VMO to MMO
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Hi bio161,
Since TAS depends on a density correction applied to IAS, and LSS varies with temperature (which affects Density Altitude), the net result is that temperature is cancelled out.
i.e. Even if the temperature is different from ISA, for a given IAS at a given FL (But your Density Altitude will be different) = the same Mach Number.
ASI measures (Pitot dynamic + static pressure) - (Pitot static pressure) = ( Pt - Ps)
Machmeter measures (Pt-Ps) / Ps.
Since TAS depends on a density correction applied to IAS, and LSS varies with temperature (which affects Density Altitude), the net result is that temperature is cancelled out.
i.e. Even if the temperature is different from ISA, for a given IAS at a given FL (But your Density Altitude will be different) = the same Mach Number.
ASI measures (Pitot dynamic + static pressure) - (Pitot static pressure) = ( Pt - Ps)
Machmeter measures (Pt-Ps) / Ps.
Last edited by rudderrudderrat; 15th Sep 2010 at 09:49. Reason: punctuation for clarity
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Hi rudderrudderrat,
Thanks a lot for your explanation. Short but i have to say precise and clear! There's no better way to do it!
I just have one more doubt in my mind. I understand that a variation in Temperature will affect both TAS and LSS so, at the end, the result MACH will not vary because both factors vary at the same time of the same (i hope i don't say something wrong now..) amount and they cancel themselves out by their own. So temperature is not a factor. This i got..
Now. Taking back for a moment the temperature of a given air mass a change of this, as you said as well, will affect density altitude.
But now my head crashes again. A change in temperature which is followed by a change in density does not change as well the pressure of the air?
So here now i come back to my problems. How can it be possible that we ALWAYS find the SAME pressure at the SAME FL which allows us to make the crossover from CAS to MACH if temperature's changes affect as well pressure?
Thank you again guys. I'm sorry if maybe i ask something that should be obvious.
Regards to all of you,
bio161
Thanks a lot for your explanation. Short but i have to say precise and clear! There's no better way to do it!
I just have one more doubt in my mind. I understand that a variation in Temperature will affect both TAS and LSS so, at the end, the result MACH will not vary because both factors vary at the same time of the same (i hope i don't say something wrong now..) amount and they cancel themselves out by their own. So temperature is not a factor. This i got..
Now. Taking back for a moment the temperature of a given air mass a change of this, as you said as well, will affect density altitude.
But now my head crashes again. A change in temperature which is followed by a change in density does not change as well the pressure of the air?
So here now i come back to my problems. How can it be possible that we ALWAYS find the SAME pressure at the SAME FL which allows us to make the crossover from CAS to MACH if temperature's changes affect as well pressure?
Thank you again guys. I'm sorry if maybe i ask something that should be obvious.
Regards to all of you,
bio161
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Hi bio61,
Sea Level pressure depends on the mass of air over each square unit of area (sq. inch). If you change the temperature, you will have changed the height of the column of air.
That's all an Altimeter does. It may be graduated in feet - but it only measures pressure (Pressure Altitude) - you're real Altitude will change with air density.
A change in temperature which is followed by a change in density does not change as well the pressure of the air?
How can it be possible that we ALWAYS find the SAME pressure at the SAME FL
Last edited by rudderrudderrat; 15th Sep 2010 at 19:08. Reason: syntax
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Hi again rudderrudderrat and thnx again for your reply!
Slowly i'm getting it..The atmosphere does NOT behave in a fixed volume way but this one varies according to the temperature so to keep a constant pressure.
As you said the Altimeter mesaures PRESSURE altitude. That's why we set the QNH every time we fly in order to know our true altitude (without counting now temperature variations of more than 10°).
So correct me if i'm wrong. But may be i got it now:
The changeover between EAS and MACH will always come at the same PRESSURE altitude, which indeed we can find at different REAL altitudes which depend on density, temperature ecc ecc.
Did i get it?
Sorry if i keep on asking but i'm starving to get to the solution!
Thank you guys again!
bio161
Slowly i'm getting it..The atmosphere does NOT behave in a fixed volume way but this one varies according to the temperature so to keep a constant pressure.
As you said the Altimeter mesaures PRESSURE altitude. That's why we set the QNH every time we fly in order to know our true altitude (without counting now temperature variations of more than 10°).
So correct me if i'm wrong. But may be i got it now:
The changeover between EAS and MACH will always come at the same PRESSURE altitude, which indeed we can find at different REAL altitudes which depend on density, temperature ecc ecc.
Did i get it?
Sorry if i keep on asking but i'm starving to get to the solution!
Thank you guys again!
bio161
The changeover between EAS and MACH will always come at the same PRESSURE altitude, which indeed we can find at different REAL altitudes which depend on density, temperature ecc ecc.
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I'm a bit late on this thread. I'm glad BIO 161 has got this sorted. He's not the first and won't be the last to have found this confusing.
I think this is an issue which the flight schools don't teach well. They teach the relationship between TAS and mach number (which depends on temperature) but they dont teach the analogous relationship between EAS and mach number (which depends on static pressure). The equations are simple (one was quoted earlier in this thread)
TAS = M x 661.48 x sqrt(T/T0)
; T0 = 288.15 kelvins
EAS = M x 661.48 x sqrt(p/p0)
; p0 = 1013.25 hpa
661.48 is speed of sound at ISA sea level.
Perhaps a reason for this is that our speed tapes display CAS not EAS. The equation relating CAS and Mach number is too complex for the ATPL courses so they don't teach it. This does not alter the fact CAS and Mach number are related by static pressure. (temperature is irrelevant)
CAS exists only because it is the best you can do with a mechanical ASI. With EFIS, CAS should eventually become obsolete. I think the Eclipse buisness jet displays EAS on the speed tape and so did the space shuttle. Perhaps Boeing and Airbus will eventually ditch CAS. Then compressibility error will be just a historical curiosity.
I think this is an issue which the flight schools don't teach well. They teach the relationship between TAS and mach number (which depends on temperature) but they dont teach the analogous relationship between EAS and mach number (which depends on static pressure). The equations are simple (one was quoted earlier in this thread)
TAS = M x 661.48 x sqrt(T/T0)
; T0 = 288.15 kelvins
EAS = M x 661.48 x sqrt(p/p0)
; p0 = 1013.25 hpa
661.48 is speed of sound at ISA sea level.
Perhaps a reason for this is that our speed tapes display CAS not EAS. The equation relating CAS and Mach number is too complex for the ATPL courses so they don't teach it. This does not alter the fact CAS and Mach number are related by static pressure. (temperature is irrelevant)
CAS exists only because it is the best you can do with a mechanical ASI. With EFIS, CAS should eventually become obsolete. I think the Eclipse buisness jet displays EAS on the speed tape and so did the space shuttle. Perhaps Boeing and Airbus will eventually ditch CAS. Then compressibility error will be just a historical curiosity.
Last edited by Rivet gun; 17th Sep 2010 at 14:04.
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Thank you all guys! Finally this is clear into my mind as well! Overall thanx to Old Smokey for the explanation via PM! It has been really helpfull!!
I really have to say that this chapter is not so well explained in the flight schools..But better late than never..isn't it?
I just have one further question concerning EAS and CAS. Is there a kind of rule of thumb which tells us the amount of change during our increase in speed?
For example at 200 kts CAS we get 10%less on the EAS due to the compressibility error..or something like that (i'm just inventing)
Thank you again!
Regards,
bio161
Overall thanx to Old Smokey for the explanation via PM! It has been really helpfull!! I really have to say that this chapter is not so well explained in the flight schools..But better late than never..isn't it?
I just have one further question concerning EAS and CAS. Is there a kind of rule of thumb which tells us the amount of change during our increase in speed?
For example at 200 kts CAS we get 10%less on the EAS due to the compressibility error..or something like that (i'm just inventing)
Thank you again!
Regards,
bio161
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I don't know if there's a simple rule of thumb for EAS - CAS because it depends on altitude as well as speed.
Remember that at sea level pressure altitude compressibility error is zero even at high subsonic speeds (because that's the altitude the ASI is calibrated for).
Unlike the Mach meter, the ASI does not know it's altitude, so it can only be calibrated free from compressibility error at one particular altitude (which is sea level by convention)
An EFIS does know it's altitude so could theoretically display EAS at all altitudes. In practice most civilian EFIS display CAS in order to be compatable with mechanical ASIs, i.e they deliberatly emulate the mechanical ASI's compressibility error.
If you search the internet you'll probably find a compressibility error correction chart. It is the same for all aircraft.
Remember that at sea level pressure altitude compressibility error is zero even at high subsonic speeds (because that's the altitude the ASI is calibrated for).
Unlike the Mach meter, the ASI does not know it's altitude, so it can only be calibrated free from compressibility error at one particular altitude (which is sea level by convention)
An EFIS does know it's altitude so could theoretically display EAS at all altitudes. In practice most civilian EFIS display CAS in order to be compatable with mechanical ASIs, i.e they deliberatly emulate the mechanical ASI's compressibility error.
If you search the internet you'll probably find a compressibility error correction chart. It is the same for all aircraft.
Last edited by Rivet gun; 17th Sep 2010 at 16:07.
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Great. Now i can say i have this chapter clear in my mind! It's incredible how many things you get to know from one you don't know..the main thing is keeping on willing to learn without being convinced to know everything! 
Thank you Rivet gun. You have been really kind in answering again!
Always happy landings to you all guys,
bio161
Thank you Rivet gun. You have been really kind in answering again!
Always happy landings to you all guys,
bio161
