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Prandtl lift distribution for conventional configurations?

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peter hudson

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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-
 

Hot Wings

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I've pondered that same question.

2 possible problems:
The Prandtl distribution is only good at one point* on the performance curve. For a speed limited ultralight that may be an acceptable trade.
Ultralights are already at too low a wing loading to allow flight in anything more than a slight breeze with no gusts. Making the wings longer just compounds the problem

*Multi-segmented ailerons/flaps that could allow a degree of "morphing" might help, but the complication.........:eek:
 

Richard Schubert

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The Prandtl distribution is only good at one point* on the performance curve.
So from what I have read most of the efforts have involved the tips going to negative lift to gain longitudinal stability in flying wing configurations.
The performance envelope may be wider if the tips go to zero or just slightly positive lift, but I don't think anyone has worked to optimize that.
I would be very interested to see any testing results, although the gains may be minimal.
 

pictsidhe

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No, the tips do not go to negative lift. They go to negative AOA, but once you add the induced angle, they are a net positive AOA and generating lift and often a little thrust, too. Shape the lift distribution and planforn correctly, you get stability and positive lift along the whole span.
As Hotwings points out. Blsd tend to be single point design. The twist needs to vary with Cl to maintain the lift distribution. Doing that without wing warping is not feasible.
 

peter hudson

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I'm thinking along the lines of a part 103 self launching sailplane or electric motor glider. Pretty much aiming at minimum structural weight and induced drag at best climb (high Cl) and or best glide. Big sailplanes tend to be raced (need better glides at speed) and classed by wingspan. But for a sport flying UL it seems like a possibility...Yet I've never heard of it being tried.
 

BJC

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Typical GlaStar and Sportsman aircraft (with 180 HP to 210 HP) have the ailerons and flaps rigged in line with the LS(1)-0413, modified. Raising the trailing edge to float up a small amount - about 1/2” - typically increases the top speed by 3 to 5 MPH. It also makes the stall speed slightly higher and decreases the roll stability with full flaps near stall speed.

These results have been demonstrated on multiple aircraft with verified airspeeds.

BJC
 

Victor Bravo

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FWIW, I asked Al Bowers directly whether this BSLD "would work on a Cub", and he said yes it would. Whether that means it would work at all CL, or all AoA, or all flight conditions... I don't know. I do have faith in Al Bowers and his judgment though. Next time I get to speak with him I will ask about whether all of this would make an airplane into a single point design.
 

Norman

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2 possible problems:
The Prandtl distribution is only good at one point* on the performance curve. For a speed limited ultralight that may be an acceptable trade.
The one point design problem argument is based on the fact that tailless designs control pitch by manipulating the lift distribution and/or airfoil pitching moment. If you have a horizontal stabilizer you're probably controlling pitch with an elevator on the stab and therefore not changing the washout with pitch changes so the planform and fuselage would be the only things affecting the lift distribution. Both the BSLD and the fuselage decrease span efficiency so having both may not be a good idea but ultralights aren't prized for their efficiency so it may not be a problem.


Ultralights are already at too low a wing loading to allow flight in anything more than a slight breeze with no gusts. Making the wings longer just compounds the problem
Why would you have to decrease the wing loading? Most ultralights have hershey bar wings that waste 12% of the outboard wing. BSLD benifits tremendously from taper (planform effects allow you to keep the BSLD over a wider speed range) which takes that wasted 12% and puts it at the center where it's useful (as long as the fuselage doesn't screw it up too badly).


Here's a video of a model with BSLD and no sweep or tail:


Multi-segmented ailerons/flaps that could allow a degree of "morphing" might help, but the complication.........:eek:
The Horten's tried that on several of the per-Argentina machines. It didn't work very well. When you have partial span control surfaces with hinges roughly parallel to the trailing edge they produce huge steps in the lift distribution which naturally produces lots of induced drag. After moving to Argentina Horten began experimenting with single elevons and it worked. Udens and Nickel added the final details on elevon shape: It must not be more than 33% span and tapering it decreases the distortion of the lift distribution.
 

WonderousMountain

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I used Fc - (Span^2)/(span^2) + Kchord taper.

Example: 40in wing Root Chord, 30 inches tapering - Tip chord 10 inches.

Two Positions: .8^2 = .64x30+10 = 29.2in
Example II: .6^2 = .36x30+10 = 20.8in

These are Two points corresponding to Span 60% & Span 80% of the 3-4-5 triangle.

The Constant section 10in is merely convenient, it's actually better to taper 100%, but
looks weird compared to other craft. You will need to twist the Airfoil or blend sections,
to prevent tip stall. At low AoA negative lifting tips is fine. High AoA will essentially put
the Plane form as lift distribution. Increasing Span is not structurally free, but BSLD will
give low induced drag for the same span.

ESLD is fine and makes sense, but single taper wings are actually easier to construct.
 

Sockmonkey

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You know, in those older hershey bar wing ultralights that are wire braced top and bottom, and use a round tube for the main spar, just adjusting the length of the bracing wires would induce the BSLD twist.
 

Norman

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No decrease in wing load - just a longer lever arm for the gusts to toss you around.
If you compare two wings of the same area, one tapered and the other not, with constant force per square foot they have about the same leverage because the centroid of the planform moves inboard with increasing taper even though the tapered wing has greater span ie the root bending moment is what would cause a rolling moment due to a gust. Or am I wrong about that?


Was not aware of that bit of history.....stored for future forgetting. :confused:
It's illustrated in figure 6 of the MSU report.
 

Norman

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You know, in those older hershey bar wing ultralights that are wire braced top and bottom, and use a round tube for the main spar, just adjusting the length of the bracing wires would induce the BSLD twist.
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.
 

jedi

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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-
Yes! Have you any knowledg of the Mitchel B-10, A-10 and related designs.
 

peter hudson

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Yes! Have you any knowledg of the Mitchel B-10, A-10 and related designs.
I'm aware of the Mitchell wings but not aware of whether they were designed for the (1-X^2)^3/2 shaped lift distribution. Are you saying they were?
 

peter hudson

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With the idea of wanting a high aspect ratio, clean, D-tube spar wing for soaring but the tight weight budget of part 103 in mind, And with the thought that Prandtl's Lift distribution was constrained to have the same bending moment as the elliptical but with 22% more span and 10 less induced drag (for a given amount of lift). It seems worth exploring. 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. Also a big taper ratio means a big root rib that can potentially be hard to cleanly attach to a fuselage or pod.

The point design issue is still valid. But 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)

With all that twist It should have a very benign stall though as a side benefit.
 

pictsidhe

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With the idea of wanting a high aspect ratio, clean, D-tube spar wing for soaring but the tight weight budget of part 103 in mind, And with the thought that Prandtl's Lift distribution was constrained to have the same bending moment as the elliptical but with 22% more span and 10 less induced drag (for a given amount of lift). It seems worth exploring. 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. Also a big taper ratio means a big root rib that can potentially be hard to cleanly attach to a fuselage or pod.

The point design issue is still valid. But 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)

With all that twist It should have a very benign stall though as a side benefit.
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.
 

Norman

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I'm aware of the Mitchell wings but not aware of whether they were designed for the (1-X^2)^3/2 shaped lift distribution. Are you saying they were?
The Mitchell wings definitely are not BSLD. I worked on a U-2 and it's a whole different beast. BSLD requires that the camber of the outboard 1/3 be variable and those stabilators don't do that.
 
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