Critical mach change with altitude?

Mattio

Mattio

Well-Known Member
Here's another one for you jet jockeys. I read somewhere online (from a questionable source) that critical mach number decreases as altitude increases. This wouldn't make sense to me because I know that, although the speed of sound decreases with an increase in altitude (because temperature is decreasing, well at least until you hit the tropopause), critical mach is a ratio to the speed of sound so the critical mach itself does not change with altitude... Can anybody back me up on this? :D
 
Mattio,

Mach is a ratio of TAS to the S.O.S. Critical Mach isn't so much a ratio as it is a speed at which an aircraft will experience a high speed aerodynamic buffet. Transonic aircraft will hit high speed buffet at a lower Mach the higher they fly (up until the TROP) because as you said, the temperature decreases and lowers the speed of sound. So, yes - critical mach does decrease with an increase in altitude.
 
So does the instrument automatically adjust so that your Mach indication is relative to the speed of sound at the current temperature, or does it just relate your TAS to the speed of sound in a standard atmosphere?
 
ljg said:
Mattio,

Mach is a ratio of TAS to the S.O.S. Critical Mach isn't so much a ratio as it is a speed at which an aircraft will experience a high speed aerodynamic buffet. Transonic aircraft will hit high speed buffet at a lower Mach the higher they fly (up until the TROP) because as you said, the temperature decreases and lowers the speed of sound. So, yes - critical mach does decrease with an increase in altitude.
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Not to be a stickler but:

Critical mach number is the speed at which airflow over any part of the wing first reaches (but does not exceed) Mach 1.0. Mach buffet begins above the mach number (that's from the PHAK page 3-35, 3-36)
 
Mattio said:
So does the instrument automatically adjust so that your Mach indication is relative to the speed of sound at the current temperature, or does it just relate your TAS to the speed of sound in a standard atmosphere?
Click to expand...

It adjusts as you go.
 
ppragman said:
Not to be a stickler but:

Critical mach number is the speed at which airflow over any part of the wing first reaches (but does not exceed) Mach 1.0. Mach buffet begins above the mach number (that's from the PHAK page 3-35, 3-36)
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Thx. You are correct. Mattio, Mach Buffet is a poor, incorrect choice of words.
 
BobDDuck said:
I had a captain tell me once that if you ain't clackin' you're slacking.
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Yeah...but doesn't REALLY count if you're clackin' at only .80????? (of worse...Less)
mshunter said:
Not a limit, but a goal.
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Mach is the goal, not the pole ;)


PS....Aircraft with Bureau numbers, block numbers and/or ejection seats do not qualify.
 

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So does the number itself that is mach crit, let's say it's 0.8, is it 0.8 at any altitude? That's what I meant in my original question but I don't know if ljg was talking about the TAS that's represented by mach crit decreasing or the actual mach number.....
 
Mattio said:
So does the number itself that is mach crit, let's say it's 0.8, is it 0.8 at any altitude?
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Probably not. Obviously, during normal operation what ever the critical mach number is will be well above redline (Vmo) so you wouldn't see it slide around like the barber poll does.

And NJA, a clacker is a writeup whether it occurs at .93 or .68.
 
Now I may be just be a simple country Hyper-Chicken, but it seems like — all else being equal — the speed that's going to get you there the fastest lives at the intersection of VMO and MMO, generally in the low FL300s. :)
 
Mattio,

While ljg is correct that the airspeed that corresponds to the critical Mach number of a given aircraft changes based on altitude (or, more correctly, based on TEMPERATURE and pressure, which in turn vary with altitude), the MACH number that corresponds to the critical Mach number of a given aircraft is constant. For example, if your airplane's Mcrit is .83, then it is .83 at any altitude, at any temperature, at any density, or at any pressure.

For my justification of this, look here. Look at formula 6.3 on page 4. This formula shows an equality of 3 quantities in the form A=B=C, right? Well let's ignore the center of the formula, and just set A=C. Notice what remains?

Well Cp,0 is a constant. It is the lowest pressure coefficient on a wing at low air velocities. Basically, you get this from testing the wing at low speeds, but it only changes when you change the shape of the wing. It does not change based on temperature, pressure, or density, and therefore it is constant as altitude changes.

Also gamma (the funky looking y-shaped letter in the equation) is also a constant. That is the ratio of specific heats, and for air it is about 1.4. This actually does change with temperature, but only VERY VERY slightly. For example, at -40 (Fahrenheit) it is about 1.401, and at 180 F, it is about 1.399. In other words, a small enough change (1/7th of 1% or about a 0.143%) that you can treat it as essentially constant.

Well, the only other quantity in the formula is Mcrit. So if Mcrit is in a formula with a bunch of quantities and none of those other quantities change with altitude, Mcrit cannot possibly change with altitude either. This would be easy to prove by solving the formula for Mcrit, but unfortunately that formula probably can't be easily manipulated to get Mcrit by itself on one side.
 
BobDDuck said:
Keep in mind though, even if the airspeed at the wing is exceeding a critical mach number, the airframe itself may not be going that fast. Picture a record player (huh? what's that?) spinning. Near the center a spot on the record is spinning much slower than a spot out near the perimeter.
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Actually, the whole definition of critical Mach number takes this into account. Critical Mach number is defined as the slowest free-stream mach number which corresponds to a mach number of 1 over some point on the wing. Freestream mach number is essentially a fancy way of saying that is how fast the airplane is going (measured in Mach, of course).

Essentially, some point on the wing will always go above the critical mach number for the airplane before the airplane gets to the critical mach number. The whole idea is that when the airplane gets to critical mach (say .85 for example), the air on the wing is going 1.0. That is essentially the whole concept of critical mach number right there.

Therefore as the airplane speeds up and approaches .85, the air on that point on the wing where it is moving the fastest HAS to hit .85 first (since it has to get to 1 when the airplane gets to .85).

Of course, that concept is similar to the whole concept of lift in the first place, right? Remember, as the airplane is flying, the air speeds up as it moves around the wing (speeding up more on the top of the wing than on the bottom). As air speeds up, the total pressure remains the same, which means the static pressure has to drop. Since the top of the wing sped up more than the bottom of the wing, it's pressure dropped more than the bottom of the wing's pressure. This means that the pressure on the bottom of the wing is higher, and higher pressure on the bottom of the wing equals lift.
 
Minuteman said:
Now I may be just be a simple country Hyper-Chicken, but it seems like — all else being equal — the speed that's going to get you there the fastest lives at the intersection of VMO and MMO, generally in the low FL300s. :)
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I wanted to expand on this with a chart! Comparing a VLJ, a cattle car, and a light twin. :) True Airspeed is the horizontal, ISA Altitude is the vertical. The lines are limits to the right of them:
TrueAirspeeds.png
The VLJ maxes out at FL240 and about 390 KTAS
The 737 at FL280 and 500 KTAS
and the Citation X at FL315 and 545 KTAS.
 
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