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Prandtl lift distribution for conventional configurations?

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Norman

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The downs sides to me are that structural weight of that type of lightly loaded wing are often driven by weight of skins and glue and preventing buckling as much as spar cap weights and bending moments..it might be hard to realize the savings.
What part drives wing weight the most depends on materials and aspect ratio. If you're building a wooden wing of AR greater than AR=8 the spar is the main source of weight. If AR is less than 4:1 the skin will drive the weight. Aluminum weight proportions will be similar to wood unless you use a piece of pipe for your spar then the spar will always be too heavy. If you use carbon fiber for the spar it doesn't become the main weight driver until you get to AR much higher than 10:1. Carbon is cheaper than aircraft grade spruce so there's no good reason not to use it unless your budget only allows aluminum. E-glass is inexpensive but the weight will be pretty close to wood. S-glass costs more than E-glass but is strong enough that a well designed spar will be a bit lighter than wood.

As for skins and ribs: At the speeds you're likely to see in an ultralight styrofoam is adequate for ribs and you can hot wire cut sheets for skin core material. I've had waste material that I could see through and know of one guy who's making styrofoam sheet less than 1mm. Many people will tell you that foam absorbs a lot of epoxy but hot wire cutting seals most of the pores that soak it up and a skim coat of dry micro reduces the density of the layer in contact with the foam.

Also a big taper ratio means a big root rib that can potentially be hard to cleanly attach to a fuselage or pod.
I'm not visualizing the problem here. Many high wing airplanes have a transparent wing panel above the cockpit. It should be high so the fuselage doesn't mess up the working side of the wing. It's also a plus to let the leading edge stick out a few inches in front of the cockpit. In fact the cleanest configuration would be a pylon of length about equal to the fuselage diameter but that's impractical.

in the case with a conventional tail it wouldn't be messed with by pitch control surfaces. but even so the distribution appears to change with alpha. (unlike the elliptical)
That's only true if the planform is elliptical and not twisted but that wing would also have a wicked stall.
 
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Heliano

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I want to add a few comments to this very interesting thread:
1 - If the idea is an aircraft with fuselage, be careful with spanwise lift distribution methods, be it Prandtl's lifting line, Schrenk, CFD or whatever: the fuselage has an important effect: a drop in lift in the center portion, causing an increase of bending moment at the wing root, due to the center of lift moving towards the tip. And each fuselage configuration has a distinct effect.
2 - Tube spars are an insult to the engineering community;
3 - D-shaped spars are in principle interesting because they are both strong in bending and strong in torsion.
4 - Using slotted ailerons may be helpful at preventing tip stalls. This kind of solution adds very little drag in cruise but retards the tip stall and, depending on hinge position, mitigates adverse yaw.
 

peter hudson

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All the twist that is required is needed to prevent tip stall. As the required twist increases with Cl, you need to be quite careful about the stall regime. I favour the use of inboard elevators. They can provide both effective twist and help the root stall first. Combine those with outboard tapered elevators, you can get approximate BLSD over a wide speed range and a non deadly stall. The outboard elevators are best tapered from 0 chord at partial span, to full chord a bit before the tips.
It's a tricky problem to analyse. A scale model is highly recommended if you try a BSLD wing.
I think your suggesting control surfaces for a BSLD flying wing like the Prandtl, Horton, Dragonwing. This thread is exploring the idea of using that lift distribution in a conventional configuration with a separate tail. But, I think the idea of designing a flaps planform to effectively change twist with deployment. would still have merit for an unswept wing with a tail. I wonder if a model with a ESLD on one side and a longer wing with BSLD on the other would be flyable as a way to compare wing performance. Maybe a model with swappable wing panels as a first test.
 

Jay Kempf

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Hate hate hate them!
Grumman after Bede and a lot out there. I know, not PERFECT usage of structural materials but makes for a simple to manufacture wing. Bede had some good concepts, some, most implemented badly, and supported atrociously, but still good concepts. Sort of like the start of a good idea that never quite got finished as it should. The Bede 4 guys have a really good airplane over a long time with a good record.
 

WonderousMountain

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I'd like to see an tube with spar caps included.
Something like 1/16th inch by a quarter inch wall.
A good crossover is needed to prevent spar print.
 
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Norman

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Grumman after Bede and a lot out there. I know, not PERFECT usage of structural materials but makes for a simple to manufacture wing. Bede had some good concepts, some, most implemented badly, and supported atrociously, but still good concepts. Sort of like the start of a good idea that never quite got finished as it should. The Bede 4 guys have a really good airplane over a long time with a good record.
I helped patched a hole in a BD-4 wing a few years ago. I was shocked by how heavy the wing was and that the skin is so thin. Didn't weigh it, just puled it down from the rafters where it had been stored. The airfoil bucket sections that BD supplied are one ply. Full of pin holes and not very stiff. I'd guess that 80% of the weight is in the spar. If he had used any other cross section for the spar he would have saved enough weight to make the skin thick enough for a D-tube and still had enough weight savings for lunch.
 

peter hudson

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So I'm starting to play with comparisons using OpenVSP. The conventional approach (bottom) has a 40 foot span and untwisted mostly constant chord wing (ala Alex Strojnik). The upper version has a 49 foot span (everything else is the same) and pretty close to the BSLD by assuming each wing half is built in 3 panels and each panel has it's own linear twist. I wanted to leave the planform basically the same for the first look. In theory these wing have the same root bending moment. compare.png
 

Steve C

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In fact the cleanest configuration would be a pylon of length about equal to the fuselage diameter but that's impractical.
Many have attempted to take advantage of this theory with model aircraft. It never has worked out. They have always been slower....and it doesn't look good.
 

peter hudson

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After a little more thought the two wings should have the same area which reduced the chord on the longer span BSLD (upper) version. But that reduces the thickness. SSo the same moment has more stress...Turns out if you maintain area, account for the chord length (and therefore thickness) and aim for the same spar cap stress, the span can only increase by the Sqrt (1.2247). It does allow a slight smaller horizontal tail to maintain tail volume too. so I'll be comparing to this 44.25 ft span version.44ft_bell.png
 

pictsidhe

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After a little more thought the two wings should have the same area which reduced the chord on the longer span BSLD (upper) version. But that reduces the thickness. SSo the same moment has more stress...Turns out if you maintain area, account for the chord length (and therefore thickness) and aim for the same spar cap stress, the span can only increase by the Sqrt (1.2247). It does allow a slight smaller horizontal tail to maintain tail volume too. so I'll be comparing to this 44.25 ft span version.View attachment 102150
You need a lot more taper with bsld, or your roots will stall very early. It'd be like an elliptical distribution with wider tips than roots. Hortens went to enough taper to have Re headaches.
 

WonderousMountain

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In the original critique from NACA,
the ideal planeform from drag view
stretches into infinity as an Eiffel
tower turned on it's side, Anomalie.

So root bending was assigned priority.
That's also kinda inconclusive, because
you can have a 25% thickness ratio, and
there's still no fully reliable study on thick
wing sections over a BSLD wing, maybe
single taper.

Also, you want to do critical gust load for
an actual build, not just fatigue equivalency.
Happy hunting, but do quit before insanity.
 

Norman

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You need a lot more taper with bsld, or your roots will stall very early. It'd be like an elliptical distribution with wider tips than roots. Hortens went to enough taper to have Re headaches.
Reimar Horten's choice of taper ratio may have had more to do with volumetric efficiency than control issues ie he was anticipating filling as much of the span as possible, on later designs, with cargo and fuel. A taper ratio of zero would allow the whole span to be filled with fuel and stay in balance. As you say he had to settle for a finite tip chord for practical reasons but BSLD wasn't one of them. The glider in the video I linked to in post #8 looks like it has a taper ratio of about 0.4 . To get the induced thrust effect near the tip you have to have some induced AoA there which doesn't neceasseraly require a lot of taper. Stall at the root of a swept wing might cause a too abrupt pitch down but without sweep I don't see a problem.
 

peter hudson

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You need a lot more taper with bsld, or your roots will stall very early. It'd be like an elliptical distribution with wider tips than roots. Hortens went to enough taper to have Re headaches.
With an elliptical distribution the" ideal" planform is an ellipse and no twist and the whole wing stalls at once. I imagine the same would result from a bell shaped planform and no twist. I take your point and may add a single or double tapered planform to the comparison to see if there is a big advantage to getting closer to that shape (in the same way a double taper and a little twist can approach the ellipse). In the end, a sort of compromise between a buildable planform, twist and stall behavior. is always struck...I guess I shouldn't assume what that shape is for the BSLD wing.
 

pictsidhe

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Bsld requires twist. The down wash angle varies along the span. Elliptical is a special case where down wash angle is constant across the whole span.
 

Sockmonkey

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I absolutely hate tube spars! They're a terrible use of material but, yes, they do alow the ribs to twist if the ribs are not rigidly attached. I don't think it would be easy to get anywhere close to BSLD with wire tension though, unless you had a lot of wires attached in the right places for getting the precise AOA at 5 points along the span and the panels between those points would have to be fairly rigid. It might work in a biplane configuration but I think a monoplane really should have a proper D-tube with an I-beam or C-channel spar.
With a fabric covered wing using fore and aft spars you could get away with fewer attachment points. It's just an idea anyhow.

I remember seeing a wing that had holes in between the ribs near the leading edge of the wingtips so the overall impression was of an integral fixed leading edge slat. So, I'm thinking that build-wise instead of adding twist or varying the shape of the ribs from root to tip, say you just added some slots between the ribs.
 

peter hudson

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Here's a preview of my BSLD vs ESLD trade study. The top 3 wings are based on the Prandtl BSLD and the bottom 3 on ESLD. The top wing in the series approaches the desired lift distribution with a three segment tapered planform only and no twist (with some small extra chord as we approach the tips to assure inboard stall). The middle wing in each series is a single taper and will be twisted to approximate the distribution of the 3 taper segment version. The bottom in each series is an easier to build, mostly constant chord section, and may have a linear twist to get a little close to the desired distribution. The tricky bit is that these all have the same planform area, and the aspect ratios are varied get similar (span/root_chord^2) values which means the stress in the spars are the same across the board. (Also the BSLD wings get the 1.2247 factor advantage in span to produce the same moment) So in principle all 6 wings have the same area, lift, and structural weight.

Next up is to adjust the twists of the twisted wings to get the desired distributions, and ultimately compare the results. I'll consider the 3 tapered ellipse as the baseline "really good wing" as the sort of the "accepted" idea.

-Peter-
trades.png
 

AJLiberatore

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Hi All,

So after Prandtl convinced the world that elliptical lift distribution was the most efficient for a given span, he went on to explore his "bell shaped distribution" as the most efficient if structural weight is the fixed parameter. The flying wing guys (Horton and his fans like Al Bowers) jumped on board as it also could solve the adverse yaw problems with flying wings.

So here's my question: Since Part 103 ultralights are restricted in weight, and not span, it would seem logical that they employ the Prandtl lift distribution even in conventional configurations. And they may further benefit from a reduced need for vertical tail volume. Are there any examples out there that tried it?

-Peter-
Is this wing extension (Planform & Twist) moving in the direction you are thinking, it may not be true Prandtl D, but is it something to look into.

 

proppastie

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I guess I am missing something.....I thought Lift Distribution Calculations were attempts to calculate the lift distribution of a wing, not a method to design a wing. In other words any wing could be have its lift distribution calculated using the various methods, each to give it a different answer and each at a variance from the true lift distribution. I see here the attempt to match the profile of the wing to the distribution but question as to if the results in the wind tunnel or CFD software give the desired results. For example I have been told the Carbon Dragon area platform distribution and the ESLD are very close given the shape of the wing, and been told by others that however you calculate the distribution it is ESLD which is the best calculation.
 

pictsidhe

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I played with a spreadsheet that calculated required twist for a given planform and bsld of any exponent over 1. It was quite educational. I got a feel for shapes that don't send the lift distribution to hell as I changed CL. It also calculated span efficiency. I didn't get around to root moment. I was trying to get it to work for swept wings when I lost my USB drive. 😫
 
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