Bell shaped lift distribution

Discussion in 'Hydrodynamics and Aerodynamics' started by container, May 19, 2020.

  1. DCockey
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    DCockey Senior Member

    An exception would be to use a symmetric foil section with no twist, and design the planform section to provide the desired spanwise load distribution. In that case the shape of the load distribution would be independent of the angle of attack. A disadvantage of that approach is the symmetric foil section will have higher drag than a section with optimized camber. Also the required planform shape may have drawbacks for structural and/or manufacturing reasons.
     
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  2. container
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    container Junior Member

    One would have to assume the ideal planform shape would be that of a soaring albatross or seagull? Obviously their wings are perfectly suited to bell shape load distribution so it makes sense. I am already using a gull wing shape for my elliptically loaded foils, I much prefer the feel of a 'cranked' wing over a traditional straight H/A foil.
     
  3. Doug Halsey
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    Doug Halsey Senior Member

    Maybe if your planform has to fold, flap, and encounter all the same mix of conditions that the birds do.

    Otherwise, maybe not.
     
  4. patzefran
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    patzefran patzefran

    It was just a reference to Jesus !
     
  5. container
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    container Junior Member

    I disagree, gull wings feel amazing to fly compared to straight or anhedral wings. I have no numbers or data to back that up other than the fact I have used alot of different foils, production ones and my own designs, and in my opinion without a doubt the gull wing is the smoothest, most forgiving and most maneouverable to ride.
    Seagulls arent flapping or folding their wings when gliding or performing a diving turn, so i think its relevant. Hawks and eagles have to do the same flapping and folding but use a drastically different wing shape, must be something to do with flight characteristics
     
  6. Doug Halsey
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    Doug Halsey Senior Member

    It's not surprising that birds' wings would have evolved to provide the favorable qualities that you mention. However, I doubt if their lift distributions are perfectly bell-shaped, and I've got to believe that they would be shaped somewhat differently if they didn't have to fold or flap.
     
  7. tspeer
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    tspeer Senior Member

    In my opinion, Bowers is only belatedly realizing some important points.

    First, the reason there is thrust produced at the tips of a bell-shaped lift distribution is because the effective span is shortened compared to the physical span, and the induced drag is higher than it could be. The proverse yaw that he finds so useful in a flying wing actually comes from the lift distribution on the outer wing becoming less bell-shaped and moving more toward a shape with less induced drag, while the lift distribution on the inside wing becomes even less favorable than it was before the rolling moment was applied. In other words, the tip thrust is just recovering some of the drag that is already higher than it should be. If there weren't some other constraints on the flying wing, it would be better to use a lift distribution that had lower drag to begin with, even though it didn't produce thrust at the tip.

    Second, for a swept flying wing there is a coupling between the bending moment produced by the spanwise lift distribution and the pitching moment. A stable airplane needs to have a positive pitching moment about the neutral point. A swept flying wing can satisfy this with reduced lift (or negative lift) at the tips and increased lift in the center. So there is a requirement to not only produce a total lift equal to the weight, but to do so with a particular pitching moment. And, because of the pitching moment is proportional to the root bending moment, this means the swept flying wing needs to have a particular bending moment. The question becomes, "How to satisfy these two conditions with minimum induced drag?"

    R. T. Jones (NACA TN-2249) showed the minimum induced drag for a given bending moment is obtained when the downwash varies linearly from root to tip. This produces a bell-like lift distribution. So I believe it is more useful to consider the bell-shaped lift distribution to be the result of minimizing the induce drag, and not an end in itself. In his more recent papers, I think Bowers is starting to come around to this realization.

    If there aren't some other constraints on the design of a hydrofoil, the best planform shape is one that produces a uniform dowwash in the wake. If there's a structural constraint on the bending moment, then the planform shape should produce a linear downwash distribution. Hydrofoils can have some complicate 3D shapes, so even for the uniform downwash case the planform that results may not be elliptical. I think it's best to start with the downwash distribution and let the spanwise lift distribution and planform shape fall out from that.
     
  8. gonzo
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    gonzo Senior Member

    After watching the videos, I had to reassess my opinion on foiling boards. My preconception was based on boat applications. The foil on the board is operating in a completely different mode. The operator is using the foil as propulsion by applying a pitching moment to create lift and forward thrust.
     
  9. Maarten88
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    Maarten88 Junior Member

    I am also designing and building foils (for kite and wing) and aim for a bell shaped lift distribution at max speed when designing my foils, using twist. I found that having a bell shaped load distribution at design-speed leads to a foil that handles poorly at higher-than-design speeds.
    A foil needs to work over a range of speeds. More importantly, the trade-off for efficiency is agility: you want to steer the foil sharply through the waves and make bottom turns. The bending moment also determines the resistance to direction change, so it seems logical to optimize that and use the bell load distribution.

    Lower load at the wingtips also leads to better control when the wingtips breach (or get close to) the surface, you won't suddenly loose control of the board because the lift is more centered. Also it can avoid tip-stall at take-off speed (when the wing doesn't have too much taper).

    When I see these video´s of AC foiling yachts pulling a huge vortex that persists behind the wingtip of the foil, I think that can´t be good, and bell shaped load distribution (or winglets) should be more efficient.

    Attached my current project: a big 2000 cm2 wing. I also take inspiration from nature, but use fish :)
     

    Attached Files:

    Last edited: Jun 22, 2020
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  10. Doug Halsey
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    Doug Halsey Senior Member

    Very pretty ! It looks a lot like a manta-ray.

    Can you give more details about the twist you used, and how the load distribution changes in varying conditions?
     
  11. Maarten88
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    Maarten88 Junior Member

    I am using a hydrofoil section that has close to zero CL at alpha=0. It performs similarly to H105, but with a constant, neutral Cm. At the root, the wing section is set to around +2 degrees. Going outward, the angle goes slowly down, and then near the tip it goes down quickly into negative, to somewhere around -3 degrees at the wingtips. When designing the wing, I take the top speed, (depending on the size somewhere between 11 and 20 m/s), and then specify the twist so that the lift distribution approximates the bell curve (see the first graph). At lower (more typical) speed (like 8.5 m/s), the lift curve is closer to the elliptic distribution. When I built a wing that had the bell curve lift distribution at these typical speeds, I found that it did not behave well at higher speed, so now I try to avoid negative lift at the wingtips at all realistic speeds.

    Below is a graph from a 900 cm2 foil wing that works well. The two grey lines are the optimal Bell and elliptic curves. The red line in between is the main wing lift. The lower red line is the stabilizer.

    Top speed:
    lift-distribution-top-speed.png


    Medium speed:
    lift-distribution-medium-speed.png
     
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  12. Doug Halsey
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    Doug Halsey Senior Member

    Very interesting!

    Can we assume that VLM2 is a Vortex-Lattice lifting-surface code? If so, are the results shown above including the mutual interference of the main foil and the stabilizer? And nonplanar?
     
  13. Maarten88
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    Maarten88 Junior Member

    Let me begin by stating that I do not really know what I am doing... I do this as a hobby, although I do remember some things I learned 30 years ago studying aerospace at the university.

    In short, what I do is use XFLR5, a program intended for analysis of model airplanes, that internally uses XFoil. It is possible to input viscosity and density of the analysis, so I use that of water instead of air, and that seems to work. I simply watched Youtube instructions and click around in that program, designing airfoil sections and wing configurations until I have something that I like, then I design it in cad, 3D print a mold or plug, build it from carbon fiber and try it on the water. I have some help for building and testing, my skills are limited. My designs optimize for stability and behavior in the waves, performance and speed are less important. I found there are many practical things that the software can't predict, the hardest part is understanding what to design for. Still, I think doing this leads to better results and better understanding than not doing any CFD calculations. I think my designs are better than the majority of commercial products.

    To get back to your question, yes, XFLR uses the Vortex-Lattice method. It has several limitations: http://www.xflr5.tech/docs/Part IV: Limitations.pdf. As I understand, main foil and stabilizer can interact, but the wake model is simplistic (flat) and their advise is to try to avoid interaction, the results are probably unreliable.

    If there are better ways to analyze foil-wings or complete configurations (including mast and fuselage) on a budget, or you have additional tips, please let me know!
     
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  14. Doug Halsey
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    Doug Halsey Senior Member

    I disagree with your first sentence. It's clear that you know quite a bit, and you are very proficient in using some of the best tools available to the advanced amateur.

    I doubt if the tools available to the pros would do much better, or could allow them to skip the experimental testing.

    Well done!
     
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  15. Jean Baptiste
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    Jean Baptiste Junior Member

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