Airfoil selection for a flying plank, how to achieve statical equilibrium?

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oriol

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Hi!

I am reading Anderson Aircraft design book. He covers everything, but there are some details that are spared. Hopefully other books will come next to study the specific details.

So far, I am working, as an exercise/divertimento, on the conceptual design of a very simple and affordable light aircraft. That is why I picked a flying plank with a vertical stabilizer as the potential layout.

I know very little of aircraft design, but I understand that, roughly speaking, you set some parameters to be able to pick the best airfoil for your requirements. Once you set a given weight, v cruise and v stall. You get a CL for your desired cruise speed. This v cruise has to be that of your best CL/CD, to get the best fuel economy. Then you have to find an airfoil that has a similar best CL/CD of the one you require for your cruise speed.

In my particular case I would like to build a tube and fabric wing. Thus I am considering flat bottom airfoils. My cruise speed would be like that of a Nano trike.

Anderson encourages to get a copy of theory of wing sections to use all the data collected of NACA airfoils. I just received a copy yesterday, I am using that book to choose my airfoil.
I guess that picking a laminar airfoil is perhaps unnecessary. The 4412 seems to be a good candidate, because the bottom is almost flat.

The 4412 has a moment of 1. OTOH the 23012 has a moment close to 0 but the bottom of the airfoil is not flat.

From what I have read on the net, most flying wings, like those used by Fauvel, use airfoils that are called auto stable airfoils; because their moment is next to zero. The auto stable airfoils I have seen, do not seem to have a flat bottom.

My doubts are those below;

Is it compulsory to use for a flying wing an airfoil with a CM that is very close to 0, or can you fix a CM that is >0 with the weight of the pilot, or with the engine weight?
When you read the CL curves You have to pick the one with closest Reynolds number to your wing chord. But what about the curve that is labelled as standard roughness, what is it for?
Given that you have to adapt the ideal CL of an infinite wing to that of a finite wing. DO you have to do the same for the CM?

Sorry if I ask something very dumb. I am just trying to digest all the info and the more I learn the more doubts I have!

Thanks for your comments, it is really helpful!

Oriol
 

Aerowerx

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To answer some of your questions....

Get yourself a copy of "Tailless Aircraft in Theory and practice", by Karl Nickel. Although it is biased towards swept wing aircraft it does discuss planks.

Yes, you can balance the pitching moment of the wing with the location of the pilot, fuel, and engine. It all has to balance out (pun intended). However, you will be designing for a single pilot weight if you do that.

Several years ago I did some virtual experiments using XFLR5, and determined that it is feasible to design a tailless aircraft such that the pilot weight does not matter. A summary of the process is: 1. determine what static margin you want. 2. place the components to achieve this margin without the pilot. 3. find where the CG is located. 4. put the pilot's seat at that location. Difficult, but feasible, and I was looking at a swept wing so I don't know how hard it would be with a plank.

Keep in mind that (according to Karl Nickel) the static margin for a tailless aircraft has to be 3 or 4 times that of a conventional tailed aircraft.

Take a look at what the Marske designs used. He invented his own airfoils.

Look in the archives here. Several years ago there was much discussion here on HBA over tailless aircraft.
 

AeroER

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Marske's book is a good start. Then, build hand launch models of increasing size based on the example in the book, and after that, modified with a constant chord wing.
 

Topaz

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Hello!

... From what I have read on the net, most flying wings, like those used by Fauvel, use airfoils that are called auto stable airfoils; because their moment is next to zero. The auto stable airfoils I have seen, do not seem to have a flat bottom.

"Auto-stable" is a bit of a misnomer, but we'll get to that in a moment.

Is it compulsory to use for a flying wing an airfoil with a CM that is very close to 0...

The short answer is "no," but there are caveats. The airplane has to have a balance of moments around the CG, such that when the speed slows, the nose drops, and when the speed rises, the nose comes up. There's more to it than that, really, but let's keep it that simple for now.

The easiest way to do this (sans computers and other gimmicks) is to have something that's "lifting" down at the rear end of the airplane and have the center of gravity be ahead of the lift of the wing. It's easiest to visualize with a traditional tail, which you'll find almost always "lifts" down. When the airplane slows down, the lift of the tail decreases and allows the weight of the airplane, concentrated towards the leading edge of the wing, to pull the nose down. The opposite happens when the airplane speeds up - the tail "lifts" down more and shoves the nose up.

With a tailless airplane, you still need to accomplish this, but you don't have a tail back there with which to do it. So the wing has to accomplish this task also, in addition to everything else you're asking of it.

With a swept-wing tailless airplane, you can twist the wing tips so that they "lift down," so that they act just like they are "phantom" horizontal tails because they're well aft of the CG. If they're doing that job, the pitching moment of your airfoil section doesn't really matter too much, other than it makes the job of the tips a little harder if it's trying to pitch the wing down strongly.

For a flying plank, the wing tips aren't aft of the CG much, if any at all. That trick won't work. So instead designers choose an airfoil that has a positive pitching moment: the faster the wing goes, the more it tries to rotate nose up, just as if there were a tail back there. The wing airfoil does the job of twisted wingtips on a swept flying wing, or an aft horizontal tail on a conventional airplane. A regular negative pitching-moment airfoil would do exactly the opposite of what you want: As the wing flies faster, it tries to rotate nose-down all the harder.

...But what about the curve that is labelled as standard roughness, what is it for?

Bugs exist. Dirt exists. Your wings get dirty, both on the ground and in-flight. "Standard Roughness" is literally a strip of about 60-grit sandpaper they glue to the leading edge of the wind-tunnel airfoil model to simulate the worst blast of dirt and bugs you could possibly imagine. The roughness (like dirt and bugs) disrupts the airflow and changes the aerodynamic characteristics of the airfoil. This lets you simulate what might happen if you flew through a gigantic plague of locusts.

Given that you have to adapt the ideal CL of an infinite wing to that of a finite wing. DO you have to do the same for the CM?

If I understand your question correctly, yes. Both CL and CM are affected by the fact that an airplane has a finite-length wing instead of an infinitely-long airfoil. The formulas for calculating real-wing performance aren't monsters.

Sorry if I ask something very dumb. I am just trying to digest all the info and the more I learn the more doubts I have!

You're not dumb, and questions are why HBA is here. I could never thank the other members here enough for the knowledge that they've shared over the years. We're truly and amazingly lucky to have each other.
 

Dana

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For a flying plank, the wing tips aren't aft of the CG much, if any at all. That trick won't work. So instead designers choose an airfoil that has a positive pitching moment: the faster the wing goes, the more it tries to rotate nose up, just as if there were a tail back there.
Commonly called a "reflexed" airfoil, where the airfoil's camber line reverses in the aft part so the trailing edge is curved slightly up.
 
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The auto stable airfoils I have seen, do not seem to have a flat bottom.

Actually, the Fauvel airfoil does have a flat bottom for a significant portion of the chord. It was done this way to make the wing easier to build on a table.

Tailless Aircraft by Nickel and Wohlfart is the "bible" for tailless aircraft but it is probably a little intense of a read to start out with. Get a copy of Airplane Performance Stability and Control by Perkins and Hage. Once you understand the basics from chapters 5 and 10 (longitudinal stability and dynamics) then you can move up to Tailless Aircraft.
There is nothing really unique about a tailless aircraft. "We just hide the tail"

For even more flying wing fun look up Prandtl-D
 

oriol

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Thanks so much for the repplies. It is wonderful to have a place in where to ask Aero technical questions!

Thanks Aerowerx, AeroER and Hotwings for the book the recommendations. As already said there are some books that are too technical. OTOH some others are too simplistic. Sometimes it is hard to grab the right one.

I ordered Dan Raymer's Aircraft design, but there seems to be a problem with the delivery. Another option to get an overall picture would be Raymer´s simplified book; Aircraft design fo homebuilders. Perhaps if I am about to get the expanded version, I do not need the small one, so I need to be patient.

After reading Anderson´s Perfos and design, I will dare to read some spanish books I have covering aircraft stability.

All the books seem worth reading! One thing for sure, is that I will be reading one book after another. I thought that Jim Marske book was a sort of biography, but it also contains applied theory which is very helpful.

As you pointed out AeroER. I was looking forward to get a general theoretical idea, then build an RC airplane and try different layouts, before jumping on a full scale aircraft adventure.

Thanks Topaz for your explanation!

Now I get the point of what standard roughness is.

I guess that if you are building a tube and fabric wing, instead of wood or aluminium. Then the final real wing, will loose some of the accuracy of the wind tested airfoil, probably the max CL/CD you are goind to get is a bit lower, etc.

I was thinking that a reflex/"auto stable" airfoil, looks more or less like an average airfoil, with the aileron shifted upwards. Perhaps you can generate a neutral momentum with a NACA airfoil by deflecting the elevons upwards?

Engineering is all about trade offs. Everything has to be very well balanced in order to achive an induced drag of a flying wing/plank that is, if no less, at least the same of a traditional aircraft with tail.

Regarding static and dynamic stability on a reflex airfoil, with the center of gravity located on the Center of Pressure. Having both, the center of Pressure and the center of gravity, on the same spot would make the aircraft good for aerobatics but not for quiet flying. I bet that placing the center of gravity below the center of pressure, like in a high wing, would result in a stable aircraft.

In any case I have to read more, to be able to tell what is the exact distance between the center of gravity with respect to the center of pressure, to make an aircraft stable.

I picked flying planks intead of swept wings because I thought it would be much simple to calculate the loads on a rectangular wing alone. I thought that by eliminating the tail from the equation, was to allow for a simple overall calculation, perhaps at the expense of some lower performances?

Perhaps I am wrong, and building a flying plank is more hard than building a conventional aircraft? The idea is the simple the calculations, the less the risk of calculation error.

Thanks again for your comments!

Oriol
 
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nestofdragons

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Flying planks. I like them a lot. Be sure to also look at the airfoils invented by Jim Marske. Those were proposed as leading to a better design by the designer/builder (Mike Whittaker) of this beauty. Special: MW9 Plank - Nest of Dragons

Also keep one thing in mind. Most flying wing beginner websites explain that balance is made in a swept wing by twisting the wing towards the tips so they create negative lift to compensate the missing elevator. I admit ... my own website tells it also that way (i will update it soon). But in fact it is better to keep all airfoils lifting. There is also balance possible if you give all parts of the wing a positive lift. Try to imagine it like this:
Place a swept wing on a ruler on the table.
Slide the wing back and forwards till the wing stays level on the ruler. Balance is possible.
All the forces in the wing are gravity-forces pulling the wing downwards. Ok, now ... put on your upside-down glasses and you see all those forces pushing upwards. Still balance is possible. All parts give positive lift. The center section of a swept wing will have its lifting point in front of the CG. It will generate a large force, but ... close to the placement of the CG (in sideways view). The wingtips generate lesser force behind the CG, but they are at a longer distance from the CG (in sideways view). Both moments can compensate each other.
Keep in mind that this explanation does not take in count the generated moment Cm of the airfoil. You can simulate that moment by placing a weight on the nose of your wing. That will resemble to the extra moment generated by the Cm of the airfoil. So ... the center section will have to push harder upwards to compensate that moment (which gives the nose a nose down atitude normally).
So it is no longer the wingtips that push down to keep balance in a swept wing. It is the center section that pushed upwards to keep balance. Just a bit like a canard does.

My apologies to the experts if i made any mistakes here.

I hope i explained it in easy words.
 

oriol

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Thanks Nestofdraggons for your clear explanation!

I just downloaded, and read(!), the article by Al Backstrom. It is so nice that you have bothered to collect so much information sprawled on the net, and put it available for other aero enthusiasts!

I was interested on a flying plank for the simplicity of a light tube and fabric structure, but also because of the potential bennefit of using a single surface lifting upwards, without interferences among different lifting surfaces, like in a canard. I know that swept wings, or even hangliders, achieve to simulate a tail by using downwash. I would like to avoid a complicated build and also keep the theoretical complexity as minimum as possible.

I am excited about building an aircraft using 1930´s diagrams, and avoiding computer simulations! I like it raw and simple, experimenting with RC models sounds also very appealing.

I am looking forward to carry on with my reads, and learn some formulas covering oscillation dampening and longitudinal stability. It is clear that I have to learn more to be able to tell if a reflex airfoil might work better than a conventional one? And if so, which airfoil suits me best.

Thanks BJC!

I need to learn and assimilate the basics before jumping to the most advanced considerations.

Thanks again for sharing your thoughts!

Oriol
 

ragflyer

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1. The benefit of using an +ve cm airfoil in a plank is it allows the airfoil to fly at some speed (cruise) without deflection of the (trailing edge) elevator . Reflex and trailing edge flaps do the same thing with the former just being more efficient.

2. Airfoils are made stable not by their shape but by simply putting the CG forward enough from their aerodynamic center. All airfoils can be made stable in this way. But this forward CG position means there is a unbalanced nose down moment. The reflex at the trailing edge helps balance (trim) the nose down moment caused by the forward CG position without deflecting the elevator. You could of course deflect the elevator instead of reflex.

3. If you used a zero cm airfoil it will require up elevator at all flying speeds. If you used a traditional airfoil with -ve cm then you will need significant up elevator at all flying speeds. A typical plank airfoil will have small +ve cm resulting in up, neutral, and down elevator position across the speed range.

4. The AC will be very close to 25% of chord for most all airfoils irrespective of reflex. The exact number can be found in publications such as Theory of wing sections or online tools.Best source for guidelines for the plank is by Al Blackstorm in sport aviation a few decades ago.
 

rotax618

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The early Arups (were flying wings but not planks) used a Clark Y airfoil, I presume the pitching moment was controlled by the large elevator. The problem becomes less if the chord is increased (lower the aspect ratio). The UFO appears to have an almost flat bottomed airfoil with a relatively sharp LE.
 

oriol

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Airfoils are made stable not by their shape but by simply putting the CG forward enough from their aerodynamic center. All airfoils can be made stable in this way

Got it, thanks ragflyer!

In Anderson´s book there is this very straighforward formula for longitudinal stabilty:

Static Margin = (X neutral point - X Center of gravity) / Medium Aerodynamic Chord

According to the book, a conventional aircraft should have a static margin of 5 to 10% (0,05 to 0,1). Aerowerx mentionned that for a tailles aircraft this value has to be 3 to 4 times higher. That would be something in between 15/20% to 30/40%.

This formula is really helpful in previsualizing the overall possible layout of the aircraft!

Hi Rotax618!

Perhaps you can reduce the moment coefficient by going with a low aspect ratio? I do not know, but then you will pay a price in your CL/CD which will result in a higher fuel consumption. I guess that everything has to be very carefully balanced to make it a nice aircraft.

Cheers,

Oriol
 

Aerowerx

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According to the book, a conventional aircraft should have a static margin of 5 to 10% (0,05 to 0,1). Aerowerx mentionned that for a tailles aircraft this value has to be 3 to 4 times higher. That would be something in between 15/20% to 30/40%.
It has been a while since I read the "Tailless Aircraft" book, but IIRC the reason for this, according to Nickels is...

You need to maintain a sufficiently high static margin during all flight modes and attitudes, particularly nose-up.

Nickels states that some people get themselves in trouble by trying to move the CG back to far in a tailless aircraft in order to get the 5-10% conventional static margin. Then they get in a too-nose-high attitude and the thing flips over backwards, with tragic results. By keeping the static margin at 20-40% this is avoided.

Also note that conventional flaps are not possible on a tailless plank. It is possible, however, with a swept wing by careful placement of the flaps.
 

Aesquire

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Just as a mind tweak... :)

Every explanation of stability and how wings actually fly is a degree of simplification.

A modern flex wing hang glider has wing tips that, in normal flight, are lifting. Not pushing down. What's more, they are lifting both up and forward, at a different angle that the inner parts of the wing. Making that even more weird, there are structures in/near the tips that Will push down if AOA falls below a designed for point, in case of turbulent or maneuvering induced dives. But essentially do nada in level flight.

The overly technical explanation uses terms like total flow field vectors and involves the wing moving air in a surprisingly large volume above, below, behind, and in front of the wing. I don't try to do the math in my head. That takes supercomputers far more sophisticated than NASA had going to the Moon, or maybe better than your cell phone!

It's much easier, and generally true, to just look at the pitching moments from the wing airfoil & Tail/Elevon/whatever, using the books listed above.

What makes a Plank hard, is everything is shorter in distance front to back than most normal, aka boring designs. Less margin of error, less damping of forces.

Everything in life is more complex than they teach you. But once you grasp the synthesis of the different, and often competing ideas, it seems so simple.

Except Economics. That's competing religious cults. They're all nuts. ;)
 

rotax618

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The 2D behaviour of airfoils is not relevant in the case of low aspect 3D. Consider the case of the Facetmobile, its profile wouldn’t work too well on a conventional straight AR >6 wing. An unswept medium AR plank requires careful design, a flat bottomed airfoil is probably not advisable.
 

ragflyer

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Got it, thanks ragflyer!

In Anderson´s book there is this very straighforward formula for longitudinal stabilty:

Static Margin = (X neutral point - X Center of gravity) / Medium Aerodynamic Chord

According to the book, a conventional aircraft should have a static margin of 5 to 10% (0,05 to 0,1). Aerowerx mentionned that for a tailles aircraft this value has to be 3 to 4 times higher. That would be something in between 15/20% to 30/40%.

Oriol

No, typical CG positions on a tailless plank is 18% to 20%. Consequently the static margins are not huge (3% to 5%) in tail less airplanes. Part of the reason is there is limited elevator control power on a plank for too forward a CG. Also damping in pitch is so low that a high static margin can make the dynamic pitching mode a little too active- I think it is called pecking in Nickle's book.

You should check out Al Backstrokes article in sport aviation for design guidelines.
 

raytol

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Nickel's book is definitely a gem! It allowed me to warn an investor in a flying wing project that it could "Peck". It did!
Also have a look at Charles Fauvel's AV-60 and the Fraser Technology F5Fras13 and 15 airfoils. The Fraser site is mainly a Flying Flea site but has some flying wing info.
Another interesting plank design is Scott Winton's Opel from Australia. Scott only weighed 140 pounds and it didn't have much provision for differences in pilot weight but it sure did go!
 

oriol

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Thanks Aesquire for your comment,

When I was preparing my exam to become a pendular pilot, our instructor, who was also the dealer of DTA, showed to us a paper from the manufacturer explaining the aerodynamics of a modern pendular wing. If I do not recall it bad, on the wing tips lift was pointing downwards. Perhaps I am wrong and this only happenned when flying close to stall, to make the wing stable.

Hi Rotax618,

I am not an expert at all. Form hwat I have read very low aspect ratio subsonic delta wings; like the facetmobile or the Lippsich glider, have very different aerodynamics, if compared with 2D NACA airoils. Its is very hard to predict the flow properties on paper and translate them into 3D.

Hi Blane.C,

I love tandem wings and biplanes, but I like a flying plank because it is in theory less draggy and this might result in a lighter aircraft.

Hi Aerowerx,

I am looking into a flying plank with very modest performances and thus it would not require high lifting devices.

The formula I took from Anderson´s book considers the distance between the aerodynamic center and the center of gravity on the horizontal axis. I guess that if you use a high wing the lower center of gravity with respect to the aerodynamic center will also help to provide better static stabillity.

Hi ragflyer,

I read an article by Al Blackstrom on nest of dragons. I have ordered Jim Marske book because he seems to enter into technical details regarding the aerodymamics of his slightly tapered wings; that seem very similar to a flying plank.

I understand that you mean that flying planks do not have their CG on 18%, 20% of the chord. Do conventional aircraft have their center of gravity on that position?

The static margins are of far less value than what Aaerowerx was suggesting on?

I thought that the formulas that serve for a conventional aircraft also serve for a flying wing?

The only difference is that you eliminate the tail momentum contribution of the equation. Then you have to either generate an equivalent momentum by the wing with respect with the CG, or viceversa.

I understand that most flying wings seem to be swept wings, with different airfoils at the root and the tip, to create a downwash that compensates the momentum of the wing.

Thanks!

Oriol
 
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