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.