Critical Mach Number
 

Hi everybody, technical question. Any engineers or other technical people have solid knowledge of this?:

What, if anything, has an effect on Critical Mach Number?

"Critical Mach Number is the free stream Mach number which produces the first evidence of local sonic flow."

My interpretation is that for a given airfoil, the Critical Mach Number is a constant and doesn't change. Is my interpretation correct?

I would also go on to say that the Indicated Airspeed corresponding to Critical Mach decreases with altitude (since we all know that due to the decrease in temperature as altitude increases, TAS increases for a given IAS), but the mach number which produces the evidence of local sonic flow does not change. .80 mach is .80 mach

Thanks for your help!

Mcrit also varies inversely with angle of attack. This is because the local peak velocity of the airflow over the wing increases with angle of attack.

Also your interpretation of IAS vs TAS leaves much out. The difference between IAS and TAS has to do with temperature, pressure altitude, installation errors, and compressibility. Temperature is but one factor.

Could you elaborate on this? I'm trying to wrap my head around this...

So, as angle of attack increases, Mcrit decreases? This is because as the AOA is increased, local peak velocity of the airflow over the wing increases.

I've read from a questionable source that as altitude increases, Mcrit decreases. Was this statement made with the assumption that in order to maintain lift at a higher altitude, AOA must increase, thereby decreasing Mcrit?

Thank you very much for your help.

That is 100% correct. For an aircraft at a given weight, steady state flight, increases in altitude will decrease Mcrit for exactly the reason you stated.

Keep in mind Mcrit is not a limitation like Mmo. Most jet aircraft cruise around .02 or .03 faster than Mcrit, which is just the "onset" of mach effects such as tuck and wave drag. The faster you go past Mcrit, the more those effects begin to be felt until eventually the designers impose the Mmo.

Great. That is what I needed to know. Do you have idea of any documents or books that I could review to learn about this even more? I've got the Aerodynamics for Naval Aviators but really, it just confused me more. Or perhaps I should reread it with this knowledge and it might make more sense....

AoA does increase the local flow velocity on top of the wing as mentioned, but recall the speed of sound decreases in thinner air as air molecules are spaced farther apart and are not as fast at transferring the kinetic energy. Speed of sound is greater in higher density flows, like sea-level atmosphere and water. In water the speed of sound is highest, so water going vessels use audible pings because they are quick in the dense medium. In thin air you need something a bit faster and we use radio waves and microwaves. M critical is the speed at which sound goes supersonic as mentioned, and occurs where the airfoil is the most cambered. Designers look at the required AoA for a given aircraft wing in cruise and make sure it is compatible with Mcrit for acceptable drag. If not, there are tricks you can do to raise Mcrit like wing sweep, flat airfoils, washout, etc.

My 2 cents worth: Mcrit for a given airframe will not change with respect to changes in altitude/airspeed/density. What does change however, is the True Airspeed at which that Mcrit number is achieved. As altitude increases all forms of airspeed for a given mach number will decrease (ie IAS, Calibrated, Equivalent, and True). What does not change however is the Mach speed of the airflow which causes the first evidence of local sonic flow. And that can be on ANY part of the aircraft, not just the wing.
It is true that increasing AOA will increase the velocity of airflow over the wing but this does not change the Mcrit number for that airplane, it just reaches that critical number sooner than if you simply accelerated in level flight.

The shape of the airfoil affects the Critical Mach Number.

Forgive me if I appear to be redundant, by shape you mean swept wing?

See, now that's what I thought. That makes more sense to me....but what is correct? Does Mcrit change inversely with AOA on an airplane or is it a constant?

That's a good question. With a straight, (non swept), wing the Mcrit number can be increased by reducing the thickness of the airfoil. The velocity of airflow over the wing at any given TAS will be slower for a thinner wing than a thicker wing (assuming a positive camber wing). So a thinner wing will have a higher Mcrit than a thicker wing.

The problem is that a wing can only be made so thin before it is no longer structurally sound so the idea of sweeping the wing came about. When a wing is swept back the chord line of the wing is no longer perpendicular to the relative wind. The result is that the airflow is split into two components: 1) Spanwise Flow, which travels parallel to the leading edge of the wing, is not accelerated over the wing at all, and produces no lift.
2) Chordwise Flow, flows parallel to the chord of the wing and is the only flow which produces lift.
Since the wind is split into these two components, the more the wing is swept back the more Spanwise (bad) flow, and less Chordwise (good) flow you get.

Ex: A sweep angle of 37 degrees produces a chordwise flow that has 80 percent of the free-stream speed; at 45 degrees of sweep, it's 71 percent. Therefore the aircraft can move through the air at a higher TAS before reaching its Critcal Mach number.

Last two points: First, the more the wing is swept the less lift is produced for any given TAS, which results in poor slow speed handling. Think of all the crap on the front and back of a 727 wing. Second, fuselage components such as the canopy can now have a lower critcal mach number than the wing. Remember that Mcrit is for the entire airframe and not just the wing.

Sorry for the long, drawn out explanation, but hope it helps.

RJ, AoA does affect Mcrit. Think of the "coffin corner" example- AoA goes up with altitude due to the reduced pressure available from thin air. However speed of sound also goes down. So while Mcrit goes down due to higher AoA, speed of sound goes down too. This leads to a crisis between what the airplane needs to fly in terms of AoA that high, and the reduced speed of sound at higher altitude. The upshot of it is, the airplane can be on the verge of a stall at the same time it is going supersonic at some places on the top of the wing. The latter is a bad situation, drag goes high and the airplane falls out of flight into a dive. Continuing the story- an uncontrolled dive can perpetuate the nonflying situation by putting the airplane in a regime it is unable to accommodate aerodynamically and is unable to recover from no matter how good the pilot. This was what happened in WWII to some single engine fighters- they exceeded their max speed for recovery due to SS flow over the tail. The solution was all moving tails as well as a host of other high speed aerodynamic techniques (sweep, flatter airfoils, area rule, delta wings, etc.).

Another quick thought here- sweep is often thought of as the only way to make an airplane capable of a higher Mcrit. However, sweep is chiefly motivated by the need for wing volume. You can obtain higher Mcrit by tucking the wings behind the bow shock. This was how the early SS aircraft (Bell X-1 and other early NASA experimental airplanes) were designed: a flat, thin, short, unswept straight wing tucked in tightly behind the bow shock formed by the nose. It worked fine but as mentioned the wing was very flat, short, and thin. The fuel space was minimal, no place for guns bombs or wheels, which is what fighters need to carry. The practical solution was to simply sweep a fat wing to get ample space inside the wing with drag levels of a short low AR wing.

Thanks for the response. I think that helps. My original question was pertaining to Mcrit of a certain airplane. I understand the concept of Mcrit and how engineers and aircraft builders can use certain design techniques as you have mentioned (sweep, chamber, etc) to raise Mcrit. I as trying to determine what, if anything, can change Mcrit for a certain airplane (not withstanding swing-wing types ie F-14), such as AoA, altitude, temperature, pressure, etc....

I think I have determined with the help of you knowledgeable folks that Mcrit varies inversely to AoA, thus as altitude increases, Mcrit decreases on a certain airplane.

I think my original confusion for all of this was assuming the upper limit of the barber pole (Mmo) had a defined relationship to what Mcrit was (ie my plane's Mmo is .80 mach so, therefore, Mcrit was .80). I now see that Mmo and Mcrit is most likely not the same in a swept wing turbojet airplane and is a design limit imposed to ensure the airplane remains controllable in this flight regime.

A source of confusion over the AoA-Mcrit discussion is grouped around the fact that AoA's for typical jets in cruise flight are fairly small, a degree or two, and variation with altitude is minor as well. The focus goes to critical mach number while holding AoA constant. You can even use an AoA of zero if you want. That's smart because a meaningful comparison is aided by removing the variables to allow direct comparisons. AoA, dynamic pressure, sometimes even speed is eliminated. It's sort of like trying to find a short circuit in your house, you need to figure out which circuits are not affected before you can determine those that are.