated.
Thanks, Hawk
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Yes. But it's essentially impossible to do so.
The relationship between CAS, Mach and pressure altitude (FL) is fixed. Therefore if you do as suggested, and
you MUST maintain a fixed Mach also.
I think the problem is that the original text was presumably talking about flying into a frontal system at a fixed GEOMETRIC altitude - in which case the FL won't stay fixed, and there will be a change in Mach for constant CAS. Since it's talking about a case with a sharply delineated temperature profile, changing quite rapidly over a short distance, unless one flew a sudden climb or dive to maintain fixed FL, one CANNOT actually do what the question posits, i.e. fly at constant CAS and FL across a temperature change.
The original article has chosen a bad example to try to explain the difference between CAS and Mach, IMO. They might have done better to consider a constant CAS descent, where they could have talked about the Mach effects just as easily.
The relationship between CAS, Mach and pressure altitude (FL) is fixed. Therefore if you do as suggested, and
maintains a given Flight Level, and given CAS,
I think the problem is that the original text was presumably talking about flying into a frontal system at a fixed GEOMETRIC altitude - in which case the FL won't stay fixed, and there will be a change in Mach for constant CAS. Since it's talking about a case with a sharply delineated temperature profile, changing quite rapidly over a short distance, unless one flew a sudden climb or dive to maintain fixed FL, one CANNOT actually do what the question posits, i.e. fly at constant CAS and FL across a temperature change.
The original article has chosen a bad example to try to explain the difference between CAS and Mach, IMO. They might have done better to consider a constant CAS descent, where they could have talked about the Mach effects just as easily.
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Sure, ok, if maintaining a constant GEOMETRIC altitude then I can see that the same CAS will not mean the same mach when flying through a temperature change. I don't think anyone was having difficulty with that. thanks for your input
Hawk
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