|Jan 28, 2013, 03:57 PM|
"Plank" wings and pendulum stability
I've got yet another question to try to sate my seemingly endless curiosity when it comes to speculative analysis on different aircraft designs. I've been thinking for a while about making a "plank" flying wing. Firstly, due to interest in the simplicity of the design, but also because it seems to be a rather unique creature when it comes to "full-scale" aircraft. The only instance of such designs being operated outside of a lab seem to be the NASA solar planes that buzzed around in the 80's and 90's with their tiny electric motors and solar-paneled wings.
Despite the stability issues associated with flying wings, these things seemed to fly alright (granted...it was completely run by a computer. Perhaps that's the entire reason.). What I noticed is that they had narrow pylons suspended from the wings, and wondered if perhaps this was the key to stability of a flying wing. Now i understand a flying wing isn't "truly" a flying wing unless it's a wing and nothing else, but it seems that little harm could be done in the way of drag if a tall, thin pylon was added at one or several points beneath the wing, putting the center of gravity below the airfoil itself, and thus cancelling out the need to produce a lot of extra drag by having elevons trimmed upward in order to compensate for the forward CG that's providing your stability?
Unless they're just made out of some ridiculously lightweight tissue-paper like material, I can't help but imagine all these under hanging pylons must be lowering the CG at least somewhat below the chord line.
Say your CG is at 25% or 30%, or some place very very close to the center of lift - but several inches (or feet, depending on the overall scale, you get the idea) below that actual point? What i mean is, longitudinally, your CG is very close to your center of lift, but lower vertically. It seems like a disturbance like turbulence, a gust, etc that would knock the aircraft out of its trimmed attitude would be corrected by simply having the CG well below the center of lift, like a pendulum, and the weight would just settle the plane back to trimmed attitude.
Now, i realize that an elevon on a straight flying wing has a VERY small moment, and must therefore have either a lot of surface area, or deflection angle to be effective. I'm sure this creates quite a bit of drag as well, so perhaps it would be possible to have a very small weight that trims the balance of the aircraft at the bottom of the pylon. This weight could be a small battery, or a small fuel tank that's moved forward or aft very slightly based on the trim requirements of the aircraft, controlled by some sort of "back/forth" servo, thus alleviating the need for excessive elevon deflection as a result of small moment arm.
With all this being said, obviously this would NOT be an aircraft for aerobatic maneuvering, or any fancy flying. But I don't mind that. I'm mostly interested in aircraft designs for their maximum figures of L/D efficiency or max altitude, since my goal is to find ways to fly higher and longer with less power.
Am I crazy, or could this work?
|Jan 28, 2013, 04:31 PM|
|Jan 28, 2013, 04:39 PM|
|Jan 28, 2013, 04:46 PM|
However, a low-mounted powerplant could be one more means to maintain a desired pitch without extreme elevon deflection.
That's the basic idea anyway. The plane itself isn't really much to look at. I've just thrown it together in a CAD program to flesh out the basic dimensions.
If the prototype works, I'll probably build a 120" by 10" or 12" plank, depending on whether or not I get excessive wing stress from the higher aspect ratio.
|Jan 28, 2013, 05:01 PM|
One streamlined body will have considerably less drag then two. Half the intersections, more enclosed volume for the wetted area, etc. The performance would be better with just one pylon, drag wise.
Pendulum stability works for flying wings. That is entirely how paragliders work, and contributes to hang glider stability.
There is an unfortunate side effect, especially for a plank where you want the CG very close to the neutral point. The CG moves forward and back as the wing pitches up and down to different AoA. It moves forward relative to the wing MAC as the wing pitches up to higher AoA, which increases the stability margin for slow flight. This means it requires more up elevon to hold it at higher Cl, which results in a lot of reflex in the airfoil when you are trying to fly slow.
The CG moves back as the wing goes to lower AoA, which reduces the stability margin for fast flight. For a plank, it may be quite possible that the CG moves behind the aircraft neutral point at low AoA. This can make the airplane pitch unstable when trying to fly fast or if the wing is gusted to a low AoA. This has always been a problem with hang gliders.
Hmm. Maybe a pylon with the mass above the wing?
|Jan 28, 2013, 05:15 PM|
That's a good point. It makes me wonder whether it's better to go to one of the extremes (very low CG OR high elevon deflection), or whether its best to settle on some compromise between having a *slightly* low CG, while still maintaining most trim with elevons?
I guess I'm making the assumption here that most of the flight would be done at a given speed/angle of attack that I'd be trimmed for, thus not requiring much elevator. And to reiterate, there may be a possible system that could be made to move a weight like a battery to shift the CG to maintain a given attitude. This could be a servo connected to the weight that's on it's own channel mixed just the right amount to respond to elevator input. Obviously a measure like this wouldn't be perfect or precise, but it would help.
It seems like this idea has a lot of potential as long as I'd be willing to settle with a very narrow maneuvering envelope.
Here's a very rough CAD sketch of what I'm proposing
The elevator is represented by red, and the ailerons by blue, with the green circle being the prop arc. (I prefer not to mix channels)
|Jan 29, 2013, 12:26 AM|
Having the weight lower than the wing will help but it's not a replacement for a proper airfoil that has a positive pitching moment airfoil. THAT is still your first and main line of "defense" towards getting a good flying model.
You will also have a serious issue with the lack of any fin area. That solar powered NASA design used computer guidence for the stability. Our models are not so lucky. So you still need a bunch of fin area behind the CG location. The further back the less you require.
Now the paragliders and hang gliders do use a very low CG location for their stability. So the pendulum stabilty IS a factor. But to achieve this with your model I'd suggest that you need to make the pylon deeper and put lots of the airborn gear deep in the base of the body fin. Or if you were to make the wing with a TALLLLLL pylon and a little streamlined pod about 1.5 to 2 chords below the wing and put as much gear as possible down that low then you could quite likely get away with an airfoil with a low negative pitching moment. Airfoils such as the MH 62 that has a nominal -.004 Cm. Such an airfoil would not require a great degree of pendulum effect to provide the stability needed.
By the way, you're wrong about there being no regular plank style aircraft. There's been lots of various model plank style flying wings and some full size ones. Keep in mind that the factor that determines if the wing is a plank style or not is very little or no sweep angle to the wing's quarter chord line. Fauvel has a whole bunch of plank flying wings in full size flying. And there's been oodles of model designs done over the years. What all these airplanes, full size and model, have in common is the use of airfoils with positive pitching moments.
The shifting weight idea has been done on plank style wings before as well. The weight shift works well for trimming the flight speed and the elevator for use in turns or where a sudden correction is needed.
|Jan 29, 2013, 03:25 PM|
Joined Oct 2004
Weight shifting has also been done in hang gliders, and works well if you have a human in the control loop that can evaluate forces and adjust controls accordingly. It might be feasible with onboard logic, but I don't think it to be trivial.
|Jan 29, 2013, 04:03 PM|
I don't think it would necessarily be trivial, but i think with the right channel mixing it could be easy to handle. You could basically just have a servo with the arm facing downward, attached to a little rod or stiff wire, with either a small lead weight at its base, or perhaps a small auxiliary battery. The servo would probably be on a channel controlled by a knob on the radio for fine-tuning, and then mixed to the elevator so that it only moves out of its trimmed position in order to compensate for the change in pitch angle. The CG would ideally be close enough to the center of lift that even the small shift in CG caused by the servo moving its weight back and forth would accomplish most, if not all of the trimming required, so that an excessive amount of drag wouldn't be brought on by constant elevator deflection.
I've heard from a few people who've built and flown planks that the "by the book" way to do it is have an airfoil with reflex camber, thus giving a positive moment, which is then countered by forward CG for stability, however, from what I'm told, these types of airfoils have very poor drag polar characteristics, and almost cancel out the benefits of a flying wing in the first place. Rather than doing that, I'd like to use an airfoil with more desirable drag polar characteristics, and then use the pendulum idea to stabilize it.
While i realize, given all the potential measures taken to make this work, it may cancel out the advantages, as mentioned with the reflext camber example, it seems like a project worth pursuing, if nothing else than simply to see how efficiently a design like this could perform, and knowing for sure whether or not this is viable compared to conventional archetypes.
Any thoughts on these points?
|Jan 29, 2013, 04:29 PM|
Check out the Wihock 60, Pg. 5:
I think you need to shift more than a servo, at least the battery pack. And the shifting mechanism should prevent stripping of the servo on a hard landing.
|Jan 29, 2013, 07:48 PM|
You will need to either shift a small weight over a longer distance or a bigger weight over a short distance. Either way it'll need to be more than you seem to think it needs to be to get a reasonable CG shift. And either way simply hanging that sort of weight off the arm of a servo is just asking for landing impact to bust the gear train.
In any event a good first place to start is to build a free flight test glider. If you can't make a concept glider fly in a stable manner for even a regular straight ahead test glide then you sure won't be able to make a radio control model fly correctly either.
Because you want to try stabilizing a negative pitching airfoil that has at least a slight to moderate camber a good aproximation would be a flat sheet balsa wing that has an arched shape camber bent into it by adding ribs to hold the camber.
Generally an airfoil for a glider has around a 1.5 to 3% camber value. So if we compromise on 2% and form this into some 1/16x3 inch balsa it means we need 3 x .02 = .06 or 1/16 inch worth of camber at the high point along the bottom surface of the wing. Now that's pretty thin so you'd likely want to make the ribs from 1/8x1/16 and sand the arc shape over only the first 1/16 and leave the rest to stiffen the ribs to hold the camber in the wood.
Alternately you could make the wing from 3/16 balsa and carve and sand a hand launch glider like airfoil into the thickness to get your camber. A 3x16 or 3x18 wing should prove stiff enough and sized suitably to give you enough wing area to carry up to a good 1/2 to 3/4 oz of lead as the pendulum.
Once done you can play with a weight on a longer than you think you need length of a pylon that extends down from the center of the wing. I'd start with more weight and lower down than you think you need and work at getting it to glide in a stable manner first. At the same time start with the CG location further ahead in the "normal" plank region of around 15 to 17%.
Assuming you can achieve stable long test glides with this setup then start playing with how much you can reduce the weight before the wing misbehaves. Then go back to the heavy weight and see how far up the pylon you can get it before the wing similarly misbehaves. In each case note where the vertical location is of the model by measuring the balance point along the pylon. The idea is you want to see the relationship of weight to CG vertical position for smaller and heavier weights. Now you can similarly start playing with shifting the CG back and see what it takes to restore stable flight.
At some point if you get this all working you can then play with how much of a portion of the pendulum weight you need and how far it has to shift to shift the glide trim from near stall to fast but non diving high speed flight.
Remember that you still need a fin. ESPECIALLY since the pylon is going to be a destabilizing surface.
|Jan 29, 2013, 09:02 PM|
Using the normal aircraft stability equations, it is actually the drag of the high mounted wing that develops the moment around the CG, not the weight acting as pendulum. The CG will be below the wing but not as low as the weight in the pylon because of the weight of the wing up high. You must use the vertical CG location of the entire airframe.
It is the change in drag with a change in wing Cl that matters to the slope of the stability curve (dCm/DCl). The curve must have a negative slope for stability
For the wing:
dCm/dCl = x/c + Cl * [ 2/pi*e*A - 0.035/(dCl/dalpha)] * z/c
x = horizontal distance from CG to wing MAC, negative if CG ahead of MAC
c = mean chord
e = wing efficiency factor (maybe 0.95 for a good planform wing)
A = aspect ratio
(dCl/dalpha) = the change in lift coefficient per degree change in the wing angle of attack
z = vertical height of the wing MAC above the CG
It is interesting that the stability contribution from the high mounted wing is a function of wing Cl. At low lift coefficients (fast flight) the stability contribution will decrease to maybe 1/10th what it is at high Cl. The high mounted wing will be unstable at negative Cl, such as inverted flight or if a vertical gust causes a negative Cl.
The second term is somewhere in the neighbourhood of - Cl/10 * z/c. For a Cl = 1, the vertical distance of the wing above the CG is about 1/10th as powerful as the horizontal distance term.
How far can you get the CG below the wing, when you take into account the weight of the wing? Do you want your stability a function of wing Cl?
Hang gliders have always had to have luft lines or dive sticks to add reflex to the airfoil at low Cl to overcome these problems. Paragliders just collapse into that nice defensive ball...
|Jan 30, 2013, 01:36 PM|
Also for more 'planks', try the - Flying Wings forum
Click on the - Search this Forum, (right hand side), type, plank, set it to Show Threads, click Go.
You should get around 40 threads with plank in their titles.
Plus there other various shaped flying wings in that forum.
|Jan 30, 2013, 10:41 PM|
I'd just like to comment a bit on this:
One of the earliest is the Stabiloplan:
The marines used to operate a plank style UAV. It was called the Dragon Eye:
And the French aircraft designer Charles Fauvel built a series of planks, mostly gliders:
There are many others. These were just the few I remembered and managed to google in the past few minutes.
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