The P-51 and its laminar-flow wing

[Pyro]

I would be willing to bet a large sum of money that a P-51 with wing at 8 degrees angle of attack has substantially more drag than a P-51 with wing at zero degrees angle of attack.

Here's a chart.  8 degrees AOA corresponds to a lift co of about .75 with flaps up.

[Stoney]

Stoney I believe the problem you are having is that you are unable (due to limitations of XFoil) to get away from the region of flight in which vortex drag (the poorly named "induced drag") is the overwhelming drag on aircraft. What you cant see in the comparison chart I submitted is the AOA points and airspeeds (constant CV) which were in the range where profile drag and parasite drag overwhelm vortex drag significantly.

Mapping a laminar profile at such a low speed (outside of radio control airfoils) is a little unfair and not at all practical considering the full range of these aircraft.

Well, the drag shown in most drag polars is profile drag, not induced drag.  I shouldn't have said the drag polar proves Brooke's contention.  But, given the formula:

Cdi = Cl^2 X pi X e X AR

Where:

Cdi = induced drag coefficient
Cl = lift coefficient
pi = 3.14...
e = Oswald's efficiency number
AR = Aspect ratio

Its obvious that any increase in lift coefficient (aka AoA) will result in a higher Cdi, and thus, induced drag must increase with effective AoA.

In 2-D modeling such as XFOIL, there is no induced drag as the 3-D effects of lift are not considered as the wing is considered to be of infinite span.  What it shows is purely the drag created by increasing the AoA of the airfoil section.  In order to create induced drag modeling, the entire wing must be considered.  So, for pure comparisons between airfoils, the drag polars should suffice.  As to the Reynolds number used, the drag numbers will only be lower, and would compare approximately the same--perhaps with the laminar airfoil showing even more of a low-AoA advantage, as they're performance generally improves with higher R-numbers.  At that speed and using the MAC of the P-51, we're still talking about a mid-7 figure R-number (around 6,000,000 or so), which is not nearly as low as the mid-6 figure R-numbers (around 400,000 or so) normally associated with drag polars of RC airfoils.

[Ardy123]

Just the Pony...  According to Dave Lednicer, the Ki-84 shared the 23000 series airfoil with most of the other WWII fighters.  The Tempest used a proprietary airfoil developed by Hawker, but if the plots I've seen of it are correct, it isn't going to be a laminar airfoil.  The P-63 used one, but I don't really count it in the mix.

Stoney,
I't doesn't have much relevance to the discussion I know... but just for clarification,
I don't know for all airplanes, but I know that the 109 Fs and later did not have the same 2300 series airfoil that the 109Es had.
109E arifoil - NACA 2314(root)- NACA 2310(tip)
109F+ airfoil - NACA 2R1 14.2(root) - NACA 2R1 11.35(tip)

how close is a NACA 2R1 to a 2300 series airfoil?

[Stoney]

Stoney,
I't doesn't have much relevance to the discussion I know... but just for clarification,
I don't know for all airplanes, but I know that the 109 Fs and later did not have the same 2300 series airfoil that the 109Es had.
109E arifoil - NACA 2314(root)- NACA 2310(tip)
109F+ airfoil - NACA 2R1 14.2(root) - NACA 2R1 11.35(tip)

how close is a NACA 2R1 to a 2300 series airfoil?

Dave Lednicer's list:  http://www.ae.illinois.edu/m-selig/ads/aircraft.html shows all models of the 109 using the NACA 2R1 series airfoils.  An older version of this list had the 2300 series listed for the early 109's, but it appears to have been changed.  The 2R1, from what I've been able to find online, was a modified Clark Y airfoil that reflexed the lower surface right before the trailing edge.  Apparently this was done to minimize the pitching moment.  I still cannot find a profile for it, but one message board I found stated that it is in the Profili database, if anyone has access to that program.

[Brooke]

Here's a chart.  8 degrees AOA corresponds to a lift co of about .75 with flaps up.

(Image removed from quote.)

Many thanks, Pyro.

[Brooke]

I also do not believe the B-24 had any laminar flow (beyond 2-3mm). Please site anything other than wikipedia if you have it.

http://www.dreesecode.com/primer/airfoil5.htm

It shows the shape of the Davis airfoil vs. the NACA 6-series laminar-flow airfoil:



Also, this, showing the Davis airfoil.  Not as good as the P-51 airfoil, but quite good for its day:



Of course, with dirt, dents, scratches, propwash, design variation, wing vibration, etc., the laminar flow wouldn't be at 20% of chord anymore.  For all I know, maybe it is, in real-world application on real, in-service B-24's, down to something quite low.  But -- it looks like Davis did make a very nice airfoil shape back in the days before widespread laminar-flow airfoils.

[Stoney]

But -- it looks like Davis did make a very nice airfoil shape back in the days before widespread laminar-flow airfoils.

No doubt, especially considering the knowledge base and technology of the day.  I didn't mean for any of my explanations to imply otherwise--just wanted to tune up the terminology.  

It actually looks very close to a NACA 4418...

[Brooke]

OK, since the bet didn't go through, I guess now I will go through my reasoning.  (Altough I'm still willing to take the bet! )

Here is a graph of a NACA 6-series airfoil, actual test data.  The P-51 wing is based on a 6-series airfoil.  So while I didn't have the data for the actual P-51 itself (although Pyro provided it -- thank you, Pyro), I figured this would be quite close.

From Aerodynamics, Aeronautics, and Flight Mechanics, by McCormick, p. 69:


An 8 degree angle of attack of the airfoil (which is a 7 degree angle of attack of the P-51, since wings are mounted with an angle of incedence at root of about 1 degree, so I could really be looking at a 9 degree AoA for the airfoil, but let's use 8 for sake of argument) equates to a Ct of about 1.0.

At a Ct of about 1.0, clearly the drag is higher than at an AoA of zero degrees.  This is true both for the "ideal condition" airfoils (very clean, no scratches, no dirt etc.) and certainly for the airfoil with "standard roughness" (just painted -- still no bugs, dents, scratches, etc.).  Note two things.  First is that "ideal condition" airfoil has the so called "drag bucket," which is the low-drag, laminar flow characteristic Chalenge was correctly indicating in principle, but it is not close to encompassing 8 degrees AoA -- it goes out to only about 2-4 degrees AoA.  Second is that "standard roughness" totally eliminates all of that, and you have the more-typical parabolic shape to Cd vs. Ct, where you are quite guaranteed (as Stoney was pointing out from the usual modelling equations) to have higher Cd at a higher Ct.

[smoe]

Having the 51 radiator scoop were it is should help with reducing air turbulence from entering the intake. The scoop design looks similar to the F-16 Falcon.  I've read/heard the air turbulence is pretty bad along an airplanes skin and is especially bad for air intakes.

[FLS]

...

An 8 degree angle of attack of the airfoil (which is a 7 degree angle of attack of the P-51, since wings are mounted with an angle of incedence at root of about 1 degree, so I could really be looking at a 9 degree AoA for the airfoil, but let's use 8 for sake of argument) equates to a Ct of about 1.0.

...

This is confusing me. Isn't AOA always determined by the wing regardless of incidence?

[Stoney]

This is confusing me. Isn't AOA always determined by the wing regardless of incidence?

The angle between the chord line of the wing and the relative wind = angle of attack.  Therefore, it doesn't matter what the angle of incidence is.

[Chalenge]

First is that "ideal condition" airfoil has the so called "drag bucket," which is the low-drag, laminar flow characteristic Chalenge was correctly indicating in principle, but it is not close to encompassing 8 degrees AoA -- it goes out to only about 2-4 degrees AoA.  Second is that "standard roughness" totally eliminates all of that, and you have the more-typical parabolic shape to Cd vs. Ct, where you are quite guaranteed (as Stoney was pointing out from the usual modelling equations) to have higher Cd at a higher Ct.

Okay first things first...

Looking at your wind tunnel report (which is obvious thats what it is) I have to start off with the critique by saying (asking) where is the wind tunnel turbulence indicated? I dont see it and without that its not worth the graph.

Second I notice the airfoil is not a P-51 airfoil. It is similar to the P-51 tip section but it really isnt even close to that!

Here we are with the P-51D root and then tip followed by the P-51H root (which as I said was modified to assist with "Slipstream Contraction."







These same images and more data can be found at the UIUC Airfoil Coordinates Database.

I believe you can see the airfoils are quite different.

Now... back in 1959 a man by the name of August Raspet (PhD) at MU was conducting experiments with methods of flow analysis. In the glider world (soaring actually) Dr. Raspet is well thought of even now more than 50 years following his death (air accident during an experiment). He invented a technique that allowed experimenters to 'listen' to air flow over a give wing in flight. His method allowed one to clearly distinguish between laminar and turbulent flow in actual flight (not in a wind tunnel). He was particularly interested in airfoils that were of laminar design because it was his objective to eliminate (as much as possible) any form of drag. It is because of him that soaring pilots today have laminar foils on their gliders that actually experience laminar flow (like it or not).

Primarily his research focused upon foils that were laminar but not symmetrical. If you look at the P-51D you will see that as the wing transitions from root to tip the symmetry changes quite a bit. This change in symmetry has the effect of broadening the bucket. You will also discover that since the symmetry is not consistant that the wing must be analysed by local coefficients which was not easy then and isnt easy today.

However... take a close look at your standard roughness again and then consider what I just revealed to you. Not only is the graph going to sink on the scale of cd but it is also going to flatten out.

All the way up until 1979 (and perhaps beyond) the various agencies conducting airfoil analysis had a problem in that they could never correlate their data from one wind tunnel to the next. You have to be very careful what you accept and what you dont but certainly without published details on things like 'specific tunnel turbulence' you must be very careful.

Anyway... you can read more about this and other details about Raspet and the P-51D laminar research in the August 1960 issue of Soaring Magazine although it isnt really worth researching for the few details he gives.

[Brooke]

Well, then it is your lucky day.  For while you are convinced that the data I posted is irrelevant (and presumably the same for the graph that Pyro posted), I think that it is spot on and am still willing to take the bet with you.

Are you willing to bet, and if so how much shall we bet?

[Brooke]

The angle between the chord line of the wing and the relative wind = angle of attack.  Therefore, it doesn't matter what the angle of incidence is.

Angle of incendence does indeed matter when you say "This is why a P-51 can raise its nose as much as eight degrees (or a little more) and the drag remains the same".  A P-51 with its nose raised eight degrees has its wing root at 9 degrees angle of attack.  That was the point I was making.

[Chalenge]

I would be willing to bet a large sum of money that a P-51 with wing at 8 degrees angle of attack has substantially more drag than a P-51 with wing at zero degrees angle of attack.

According to Pyros graph at a cl of 0.75 (8 degrees AOA) to cd is .008. At zero degrees AOA the cl is 0 and the cd is .00025 (approximately). This chart was produced in 1946 by calculation (apparently). There does not appear to be any relative published drag coefficient in any of the evidence you have that can be accurate.

However... you can still back out of your claim or more clearly define "substantially more drag."

I will tell you that the definition of "parasite drag" in the U.S. is commonly accepted as the total drag excluding vortex drag (your induced drag). In looking at Pyros chart I would have to say the chart defines parasitic drag as only the part of drag associated with surface friction/resistance with the air flow and does not mention profile drag (which as I understand things should double the drag coefficient since profile drag is usually the equal of or slightly greater than parasite drag). In other words the total drag would be 2 x .008 + vortex drag but in reality it would be more. The published zero-lift drag coefficient for the P-51 is .0163 and so please tell me what you think the total drag coefficient for 8 degrees angle of attack would be and explain how it is "substantially more drag."

Then you can explain why you think an airfoil that is nothing like the P-51s has any bearing on the subject.