subdivide the curves and use one of these: ?

http://rcwingcog.a0001.net/V3_testing/index.html?i=1
https://rcplanes.online/cg_calc.htm
http://www.tailwindgliders.com/Files.html#Files

not a nice solution, though
trying to find something better
i just like my splines in Fusion360

not sure how (and if) to make a fuselage and tail, still thinking
need some input on that, too

hi
this was moved from the general sailplane forum to here in hopes of getting more and different input

It's still all about the Mean Aerodynamic Chord. The issue comes in finding the chord for something with this many curves and points.

I'd have to download and install the spreadsheet files in the third link before commenting on those. But your second link that takes you to the CG calculator at least has a link to a page that has an option for a 5 panel wing. You'd need to "fake" a tail section to fill the form in but what it would give you would be the MAC width and location. But with the MAC you could work on a CG location of somewhere around 17 to 22% of the MAC which is often the range used on plank style flying wings. The final CG relying heavily on the pitching moment of the airfoil used.

With 5 panels to play with you should be able to approximate your swoopy shape into 5 reasonably similar polygons that average out the area for each of the five curved portions.

The other option would be a scale size test glider. Doesn't need to be anything all that fancy. Just flat sheet wings with a touch of some reflex. Shift the balance around until it starts gliding and measure where it balances. Something around 50cm span for high of an aspect ratio would be a good size. I'd make it using 3mm balsa and shape the edges something like below to give you a sort of airfoil.

The tips are quite swept back on this shape. So using three or four degrees of washout in the outer portion of the wing would aid with giving the wing the reflex it needs for stability and also altering the spanwise lift distribution to something more Horten like where the lift at the tips is slightly negative for much of the wing's angle of attack range. Especially if the goal is to fly with no vertical fins.

You may want to make a post about this unique and interesting project in the Nurflugel forum here on RC Groups. The others and I would enjoy seeing it and there's some really good flying wing theory folks there. Especially if the idea is to go with no vertical tail fins.

Have a look at this guy. They fly ok and the fuse is more about CG and looks here...
https://www.rcgroups.com/forums/show...on-Pterodactyl

to BMatthews:
as you said, 5x subdivision worked quite well, see pics below
but i'd still build the wing with the curves, just looks better

i totally forgot about doing a small scale test, that would probably be better than software, as i read somewhere, that some calculators have errors when doing multi panel calculations
i think it was on rc universe (i did a test and the 2nd one in the list seems to be fine, same wing, one as single panel and one as multi panel, if mac is different, error)

i wanted to avoid using reflex, i once did a test in OpenVSP and bird tails seemed to be 10% more efficient (in this thread: https://www.rcgroups.com/forums/show...p-vs-bird-tail)
the program and i most likely left out quite a lot of aspects, whitch decrease the advantage, but from a purely logical standpoint, it makes sense

i actually did intend not to have vertical surfaces, horten and prandtl are both really cool
but i guess the real bird can just bend the wrist and has just created a more vertical surface

thanks for the interest, i might actually start a thread, global intelligence is pretty useful
but it would be quite a while from now to flying, as this is the very beginning



to gliderguide:
the pterodactyl looks like a really nicely done project
although there was a pretty useless discussion about locking up folding props XD

what inspired me, was the high L/D of the albatross of up to 23, despite the small reynolds numbers and surfaces made of feathers
(that last part might not actually be a negative, see this article on researchgate:
https://www.researchgate.net/publica...d%27s_Airfoils
on page 14, i guess the permeable airfoil increases the size of the low pressure bubble on top and therefore creates more lift at the same drag, might be totally wrong, i was lazily reading that day)

the L/D of the pterodactly wasn't that great, i guess
a fuse would really help to get the cg correct, without unnecessary amounts of ballast

Birds are good at shifting their wings back and forth as well to alter their CG. I'm sure that a lot of their flying is done at neutral or perhaps even slightly negative pitch stability values. But like us riding a bicycle they can make instant small corrections as needed.

Of course we've got a lot more options these days for stability enhancement. It would be interesting to build a flying wing that has an airfoil with a very low pitching moment range and then rely on a stability module and a small bird like stabilizer and elevator for the pitch control. that could allow us to fly the model with modeled in pitch stability and speed trimming between the pitch stability programming and perhaps a speed measuring module. In flight we'd trim in a desired speed with a separate dial or slider or the throttle stick. And then the elevator would command actual pitch changes for short term maneuvering like turns, dives and even loops.

Your original question is hard to answer because you're using the word "plank" in the subject which
implies an airfoil intended for a tailless aircraft, but then describe the use of a tail for pitch stabilization.
Each scenario will have a very different CG.

Originally Posted by Marc Frank

i wanted to avoid using reflex, i once did a test in OpenVSP and bird tails seemed to be 10% more efficient (in this thread: https://www.rcgroups.com/forums/show...p-vs-bird-tail)
the program and i most likely left out quite a lot of aspects, whitch decrease the advantage, but from a purely logical standpoint, it makes sense

1. If it has a tail used for pitch stabilization, it is *not* really a flying wing or plank and a more conventional airfoil airfoil should be chosen.
2. A tail or reflex on a zero pitching moment airfoil is there to keep the nose "up" not down as the OP of that linked thread, falsely asserts in his very first sentence (and then nobody corrects).

A little background:
All non-symmetrical airfoils with positive camber generate a forward pitching moment. Generally
the more lift they are capable of generating at a given loading and airspeed the greater that forward pitching
moment is. This is simply the way airfoils work because of the way they accelerate the airflow asymmetrically.
A conventional aircraft counters this forward pitching moment with a long (relative to the chord length of the
airfoil) tail boom, with a horizontal stabilizer at a negative angle of attack to push down against
the main wing's desire to rotate forward.
Tailless aircraft still need to counter this, and that's where reflex comes in. Reflex is just
the same negative angle of attack horizontal stabilizer, on a *much* shorter pitching moment,
which is why it's generally built into the entire length of the airfoil.

So back to CG question. With a conventional non-reflexed airfoil that is all producing positive lift plus a
long tail boom to provide more leverage for the horizontal stab to counter the forward pitching moment, you can move
the CG well back, often behind what the MAC based CG calculators recommend. It is not
uncommon to see the CG as far back as 50% of the chord where the CG calculator might be recommending only
30-40%. This can work for a wide speed range and may only have issues at extremely high airspeeds.

With any zero pitching moment airfoil meant for tailless aircraft, only the forward 2/3rds or so of the
airfoil is generating positive lift, while the last 1/3-1/4 or so is reflexed and providing negative lift.
This forces the CG to be well forward, and only optimal in a very narrow range.
If you go behind that range, the aircraft becomes literally unflyable.

So the question here is.. Are you really intending a conventional airfoil (non-reflexed) with
a tail doing all the work of pitch stabilization, or using a "plank" airfoil which is inherently
zero pitching moment and requires reflex, or are you trying to massage the two together,
starting with a plank airfoil, with reflex removed (essentually just pitched forward) and then
countering that with a tail? I doubt that the hybrid approach is optimal.

FWIW, photos and diagrams of most avian airfoil cross sections suggest they are more conventional
(often highly under cambered) and not zero pitching moment, although I've seen some reflex on
soaring bird wingtip flight feathers. Sweep em through the air to generate lift
and they still tend to pitch forward though.

If it has a tail used for pitch stabilization, it is *not* really a flying wing or plank and a more conventional airfoil airfoil should be chosen.

Eggzactly!

But in an extreme case like this layout I'm thinking that some of the very low pitching moment airfoils that are cambered might not be a bad option. An airfoil with a stronger sort of pitching moment could easily overpower the bird like very low aspect ratio stabilizer that is operating with a super short moment arm.

Some aerofoils meant for swept tailless have minimal reflex and pitching moments. MH45, MH64, EH range for example are used in combination with sweep and washout to create stability. Without these they are not pitch stable.

Yes they have beed used on planks, I have a plank with the MH64, but they need extra reflex adding to be stable.

The point being that everything is a compromise when designing and one of these aerofoils along with a tail may give the required stability with 'more' lift.

thanks a lot
don't have much time to write right now, but here are a bunch of flying wing airfoils
https://www.aerodesign.de/english/profile/profile_s.htm
i'll come back soon

well, today i saw a crow taking a walnut from its beak with a foot, mid flight
birds are amazing

we have digressed a bit
i guess the original question was if there were tools to calculate the mac without using a finite amount of panels and i bet there are functions, but i have no idea how to convert my drawing into something usable and also no idea how to use such a function (hopefully not proudly ignorant, at least i'm going to the wise ones to learn)

i greatly appreciate all additional info, though, it helps a lot

i found this albatros airfoil
http://airfoiltools.com/airfoil/deta...e176-il#polars

the pitching moment at the same alpha as cl/cd max is about -0.12
at the 50k reynolds numbers

i have no sense of scale, is that big or small?

i'm a bit sad, that i couldn't find an airfoil of the same name further along the span of the albatroses wing
if i'm already copying the planform of this great design, i would like to also steal the airfoil
i guess the airfoil isn't constant along the span
the tip feathers are almost flat plate, right?

i also read in another researchgate article, that the airfoil changes under aerodynamic loads, it might create reflex when more air pushes against the flexible trailing edge
i don't see a simple, durable way to recreate that and the air permeable back part, so i'll just leave that out
maybe in a future project

i think i want a normal airfoil with a tail, but not on a boom, just like the guy in the pic, although i'm not convinced that tiny tail is doing all the work reflex would do
maybe an airfoil with less reflex than necessary without the bird tail?

if it's not a plank, does a new thread belong in the Nurfügel category?

oh and another thought i had, was automatic iterative design, maybe it exists already (xflr5?)
the program could try out a bunch of combinations of airfoils and chords and sweeps and twists and alphas and positions of tail and and and
with some constraints, maybe max span, min span, max volume, min volume, min/max cl ...
and then the program shows me all the progressions in L/D and stability depending on the iterative changes of the values and shows me the "best" combination
might take a week to calculate, and much much longer to program, but i guess it would be worth it

It might be that the albatros wing has a bell-shaped lift distribution. Depending on the swept angle, it´s possible to choose airfoils witch are cm negtive in the middle section. If the swept angle is zero, normally the airfoil should have a cm0 which is zero or positive.
This paper might help: i like the idea of a blended wing body for a albatros inspired plank.
https://openscholarship.wustl.edu/cg...ontext=mems500

/Bernd

Hey, that named airfoil doesn't look like anything off a bird. So I'd suggest that you're looking at an airfoil originally drawn out by the old WWI Albatross aircraft company.

The strongly undercambered shape shown in the link would have a very strong negative pitching moment. And yes a Cm of -0.12 is pretty strong.

By comparison have a look at this link to the MH45 AIRFOIL GRAPHS. Note the last chart for Cm values. Only for the lowest 50K Reynolds number is the Cm drop to -0.05 for angles of attack really near to zero. But if flying that slow to get the number that low you would never really be at anything like 0 to 3°. So even for flying slowly it would be up a bit higher.

Mind you for a larger size glider the wing chord would be such that it would likely never fall below around 100K And the upper angle range for the 100K curve is all around 0 pretty closely with the useable model values being in the -0.01'ish range. An amount of negative pitching which could be easily countered with just a whiff of up trim.

Your layout to follow the bird's wing puts the outer portion of each side in a fairly strongly swept back configuration. So much so that it would be a perfect wing to use with a fair bit of washout to promote a negative lift at the tips which being behind the wing's neutral point would promote some amount of pitch stability.

You say you want to avoid reflex. But really your wing is so close to being a plank style that this won't really work out for you. That Mh45 airfoil is what I'd call a Cm=0 for the most part. At least for model use it is. Any reasonable model size glider isn't going to see angles of attack greater than 10° which is where the MH45 actually ends up slightly positive for the Cm. So we're stuck with a slightly negative pitching moment..... unless we go with strongly positive pitching moment airfoils along the lines of the MH110 which is a true plank wing airfoil with a far more consistently positive Cm value across the whole useable range of Reynolds numbers and in flight angles of attack. But which also limits the maximum Cl value at "our" angles of attack below 10° as a tradeoff for this.

What I'm thinking is that something like an MH45 for the majority of the wing with the outer 1/3 transitioning to where the last 15% or so of the wing was a fairly heavily washed out symmetrical section might work well. The washout at the tips should reduce much of the tip vortex formation but likely it would cause some issues with spanwise circulation that might not be good.

Now this is just a doodle with some thoughts behind it. Picking the nearly Cm=0 MH-4x series as the basis for this I did this sketch below from your picture in the first post. It would use the MH-45 at 9.6% thick at the center for a little more strength. It would taper to the MH44 as shown and stay that way to the outer MH-44 label and then transition to fully symmetrical at the point of the arrow head out near the wing tip.

I'm also thinking that the elevons would be sized and hinged as shown so any "up" inputs increase the washout at the tip rather than altering the camber through the middle of the wing.

There's some mention about keeping this light and floaty. But you'll get that through having a relatively light wing loading for the size of the model. Any plank style flying wing is going to be a compromise in this area because of the lift vs alpha for any airfoil which could be used on a plank style wing.

And despite the narrow little tail this really is a plank style flying wing in almost ever manner that counts. If you stick an elevator on the scale bird's tail it would help for sure. But I'd suggest that there isn't enough tail area to matter so you won't be using airfoils with more serious camber any way you look at it.

If you want to make a little scale test glider I'd suggest that the outer portion be cut and hinged with some soft copper wire or soft aluminium like that off the top of a beer or pop can. or even just glue on such a feature at the tips so you can flex in some washout. Then play with some nose weight to set the glide.

I'd skip the gull dihedral shape for now though. The real bird flies with a fair amount of droop in the outer wings. With ailerons and perhaps some gyro stability in the Rx you could copy that. But if you include that on the test glider you'll find it trying to roll into inverted. stick with flat or slightly angled up wings.

Since I already had the drawing seen above.... I got a little carried away....

Built as indicated on the PDF it flew without any nose or tail weight. The popsicle stir sticks must have been just heavy enough. The balance point is fairly strongly ahead. You can see it in one of the pictures where I marked it on the lower side of the wings. Balanced as indicated and with the washout and reflex effect of the tips the wing flew a nice flat and fairly fast pass across my living room and bounced off the back of the sofa. So it's not far off for trim.

Throwing it a few degrees down and with more energy saw it curve up to an expected stall and fall away into the couch. The pitch up curve looked pretty good. As in pitch stable but not too strongly pitch stable.

Yaw stability seems to be marginal though. On one of the flights it did yaw one wing forward of the other and did not show signs of recovering. So that could be an issue. The reverse bell curve at the tips does seem like it's working to some degree. And to be fair this little thing is far from having the proper twist distribution to achieve a proper Prandtl or Horten style lift distribution where it would self correct any yaw excursions. But perhaps keeping the idea of the split tip rudders as seen on the B2 and early Northrop N9M flying wings might be needed. But then that's part of the fun, eh?

And a PDF of the plan I used. It's 24" span so you'll want to print it onto legal size paper or equivalent, Or use the Poster option in Acrobat.

I have to say that the glide slope, while a bit quick at present, was very flat. The test glider is pretty darn encouraging. And after a bit of outside testing up at the local dead end cud-de-sac if it ever dries up I think it'll look darn nice hanging up with the other models that have been retired or that were test models.

Bruce, that test model looks amazing already
but i'm not at all a fan of the split elevons of the b2

first thing i did, was to loft between the airfoils like you said, the mh45 & mh44 and naca 0007, i did it in Fusion360 and OpenVSP (so that i can check out the lift distribution)
i tried to adjust the twist to get a bell curve, but i have no way of comparing what i did to the ideal bell curve
i also tried a bit in xflr5 and what i found was, that it can calculate the mac of many more panels than just 5, so thats what i'll use in the future

so the next thing i did, was to model the Prandtl-D in Fusion360
that way, i can get an idea of how something actually good looks like
the curvy trailing edge looks kinda funny, but it isn't as extreme as is appears

what i got by doing that, are all the intermediate airfoils
in the paper by Albion Bowers, we only get the root and tip airfoils, but now i have all of them

i made one untwisted loft from root to tip airfoil, then sliced into 20 pieces and twisted like the paper states
and another loft between all those intermediate twisted airfoils

what i think i can do now is, match the chords of the intermediate airfoils with the cords of my planform at their position
then align the leading edges of the airfoils with the leading edge of my planforn and loft between those

should result in something a little better, but i guess it doesn't directly translate from the prandtl to mine, probably still not a real bell curve spanload
your "doodle with some thoughts behind it" looked very similar, actually

in the paper Bernd (moin moin) linked it says:
"simply using a bell-spanload is insufficient to guarantee strong proverse-yaw characteristics" (conclusion)
so that might still be a problem

i uploaded "my" model of the prandtl to grabcad:
https://grabcad.com/library/prandtl-d-1