BobDDuck
Island Bus Driver
Does airflow over specific portions of the wing change based on AoA on a super critical wing? I honestly can't remember. If so, wouldn't your critical mach then vary based on AoA? Or am I way over thinking this?
Critical mach change with altitude?
- Thread starter Mattio
- Start date
Does airflow over specific portions of the wing change based on AoA on a super critical wing? I honestly can't remember. If so, wouldn't your critical mach then vary based on AoA? Or am I way over thinking this?
fish314
Well-Known Member
Great point, and I'm going to have to revise my whole previous posts because of it. The pressure distribution around the wing does vary with AoA. See here, page 4.
The whole discussion above was predicated on the fact that the pressure distribution around the airfoil changes by the Prandtl-Glauret relation due to changes in velocity (basically, you divide by the square root of 1-Mach^2). Therefore, an airfoil AT a particular AoA will have the same Mcrit regardless of altitude. That Prandtl-Glauert relationship doesn't say anything about changing the AoA.
So, before we begin worrying about whether the change in AoA would change the Mcrit, we should figure out if the AoA changes as the altitude increases.
Well, lift is going to equal weight regardless. From the Lift equation, W = L =1/2Cl*rho*V^2*S. As altitude increases, S (area of the wing) stays the same, and rho (air density) decreases. At a particular altitude, a given Mach number does not equate to the same true airspeed. As altitude increases, the speed of sound decreases (due to temperature decreasing), which means if we keep Mach number the same then the Velocity will be decreasing (for example, at FL200 Mach .85= 522 knots true, but at FL350 Mach .85 =490 knots true).
Therefore, as altitude increases if we keep Mach number the same, rho AND V are both decreasing and S stays the same. This means that Cl must increase to make up the difference and keep lift equal to weight. This is done by increasing AoA. So now we know not only does AoA change, but we also know which way it changes. It increases.
That increase in AoA would change both the location and the magnitude of the Cp,0 in the formula I quoted in my first post of this thread. Specifically, the Cp,0 value would increase (actually it's a negative number, so it's absolute value would increase) with an increase in AoA, and this would cause the Mcrit to decrease. (Reference the same page 4 from the link in this response. Coefficients of pressure are the basically the change in static pressure at a particular point on the wing from the free stream static pressure, divided by the freestream dynamic pressure. Clearly from the diagram, as AoA increases, this change gets bigger.
As Cp,0 gets bigger, Mcrit gets smaller. This is difficult to see from the formula that I posted in my first post, but if you put in 1.4 for the gamma and a couple of different Mcrit values it's easy to see. For example, with a Cp,0 of -.1352 corresponds to an Mcrit of .85 mach. A Cp,0 of -.2086 corresponds to an Mcrit of .80 mach.
Which means I need to revise my earlier statement. Although Mcrit should remain the same regardless of a change in altitude, (and the corresponding changes in pressure, temperature and density) this is only true if the AoA were to remain constant. Since the AoA does NOT remain constant, but rather must increase with altitude if you hold Mach number constant (until the tropopause) due to the drop in true airspeed and density, the critical Mach number would have to decrease slightly with altitude. How much would be determined by how much the AoA changed.
Take as an example a 200,000 lbs. airplane holding .85 mach at FL 200 and then at FL 350. We'll say the airplane has a wingspan of 200 feet, and a mean aerodynamic chord length of 20 ft. This makes S 200*20=4000 ft^2.
FL 200, V=.85 mach=.85*1036.9 (ft/sec)= 881.4 ft/sec (522 KTAS).
rho= .0012673 slugs/ft^3
1/2*rho*v^2*S= .5*881.4^2*.0012673*4000= 1969044.
200,000/1969044=CL, which in this case makes CL .1016
On an infinite wing, that would equate to just shy of 1 degree AoA (an infinite wing has a lift slope of about .11 per degree, so the exact value would be .923 degrees).
Now let's look at the same airplane at FL350 and .85 Mach.
FL350, .85 Mach, V=.85*973.1 ft/sec=827.1 ft/sec (490 KTAS)
rho = .0007382
.5*.0007382*827.1^2*4000=1009997
200000/1009997=CL = .1980. Assuming that same .11 per degree that is a 1.8 degree AoA.
I think this is enough of a change in AoA that the Cp,0 would change (it's absolute value would increase... it would become more negative). This would cause Mcrit to decrease.
So Mattio, if you are still reading, I think I was wrong before. On a real airplane, IF AoA is kept constant, Mcrit is constant with altitude. But on a real airplane, AoA would need to increase to maintain the same speed, and the increase in AoA would result in a decrease in Mcrit as altitude increased.
Therefore, assuming the barber pole is indeed based on critical Mach, the designers probably use the highest anticipated altitude and the greatest anticipated weight as the worst case Mcrit (since that would be the lowest Mcrit).
BobDDuck
Island Bus Driver
Thanks Fish. I followed about 1/2 of that (and I'm impressed with myself for keeping up that much).
On the CRJ200, Mmo backs off as altitude increases and I've always understood that to be due to the critical mach number rolling back due to AoA changes. Even with out looking at all the numbers, anybody who's taken an airframe up near it's altitude limit can tell you that you tend to be pitched up more than down low at a comparable mach speed. There are probably other reasons too that the Mmo speed comes back up high as well.
On the CRJ200, Mmo backs off as altitude increases and I've always understood that to be due to the critical mach number rolling back due to AoA changes. Even with out looking at all the numbers, anybody who's taken an airframe up near it's altitude limit can tell you that you tend to be pitched up more than down low at a comparable mach speed. There are probably other reasons too that the Mmo speed comes back up high as well.
Mattio
Well-Known Member
BINGO!!! That's what I was trying to find out. It didn't make sense to me that the number would change.. Thanks for clarifying that!
Either way, thanks for everybody's input. Definitely a lot of good info in this thread. Fortunately, I didn't get that question at my interview while I was still unsure about it. Kudos
fish314
Well-Known Member
Actually Mattio, I was wrong there. Check out my second post (although I found a few mistakes in that as well... I SUCK this week! Don't worry, though, the mistakes don't change the second answer).
What I wrote originally about critical mach not varying due to temperature, pressure or density is true if you assume a constant CL (and, hence, for a given airfoil a constant AoA). I found out after that first post that Critical Mach number DOES vary inversely with changes in CL, though. So if the airplane were to change altitude and keep the same AoA (and hence the same CL)... no change in critical mach.
But.... when you increase altitude (and hold mach number constant), velocity and density both decrease. To keep lift constant (equal to weight), CL needs to increase (and hence AoA needs to increase). THIS is what causes the decrease in critical mach number.