Which speed should be used in calculating the mach number?
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Which speed should be used in calculating the mach number?
Hi ,
there is a question that is bothering me about the mach number calculation...
I have seen in the "pilots handbook of aeronautical knowledge" that mach number is using CAS in calculation.
However in "ace the pilot interview", they use TAS in the calculation above FL260 and IAS below FL 260.
Can someone tell me which airspeed should be used in the calculation?
And also why we should use two different airspeed at above or below FL260??<in the case in Ace the pilot interview>
Thanks a lot!!
there is a question that is bothering me about the mach number calculation...
I have seen in the "pilots handbook of aeronautical knowledge" that mach number is using CAS in calculation.
However in "ace the pilot interview", they use TAS in the calculation above FL260 and IAS below FL 260.
Can someone tell me which airspeed should be used in the calculation?
And also why we should use two different airspeed at above or below FL260??<in the case in Ace the pilot interview>
Thanks a lot!!
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This crops up again
Mach Number is a number, it has nothing to do with speeds which have you left you confused and wishing to "know" which box to tick.
It is normal to use CAS in climb until "cross-over" after which Mach Number is used. The point at which CAS and Mach Number "match" is the crossover. That point is essentially temperature dependent.
Say alt 28000ft is ISA +10, then OAT is -30*C; use your whirly-wheel to deduce TAS is 504kts and TAT is 3.5*C; as a further exercise use the same wheel and settings to show that CAS is 330kts. The two exercises are mutually explanatory.
In other words if PAlt is 28000ft, and OAT is -30*C then Mach Number is 0.83...... don't think of "ace-ing the interview" until you can swop the "wheel" numbers or the electronic calc version in your sleep. You are trying to quote numbers without understanding the underlying physics.
Best of Luck!!
It is normal to use CAS in climb until "cross-over" after which Mach Number is used. The point at which CAS and Mach Number "match" is the crossover. That point is essentially temperature dependent.
Say alt 28000ft is ISA +10, then OAT is -30*C; use your whirly-wheel to deduce TAS is 504kts and TAT is 3.5*C; as a further exercise use the same wheel and settings to show that CAS is 330kts. The two exercises are mutually explanatory.
In other words if PAlt is 28000ft, and OAT is -30*C then Mach Number is 0.83...... don't think of "ace-ing the interview" until you can swop the "wheel" numbers or the electronic calc version in your sleep. You are trying to quote numbers without understanding the underlying physics.
Best of Luck!!
Last edited by Dr Syntax; 18th Jun 2013 at 18:53. Reason: spelling, grammar
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Mach Number / LSS
Eagleflier
hin027, Hi,
As Eagleflier says Mach Number is the product of LSS
LSS is the Local Speed of Sound, and, the LSS is based on Temperature (your Local, that is Outside Air Temperature (OAT))
Its a really easy calculation to do - just do it loads of times over and over again for different temperatures.
Base all your calcs on the magic number Kelvin which at 0 degrees C is 273 Degrees Kelvin.
So, if LSS is based on temperature then Mach Number is based on temperature - remember this and you will never go far wrong.
So say the OAT is -20
the calculation is the Sq Rt of 273+/-T x 38.94
So, using your calculator (just for now) enter 273-20 and hit the Sq Rt button times that by 38.94 = a TAS of 619 knots (kts) therefore the Speed of Sound in your Locality is 619kts TAS, (or LSS), and this is Mach1.
if you multiply this 619 by .78 then you get a TAS of 483 kts.
So, at your OAT Mach .78 is a TAS of 483 kts (obviously this is important for flying jets because with this information added to the windspeed you get a ground speed giving you time and hey, you can now work out how much fuel you need).
The calculation is based on ambient air temperature or OAT so the aispeed is True Airspeed TAS
Now to mess it up. Calibrated airspeed and Equivelant Airspeed have nothing to do with True Airspeed and therefore have nothing to do with mach number, UNLESS you are having to calc through CAS to get TAS,
in which case, go back to your books, find the definition of CAS and learn about CAS only. Then do the same for EAS only.
Then when they try to faze you by asking stupid questions, you will be able to calculate it all back to TAS, ok? But don`t go directly from CAS or EAS to Machno or you will do yourself a head injury.
When you have done a few LSS Machno calculations for different air temperatures - then just look at the little book that came with your whizz wheel or computor and learn all about how to determine Mach number by putting in the temp, looking at where the little 10 number is (Mach1) which should be bang on your TAS.
A word on CAS and EAS one of these is due to compressibility error, i.e., the error in airspeed cause by the air ramming into the pitot tube and getting squashed in the process - the difference in CAS to TAS is not that much, and you can use your whizz wheel to do this = just as you can for EAS.
The other one is due to Temperature Rise, i.e., the rise in temperature of the air as it is going so fast into the pitot tube. What you must do is go to your little book that came with the computor and find out which is which.
Aeronautical engineers (and pilots) came up with a brilliant idea and invented a nice pitot tube/temp sensor that could do all these calculations for you this was called a Rosemont Probe - unfortunately, because it was logical and worked very well, they have stopped using them.
Machno TAS Geddit?!
Now, you should really know the difference between IAS and TAS - because if you do not, then you should not be at a pilot interview or even out on the street!
Also - you should know very well how to get your TAS from your IAS, if not and due to the possibility you are using American terminology instead of Brit terminology then you need some help further on this. For example the Yanks (said with much love and affection for the Yanks) use Course, whereas the Brits don`t (don`t worry about Europe, they just follow us Brits) the Yanks also use CAS moreover than TAS - which is not a bad thing but is a different way of hitting the problem - in short, if your schooling and studying is done Stateside - then I cannot help you, but an American pilot can and will, watch this space.
hin027, Hi,
As Eagleflier says Mach Number is the product of LSS
LSS is the Local Speed of Sound, and, the LSS is based on Temperature (your Local, that is Outside Air Temperature (OAT))
Its a really easy calculation to do - just do it loads of times over and over again for different temperatures.
Base all your calcs on the magic number Kelvin which at 0 degrees C is 273 Degrees Kelvin.
So, if LSS is based on temperature then Mach Number is based on temperature - remember this and you will never go far wrong.
So say the OAT is -20
the calculation is the Sq Rt of 273+/-T x 38.94
So, using your calculator (just for now) enter 273-20 and hit the Sq Rt button times that by 38.94 = a TAS of 619 knots (kts) therefore the Speed of Sound in your Locality is 619kts TAS, (or LSS), and this is Mach1.
if you multiply this 619 by .78 then you get a TAS of 483 kts.
So, at your OAT Mach .78 is a TAS of 483 kts (obviously this is important for flying jets because with this information added to the windspeed you get a ground speed giving you time and hey, you can now work out how much fuel you need).
The calculation is based on ambient air temperature or OAT so the aispeed is True Airspeed TAS
Now to mess it up. Calibrated airspeed and Equivelant Airspeed have nothing to do with True Airspeed and therefore have nothing to do with mach number, UNLESS you are having to calc through CAS to get TAS,
in which case, go back to your books, find the definition of CAS and learn about CAS only. Then do the same for EAS only.
Then when they try to faze you by asking stupid questions, you will be able to calculate it all back to TAS, ok? But don`t go directly from CAS or EAS to Machno or you will do yourself a head injury.
When you have done a few LSS Machno calculations for different air temperatures - then just look at the little book that came with your whizz wheel or computor and learn all about how to determine Mach number by putting in the temp, looking at where the little 10 number is (Mach1) which should be bang on your TAS.
A word on CAS and EAS one of these is due to compressibility error, i.e., the error in airspeed cause by the air ramming into the pitot tube and getting squashed in the process - the difference in CAS to TAS is not that much, and you can use your whizz wheel to do this = just as you can for EAS.
The other one is due to Temperature Rise, i.e., the rise in temperature of the air as it is going so fast into the pitot tube. What you must do is go to your little book that came with the computor and find out which is which.
Aeronautical engineers (and pilots) came up with a brilliant idea and invented a nice pitot tube/temp sensor that could do all these calculations for you this was called a Rosemont Probe - unfortunately, because it was logical and worked very well, they have stopped using them.
Machno TAS Geddit?!
Now, you should really know the difference between IAS and TAS - because if you do not, then you should not be at a pilot interview or even out on the street!
Also - you should know very well how to get your TAS from your IAS, if not and due to the possibility you are using American terminology instead of Brit terminology then you need some help further on this. For example the Yanks (said with much love and affection for the Yanks) use Course, whereas the Brits don`t (don`t worry about Europe, they just follow us Brits) the Yanks also use CAS moreover than TAS - which is not a bad thing but is a different way of hitting the problem - in short, if your schooling and studying is done Stateside - then I cannot help you, but an American pilot can and will, watch this space.
Last edited by Natstrackalpha; 18th Jun 2013 at 22:23.
Moderator
This question (and variants) crops up periodically.. as often is the case, a search will bring up the history. This thread has enough of the story for the purpose at hand ..
Suggest you don't fuss too much about the previous answers - the boys appear to have gone off at a bit of a tangent. Certainly, one can use temperature to facilitate LSS and TAS calculations to end up with Mach number but you don't need to do so - temperature, per se, has naught to do with Mach Number - LSS and TAS, yes, but not M. Indeed, have a CLOSER look at what you are doing on the Jepp and it should become a bit clearer that CAS and Hp produce M as the underlying thing being done.
Mach number depends on static and dynamic pressures, think flight level and CAS .. in effect, the machmeter is just a fancy ASI with some extra internal bells and whistles.
Likewise, a search for information on "Ace the .." should give you a picture regarding that document ...
Suggest you don't fuss too much about the previous answers - the boys appear to have gone off at a bit of a tangent. Certainly, one can use temperature to facilitate LSS and TAS calculations to end up with Mach number but you don't need to do so - temperature, per se, has naught to do with Mach Number - LSS and TAS, yes, but not M. Indeed, have a CLOSER look at what you are doing on the Jepp and it should become a bit clearer that CAS and Hp produce M as the underlying thing being done.
Mach number depends on static and dynamic pressures, think flight level and CAS .. in effect, the machmeter is just a fancy ASI with some extra internal bells and whistles.
Likewise, a search for information on "Ace the .." should give you a picture regarding that document ...
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Temperature effect on the speed of sound and true airspeed
I understand that Mr Tullamarine is saying that both LSS and TAS depend on temperature in the same way - root(T), so the Mach number isn't affected by temperature.
To answer the OP, if they want the answer from CAS, do it on your whizz wheel: Put the Cal Airspeed on the Pressure Altitude and read the Mach No in the "Mach Number" window.
If they want the answer from TAS, in the True Airspeed section, put the OAT on the Mach Index arrow, then read Mach and TAS on the main scale. Alternatively, use the formula TAS= 39M x Sqrt (OAT°C +273.15)
You can use the two methods above to calculate the IAS for a TAS without worrying about the Cr value.
Local Speed of Sound and Temp/RAM rise are irrelevant.
Hmm, that's not right. At ISA sea level, yes, at 40,000ft, almost half.
If they want the answer from TAS, in the True Airspeed section, put the OAT on the Mach Index arrow, then read Mach and TAS on the main scale. Alternatively, use the formula TAS= 39M x Sqrt (OAT°C +273.15)
You can use the two methods above to calculate the IAS for a TAS without worrying about the Cr value.
Local Speed of Sound and Temp/RAM rise are irrelevant.
Originally Posted by NTA
the difference in CAS to TAS is not that much
Moderator
Useful thread as this is a very common misconception regarding OAT and Mach number. Much of the blame is sheeted home to ineffective basic theory training courses, methinks .. or, perhaps, theory instructors' not qualifying their explanations in such courses. (I come from a long ago history of such activity and certainly was not immune to the problem myself).
Temperature has nothing to do with the speed of sound? If so I need to burn a lot of old books
I didn't say that ... indeed, quite the contrary !
Suggest, first, that you re-read the old books. I suspect that they will be talking about temperature's having an involvement in both LSS (directly) and TAS (indirectly), but not Mach number - which is calculated directly from dynamic and static pressures ?
Tullamarine is saying that both LSS and TAS depend on temperature in the same way
Not quite .. what he is saying is that the equation for Mach number involves static and dynamic pressures and has naught to do with temperature.
Put the Cal Airspeed on the Pressure Altitude and read the Mach No in the "Mach Number" window
Precisely and that implements the equation to which I hyperlinked earlier. Once the Mach number is set, subsequent calculations to other values can follow
More particularly, how do you figure your Mach number in flight ?
(a) look at the Machmeter - which implements the equation for Mach number, or
(b) pull out your whizz wheel and set CAS against FL to read off M
If you want to end up with the value in a round about, more difficult fashion, you can work out the LSS, work out the TAS (or read them off the appropriate page on the box) and figure Mach from that .. but why do things the difficult way when there is an easy solution ?
Temperature has nothing to do with the speed of sound? If so I need to burn a lot of old books
I didn't say that ... indeed, quite the contrary !
Suggest, first, that you re-read the old books. I suspect that they will be talking about temperature's having an involvement in both LSS (directly) and TAS (indirectly), but not Mach number - which is calculated directly from dynamic and static pressures ?
Tullamarine is saying that both LSS and TAS depend on temperature in the same way
Not quite .. what he is saying is that the equation for Mach number involves static and dynamic pressures and has naught to do with temperature.
Put the Cal Airspeed on the Pressure Altitude and read the Mach No in the "Mach Number" window
Precisely and that implements the equation to which I hyperlinked earlier. Once the Mach number is set, subsequent calculations to other values can follow
More particularly, how do you figure your Mach number in flight ?
(a) look at the Machmeter - which implements the equation for Mach number, or
(b) pull out your whizz wheel and set CAS against FL to read off M
If you want to end up with the value in a round about, more difficult fashion, you can work out the LSS, work out the TAS (or read them off the appropriate page on the box) and figure Mach from that .. but why do things the difficult way when there is an easy solution ?
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Confusion reigns...
Right, lets get to the bottom of this.
IAS = speed calculated from dynamic pressure (i.e. total - static), assuming ISA SEA LEVEL air density. IAS is therefore a representation of DYNAMIC PRESSURE, not actual speed though the air in the sense of speed = distance/time. IAS also has errors because there is no pressure error correction on the static source(s).
CAS is IAS with the static pressure errors corrected, but it is only valid up to about Mach 0.3 because it assumes zero compressibility error. CAS will over-read once compressibility of the air in the pitot tube becomes significant; this discrepancy increases with altitude.
EAS is CAS with a compressibility correction, but still assumes ISA sea level density when deriving the speed from the dynamic pressure.
In a perfect aircraft with no static pressure errors and no compressibility errors, IAS = CAS = EAS, but these still only represent dynamic pressure, not the actual speed of the aircraft through the air. So why use them? Well, all your limiting speeds (e.g. stall, flaps/slats, gear, Vne, etc) are dynamic pressure related and will be constant regardless of actual local air density provided they are expressed in terms of EAS, which means they are easier to remember and comply with throughout the flight envelope. If they were expressed in TAS you would have to recalculate the limits frequently as temperature and altitude changed.
TAS = EAS corrected for density. See below:
0.5 * density(ISA sea level) * EAS^2 = 0.5 * density(actual) * TAS ^2
thus:
TAS = EAS / SQRT(sigma) where sigma = Rho(actual) / Rho(ISA sea level)
Clearly we need to know TAS for navigation, and also because speed of sound is a true air speed. Both TAS and speed of sound depend on temperature, so when you calculate Mach Number the temperature dependency cancels out.
Mach No = TAS / Local Speed of Sound
If you plot a graph showing a constant EAS climb, TAS increases with height but speed of sound decreases with height. Therefore there will be a height where a given Mach No will be equivalent in TAS to a given EAS expressed as TAS. Therefore at low altitude Vmo takes precedence (dynamic pressure limit), but at a certain height Mmo becomes more limiting (e.g. wave drag, mach tuck and possible control problems).
Hope this helps.
IAS = speed calculated from dynamic pressure (i.e. total - static), assuming ISA SEA LEVEL air density. IAS is therefore a representation of DYNAMIC PRESSURE, not actual speed though the air in the sense of speed = distance/time. IAS also has errors because there is no pressure error correction on the static source(s).
CAS is IAS with the static pressure errors corrected, but it is only valid up to about Mach 0.3 because it assumes zero compressibility error. CAS will over-read once compressibility of the air in the pitot tube becomes significant; this discrepancy increases with altitude.
EAS is CAS with a compressibility correction, but still assumes ISA sea level density when deriving the speed from the dynamic pressure.
In a perfect aircraft with no static pressure errors and no compressibility errors, IAS = CAS = EAS, but these still only represent dynamic pressure, not the actual speed of the aircraft through the air. So why use them? Well, all your limiting speeds (e.g. stall, flaps/slats, gear, Vne, etc) are dynamic pressure related and will be constant regardless of actual local air density provided they are expressed in terms of EAS, which means they are easier to remember and comply with throughout the flight envelope. If they were expressed in TAS you would have to recalculate the limits frequently as temperature and altitude changed.
TAS = EAS corrected for density. See below:
0.5 * density(ISA sea level) * EAS^2 = 0.5 * density(actual) * TAS ^2
thus:
TAS = EAS / SQRT(sigma) where sigma = Rho(actual) / Rho(ISA sea level)
Clearly we need to know TAS for navigation, and also because speed of sound is a true air speed. Both TAS and speed of sound depend on temperature, so when you calculate Mach Number the temperature dependency cancels out.
Mach No = TAS / Local Speed of Sound
If you plot a graph showing a constant EAS climb, TAS increases with height but speed of sound decreases with height. Therefore there will be a height where a given Mach No will be equivalent in TAS to a given EAS expressed as TAS. Therefore at low altitude Vmo takes precedence (dynamic pressure limit), but at a certain height Mmo becomes more limiting (e.g. wave drag, mach tuck and possible control problems).
Hope this helps.
Last edited by Jetdriver; 20th Jun 2013 at 17:40.
IAS = speed calculated from dynamic pressure (i.e. total - static),
Dynamic Pressure = 1/2Rho Vsquared where V is the TAS.
Impact Pressure = Total Pressure - Static Pressure.
I know that's not they way we all used to explain it in the past, but it is the way that we should be explaining it in these modern times.
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IAS,RAS,TAS,CAS,EAS
I thought IAS was what you see on the airspeed indicator dial - subject to position error / mechanical error (of all the things that make the a/s indicator . . .work). Take these out in your calcs and you get
RAS (which you did not mention) So RAS is IAS with all the errors taken into consideration
So far then its
IAS
RAS
So with your RAS you then work out your temperature (OAT/Ambient - i.e., the air around you, only) and Pressure i.,e your altitude. So at 5,000ft it will be less pressure than at Sea Level, as you know full well.
On your computer / whizz wheel you just stick the temp against the altitude you want to fly at. you, get, your, TAS, which is found against your RAS - see?
So far then its
IAS
RAS
TAS
then take that true airspeed and adjust on your computor for commpressability error? This gives you CAS [and for some reason the Yanks go to CAS all the time - which is which is there way of doing it and is fine]
IAS
RAS
TAS
CAS
Now, the air going into the tube [pitot] is going to cause a rise in temperature of the air - obviously we don`t bother about this flying a little old puddle-jumper, but when flying along at some 450 kts - this will happen. . . So, we . . .adjust the speed we have to accommodate the temperature rise (we are still in the briefing room) at that alt and that speed by the method used to obtain EAS (see your little book that came with your big fat CRP5 -don`t leave home without it) to get our EAS therefore we get
IAS
RAS
TAS
CAS
EAS
e` voila! However, if they are teaching you in America-land to do it straight from CAS - then do it.
Just when you thought it cool to pop a valium, hang on a sec. The question is - now, do we use the EAS speed or TAS for Mach calcs?
Well, a super sonic aircraft flying through the air at the LSS or shall we say Mach one is going to break the sound barrier - which will be a different airspeed when it is cold outside to when it is hot!
In minus 35 deg C the Speed of Sound is 600 kts
at +35 deg C its 683 kts
Even though the air popping down the tube is compressing or rising in temp
(due to compressibility and temperature rise) the fast aeroplane is moving through the atmosphere at, the, speed, of, sound, based on temperature of that air.
RAS (which you did not mention) So RAS is IAS with all the errors taken into consideration
So far then its
IAS
RAS
So with your RAS you then work out your temperature (OAT/Ambient - i.e., the air around you, only) and Pressure i.,e your altitude. So at 5,000ft it will be less pressure than at Sea Level, as you know full well.
On your computer / whizz wheel you just stick the temp against the altitude you want to fly at. you, get, your, TAS, which is found against your RAS - see?
So far then its
IAS
RAS
TAS
then take that true airspeed and adjust on your computor for commpressability error? This gives you CAS [and for some reason the Yanks go to CAS all the time - which is which is there way of doing it and is fine]
IAS
RAS
TAS
CAS
Now, the air going into the tube [pitot] is going to cause a rise in temperature of the air - obviously we don`t bother about this flying a little old puddle-jumper, but when flying along at some 450 kts - this will happen. . . So, we . . .adjust the speed we have to accommodate the temperature rise (we are still in the briefing room) at that alt and that speed by the method used to obtain EAS (see your little book that came with your big fat CRP5 -don`t leave home without it) to get our EAS therefore we get
IAS
RAS
TAS
CAS
EAS
e` voila! However, if they are teaching you in America-land to do it straight from CAS - then do it.
Just when you thought it cool to pop a valium, hang on a sec. The question is - now, do we use the EAS speed or TAS for Mach calcs?
Well, a super sonic aircraft flying through the air at the LSS or shall we say Mach one is going to break the sound barrier - which will be a different airspeed when it is cold outside to when it is hot!
In minus 35 deg C the Speed of Sound is 600 kts
at +35 deg C its 683 kts
Even though the air popping down the tube is compressing or rising in temp
(due to compressibility and temperature rise) the fast aeroplane is moving through the atmosphere at, the, speed, of, sound, based on temperature of that air.
Last edited by Natstrackalpha; 23rd Jun 2013 at 07:53.
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I think that in the days when the density of air at sea level was 0.002378 slugs/cu.ft people had no trouble calculating a Mach No without any spin wheels. Mind you there was no t'internet to confuse people then.
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Thank you everyone!!
I guess I got the concept now!
But concerning the temperature effect on mach no,
is it like the mach no at a specific altitude is independent of temp?
Becoz the effect of temp on TAS and that on LSS has canceled out each other?!
I guess I got the concept now!
But concerning the temperature effect on mach no,
is it like the mach no at a specific altitude is independent of temp?
Becoz the effect of temp on TAS and that on LSS has canceled out each other?!
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Mach No and altitude
The speed of sound (a) at any alitiude in air is given by:
a = sqrt(gamma*R*T), where:
a = true air speed in m/s
gamma = 1.4
R = gas constant fo air, usually taken to be 287 J/kg.K
T = temperature in Kelvin
Some useful conversions for you to use with the above:
1 kt = 0.51444 m/s
Temperature in kelvin = Temperature in deg C + 273.15
If you intend to maintain a constant Mach No as you climb, the TAS required to maintain that constant Mach No will DECREASE as you climb, because the outside air temperature is decreasing as you gain altitude.
If you maintain constant TAS as you climb, the Mach No will slowly increase because the speed of sound is decreasing (due to the temperature decreasing). As a guide, Mach 1 at ISA Sea Level is 340.29 m/s (661 kt), reducing to 295 m/s (573 kt) at the tropopause (36,089ft in the ISA).
a = sqrt(gamma*R*T), where:
a = true air speed in m/s
gamma = 1.4
R = gas constant fo air, usually taken to be 287 J/kg.K
T = temperature in Kelvin
Some useful conversions for you to use with the above:
1 kt = 0.51444 m/s
Temperature in kelvin = Temperature in deg C + 273.15
If you intend to maintain a constant Mach No as you climb, the TAS required to maintain that constant Mach No will DECREASE as you climb, because the outside air temperature is decreasing as you gain altitude.
If you maintain constant TAS as you climb, the Mach No will slowly increase because the speed of sound is decreasing (due to the temperature decreasing). As a guide, Mach 1 at ISA Sea Level is 340.29 m/s (661 kt), reducing to 295 m/s (573 kt) at the tropopause (36,089ft in the ISA).
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is it like the mach no at a specific altitude is independent of temp? Becoz the effect of temp on TAS and that on LSS has canceled out each other?!
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Not quite .. what he is saying is that the equation for Mach number involves static and dynamic pressures and has naught to do with temperature
ahh, I see it all now. . . !
You mean Mach is D over S
D/S
?
So just to make it totally indecipherable, pitot Dynamic increases with speed whereby static reduces with alt . . .
dynamic reduces with alt due to reduction in density (less air per cubic . . space) speed speeds up due to less density thus being the TAS
la di da di da ends up with D over S D/S
No mention of temp here though, ? Except that less temp = greater rho and
Last edited by Natstrackalpha; 26th Jun 2013 at 01:23.
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Natstrack,
try this for an explanation and the relevant equations:
Machmeter - Wikipedia, the free encyclopedia
Put simply, the Machmeter does not need to know temperature. For subsonic speeds it simply uses the ratio of impact pressure to static pressure and then does some additional maths. The maths is simple enough to be implemented with a purely mechanical mechanism, which is exactly what was done in early Mach meters, prior to the invention of air data computers. You don't need to know local air density to calculate mach number - it does not appear in the equation at all (although you could ague it is implicit within impact pressure, but to determine it you would need to know your TAS first).
You DO need temperature to calculate TAS, because you need to calculate the local air density from the temperaure and static pressure. Air follows the perfect gas law well enough:
P = Rho * R * T therefore Rho = P/(RT)
thus if you need to calculate TAS your aicraft will amost certainly have a total temperaure probe, which will supply the information the air data computer needs to calculate local air density and thus derive TAS from EAS.
Total air temperature - Wikipedia, the free encyclopedia
try this for an explanation and the relevant equations:
Machmeter - Wikipedia, the free encyclopedia
Put simply, the Machmeter does not need to know temperature. For subsonic speeds it simply uses the ratio of impact pressure to static pressure and then does some additional maths. The maths is simple enough to be implemented with a purely mechanical mechanism, which is exactly what was done in early Mach meters, prior to the invention of air data computers. You don't need to know local air density to calculate mach number - it does not appear in the equation at all (although you could ague it is implicit within impact pressure, but to determine it you would need to know your TAS first).
You DO need temperature to calculate TAS, because you need to calculate the local air density from the temperaure and static pressure. Air follows the perfect gas law well enough:
P = Rho * R * T therefore Rho = P/(RT)
thus if you need to calculate TAS your aicraft will amost certainly have a total temperaure probe, which will supply the information the air data computer needs to calculate local air density and thus derive TAS from EAS.
Total air temperature - Wikipedia, the free encyclopedia
Last edited by WeekendFlyer; 26th Jun 2013 at 09:13. Reason: Typos and Web link
The mach meter gives an indicated mach number that is the ratio of dynamic pressure to static pressure.
Mach Number = Dynamic Pressure / Static Pressure.
Dynamic Pressure = 1/2 Rho V squared
Static Pressure = Rho g H, where H is the height of the column of air above us.
So we have Mach Number = 1/2 Rho Vsquared / Rho g H
Dividing both sides of this equation by Rho gives us
Mach Number = 1/2 Vsquared / gH
Rho is not in the above equation, so changes in Rho do not change the indicated mach number.
Or to put it in a slightly different way, if the temperature changes it causes the value of Rho to change. But because Rho is in both sides of the mach number equation, this change in Rho is self-cancelling.
So changes in temperature do not affect the indicated mach number.
Also because both CAS and mach number are determined using the same dynamic pressure, the mach number at any fixed CAS does not change with temperature.
But because changes in temperature change the ratio of CAS to TAS, any change in temperature will change the TAS at any given mach number.
Mach Number = Dynamic Pressure / Static Pressure.
Dynamic Pressure = 1/2 Rho V squared
Static Pressure = Rho g H, where H is the height of the column of air above us.
So we have Mach Number = 1/2 Rho Vsquared / Rho g H
Dividing both sides of this equation by Rho gives us
Mach Number = 1/2 Vsquared / gH
Rho is not in the above equation, so changes in Rho do not change the indicated mach number.
Or to put it in a slightly different way, if the temperature changes it causes the value of Rho to change. But because Rho is in both sides of the mach number equation, this change in Rho is self-cancelling.
So changes in temperature do not affect the indicated mach number.
Also because both CAS and mach number are determined using the same dynamic pressure, the mach number at any fixed CAS does not change with temperature.
But because changes in temperature change the ratio of CAS to TAS, any change in temperature will change the TAS at any given mach number.