Bell Spanload Implications for Sailing?

Discussion in 'Hydrodynamics and Aerodynamics' started by lunatic, Nov 19, 2017.

  1. CT249
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    CT249 Senior Member

    Thanks. Until I had a good hard look, I didn't realise how much higher the X 41's forestay was in proportion. I should have checked the available figures rather than eyeballing it off small sailplans.
     
  2. tspeer
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    tspeer Senior Member

    Yes, and yes. For example, the AC72 yachts in San Francisco even took it a step further and used negative lift at the head! They would have had to sheet out more and been less powered up if they'd used a more elliptical lift distribution.

    The bell-shaped lift distribution is simply a by-product of tailoring the lift distribution to reduce the root bending moment (same thing as the heeling moment for boats), allowing a greater span for the same moment. The minimum induced drag is obtained when the wake wash distribution is linear along the span. If you have a constant wash in the wake, then the lift distribution will be elliptical for an isolated wing. If you choose the right slope to the wash distribution across the span you'll get a bell-shaped lift distribution.
     
  3. lunatic
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    lunatic Senior Member

    Confusion: the outboard forward tilted lift and thrust,as presented in the NASA paper's diagram, should increase heel. The trade off looks bad, the thrust would have to be substantial and the thrust's leverage would bury the bow. Maybe this should all stay in the air, but the paper has provoked my curiosity that there might be other options to lift distribution.The idea of negative drag is quite appealing and seems to be successfully exploited in nature. Years ago large twist-off sails for sailboards enabled us lightweights to stay on board in conditions not conducive to musing about negative lift, I now assume it was what left me standing.
     
  4. philSweet
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    philSweet Senior Member

    lunatic, no, it decreases heel over the entire range of headings. The result, from a sail trim perspective, is that the top of the sail is eased out further while generating the same amount of force. Thus the local total aerodynamic force is rotated some amount from the leeward to bow-ward direction.

    One source of confusion is the standard method of showing the centroid of the sail and assuming the total aero force acts there. This only works if the sail projection that you used to determine the centroid is perpendicular to the forces, and also that the force component is uniform. So you have decompose all the local aero forces and only use the sideforce portion of the force. Only if the sideforce is uniform will the applied heeling force act at the centroid of the profile view of the sail plan. When you twist the force at the top bow-ward, that sideforce decreases, and the center of effort for total sideforce gets lower. The drive force increases, and the center of effort of total drive rises. There are separate centers of effort for drive and sideforce.
     
  5. lunatic
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    lunatic Senior Member

    Thank you, very use response. Poor wording can confuse the novice, relative to the wing chord at the tip (Fig 2b) the upwash (angle) seems a diminished downwash on its way to negative lift. On the NASA wing the diminished tip vortex moves inboard, what is the distribution going to full negative lift.
     
  6. philSweet
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    philSweet Senior Member

    There isn't an easy way to answer that. A local added bit of lift (a bump) will be modeled as a horseshoe vortex, and the entire flowfield can be updated by adding the influence of this horseshoe vortex to the preceding flowfield. Thus a local bump in lift changes the entire wash, across the wing, outboard the wing, everywhere. If you go from positive lift to negative lift near the wingtip, you are adding a vortex with 'backwards' rotation, and the added vortex will increase downwash/decrease upwash across the entire span of the wing inboard of the 'bump' and outboard of the bump, but will have the opposite effect across the span of the bump itself. Pretend you are superimposing a similar, but smaller wing upside-down, and then add the similar, but weaker inverted flow field. None of this depends on whether the bump happens to be in an area upwash or downwash.

    So if the reverse in lift occurs entirely outboard the vortex, the primary vortex moves outboard, perhaps right to the inboard bump vortex, then there is the outboard bump vortex. However, a smooth transition towards negative lift which begins inboard of the vortex would tend to move it inboard.
     
  7. patzefran
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    patzefran patzefran

    https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20160003578.pdf

    Interesting study, but it seems those young (?) NASA people using flowfield codes missed the exact analytical solution found by Robert T. Jones (1950).
    Ref : NACA TN 2249 " The spanwise distribution of lift for minimum induced drag of wings having a given lift and a given bending moment "
    Without bending moment constraint the exact lifting line solution corresponds to constant downwash angle along the span (elliptical lift distribution).
    With bending moment constraint it corresponds to linear decrease of downwash angle from root to tip !
     
  8. philSweet
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    philSweet Senior Member

    Here's a little summary I found. I'm not especially confident in its accuracy, though. I think Prandtl and Jones were using different optimization criteria, contrary to what this suggests. (I think they used different expressions, when taking the derivative and setting it to zero.) That could have stemmed from using different linearization techniques, or from applying different physical constraints. But see the note that Jones's work was less general than Prandtl's and derived independently.

    http://www.twitt.org/Bowers Slides.pdf

    (still looking for Prandtl's 1933 derivation)

    Edit - I think I found what I was looking for. It seems Prandtl minimized the integral of the bending moments over the span, while Jones minimized the root bending moment. See para 16 here - Full text of "Effects of winglets on the induced drag of ideal wing shapes" https://archive.org/stream/nasa_techdoc_19810065587/19810065587_djvu.txt

    exerpt -
    Prandtl assumed that a fraction of the weight of the wing
    structure is proportional to the bending moment integrated over the whole span<
    For a planar wing the average or integrated value of the bending moments turns
    out to be just the second moment or "moment of inertia" of the load curve.
    Prandtl 's criterion seems more appropriate than the criterion used by one of
    the present writers (see ref. 7) in which only the bending moment at the wing
    root was considered.

    Jones was one of this document's authors.
     
    Last edited: Dec 31, 2017
  9. patzefran
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    patzefran patzefran

    PhilSweet, thanks for your interesting data, I am surprised by the results ! I think T. Speer will be too. I had to download "Full text of "Effects of winglets on the induced drag of ideal wing shapes" https://archive.org/stream/nasa_techdoc_19810065587/19810065587_djvu.txt" in .pdf format to get the formula and figure right. So it seems constraint on integrated local bending moment (L. Prandtl ) results in parabolic downwash variation as
    optimum solution for minimizing drag. However, it seems for sailing application, root bending moment represents heeling moment and linear downwash is best suited.
     

  10. tspeer
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    tspeer Senior Member

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