Undercambered vs. flat bottom airfoils

[waco10]

I have read that undercambered ("birdlike") airfoils are more efficient at slow flight speeds, compared to flat bottom airfoils. I must display my ignorance, but have to ask this question: why? Many slow flyer type planes use undercambered airfoils with great success, but it seems to me that the airflow over and under such a wing (say, a Slowstick wing) must travel about the same distance, seperated only by the thickness of the foam sheet airfoil. Given Bournelli's principle, wouldn't a thick flat bottom airfoil (say, a Mountain Models Dandy wing) create much greater lift due to the airflow on top traveling so much farther than that on the bottom? Yet, the Slowstick and the majority of indoor, micro and many parkflyer models use undercambered airfoils with great results, vintage and old timer models sometimes, and sailplanes almost never. Is it a Reynolds number thing? Do undercambered airfoils excell at slow speed flight at the expense of higher induced drag by comparison to flat bottom airfoils?

[Ollie]

"Given Bournelli's principle, wouldn't a thick flat bottom airfoil (say, a Mountain Models Dandy wing) create much greater lift due to the airflow on top traveling so much farther than that on the bottom?"

Your simple idea is myth about lift. Read this:

http://www.allstar.fiu.edu/aero/airflylvl3.htm

You could better compare mean cambered airfoils, not undercambered vs. flat bottomed airfoils.

Thin, mean cambered airfoils do well at slow speeds but do poorly at high speed. With same mean camber (flat bottomed vs. undercambered) both do well at slow speed but at high speed the flat bottomed airfoil is better. The sweeped up bottom ahead the spar airfoil is even better at high speeds. The thick airfoils have room for strong, stiff spars. Thin air foils don't have room for strong, stiff spars.

[Ollie]

There is more:

For the mean camber airfoils compare thickness. With thick airfoil the drag is higher compared to thin airfoil. The reynolds number is proportional to chord times airspeed. As reynolds number smaller the airfoil's maximum lift smaller and the airfoil's minimum drag increases.

Air is normaly not seen directly. The flow of air is not seen directly. That is why air is complex to see directly. You have to measure airspeed and angle direction with out seeing. In air flow around an airfoil is not seen and the behavior with out speed and direction are subject to myths.

[waco10]

Thank you Ollie, great site, I'm printing it out so I can study it at leisure. While thinking about this, I remembered reading in the Parkfler section long ago about someone covering the bottom of a slowstick wing to see what difference it would make. As I remember, they reported that it flew slightly faster and not so "floaty". Not sure what to make of that, but it fits in with the discussion above. Someone once covered the bottoms of a pico tigermoth wings and reported that it flew well, but had lost the very low speed flight capability that the pico moth is so famous for, and was therefore not as much fun. This is great stuff to learn about, and I really appreciate this forum and your responses.

[Ollie]

The mean camber line is half way from the top and bottom of the airfoil. With the very, very thin airfoil (almost zero thickness), the top camber, the bottom camber and the mean camber are almost the same. When the thin cambered wing is converted to flat bottom, the new airfoil has same camber for the top, zero flat for the bottom camber and half way (mean) camber for the new airfoil. The new airfoil has half of the (mean) camber compared to the first airfoil. So, the new airfoil as not as good at low airspeed but better at high speed. Fun equals slow for you. For some other people,"fun equals fast."

A thin, mean cambered airfoil at slow airspeed, high attack of angle but not too high before stall, the mean camber has smooth flow over the bottom. With smooth flow on the bottom and the top, the drag is low. With fast airspeed, low attack of angle, the thin, mean cambered airfoil has turbulent flow on the bottom of the airfoil. With turbulent flow, the drag increases greatly.

The wing drag is due two main things, airfoil and aspect ratio. At low speed and low aspect ratio, the wing swamps the induced drag over the airfoil drag.

To understand the whole wing, all functions must be included. The wing is a complex thing with airspeed, size, angle of attack, twist, aspect ratio, sweep back, lift, drag, pitching moment, strength, stiffness, dihedral, rough surface, etc.

I hope you will have more fun by studying about areodynamics. I have had fun that way since about 1937. I am 74 years old, still learning, I hope.

[waco10]

Very good points. You are right, my conception of lift using only Bernellis principle was incorrect. The text from the websight points this out. I have noticed that the Slowstick and other undercambered wing planes have a very pronounced high angle of attack, measured from the fuselage and horizontal tail. A Gentle Lady sailplane wing is flat and on line with the horizontal tail. The slow flyer undercambered wings seem to be flying around with about 10 degrees of full span flaps down all the time. It seems the slow flyer wings are more like the "scoop" as described in the text, creating high lift partly by high angle of attack, the penalty of increased drag being unimportant to these planes. The flat bottom wing of the Gentle Lady creates less lift, but is far more efficient for its intended use, where aerodynamic efficiency is of prime importance, and drag is a very bad thing (unless desired for landing). The text describes the fact that the air on top and the air on the bottom do NOT have equal transit times, and that is a key factor I had not considered. It states:"the lift of the wing is proportional to the amount of air diverted down times the downward velocity of that air". This would explain why even flat airfoils such as used on 3-d flyers and the GWS Pizza work. Given Bournellis principle only, these "flat plate wing" planes could not fly at all. I once saw an amazing display of aerobatics by a friend flying a simple GWS flying Pizza...I couldnt believe the thing could fly at all, but was astonished at the ability of this plane to cruise, maneuver and perform aerobatics..... it certainly was food for thought. Is this fun or what? Thanks again for your help. By the way, I'm 54, and just now starting to question a lot of the conventional wisdom about this sort of thing.

[Ollie]

You have to put a a flat airfoil into a smoke windtunnel too see the airflow. At a positive AoA the flow splits just under the leading edge on the bottom. The top flow goes back and around the leading edge and over the top. The air sticks to the airfoil. The boundary layer has some thickness before getting to full speed. The boundary layer thickness depends laminar some spots, turbulent other and turbulent type eddy or bubble. Just at the leading edge on the top, the flow can't bend the flow around the too sharp LE. The flow makes a short turbulent bubble in the thick boundary layer. It is the streamline flow for the solid airfoil plus the boundary layer and bubble. The streamline flow applies with all B. principle, Newton, etal. You can't see the flow behavior without smoke or fog.

[BMatthews]

Waco, it's a weird and wonderful phenomenon.

I was part of a rather heated debate between two camps that asked the question of "what effect generates lift". One says you can measure the pressure differential between the upper surface and the lower surface (basically your Bernulli effect) and when you integrate it all you arrive at the lift needed for flight at that speed that generates that pressure differential.

Then there's the other camp that says that if you study the downwash behind the wing you'll see that X mass of air has been accelerated to Y speed downwards and that the weight of that volume of air accelerated to Y speed is equal to the lift needed to hold the plane up.

But the two phenomenon are present at the same time and are linked such that each is dependent on the other and each can be shown to separatley account for the wing's lift. In the end both camps agreed to disagree for the most part. What I got out of it was that the two effects were indeed one effect. After all if you have two effects that can be shown to EACH account for the lift needed and both are happening to the same wing that would imply that there's TWICE the lift you need unless you realize that the two effects are actually just different aspects of the same SINGLE effect.

Confused yet? :D

[waco10]

Yup :D .
But thats part of the fun, and I'm sure learning a lot. Isn't it amazing that more than a century after the Wright brothers success, the "laws" of aerodynamics are still open foir debate? As an aside, back in the seventies, Volmer Jensen built and flew a hang glider, the VJ-24 I think it was, that flew at very slow speeds and had a fascinating airfoil. Sort of a combined undercamber and semi-symmetrical (not flat bottom) center section. I read that it flew rings around the typical rogallo wing types of the day. This just opens the field up even more doesn't it? It interesting to compare slow flyer type planes designed for the same speed range and of about the same size and weight, the Mountain Models Duskstick which has a flat bottom airfoil, and the GWS Slowstick which has a classic thin undercambered airfoil. Why did their respective designers pick such different aifoils? Which is "better"? I sure don't know, but they both fly great :rolleyes:. My totally untrained mind tells me that, in general, the flat bottom airfoil requires less power but more area to create the same lift at the same airspeed as an undercambered airfoil, that the undercambered airfoil needs an angle of attack slightly higher than the flat bottom airfoil to perform at its best (at the expense of higher drag), and that the flat bottom airfoil is somewhat less affected by turbulence (has better penetration) and a wider speed range (due to slightly less induced drag). I could be entirely wrong about all of this :D ! But again, its the variables that make the difference. From the great website that Ollie showed me, I learned that Bournellis principle is only one part (and a fairly small part at that) of a much larger equation. Fair enough, but all other variables being equal, would not a flat bottom airfoil (such as the Duskstick) still have a slight advantage, even if only a few %, because the air on top really does have to travel farther than the air on the bottom, as opposed to an undercambered wing (such as the slowstick) which is only as thick as the foam from which it is made and therefore the air on top and bottom is traveling almost exactly the same distance?

When I get the chance, I will do a totally unscientific experiment. I have a plans built profile Champ from Randy Randolph plans. Its a great little flyer with an undercambered airfoil. I can build a second wing, identical except for covering the bottom to make it a flat bottom airfoil, and then compare the performance to the original wing. One variable I have to deal with is angle of attack of the wing, but I suppose I could start by leaving it identical for both wings and see what happens. Please keep the info and comments coming, I really enjoy learning about these things :) .

[Ollie]

"One variable I have to deal with is angle of attack of the wing, but I suppose I could start by leaving it identical for both wings and see what happens."

Please don't confuse incidence with AoA. Incidence is how to mount or rig a wing at the shop bench. AoA is how the wing flies at a pitch angle. From moment to moment the plane flies as airspeed changes with the AoA. v~(wing loading/AoA)^-2.

[BMatthews]

Waco, for very slow speed flying it's been found by legions of free flighters that thin is in. And when you remember that the camber of many free flight airfoils is up around 5 to 6% often and higher in some cases it's no wonder that the final shape shows a lot of undercamber.

Be careful with the idea of just covering the lower surface. If the wing is just a simple arc then covering the lower surface won't really produce an airfoil that works well. You'd be far better off making two totally separate wings with proper airfoils. It gets even more complex when you need to consider that you want the camber (the airfoil's centerline arc, not the concave lower shape) to try to be the same for both airfoils to actually do a fair test.

Just covering the lower surface will produce an airfoil with basically 1/2 the camber. So it won't be any surprise if it flys faster and doesn't slow down quite as well.

[waco10]

Ollie, You're correct, I got sloppy with my terminology...I did mean angle of incidence.
BMatthews, good points, I should have explained that the wing is balsa with undercambered ribs, covered on top and bottom with solite..it would be simple to build a second wing right on the same plans, but add a few balsa sticks across the bottom from the leading to the trailing edge to create a flat bottom. Both wings would be covered top and bottom. I think the plane is intended to be an indoor flyer (about 6 oz. with an ips motor) but I usually fly it in the front street early on weekend mornings. I'm coming to the conclusion that I'm in over my head on the technical end of all this, but thanks to everyones help, still learning a lot ..heavy sigh. I've got a couple of books that cover the subject, but they are focused on full scale aircraft or man powered aircraft...pretty technical stuff. Too stubborn to give up though :D . Thanks again guys.