Aerodynamics Question

[Amish RakeFight]

Critical mach remains the same regardless of altitude. Mach crit is expressed as a percentage of mach. This percentage remains the same for a specific wing. Only mach itself differs depending on temperature and hence, altitude.

For instance, mach is achieved at a higher speed at lower altitudes and as you ascend in altitude (decreasing temp) mach will be attained at a lower speed. However, the percentage of mach at which mach crit occurs is fixed in relation to the mach number itself which will vary.

 

[LearLove]

Nothing in Aerodynamics for Naval Aviators really answers the question.

thats because that book is nothing but a glorified cookbook on aerodynamics.

off the cuff I'd say the above post is best but i'd have to look at something wrt shockwave formation before laying down my opinion/answer.

All of my research and windtunnel exp. (done 10 years ago now) was in the area of low speed aerodynamics, Reynolds number around 500,000 and less.

Only the smart grad students/kids (China/Korean and Russians) got to play with the high-speed wind tunnels. I was only a C average white kid engineer.

 

[SkiFishFly]

Mach number stays the same. It is a percentage of Mach 1. Critical mach number stays the same for a specific wing design.
The indicated/true airspeed at which you reach a specific mach number decreases with altitude.

 

[BEECH-SLAPPED]

It is aircraft dependant

Critical Mach will change slightly with altitude depending on the design of the wing. It is tempting to say "no, it doesn't change" because Mach is Mach, regardless of altitude. However, very few things are linear with regard to flow around bodies. The local speed of flow around at any given point depends on several factors, not just freestream velocity. Two of those factors are density and temperature, both which change with altitude. To compare two conditions you need to keep the same Reynolds number, which is dependant on density, velocity, and viscosity of the air. Calculating the local velocity at a given point on a wing is very difficult and even with sophisticated compututational fluid dynamics software, the result is never exact with what is measured.

Now without all the engineering terms. Let's take a hypothetical jet with a published Critical Mach of .87. Let's say at M 0.87 at 30,000 ft, you have Mach 1 flow at a certain point on the wing. You measure and calculate the local SPEED of the flow at that point to be 589 kts. At M 0.8 at 30000, your TRUE airspeed of the aircraft is 512 kts (assuming standard atmosphere). Now, let's climb to 37,000 and hold a Mach of .87. Your true airspeed at this altitude is now 499 kts. Let go back to the the same point on the wing and measure and calculate the speed of the air. We get a value of 557 kts, or M .97. Wait! Shouldn't this value be 573 kts, which is the speed of sound at 37,000 ft? What this means is that you will not necessarily get supersonic flow at the same point on the wing at the same aircraft Mach # at every altitude. It depends on many factors! So basically the aircraft manufacturer publishes the most conservative number and that is what we use to fly by.

Few people also realize that the indicated stalling speed of a wing actually changes with altitude as well, due to the changes in density and viscosity of the air. I'm not talking about low-speed buffett at high altitudes either. A Cessna 172's stalling caliberated airspeed at Sea Level is not the same as at 8000 feet. It's just that the difference is very small.

 

[Bjetset2]

Yep

And that is why the Mmo for airplanes vary by altitude, some more than others. Good explanation sir.

 

[AcroTim]

Question?

Now without all the engineering terms. Let's take a hypothetical jet with a published Critical Mach of .87. Let's say at M 0.87 at 30,000 ft, you have Mach 1 flow at a certain point on the wing. You measure and calculate the local SPEED of the flow at that point to be 589 kts. At M 0.8 at 30000, your TRUE airspeed of the aircraft is 512 kts (assuming standard atmosphere). Now, let's climb to 37,000 and hold a Mach of .87. Your true airspeed at this altitude is now 499 kts. Let go back to the the same point on the wing and measure and calculate the speed of the air. We get a value of 557 kts, or M .97.

I'm not an engineer. Started on it but didn't finish. Got my first REAL flying job instead. Did very well in aerodynamics classes, however, and I'm stumped at one point in your calculations. How are you calculating the speed of the air at the point on the wing at 37000 ft after you have calculated aircraft TAS? And...are you taking into account that 37000 ft lies in the Stratosphere for a Standard Atmosphere? As we all have learned the initial layer of the Stratosphere is isothermal. The density ratio does continue to decrease obviously with decreasing static pressure. Was this accounted for in your calculation?

 

[BEECH-SLAPPED]

AcroTim,

I should have been a bit clearer on that number. I didn't calculate that value at all. I made it up just to show that although the aircraft Mach # didn't change from FL300 to FL370, the Mach # at the same point on the wing CAN change due to the different properties of the flow at that altitude. Also, the AOA of the wing will NOT be the same at the higher altitude either (weights being equal), so that will definitely change the point on the wing where supersonic flow begins. So, although this particular point on the wing had supersonic flow at M.87 and FL300, it won't necessarily have it at M.87 and FL370. Therefore the critical Mach # must be adjusted up or down depending on where the FIRST sign of supersonic flow is measured. All of the other numbers were calculated from Standard Atmosphere tables and are actual values for FL300 and FL370 at standard temperature. Hope this clarifies.

 

[igneousy2]

Critical mach does not vary with altitude just like critical angle of attack does not vary either.

Maybe if you take the calculations out to 3, 4, or 5 decimal places you may find some Aero-engineer types that can create scenarios that would "change" those numbers...Maybe the sun is behind you and your tail is casting a shadow and the difference in temp at the boundry of the shadow is creating localized convective currents that change the critical mach number of the airfoil from .800001 to .800002...Maybe there is a fat guy in 8F that is causing the fuselage adjacent to his seat to bulge out by .5 microns which disrupts the airflow which changes the AoA of the wing immediately behind the disruption which alters the critical Mach of the airfoil...Maybe the 737 on the J-route just ahead of you created some wake turbulence...maybe there was a butterfly in Beijing that flapped it's wings which caused...blah blah blah

Critical AoA is Crtical AoA just as Critical Mach is Crtical Mach.

I highly doubt the argument about variance because of temp/altitude because this is already accounted for in the calculation of Mach. An airfoil does not "know" what the "altitude" is or what the "temp" is...it only "knows" what the density of the air is. The TAS or True Altitude may vary, I might even be able to be convinced that "Indicated Critical Mach" may vary...but I would bet that when push comes to shove, critical Mach is crtical Mach.

Another clarification...Critical Mach is NOT a limitation, it is the point at which there is supersonic airflow SOMEWHERE (even one air molecule) on the airfoil. This occurs BEFORE a shockwave develops. I forget the exact term...but there is another Mach number that engineers use that is higher than Critical mach...this Mach number is where the supersonic airflow starts to form drag on the airplane. One example of an attempt to combat this, is a super-critical airfoil - the most obvious feature being a reversal in direction of the lower camber of the wing. On a supercritical airfoil above its critical Mach an airmolecule accelerates in the early part of the airfoil to a speed above Mach 1 then is decelerated again below Mach 1, delaying the point at which drag (from supersonic flow) starts to develop on the airfoil...which allows the airplane to go faster then it would otherwise.

confused yet?

Later

 

[igneousy2]

forget the exact term...but there is another Mach number that engineers use that is higher than Critical mach...

I had to look it up...

Drag-Divergence Mach Number

Later

 

[BEECH-SLAPPED]

Another clarification...Critical Mach is NOT a limitation, it is the point at which there is supersonic airflow SOMEWHERE (even one air molecule) on the airfoil. This occurs BEFORE a shockwave develops. I forget the exact term...but there is another Mach number that engineers use that is higher than Critical mach...this Mach number is where the supersonic airflow starts to form drag on the airplane.

You are referring to the Drag Divergence Mach Number. And yes, you are correct in that it is higher than the critical mach number. The original poster wanted to know if critical mach changes with altitude. The answer is yes. I was merely trying to show things aren't necessarily what is written in the "pilot aerodynamics" books. Those books don't tell the whole, or sometimes even correct, story. The FAA teaches that lift is produced because the airflow moves faster over the top of the wing because it has "further to travel." This is absolutely wrong and it has been proven wrong. Just because we're pilots, it doesn't mean that we have to accept the FAA's "dumbed down" explaination of things. Critical AOA also changes slightly with altitude as well due to VISCOSITY of the air. Will it be noticable on the airspeed indicator? Probably not. But that still doesn't change the facts.