Suggested references for "low" Reynolds number airfoil performance?

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Grimace

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I'm looking for references that discuss, or provide equations, or even pretty pictures for standard aircraft airfoils in the Reynolds number range of about 1 million and up...

I've seen lots of stuff about wind turbines and R/C models in the under 400K range, however I'm looking for some information in the middle... specifically the 1 to 3 million range that isn't covered by the NACA data.

Someone had previously brought up the issue of low-Reynolds stall characteristics on "normal" airplane wings, but I can't find much on the topic. Approaching stall, my Re would be around 1.00E6 on a 24" chord... 1.3E6 on a 30" chord and so forth... And I'm really inclined toward smaller wings to get a greater aspect ratio for a given wing area, but I don't want to push things too far...


And as a little side question... in general, it's my observation that the effect of reynolds numbers on low-speed flight is less significant on a thinner airfoil... the thicker sections, for example, have greater changes (for the worse) in lift/drag/aoa as the Re drops down to 3E6. And flaps/slats/etc are also less effective at low Re numbers as well. Is there any data available for low Re flap systems? Does any book/reference/research cover this topic?
 
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Topaz

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You've fallen into the 'Black Hole' of airfoil testing - not a lot of wind-tunnel testing has been done in this Re range for 'sportplane' type of airfoils.

The problem is that the aerospace engineering community (our Orion notably excepted) generally considers "General Aviation" to end with airplanes down about King Air size and performance, whereas the RC folks consider a model to be "HUGE!" if it's got a span of eight feet or so. Everything in-between, from BD-5's to Van's airplanes to a piston Cessna is pretty much ignored by both sides, leaving the work on airfoils for these airplanes up to either their specific manufacturer, or specialists such as Drs. Selig, Eppler, Wortmann, and Roncz.

Sounds like you've already visited Selig's group at UIUC, and they're pretty much the torch-bearers for low Re airfoil design these days. There are quite a few sailplane airfoils (even thick ones) optimized for low-Re usage, but they just have too much camber for a sport plane. Not much use to you.

There's a great debate (or has been) about the validity of wind-tunnel testing of airfoils versus computer simulations. There are pros and cons on each side of the argument - too long to go into here. The really important thing to glean from the arguments is to compare apples to apples - don't compare results from one method to those obtained with the other, beyond general characteristics and broad performance 'ranges.' One of the points on the pro-computer side is that you can see more variance between the same airfoil tested in two different wind-tunnels than you can between 'real life' and a well-done computer run on the 'foil.

That said, if you have an airfoil in-hand that hasn't been tested down to the Re you want (and you aren't independantly wealthy so that you can afford wind-tunnel testing), your best bet is to learn Profili (or the core program, XFoil) and run your airfoil at two conditions:

1) The lowest independantly-tested Re number. This establishes a baseline of comparison for your results against those in the wind-tunnel. Whatever differences you see between the two here will probably carry across to other test points. The two should be broadly in agreement in terms of the performance characteristics of the airfoil. If not, you'll need to figure out why.

2) A second run at your target Reynold's Number. Don't trust this as an absolute set of numbers for your airfoil, but rather watch what happens to it under these different conditions. How radically does the maximum lift degrade? How much does the drag change. Does the shape of the stall indicate that the stall transition is moving significantly forward, resulting in poor stall characteristics? Again, you're looking for trends rather than absolute numbers. You can broadly take the numbers from this kind of testing, but things get to be a little funky at low Re, as the air "thickens up" from the point of view of the wing. Don't expect an exact match to your actual airplane.

My understanding is that yes, you're generally correct that thinner airfoils do better at lower Re numbers. However, you can take that too far. Thin (<10%) airfoils have a propensity for a sharp leading edge stall (unless there's radical sweep to set up vortex flow). You don't want that, either. There have been a number of 'thick' (15-18%) low-Re airfoils designed, but again, that was for specialized low-speed usage.
 
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Grimace

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There are quite a few sailplane airfoils (even thick ones) optimized for low-Re usage, but they just have too much camber for a sport plane. Not much use to you.
How much are you thinking is too much?

There have been a number of 'thick' (15-18%) low-Re airfoils designed, but again, that was for specialized low-speed usage.
What kind of low speed usage are you referring to? I am looking for an airfoil with excellent low speed performance. The "high speed performance" that I expect to get from the plane will come from having a small wing area that allows me to cruise at a high lift coefficient and a moderately high (for a powered plane) aspect ratio around 8 or 9. As I see it, that alone will give me "good enough" high speed performance... I don't need to push that edge of the envelope any farther. Cruising with a CL around 0.2 to 0.25, I'll have a l/d ratio of 25 or possibly much higher regardless of what airfoil I choose (within reason). Good and efficient.

So what I really will need is to push the low-speed envelope... because that's what will determine whether this airplane is a hot ship or a pussy cat. I'm not trying to design the next BD5/Cassutt/AR5. The way I think about it is that I'm really trying to emphasize the low speed performance... it's just that I'm handicapping myself with a tiny wing... ;)
 
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Topaz

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How much are you thinking is too much?
Unfortunately, that's about like asking "how tall is tall?" The answer is completely dependant upon the particulars of your design, but remember that these airfoils would be designed to have a minimum drag at a much higher lift coefficient (0.6-1.0) than would normally be the design (cruise) lift coefficient for a sport plane wing. Some of the more modern competition sailplane airfoils might be more suitable since modern soaring competition technique has more emphasis on higher-speed flight, but most of those are proprietary property of the companies that developed them, and not available to folks like you or me.
 

Grimace

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Thanks for the tips, Topaz and Orion. I'm downloading Profili right now. I've used it before, but that was many computers ago and I see there's now a new version out anyway.

If it works with Linux (Wine), I'll pop for the full version and be in business... if not, I'll have to wait until my water-cooled computer is completed so I can have something with MS Windows on it... I'm really not much of a Windows geek.

Every time I think about a tiny 32-40 sqft wing on a plane, I get excited just thinking about how little surface there will be to sand down... and how much less epoxy will wind up on my shoes as I'm glassing the wing... and then I think about the fact that the airplane will also be fast and I guess that pretty cool too!

(Edit... hrmm... it looks like wine has an issue with the limited read/write abilities of the "free" version. On the one hand, that bodes well for me getting it to work with the full version. On the other hand, it makes the option of waiting for the Windows computer more appealing)
 

Grimace

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Here's a follow up question....

When using profili, there's a lot of airfoils to sort through... When selecting an airfoil for a mission such as the one I've explained (great low speed performance, adequate high speed, decent stall characteristics, Re under 2 million), what kind of general shapes should I earmark as worth examining?

To put it another way, what general characteristic might I use to rule out 90% of the 12-18% thick airfoils off the bat? Obviously, I'll rule out anything with a sharp LE. But what else? Cusp? No cusp? high laminar flow sections? I'm not worried about one or two good ones slipping through the cracks... more about getting a handful of good ones to start examining..
 

Topaz

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It's another "depends upon your airplane" answer, I'm afraid.

If you want one that's tested at Re<2e6, then your choices are very, very limited. Off-hand, I don't know one that might be suitable. If you're looking at an airfoil that's got all the other characteristics and has at least been simulated down to Re=2e6, you'd be hard-pressed to do better than some of Harry Riblett's airfoils. Harry kinda goes "off to visit the elves" in the latter part of his book, but his actual airfoil work seems to be nearly universally liked. His airfoils are 'corrections' of some of the NACA series, and his alteration to the mean lines generally preserve the drag characteristics of the equivalent NACA sections, reduce the pitching moment, and improve the stall behavior quite a bit.

Which one (camber, thickness, and chordwise maximum thickness location) is the best fit to your specific airplane will depend upon the wing loading and design cruise speed, amongst some other things such as structural materials, construction methods, etc.

I personally don't think you need the cusped shapes on your particular design. The top-end performance isn't critical, and such shapes can sometimes play Hobb with aileron feel.
 

Grimace

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his book is already on its way.... I was just wondering if there are some physical characteristics of an airfoil that work at higher Re, that I could pretty easily dismiss when looking at the airfoil for lower Re purposes...

I was just wondering if there's a way to look at 500 airfoil pictures and throw away 90% of them as being likely unexceptional without detailed analysis of them at low Re numbers for a plane flying in the 45-170mph range.

I thought, for example, limiting myself to airfoils in the range of 12-18% might be a good idea...
 

Topaz

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Hmmm. Got me there. Every 'rule' that I've heard seems to be full of exceptions, so I don't know if I could make any useful generalizations for you.

I think that if it were me, I'd try and choose one that's been tested or simulated at some Re at least close (within 1e6-1.5e6) to what I'd be using, is still about 15% thickness and meets my other characteristic requirements. Starting from that 'solid' base, I'd make some runs at various Re numbers in XFoil (or Profili, if you prefer) to see what I can expect to happen to that airfoil in the Re range I need. I'd avoid something much thicker than 15% simply because "thicker is often worse" in low-Re airfoils. Kinda playing the odds there, if you will.

Some research on Selig's site or the one Orion noted might give you some general background information that could be helpful.

I know that's not really as cut-and-dried as you'd like, but that's about the best I can think of. Perhaps someone else here has more experience with this sort of thing.
 

Grimace

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Another potential site is that of Martin Heppler at MainFrame. True, a lot of the stuff may not be applicable but it might prove useful nevertheless.

Heck that Java applet is pretty entertaining...

JavaFoil - the Applet

Comparing its calculations to the 63-215 at Re 3.0 million, it's actually really close from what I've seen so far... I'm still comparing points and fiddling with it though...

Edit to add... other airfoils don't seem to fare so well though..
 
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Norman

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When using profili, there's a lot of airfoils to sort through... When selecting an airfoil for a mission such as the one I've explained (great low speed performance, adequate high speed, decent stall characteristics, Re under 2 million), what kind of general shapes should I earmark as worth examining?
Profili comes with hundreds of preprocessed polars but it doesn't search by section characteristics, it searches be physical similarity. You find one you like and then click on the “show airfoils similar to the selected one” button in the airfoil management dialog box. It gives you a list of sections of similar thickness and camber without any consideration of the polars.


If you prefer Linux you should take a look at the Linux version of Xfoil. The MSWin version has a lousy user interface but I've been told that it's a lot better on a nix platform.


You're running into the laminar separation bubble problem. The GA airfoil sections (at least the older ones) weren't designed to deal with that so they don't scale down well but the newer model airplane sections have been designed with that in mind and scale up pretty well. Attached is a section that's very popular with flying wings because of it's its low pitching moment. Shown is the original 9.86% with and without a 10 degree flap with the basic shape thickened to 11% and 12% . I haven't tried it with more flap or different hinge positions but you get the idea of what you can do with Xfoil/Profili. The pressure plot also will show very clearly when and where a bubble will occur so you can figure out if you need turbulaters and where to put them


Regarding those sections Riblet designed. All he did was buy the old Eppler code, load the NACA sections into it and then poke at it until something interesting fell out. Even I can do that, just ask Topaz. At that time all responsible people in the business, including Eppler, were saying don't trust the data that the code produces until it's been verified by actual wind tunnel testing. In his wisdom Riblet decided to sell his sections and let the home builders test his airfoils for him. Good thing Eppler's programing turned out to be right.
 

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Topaz

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...Regarding those sections Riblet designed. All he did was buy the old Eppler code, load the NACA sections into it and then poke at it until something interesting fell out....
That's not quite right. I've read the design rationale behind his modifications - it fits, and it's not 'random poking.' Basically NACA chose a really odd way to plot the airfoil series that you see referenced in Theory of Wing Sections, and the method resulted in a flattening of the mean line near the leading edge. That's why those sections have some pretty difficult stall characteristics and more Cm than they 'ought' to have. Riblett replotted the 'foils via the correct method, and in some cases tweaked the mean lines a little. Mostly it's using the correct method of combining the mean lines and thickness distributions that's causing the improvements in Riblett's sections - the mean line near the leading edge has the appropriate curvature, rather than flattening out as the NACA did it.

I recall the big controversy about computer airfoil analysis at the time. In the case of routines that didn't iterate on the boundry layer development, that concern was quite justified. The programs that take the boundry layer properly into account have proven to be relatively accurate. Eppler's routine is one, XFoil is another. I've run a few of Riblett's 'foils through XFoil, and the results match those from his book (run through Eppler's routine) quite well.

As for having builders do the 'real' testing on the airfoils, that's the way it is for all airfoils. Wind tunnels have their own set of limitations and distortions, and don't have a "lock" on accurate data by any means. I've run airfoils in the 3ft section tunnel at Cal Poly Pomona when I was a student there, and it was pretty obvious that the numbers weren't "pure" - or even consistent from run to run.
 

Norman

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I don't know how original that idea was. I read Epplars book years ago so I'm not sure but I think he may have suggested re-plotting the NACA sections I do know that way back in the fuzzy old parts of my mind tha there have been other ways to wrap a thickness form around a mean line.


I believe it was Wartman that said we should discard the idea entirely that an airfoil section has to be made up of a symmetrical shape bent around a precise curve because the air that takes the high road doesn't care and will never find out what happened to the air that took the low road. He's the one who started fixing sailplanes that had NACA sections by adding a few millimeters to the front 5% of the lower surface to make the nose shape better. That also has the effect on the mean line that you mentioned but of course the original thickness form is grossly altered. Amazing what somebody who really knows what he's doing can accomplish with some bondo and cardboard templates
 
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orion

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One other historical note here - the baseline airfoil sections that have become the standard in the industry were actually never intended for public release. In actuality they were families of test shapes that NACA was working with on the way to developing a more optimal database. But the laboratory database leaked out (actually it was published as a seres of preliminary reports) and the designers of the day started using the sections as if that's what they were intended for. The incorporation in the industry was so quick that the NACA folks just said "what the heck, it's close enough", and they let it go at that. the optimization study was never completed.

Harry Ribblet essentially just finished what NACA was eventually going to do anyway. This was passed on to me about twenty some odd years ago by the chief aerodynamicist at NASA Ames Research Center, so I have pretty good faith in its accuracy.
 

Tom Nalevanko

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Speaking of Harry Ribblet, is he still actively working on the subject? I thought his book was very well reasoned.
 

addaon

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Wow. While I found Ribblet's book interesting, provocative, worth buying, and most importantly useful, "well reasoned" never really crossed my mind. I get the sense that he had a bet with a friend to see how many times he could try to discredit himself... on each page. If the information wasn't backed by so many other people I respect, the writing style would have me write him off as a loon. As it is, I'm still leaning towards "loon with one or two good ideas."
 

Topaz

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Oh, he falls into a trap that many people do - he found an error made by a big, well-known organization. A significant thing with a famous and well-established set of data. But having "caught" the NACA in a mistake, he took it too far, and seems to have fancied himself something of a champion for 'proper' airfoil usage, and proceeded to write letters to various agencies all over the place telling them what they were doing 'wrong'. That's the process that's detailed in the latter half or so of his book, which I generally ignore. His rants are... "interesting" for a casual read, but you can almost see the eyes rolling on the people who received the letters he's published. They're a bit... "strong", given his actual background.

In reality, catching the NACA's error in plotting these airfoils and providing a catalog of corrected 'foils is his sole significant contribution. Anyone could have done it, and anyone could do it to the rest of the NACA catalog.

To his credit, he mentions what Orion was talking about - that the NACA never intended for the "NACA airfoils" to see the light of day - but he also recognizes what would be obvious to any of us except the scientists at that organization. The NACA intended that they'd come up with a database of information, and that then every single airplane designer would create custom airfoils for their specific application, based upon that data. That wasn't ever realistic, nor is it today, even with all the computing horsepower we now have. Airplane designers are rarely airfoil designers, and vice versa. Only a very ivory-tower scientist would think that a scheme like that would actualy work in general practice.

None of this should take away from the good work he did on his airfoil catalog. Sure, anyone could've done it, but nobody else did do it and we have a full catalog of some very nice airfoil sections as a result. That shouldn't be lost in this discussion - the airfoils themselves, by all accounts, really do fullfill his claims for them.
 

HumanPoweredDesigner

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that first response about using the commonly tested Re numbers and comparing to the higher Re number sounds like good advice.
 
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HumanPoweredDesigner

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The answer is completely dependant upon the particulars of your design, but remember that these airfoils would be designed to have a minimum drag at a much higher lift coefficient (0.6-1.0) than would normally be the design (cruise) lift coefficient for a sport plane wing.
Cl = 0.6-1.0 is about the area I want. What are some of these thick air foils you refer to? The thicker and easier to fabricate the better.


just found your link. Good start. And they look straight in back, which is good since I don't want to be bothered with tiny curvatures over long distances. I just want to curve where the curve is big, and then have it go straight. http://www.aircraftspruce.com/catalog/bvpages/ga_airfoils.php
 
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