Aerodynamics Question

[CesnaCaptn]

Is there a forum on here to ask technical questions? Well here's one:

Does critical mach number change with altitude?

 

[Bjetset2]

Yep

Yes it does vary by altitude. Remember the speed of sound is related to temperature. Thus for a given TAS the MACH number will be much higher at altitude than at sea level. Thus compressibility effect due to supersonic airflow will be encountered at slower speeds at high altitudes versus low altitudes.

The Lear 60 for example has an MMO of .81 from 26,750 feet to 37,000. Above 43,000 the Mmo is .78. The Falcon 2000EX, a much better aerodynamic design, only varies from .862 to .85

Hope that helps.

 

[b82rez]

no...

 

[Bjetset2]

Better Put

The wing's Critical Mach is what it is, the indicated Mach you fly to avoid it changes.

I missed the intent of the question. My bad.

 

[GCD]

A "critical Mach number" is the speed of an aircraft (below Mach 1) when the air flowing over some area of the airfoil has reached the speed of sound. For instance, if the air flowing over a wing reaches Mach 1 when the wing is only moving at Mach 0.8, then the wing's critical Mach number is 0.8.

 

[Bjetset2]

Correct

That is correct GDC. Thus I will defer to my first response that yes the critical mach number does vary with altitude.

 

[Razorback one]

Someone has a Delta interview coming up..... Best of luck, I finally decided I was going to flip a coin on that question. It never came up.

R1

 

[sg737]

I think....

Critical mach is critical mach is critical mach... regardless of altidude. It occurs at a different AIRSPEED at different altitudes... but mach is mach....

 

[Truckdriver]

Keep going guys, I have the same problem with this issue. I think it stays the same, but the airspeed at which you reach critical mach will decrease. I also see how you could go the other way so I'm not sure here. Nothing in Aerodynamics for Naval Aviators really answers the question.

 

[macdu]

I think....

Critical mach is critical mach is critical mach... regardless of altidude. It occurs at a different AIRSPEED at different altitudes... but mach is mach....

This is what I have always used as the definition also. You want to avoid critical mach for various efficiency, safety reasons, and the simple fact the commiercial wing/tail design is not meant to go Mach 1. Up high you need to be cognizant of your gross weight, CG, ISA, turbulence. You end up backing the wing in to a corner, so to speak, of narrow performance capability of stall and mach buffet I believe. Remember you are actually "flying" the wing, not the plane if you follow me.

 

[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.

 

[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.

To quote my earlier post, critical mach is fixed in relation to mach itself which fluctuates based upon the temperature which varies upon altitude.

Technically, one could argue that critical mach changes with altitude and this is correct, if you understand that it changes along with mach itself. Critical mach rides the coat tails (if you will) of mach.

But as a limitation or milestone, Mcrit is recognized as a percentage of mach and only that. It does not vary on its own, independant of mach itself. It's variance is dependant upon the present mach's variance that which a specific wing is traveling at within a certain altitude.

 

[PHXFLYR]

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.

So that's why you're a pilot ......

PHXFLYR

 

[Amish RakeFight]

So that's why you're a pilot ......

PHXFLYR

Not that I'd necessarily agree, but I once read somewhere that a good pilot is one who isn't too bright. Apparently you CAN be too smart to fly a plane. I believe it had something to do with overanalyzing and thinking too much in a perfectionist sort of way.

 

[luckytohaveajob]

A long time ago I remember reading the DC8 was actually dive tested above Mach 1 in flight testing. I can not remember the details. Does anyone have any good stories about the 8 going past Mach 1?

How about some stories about other aircraft in high speed flight.

Anyone have a B737 past .82? How about a B747 past Mmo? Or an old B727 past .92? And what about the Citation X?

 

[Amish RakeFight]

I can't recall which aircraft (L1011?), but the curvature just above the cockpit would cause flow to go supersonic before mach crit made an appearance on the wings.

 

[XJ-spartacus]

My quess is that a wings Mcrit is as fixed as it's Critical AOA. There are several variables that can change these values, but all are insignificant. With any value, there will be variances that must be averaged out. One of my profs used to say you measure with a micrometer and cut it with an axe. As pilots, we use a maul. The engineers know this, and write our manuals to reflect it. They don't want us trying to take the square root of the hypotenuse of an isosceles triangle and dividing it by one while were trying to make a crossing restriction. I like it when they keep it simple. I really like it when they install coffee holders next to where I lay my arm.

-Spartacus

 

[Amish RakeFight]

Thumbs up Spartacus!

 

[27 driver]

My quess is that a wings Mcrit is as fixed as it's Critical AOA. There are several variables that can change these values, but all are insignificant. With any value, there will be variances that must be averaged out. One of my profs used to say you measure with a micrometer and cut it with an axe. As pilots, we use a maul. The engineers know this, and write our manuals to reflect it. They don't want us trying to take the square root of the hypotenuse of an isosceles triangle and dividing it by one while were trying to make a crossing restriction. I like it when they keep it simple. I really like it when they install coffee holders next to where I lay my arm.

-Spartacus

Spartacus, I have to agree. The last thing I want to do when trying to maintain speeds, make a restriction, and read the news paper is do quantum physics calculations. Besides, Cmach means nothing until you exceed it, and to do this you are doing something you shouldn't be. Performance books are in the plane for a reason. Keep is simple stupid is a great rule. Just my .02