coefficient of confusion, Cm

[HELModels]

When I use Xfoil to look at foils I always see the moment coefficient as a negative number in viscous mode. I purposely compared a NACA 6412 to the plank foil HS 130. The HS 130 has a much smaller number, compared to 6412, for the Cm at wide range of alpha, but it still shows both as negative numbers. I dont understand this, so I used the CPV instruction and got these pressure plots. It is obvious in the plots that the forces are trying to point the nose of the HS 130 up, which would be a positive Cm. The comparison is at the same Cl of 0.6 for both foils.

Any explanations for why Xfoil always shows the cm as a negative number in viscous mode when experience says it isnt?

[HELModels]

Duh! The negative Cm only means that the Aerodynamic Center is a smidgen behind the 1/4 chord. The pitching moment is not the same thing as a coefficient. I think I get it now, maybe. If the lift increases suddenly, then the c.p. will shift back, causing a pitch up, and a CG forward of the A.C. will counter that. Is this correct? Any help appreciated.

[kcaldwel]

Actually, the 1/4C point is chosen as the reference for Cm because the pitching moment is relatively constant about that point for most airfoils. Changes in lift do not result in big changes in Cm about the 1/4C, which makes it an easy point for calculating the pitch characteristics of a wing planform or entire aircraft.

I don't have the cordinates for the HS130 you used, but if it has a negative pitching coefficient, it will need some device to provide a positive pitching moment to counteract both the remaining airfoil negative Cm, and the CG negative pitching moment. Elevons deflected up is one method, which I suspect must be used with the HS130 on a plank flying wing.

Of attached plots of the Cm for the 6412 and another flying wing airfoil over a range of angles of attack. A tail with a long lever arm would be required to counteract the strong negative pitching coefficient of the 6412. The MJP711f-3 has a slight positive Cm over most of the range of angle of attack, so it would be pitch stable in a plank configuration.

Kevin

[HELModels]

Thank you, Kevin. That clears up some of the confusion which started when I went to this site:

http://www.aerodesign.de/english/profile/profile_s.htm#sipkill

http://www.aerodesign.de/profilelight/pl09_bild_02.gif

It has the HS130 coordinates and some polars which show the Cm as positive. It looks like the polar is done in inviscid mode. :confused:

[kcaldwel]

I'm pretty sure that is actual wind tunnel data he has there. But, I think he is reading the graph wrong for the HS 130 and the JWL-065. The Cm on the centre graph is more negative going upward. I read a max negative Cm for the HS 130 of -0.055 or so - I think at Re 100k.

So I think your Xfoil results are pretty close. From the graph I see Cm = -.013 at Re = 400k, and maybe Cm = -0.014 at Re = 100k.

He's read the graph wrong I think.

Kevin

[HELModels]

Of attached plots of the Cm for the 6412 and another flying wing airfoil over a range of angles of attack. A tail with a long lever arm would be required to counteract the strong negative pitching coefficient of the 6412. The MJP711f-3 has a slight positive Cm over most of the range of angle of attack, so it would be pitch stable in a plank configuration.

Kevin

I'm not convinced the HS130 is so great a plank foil. Do you have the coordinates for the MJP711f-3, or a link to them? That has a pronounced positive Cm which I havent been able to find in other foils.

Thanks,

Harry

HS 130
1.000000 0.000000
0.992985 0.000164
0.979993 0.000630
0.965042 0.001500
0.949247 0.002676
0.933097 0.004086
0.916778 0.005669
0.900399 0.007398
0.883938 0.009255
0.867370 0.011212
0.850752 0.013236
0.834132 0.015315
0.817501 0.017448
0.800831 0.019625
0.784121 0.021833
0.767388 0.024058
0.750651 0.026284
0.733916 0.028499
0.717185 0.030698
0.700465 0.032877
0.683768 0.035030
0.667098 0.037148
0.650452 0.039221
0.633822 0.041244
0.617198 0.043212
0.600579 0.045124
0.583966 0.046974
0.567361 0.048758
0.550766 0.050471
0.534181 0.052109
0.517603 0.053667
0.501031 0.055141
0.484462 0.056529
0.467895 0.057826
0.451330 0.059031
0.434771 0.060141
0.418222 0.061151
0.401683 0.062056
0.385155 0.062852
0.368637 0.063534
0.352131 0.064098
0.335645 0.064538
0.319186 0.064847
0.302760 0.065015
0.286367 0.065034
0.270006 0.064893
0.253685 0.064584
0.237420 0.064097
0.221232 0.063414
0.205129 0.062519
0.189111 0.061392
0.173179 0.060017
0.157347 0.058378
0.141644 0.056456
0.126124 0.054226
0.110853 0.051669
0.095864 0.048749
0.081156 0.045420
0.066937 0.041665
0.053686 0.037575
0.041527 0.033156
0.030464 0.028366
0.021784 0.023841
0.015624 0.019993
0.010986 0.016506
0.007278 0.013129
0.004470 0.009989
0.002507 0.007328
0.001180 0.005114
0.000377 0.003186
0.000020 0.001398
0.000108 -0.000361
0.000644 -0.002163
0.001661 -0.004027
0.003262 -0.005892
0.005626 -0.007652
0.009007 -0.009308
0.013594 -0.011047
0.019662 -0.013091
0.027661 -0.015333
0.038143 -0.017605
0.051243 -0.019848
0.065875 -0.021891
0.081072 -0.023603
0.096773 -0.025037
0.112864 -0.026248
0.129152 -0.027272
0.145540 -0.028144
0.161995 -0.028882
0.178505 -0.029498
0.195071 -0.030006
0.211690 -0.030419
0.228357 -0.030752
0.245064 -0.031014
0.261802 -0.031218
0.278565 -0.031369
0.295343 -0.031474
0.312130 -0.031536
0.328923 -0.031557
0.345719 -0.031539
0.362522 -0.031484
0.379335 -0.031393
0.396156 -0.031269
0.412982 -0.031115
0.429807 -0.030930
0.446630 -0.030715
0.463451 -0.030469
0.480272 -0.030193
0.497095 -0.029886
0.513919 -0.029549
0.530744 -0.029183
0.547567 -0.028786
0.564383 -0.028359
0.581189 -0.027900
0.597982 -0.027405
0.614767 -0.026872
0.631548 -0.026299
0.648327 -0.025686
0.665102 -0.025032
0.681870 -0.024337
0.698628 -0.023597
0.715382 -0.022813
0.732137 -0.021983
0.748894 -0.021109
0.765654 -0.020193
0.782412 -0.019233
0.799156 -0.018230
0.815874 -0.017180
0.832560 -0.016077
0.849222 -0.014912
0.865866 -0.013679
0.882475 -0.012375
0.899025 -0.010991
0.915524 -0.009509
0.932007 -0.007929
0.948479 -0.006258
0.964601 -0.004523
0.979769 -0.002724
0.993067 -0.001008
1.000000 0.000000

[kcaldwel]

I don't know anything about the MJP airfoils. They came with the Profili database, and it said "Flying Wing" so I ran it. I've attached some text files of two MJP flying wing airfoils.

There are some others here that have a positive Cm, the E184 and E186 in particular. Also looks like the the graphs on these are identical to the one for the HS 130 you referenced, and it says that it is XFOIL output, so I guess the HS 130 polars are XFOIL results too. Notice the Cm scale is inverted on those polars also, with negative up.

http://www.ae.uiuc.edu/m-selig/flyingWingAfs/

Kevin

[HELModels]

Thanks again, Kevin. I think part of the problem is I keep running Xfoil at 100,000 Re and some of these "plank" foils dont show a consistently positive Cm until 200,000. This might explain why AR's on planks arent that high, to keep the Re up and Cm positive. Does this seem like a reasonable conclusion?

[MarkusN]

This might explain why AR's on planks arent that high, to keep the Re up and Cm positive. Does this seem like a reasonable conclusion?
Definitely. Already in the seventies it was known that the positive Cm calculated for the E184 with the Eppler code could not be realised in reality and that higher reflex was necessary to get it to fly on a plank. It was also found that higher Re helps.

As flying sub-critical and separtion bubbles mostly affects airflow over the rear part of the wing section this does make sense.

[Brandano]

Well, the AR on flying planks can't be too high for several reasons. I think that the main one is the inertial coupling that will change pretty much any control input in a tendency to enter an uncontrollable tumble. A longer and narrower shape is less prone to this, and has a bigger control arm for the pitch input.

[biber]

Planks have to have at least 200 mm chord to work well, even better 250 mm or more.
Seems to have been the valid rule of thumb since ever.

It's all about Reynolds numbers!

And with the rather low Cl_max of the typical plank airfoils you needn't to drive the AR too high, anyway.

One should be careful with theoretical Cm values that are not actually measured in reality.
One of the hardest task for the existing airfoil evaluation codes seems to be forecasting the precise Cm.
At least that is for us non professionals.
Real professionals like Dr. Drela and others might be able to give better guesses.
Codes like XFoil or the Eppler and Hepperle stuff need to be operated properly.
In addition to that, even little building imperfections will have quite a big impact on that.

In our first Multibumm prototype we had about 1.5° of washout to compensate for the slighty negative theoretical Cm.
Gave us wonderful loops with all controlls flush zero.
We then went back into theory and recalculated and estimated the actual Cm from the control offsets needed in reality to maintain straight flight at about zero lift.
Turned out that we seemed to have Cm very close to zero instead of the calculated -0.02 that lead us to believe to need the washout.

Next proto was without any washout and hit the sweet spot.

biber

[HELModels]

Planks seem trickier to me, but there are lots of examples like the zipper. I know Biber has done some nice wings with sweep and twist. His warning to use Xfoil properly is why I am asking all these questions. Xfoil has a command for changing the reference of the Cm, which is 25% by default. This suggests that some airfoils dont have a NP of 25%. I have no idea how to determine which foils should have that setting tweaked, but I tried it anyway. :eek: I tried it on the HS130 to see how much I could move the Cm plot. I moved the reference back to 27% and the Cm plot moved into the positive. I guess the safer thing to fiddle with would be the camber high point location.

[biber]

Moving the point of reference can be sensible if the Cm vs. alpha graph shows a noticable gradient.
By shifting the reference you may be able to approximate a constant Cm.
The new point of reference would then roughly be the true NP.
That makes clear what you desire a Cm vs. alpha graph to look like,
especially for flying wings and even more especially for the plank type.
You want it to be as linear as possible, because anything else would mean a hopping and suddenly shifting NP
that might give you a hard time tweaking the CG and setting up tuning the model.

biber

[mnowell129]

Why so much interest in Cm of the airfoil?

Doesn't stability require Cm(alpha) to be negative which generally means the CG is ahead of the AC and Cm(zero) to be positive meaning some kind of nose up trim (elevon, twisted swept tip, etc for a plank)?

Isn't a negative Cm for the airfoil going to be down in the noise compared to the negative Cm due to CG to AC displacement for stability?

Why not just pick a good airfoil and trim as usual?

??

[kcaldwel]

The CG has to be ahead of the aircraft neutral point for static stability, usually 5 to 15% of Mean Aerodynamic Chord. On a plank flying wing, there is no other force other than an airfoil with a positive Cm to counteract the nose down pitch from the CG location.

A "normal" airfoil with a large negative Cm would require huge elevon deflection which would destroy the performance. Airfoils with near zero or positive pitching (nose up) moments are required for plank flying wings.

Kevin

[mnowell129]

I think my point is that with 5 to 15% static margin, the nose down moment from this is much greater than the nose down moment from the airfoil. So you will carry reflex or up elevon to trim out the nose down moment from static margin. I think the additional up elevon due to differences in airfoil is small compared to the trim carried due to static margin.
I guess I should look at some numbers to verify but it looks like Cm is small compared to Cl.
Suppose a dynamic pressure (Q) of 2 lbs, a Cl of 0.5, Cm of .005 and a 1 pound model with 6inch (.5 ft) chord, with 10% SM.
The nose down moment from airfoil is 2*0.005 * (.5) (Q * Cm * chord) = 0.005 ft-lb = 0.96 ounce-inch.

The nose down from SM is 1 lb * 0.1 * 0.5 = Lift * 10% of .5 foot chord = .05 ft-lb = 9.6 ounce inches.

So of the ~11 ounce inches of nose down moment only 9% is due to airfoil and the rest is static margin. So even if the airfoil Cm is zero you still carry 10 ounce inches of nose up trim in the elevons.

Maybe I'm missing something or the math is wrong, but it still looks like the airfoil moment is a smallish part of the equation.

[kcaldwel]

Most planks have chords more like 10", and typically fly with static margins down around 2% to avoid the need for a lot of up elevon trim, which kills performance.

Why design a plank airfoil, and then have a bunch of elevon deflection that changes the performance at trim? Far better to design an airfoil with the required positive Cm. You are going to have to trim for positive Cm anyway, so you might as well optimize the airfoil for that flight point.

The airfoil has to be the entire positive Cm with a plank. Some sweep sure helps, which must be what is discussed above, or washout wouldn't provide a positive pitching moment. If the 1/4C is straight, the airfoil has to do the work.

Kevin

[HELModels]

I thought this would be interesting, so I took the phoenix airfoil and ran it without deflection and finally with flap deflected up. It has a flat Cm, so whether it needs some up trim or not, it should be stable for the reason that Biber mentioned - Cm is steady. I've read over in slope, how special mixes are needed on some planks to trim out the wild changing pitch, as speed changes. The phoenix seems like it wont be so wild.

[kcaldwel]

It's actually got quite a kink in the Cm at low alpha - 0 to 2 degrees. That will make for some interesting pitch characteristics at high speeds.

You really want an airfoil with a flat Cm line, or at least one with a constant slope that indicates the Cp is maybe slightly for or aft of the 1/4C. A kink like isn't a good sign. Any airfoil will have the Cm line move up and down with elevon deflection.

Notice how the drag goes up with elevon deflection as well.

Kevin

Kevin

[HELModels]

I hear you about the kink, but it isnt really there for the polars without any flap deflection. Maybe it is saying go gentle on the elevator, which seems typical for a plank. I only ran that one to see how a deflection up would look. Another thing about the phoenix is that a high wing loading is suggested to dampen out things, so maybe that kink is a real concern. The other thing about that kink is that all the plank foils I've looked at have some spot where the Cm goes whacky and changes direction.

[HELModels]

The phoenix isnt all that bad, but the HS130 has a better pedigree of proven applications. I found the coordinates for the PW51 which is even better. They all have some goofy spot in the Cm, but along the lines of the argument of mnowell129, the scale of the goofy spot in the Cm plot should be considered. The companion to Xfoil, Pplot exaggerates the scale and can make a blip look like a mountain.


Merry Christmas