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# Airplane Wings: Optimal Radius Curve

08/15/2008 7:51 PM

I have looked all over and I cant find the optimal radius curve of an airplane wing.

I am looking for the radius curve for maximum lift. And does the trailing edge of the wing have to tapper off ?

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#1

### Re: Airplane wind radius

08/15/2008 8:16 PM

Maximum lift also has to do with the relative size of the airfoil, speed, etc. Wings are not round or even oval, so the radius of the curve changes.

The reason there is a trailing edge on a wing is to reduce drag. All airfoils have drag associated with them, so for aircraft they work pretty hard to reduce drag at most points.

You also find many aircraft have a larger airfoil near the root, and it rotates and gets smaller near the tip. It all effects the amount of lift and drag at diffrent speeds.

When I was in high school I built a low speed wind tunnel similar to the one in the book 'A Book of Projects for the Amatuer Scientist' by C.L.Stong published by Scientific American. Building it was easy and studying simple test wings taught me a lot. I would suggest the experience for any budding aeronautical engineer. And no, I did not make it 6' in diameter, I made it a 2'x2' cross section using a trashed squirl cage fan to pull the air through. I did put flow straighteners both before and after the 'test chamber' to make it have a reasonably steady flow. The scales they show building are easy to do, they are basically small tortion springs made from solid piano wire.

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#2
In reply to #1

### Re: Airplane wind radius

08/15/2008 8:59 PM

I know that wings are not round. However they are curved. I built a wing that has a radius curve of 29 deg. on the leading edge and 29 deg. on the trailing edge as well. Looks a lot like a half pipe. And it is flat on the bottom. To create a differential pressure. So as air passes, it will create lift. I want to build a three winged horizontal wind mill. So the blades are perpendicular to the ground. I thought about it several years ago and know I have seen similar ones.

When I thought of it , it was a concept. Now I know the idea does work . So I thought I would pursue the idea.

I don't know anything about fluid dynamics. I have looked for information and all I can find is angle of attack. Referring to the angle of the wing in reference to the plane body.

I know there has to be an optimal curve for this.

Any Ideas on this, will be greatly appreciated.

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#3
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### Re: Airplane wind radius

08/15/2008 9:17 PM

You might go look at nasa.gov or call the aeronautical or mechanical engineering department at a local college, sometimes professors will be nice enough to point you to publications or where to find them. ... NASA has reports on full series of different wing shapes and their properties. I think there is even a NASA standard on numbering and defining wings and their properties.

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#4
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### Re: Airplane wind radius

08/15/2008 9:22 PM

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#5

### Re: Airplane wind radius

08/16/2008 1:18 AM

The University of Ohio has department of Aeronautics and Astronautics plus a good sized wind tunnel. They have an extensive library of research papers written by host staffers as well as those from other facilities.

They are a pretty sharp bunch of guys as evidenced by the fact that noted aerodynamicist John Rontz turned to them to resolve dangerous pitch loss problems on Dick Rutan's Voyager prior to the Round The Worlds Flight. They did and the flight was a dramatic success.

I suggest you Google that university, find their web site and start reading.

Good luck

L. J.

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#6

### Re: Airplane Wings: Optimal Radius Curve

08/16/2008 9:11 PM

I take it you are trying to determine the optimum airfoil shape for a propeller on awind powered generator. THer eis no such thing. Airfoil shape is a study of compromises. What is ideal for a given temperature, air density, and velocity, is unworkable for different velocities.

A 'fat' cross section works better for low velocity relative wind, while very 'thin' cross sections are best for high relative wind speed. Because the relative wind speed varies along the length of the propeller, the 'optimal' cross section also varies.

If, on the other hand you are trying to design the optimal shape for the buckets in a 'horizontal blower wheeel' or 'wind turbine', you should first research the prior art. Such devices are much more limited in power output than 'conventional' vertical propeller wind powered generators simply because the area of interaction with the wind is so much less.

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#7
In reply to #6

### Re: Airplane Wings: Optimal Radius Curve

08/16/2008 11:36 PM

The flat portion of the wing is currently 8 1/2" wide, with a 29 deg. radius curve on both sides.

I was hopping to make one that spin's slow, but has a high degree of torque.

Does that qualify as a fat cross section?

If I taper one side it will lower the resistance. But will that help improve the torque?

I thought that if it spun to fast that it would surpass the blower curve. So intended to add an centrifugal brake.

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#10
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### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 12:34 AM

Keith, are you by any chance related to Pete Bowers, designer of the popular Fly Baby monoplane?

L. J.

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#8

### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 12:16 AM

Check out Dover Publications for "Theory of Wing Sections" (think that' the right title). It's an old NACA (that became NASA in the 50s) publication but it's a fairly comprehensive coverage of low speed wing cross-sections and design principles. There are also computer-aided design programs (check the NASA pubs per other recommendations). They will get you close to an optimum design but wind tunnel testing is needed to get to an optimum performance. Lift and drag determinations are not an exact computational reality yet. Most explanations refer to the Bernoulli theory but lift is really developed by momentum transfer and circulation modification (Navier-Stokes equations plus a lot of fluid transfer dynamics mathematics which willl make your head hurt and requires a really fast powerful computer. Most folks settle for good enough rather than try for the absolute optimum since most aircraft cover a fairly wide speed range.

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#9

### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 12:18 AM

In Oklahoma City, there are many copies of the classic book on airfoil shapes: Abbott and Doenhoff's Theory of Wing Sections. The book provides a certain amount of theory, (thus the name), but also has lift/drag curves (obtained in wind tunnels) for perhaps 100 wing sections (shapes). Your local library might not have a copy but a university library will.

Another alternative is to use a program like X-Foil, which will show you the pressure distribution across a wing that you shape yourself. You'd want to first have a long look at Abbott and Doenhoff, though.

Some other possibilities for software are here.

Here's a pretty good intro to the basic theory of airfoils and some of the related terminology.

An ordinary airfoil does not have a single radius. But if you want to plot the curve of an airfoil, you can compute points along the top and bottom surface, according to the equations for those surfaces.

However, there are ogival sections, which have a constant radius on the top surface, and a flat surface on the bottom. The leading and trailing edges are sharp and the same. They are easy to make, and if you have a large lathe, you can machine six or at once out of a hexagonal or octagonal "tube" glued up from wood boards. Page 37 of this book shows such a section.

Yes, ordinarily the trailing edge of the wing tapers off to reduce drag.

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#12
In reply to #9

### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 12:30 PM

This is enough to dive me nut's. Especially when you consider, that as the wing spins 180 deg. That the leading edge becomes the trailing edge and vis-versa. So I dont want to taper the trailing edge. As it will be completely wrong at 180 deg.

And as it spins the angle of attack is constantly changing. The only improvement i could find is to change the flat, to slightly concaved. To add push when the wing is perpendicular to the wind.

I could also add a mechanical cam. To change to angle of attack, as it spins.

That would be expensive

Timmy's not stuck in the well, I am.

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#13
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### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 1:48 PM

Ok, please help me. What kind of a design does the wing spin 180 degrees? Almost sounds like you are trying to do a vertical windmill and get power on portion of the rotation when going against the wind too.

As far as the angle of attack changing, helicopters deal with this as they change the angle of attack continuously during rotation. It is also ajustable by the pilot using the control called a 'collective'. It is not a simple problem to solve, but it has been solved many years ago. Some more 'rudimentary' helicopters do not have collective, but that is not the popular method today. Even many RC helicopters have collective controls.

I have seen videos on YouTube of some vertical windmills that do have air foils that have ajustable angle of attack during rotation. It reminds me of dear Mr. Rube Goldberg and his inventions.

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#14
In reply to #13

### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 5:09 PM

Im really not sure how to explain it. But the photo might help Sorry for the bad photo its a bad camera. The concept is, that it doesn't matter in witch direction the wind is coming from to make it turn. So the constantly changing wind, does not effect the wind-mill, other then to make it turn. The reason the blabes are so far out is to increase torque. I want low RPM's and higher torque. That is, if im correct

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#20
In reply to #14

### Re: Airplane Wings: Optimal Radius Curve

08/20/2008 1:37 PM

After studying your photo and reading the rest of the page, I think, IMO, you're headed in the wrong direction. Your setup looks more like a paddle wheel problem than an airfoil problem. Airfoils generate lift, paddle wheels rely on direct pressure. In your setup with fixed airfoils you would probably only get lift +/- 5 degrees or so off of apparent wind direction no matter the airfoil shape. That leaves about 350 degrees of no lift and increasing drag until the foil passes perpendicular to the wind when drag will gradually decrease to the "lift" zone.

No offense but I think you need to study the differences between square sail type ship propulsion (which could only effectively sail downwind) and sloop rigged ships (whose sails were airfoil shaped and allowed sailing into the wind). Or paddle wheel ships vrs. propeller ships. Those designs are used for propulsion but effectively teach the fluid dynamics involved.

I believe, again IMO. that your design would be more effective if you think of it more as a paddle wheel where the wind pushes (forget lift) against the broader surface. This should get you a wider degree of wind effectiveness (perhaps 60 degrees on the downwind side). The trick then is to design the back and sides of the paddles to minimize resistance (drag) in the other 300 degrees.

If you look around on the net you will see that virtually all airfoil based wind generators (not propeller style) have a swivel mechanism that keeps the airfoil pointed appropriately near the direction of the apparent wind.

Hope this helps.

Dave <--- ex NASA-ite who participated marginally in wind generator design back in the 70's.

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#21
In reply to #20

### Re: Airplane Wings: Optimal Radius Curve

08/20/2008 1:53 PM

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#25
In reply to #20

### Re: Airplane Wings: Optimal Radius Curve

08/21/2008 9:02 PM

I disagree completely My design creates allot of differential pressure from one side to the other side. The proof is when I get the wind from the top and it still turns in one direction as I intended it to. Do you have a wind tunnel? Until you do, you don't know what you are writing about. Yours is just an opinion You don't deserve any mark's for a good answer.

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#22
In reply to #14

### Re: Airplane Wings: Optimal Radius Curve

08/20/2008 2:48 PM

I'm afraid I have to agree with Hooker.

If you assume that the wind is coming from you as you look at your picture, the airfoil in the rear, partly obscured by the vertical shaft, will generate lift to the right, given its current angle of attack, which might be 2-3 degrees. (Even at 0 degrees, an ogival section like the one you are using will generate some small amount of lift in the direction of the curved side.) This would tend to make the assembly rotate clockwise, when viewed from above. (But the effect would quickly disappear, as the angle of attack reduced to a few degrees below zero.)

The airfoil to the left in the picture would generate slightly more drag than the airfoil to the right. This would also tend to make the assembly rotate clockwise, when viewed from above. However the remaining foil would generate nearly as much drag, and therefore torque, in the opposite direction. There'd be a lot of lost energy.

The foils could be articulated so that each foil generates lift (let's say from left to right) as it sweeps through maybe 160 degrees in the sector away from the viewer, (with angle of attack being continuously varied) and then reset to generate lift (from right to left) as it sweeps through the sector close to the viewer. Then you'd end up with something close to this: http://www.freepatentsonline.com/4410806.html

Hooker mentioned reading up on sailing vessels. A great book on the subject (which coincidentally, I just found minutes ago while looking for another book -- it had been lost for a couple years) is Marchaj's Aero-Hydrodynamics of Sailing.

Your model looks skillfully built.

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#23
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### Re: Airplane Wings: Optimal Radius Curve

08/20/2008 5:54 PM

and other searches for 'vertical turbine' seems to find some similar models.

You might examine their airfoils (even a 'flat plate' is an airfoil in my book, just depends on its use!) by observing the video's. In these, it looks like reasonably normal airfoils, since the blades never really run 'backward', but they probably only generate power in a portion of their turning, not all the way around their path. So in the non-power producing portions you want them to have low drag, as much as possible.

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#24
In reply to #14

### Re: Airplane Wings: Optimal Radius Curve

08/21/2008 12:21 AM

Im out of the depth, but in my views, it looks like a bass trap

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#18
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### Re: Airplane Wings: Optimal Radius Curve

08/18/2008 11:29 AM

As long as you are stuck in the well, (and presuming you still have Internet access;)), check this site http://www.ae.uiuc.edu/m-selig/ads.html for airfoil data.

There will not be one perfect solution, but expect to compromise as suggested by others on the site.

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#11

### Re: Airplane Wings: Optimal Radius Curve

08/17/2008 9:25 AM

Factor the statement from Post #6 in all your design revisions and you'll save a lot of time and aggravation. "Airfoil shape is a study of compromises."

There is no perfect design, just figure out what variables are in play with your specific application and priortise them them by which ones affect your desired outcome the most to the least.

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#15

### Re: Airplane Wings: Optimal Radius Curve

08/18/2008 7:39 AM

The Supermarine Spitfire had a wing shape that was a skewed parabola.

Its intent was to ensure that the stress on the wing was the same at all places, and so use the minimum amount of material to build it, an important consideration at the time.

A parabola does not have a circular radius at any point.

Does that answer the question?

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#16
In reply to #15

### Re: Airplane Wings: Optimal Radius Curve

08/18/2008 9:29 AM

How did the create lift, angle of attack and HP ?

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#17

### Re: Airplane Wings: Optimal Radius Curve

08/18/2008 10:25 AM

Ahhh - it's not just a radius.

Look up some of the online foil generators that will give you the points for any NACA foil.

Travis

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#19

### Re: Airplane Wings: Optimal Radius Curve

08/19/2008 9:36 AM

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#26

### Re: Airplane Wings: Optimal Radius Curve

10/30/2008 8:32 AM

You seem to be designing a giromill, a type of Darrieus turbine.

These are not self starting unless you add pitch control.

A control which varies pitch throughout the rotation allows the wind to drive it over a greater part of the arc and you can minimize drag during the non driving portion.

It is unlikely that the complication will be worth it. Probably better to accept lower efficiency and make a slightly bigger windmill.

Another way to self start is to combine a savonius rotor. this is a "S" shaped drag type turbine which is self starting and can start the darrieus mill running.

You can make a savonius by cutting a 200L drum in half lengthwise and use the 2 halves as your rotor.

Depending on how your wind conditions and the power you want from the machine, a simple 200L drum savonius may be all you need. If more is wanted stack another one on top.

Savonius turbines tend to spin quite slowly with fairly good torque, but don't scale well because a lot of material is needed for a large one, making it heavy and expensive.

Google "Darrieus", "giromill", "vertical axis wind turbine", "vawt" to obtain plenty of useful (and useless) info.

Good luck

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#27

### Re: Airplane Wings: Optimal Radius Curve

02/05/2009 8:24 PM

I realise im posting anonomously.

Im currently studying Marine Sports Technology at Plymouth University, UK

I really dislike the fact that none of you have even mentioned anything about the reynolds number for this problem. Reynolds numbers are the starting point in any aerofoil/fluid interaction.

First things first. This design is in fact a paddle wheel design and very little consideration as to the aerodynamic effects of this device as far as foil (the oval shape) sections will make any difference to its design perameters. The aim of this device is to minimise drag and maximise slip of the relative wind (as the wheel passes through the air block) of the so called drag side (rear) of each paddle. The front serves as a catchment area for the wind to move the wheel around in a purely push mode. This is NOT a standard blade design by todays standards. The reason for this is that the coefficient of power of this system approaches around 20% by its mode of opperation (not using lift). This is calculated by the power output of the "turbine" through the air block which is define by the equation:

P=Cp(Coefficient of power of the turbine) x 0.5 rho (air density) x A (turbine total sweep area) x V^3 (windspeed)

The coefficent of power in this case is purely the theoretical output of a particular extraction mechanism and does not include losses due to mechanical transmision and friction. for this use a a C (losses) of ur system, usually approaching 70-90% depending. or around 0.7-0.9.

This type of system benefits greatly by having screens in front of the returning blade as it reapproaches the wind as this will reduce the return drag and decrease the losses due to friction. I realise this will not make it an omnidirectional device as the author intended.

The book so readily quoted as a must read in this thread is Theory of Aerfoil Sections which has a great appendix which shows angle of CL vs angle of attack for various foil sections and CD vs angle of attack. This is all well and good in systems where the reynolds number is 10^6+ (quite a large wing section or very fast airflows)

I can see that any airfloil in this system will have a reynolds numer of the order 5x10^4 max and the best sections for standard airblade designs for these types of blades are thin walled sections and not high thickness sections (thin being 3% of chord thickness and thick being 12% thickness due to the effect of reynolds viscocity at the low speeds/chords in air. Cl for these sections is almost double a thick section and Cd is just under half or 4 times more efficient as far as the lift to drag ratio.

A lift or drag force can be calculated thro its line of action by the equation:

CLift/Drag=CL/Cd x 0.5 x rho x V^2 x A

In this case if the section were moving in a straight line in the direction of the wind a straight up narrow wedge on the rear side and a semi hemispherical cup on the other would provide the greatest momentum flux change on to your cup. This is not possible as the blade rotates therefore the action of the wind on the flat surface as the rear of the blade moves around the circle of wind will have increasing planform drag is it approaches its rear and frontal zeniths of height on its cicumferance therefore the easiest way to reduce this is to round the nose of the cone a little more at each angle. This approaches a backside of a cup or curve/hemisphere. This is how these designs formed. These results are easily confirmed using water jet/wind tunnel experiements for equlvalent reynolds numbers.

Hope this helps.

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