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Old Sep 26, 2012, 10:23 AM
A witty saying proves nothing.
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Stability demonstrator: High CM airfoil, short coupled tail

I built a little RC model to demonstrate some points about pitch stability that are routinely misunderstood in this forum. It is basically a control line combat planform, based on the old Carl Goldberg "Jr. Satan". I used a very high pitching moment coefficient (Cm) airfoil, a modified version of the Benedek 7406F, which is a highly under-cambered free flight airfoil. My version is slightly smaller in all dimensions.


Span = 707mm
Chord = 195mm
Stab span = 200mm
Stab chord = 58mm
Wing TE to stab LE = 73mm



I had cut some wing cores for a backyard flyer for a friend that never got used, so they are the basis of the airplane. The airfoil had been reduced to 4.81% camber, and the trailing edge thickened for strength in an uncovered foam wing. The airfoil is still very under-cambered, and the Cm should be about -0.11 which is quite high.

I knew the extreme airfoil Cm would put a lot of load on the small stabilizer so I used an inverted airfoil on the stab, and used the tail booms as end plates to enhance the max negative Cl of the stab. It also made the stab easier to hinge at the 1/4c, for minimum load on the servo and pull/spring linkage arrangement. Pull/spring, in addition to being very light and keeping weight out of the tail, loads the servo gears in one direction and removes the backlash and play from the elevator. Since i knew I would have to use a very low static margin to avoid loading up the tail further, I needed all the precision I could get on the pitch control. I extended the stab span by 11mm, to give me about 5% more stab area, to help my heavily loaded stab a little bit.



I did increase the fin area and cut the tips at a slight angle to provide some yaw stability. Control line airplanes don't need much because of the lines and centripetal acceleration.


The airfoil negative Cm translates to a nose down (in upright flight) wing moment that must be counterbalanced by a nose up moment (again, in upright flight) provided by a down force form the stab:

The wing moment:
M = Cm*q*S*c
q= dynamic pressure
S = wing area
c = mean wing chord


To the first order, and assuming the CG is at the neutral point, the tail must provide a moment to balance this:

The moment created by the tail:

Mt = Lt*Clt*St*q
Lt = tail arm CG to tail 1/4c
Clt = Cl tail
St = area of tail


The only variable in these equations is the same on both sides is q, dynamic pressure. Since this approximately varies over the wing and stab the same, the tail Cl required will be constant over the speed range. For my model, in millimeters:

0.11*q*138060*195 = 245.5*Clt*11400*q
Clt = 1.05

This is quite a high Cl for such a low Re airfoil, so the stab will be near stall. If the CG is ahead of the wing 1/4c, the additional load will likely stall the tail at low speed. Fortunately, the aircraft neutral point is aft of the wing 1/4c by about 4mm, so I can have a small positive static margin and still keep the tail below stall.

I have made four test flights so far. The airplane flies very well, but has very quick responses in pitch and roll making it a bit exciting to fly. The stab does stall at low speeds with the CG further forward, so I am limited in the stability margin I can fly with. I have dived it vertically with the power off, and it just dives with no tuck or other odd behaviour. It behaves very well, with one exception.

I did overlook one factor, and got the thrust line wrong. I had aligned the thrust line with the wing zero lift line, like is done with a symmetrical airfoil. The airplane pitches up with throttle like this. The prop diameter is the same span as the stab, and the higher velocity flow off the prop increases the lift from the tail, causing a pitch up. The prop wash only effects about of the wing, so the increase in the wing moment from the airfoil Cm is much less than the moment from the increased tail lift.

I can easily trim it out at any power setting, but it would be nice to have less trim change. It is very neutral in pitch power off, and basically stays in whatever attitude I place it.

I am adding some down thrust to hopefully trim out the pitch with power. I hope to do some more test flying today, and will try to get some video of it flying.

I hope this demonstrates that short-coupled airplanes do not tuck at speed, and that static margin is what determines pitch behaviour, not airfoil Cm.

Kevin
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Old Sep 26, 2012, 11:40 AM
Herk
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subscribed -- interesting project.

It would be interesting to know the weight - you mentioned a vertical dive - I'm guessing that's with power off and prop windmilling. I wondered if the horizontal tail's high pitching moment could overpower the spring and slack the string at high speed. Of course that would promote dive divergence which you indicate is not happening.

With such short coupling and small SM, I'm surprised that the change in downwash with AOA doesn't tend to destabilize the model. Perhaps the continuous prop wash over the tail reduces that effect. It might be interesting to put a folder on it and see if the response is similar while gliding.

None of this has to do with your initial premise - which is correct so long as the surfaces don't get out of the linear part of the CL-Alpha curve.
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Old Sep 26, 2012, 11:45 AM
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Great results.
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Old Sep 26, 2012, 12:26 PM
A witty saying proves nothing.
kcaldwel's Avatar
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Originally Posted by HerkS View Post
subscribed -- interesting project.

It would be interesting to know the weight - you mentioned a vertical dive - I'm guessing that's with power off and prop windmilling. I wondered if the horizontal tail's high pitching moment could overpower the spring and slack the string at high speed. Of course that would promote dive divergence which you indicate is not happening.

With such short coupling and small SM, I'm surprised that the change in downwash with AOA doesn't tend to destabilize the model. Perhaps the continuous prop wash over the tail reduces that effect. It might be interesting to put a folder on it and see if the response is similar while gliding.

None of this has to do with your initial premise - which is correct so long as the surfaces don't get out of the linear part of the CL-Alpha curve.
The all-up weight with battery is 148g.

The stab is pivoted at the 1/4c, and that is where the torsion spring is too, so there is basically no aero loads on the spring regardless of speed. I have used these 0.5mm, 50mm long SS spring wire torsion springs on large DLG surfaces up to the 120kph or so I throw at and never had an issue, and those are not aero balanced surfaces.

This is a pretty small motor (A2204-14T), so I don't think I have any folding props that will fit. I'll have to dig through the prop box.

This is about as marginal you can go on stab volume and airfoil Cm. Anymore Cm, and the stab would be stalled. Gliding was more enjoyable yesterday than power on, because of the power pitch up. Hopefully have that sorted today.

Kevin
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Old Sep 26, 2012, 03:46 PM
Herk
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Originally Posted by kcaldwel View Post
The all-up weight with battery is 148g.
The stab is pivoted at the 1/4c, and that is where the torsion spring is too, so there is basically no aero loads on the spring regardless of speed.
Kevin
Might want to think that line through just a bit.
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Old Sep 26, 2012, 04:11 PM
A witty saying proves nothing.
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Well, the stab has maybe 1 -2% camber (sanded airfoil in 1/8" balsa), so there is a tiny Cm load. It won't be anywhere near enough to overcome the spring.

Kevin.
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Old Sep 26, 2012, 04:21 PM
Herk
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Originally Posted by kcaldwel View Post
Well, the stab has maybe 1 -2% camber (sanded airfoil in 1/8" balsa), so there is a tiny Cm load. It won't be anywhere near enough to overcome the spring.

Kevin.
Got it - OK -

From your description, I thought maybe it had a lot of camber. Couldn't really tell from the photos
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Old Sep 26, 2012, 08:45 PM
A witty saying proves nothing.
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Videos are up on Vimeo. These are my first attempt at a helmet cam! I drilled a hole in the visor of my bicycling helmet and put in a wedge washer to get the angle better, and bolted my Casio point and shoot to the helmet. Fortunately there was no one else at the field today, so I didn't have to explain why I have to wear a helmet for walking around...

This video (033) is a bit better I think:

https://secure.vimeo.com/50261376

but the other (032) has some bigger dives in it:

https://secure.vimeo.com/50258747

Anyway, they came out better than I expected, even after being compressed for uploading.

It's kind of a manic little airplane - sort of like a control line combat airplane with the strings cut! - but it behaves very well. It requires just a bit of down elevator for inverted. That also shows that the pitch trim difference between upright and inverted is almost entirely due to the static margin, and that wing camber has little to do with it.

It needs some aileron differential, but I couldn't figure out how to do that on a JR 8103 Tx with a 4 channel Rx.

The drag inverted is very high, and the airplane slows noticeably any time the Cl gets near or below zero because of the airflow separating on the bottom of the high camber airfoil. This means it doesn't pick up a lot of speed in a vertical dive even with full throttle on the mighty 2s A2204-14T. But it does fly inverted just fine, and even does outside loops although that really kills the speed.

I measured the stab angle for trim, and it is about -9 degrees to the wing zero lift line. If the wing was at 3 degrees AoA (chord line still -2 degrees to the free stream!), then the tail would be at 6 degrees to the free stream. Since the tail is very close to the wing, the down wash will have a large effect on the actual stab AoA. I don't feel like doing that much figurin' right now. It flies fine.

It still pitches up at launch, because the tail is in the prop slip stream, and the wing largely has zero airflow. The wing nose down moment doesn't come in until the wing gets some airspeed, so there is always a pitch up on launch from the tail pushing down in the prop flow. It is much better otherwise with the 5 degrees of down thrust I added.

It would be better behaved with a symmetrical airfoil on the wing. It would launch without pitch-up, it would fly inverted with a lot less drag, and would have less drag overall because the tail would not have to work so hard to control the negative wing Cm. But even the highly cambered free flight section isn't too much of a handicap for aerobatics if the CG is in the right place.

I think the neutral point is a few mm further back than Dan's excellent CG calculator indicates. The spreadsheet does not take into account the improved stab efficiency from the end plate effect of the fins, so in this case it is a bit conservative.

Many people align cambered sections by their chord line, or worse yet, the flat bottom like on a Clark Y, and then end up having to put the CG far forward to trim the large incidence angle on the wing. This makes the airplane balloon with every speed increase from the throttle or a gust, and it requires a huge amount of down elevator to fly inverted. This is not the airfoil's fault, it is because the CG is too far forward.

Anyway, off my pitch stability soap box for now.

Kevin
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Old Sep 26, 2012, 08:55 PM
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Quote:
Originally Posted by kcaldwel View Post
Many people align cambered sections by their chord line, or worse yet, the flat bottom like on a Clark Y, and then end up having to put the CG far forward to trim the large incidence angle on the wing.
Kevin
Probably because that's what "looks right" to them.
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Old Sep 27, 2012, 10:21 AM
An itch?. Scratch build.
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I think I can see what you have done, thought the maths side may need a new routine in Google Translator for me

If I have it right, you have a model with an under-cambered section that is not particularly affected in pitch by changes in speed. Ending up with a model that flies similar to one with a symmetrical section.

This is where I ask that awkward question, Why ?

Not so much why it works, that I can basically understand, (hey, I'm not quite as dumb as I thought), but why do it ?

For anyone with a conventional trainer model using a cambered section wing, wouldn't reducing the wing incidence to stop speed change nose ups, (which I think you are getting at), also affect the basic natural pitch recovery affect. Rather like removing the dihedral would also remove lateral stability recover.

If reducing the incidence angle will reduce the speed/lift relationship, isn't that like saying trainers should have symmetrical section wings ?

Or have I missed something here and this is purely related to short coupled stabs ?, as what you are then doing is adding some reflex similar to a flying wing, but with a gap between the wing and stab ?

Sorry, I'm blabbering on, and thinking while typing, (or is it typing, then thinking ).
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Old Sep 27, 2012, 12:06 PM
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Originally Posted by eflightray View Post
If I have it right, you have a model with an under-cambered section that is not particularly affected in pitch by changes in speed. Ending up with a model that flies similar to one with a symmetrical section.
It sounded to me like he was trying to demonstrate the difference between stability and trim.

Stability is entirely a function of the distance between the neutral point and center of gravity. The airfoil section of the wing is not part of the stability calculations.

Trim is a function of the aerodynamic forces that your surfaces can produce. Since the airfoil pitching moment is an aerodynamic force it counts in the trim calculations not the stability calculations.

For instance you can use a flat bottomed airfoil in a plank style flying wing chuck glider and as long as the CG is far enough forward it will be stable but it will only be in trim upside down because planks rely entirely on the airfoil pitching moment for trim.

--Norm
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Old Sep 27, 2012, 12:21 PM
An itch?. Scratch build.
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Originally Posted by nmasters View Post
It sounded to me like he was trying to demonstrate the difference between stability and trim.

Stability is entirely a function of the distance between the neutral point and center of gravity. The airfoil section of the wing is not part of the stability calculations.

..................................................

--Norm
Now that one has me confused.

Surely the airfoil does have an affect on stability, unless you reduce the incidence angle to the point where it is no longer functioning as originally designed.

Perhaps I am just not thinking in the same way as the difference between stability and trim.
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Old Sep 27, 2012, 12:33 PM
Herk
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Originally Posted by eflightray View Post
Now that one has me confused.

Surely the airfoil does have an affect on stability, unless you reduce the incidence angle to the point where it is no longer functioning as originally designed.

Perhaps I am just not thinking in the same way as the difference between stability and trim.
I think perhaps you were already confused. That is exactly what Kevin was trying to clear up with his demonstration.

The confusion is just what Norm has described. You are mixing the conditions governing flight trim with those that affect stability - somehow thinking that they are the same thing. If you understand Kevin's demo it should be pretty clear.
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Old Sep 27, 2012, 12:36 PM
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Originally Posted by eflightray View Post

Surely the airfoil does have an affect on stability, unless you reduce the incidence angle to the point where it is no longer functioning as originally designed.
Pitch stability is determined by the changes in the moments that follow a change in the angle of attack. The moment produced by camber does not change with angle of attack (as long as linearity is valid), so it does not contribute to stability.
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Old Sep 27, 2012, 01:33 PM
A witty saying proves nothing.
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Originally Posted by eflightray View Post
If I have it right, you have a model with an under-cambered section that is not particularly affected in pitch by changes in speed. Ending up with a model that flies similar to one with a symmetrical section.

This is where I ask that awkward question, Why ?
I did it to demonstrate that the wing Cm is not part of the stability equations for the good reason that airfoil Cm it does not affect stability. The neutral point of this airplane is in exactly the same place it would be with a symmetrical airfoil, and the stability is the same with a high Cm airfoil with a given static margin as it would be with a symmetrical airfoil.

It demonstrates the wing airfoil Cm only effects trim, not stability.

It also demonstrates that a high Cm wing does not over-power a close coupled stab as the speed increases. Stability (assuming airfoils without low Re hysteresis or steps in their lift curves) is basically speed independent.

Quote:
Originally Posted by eflightray View Post
For anyone with a conventional trainer model using a cambered section wing, wouldn't reducing the wing incidence to stop speed change nose ups, (which I think you are getting at), also affect the basic natural pitch recovery affect. Rather like removing the dihedral would also remove lateral stability recover.

If reducing the incidence angle will reduce the speed/lift relationship, isn't that like saying trainers should have symmetrical section wings ?
I was trying to demonstrate stability is independent of airfoil section, not that trainers should use symmetrical sections.

Incidence is not what creates stability, or what causes "nose ups". Both are function of the stability margin. The problem with having a lot of built in wing incidence, is that people try to trim the airplane out by moving the CG forward. This increases the stability. They could also trim it out by adding lots of down trim, but that is visible and looks bad.

I've never been convinced that trainers with more than about a 10% static margin are easier for beginners to fly. Big static margins cause the airplane to balloon or dive radically with every gust, and to nose up with every speed increase. It seems they end up fighting with the airplane more, and it certainly makes it harder for anyone to fly it on a windy day with the resulting turbulence down low.

Kevin
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