The Myth of Aspect Ratio

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, Feb 20, 2011.

  1. Mikko Brummer
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    Mikko Brummer Senior Member

    Leo,

    Having spent most of the 90's trying to understand & implement Lamar's papers about LES and SES in my own MacSail VLM, I congratulate and completely sympathize with your work. Unfortunately, my MacSail no longer runs in the current Mac OSX so I cannot try it on a circular planform. I'll try to find time to try it on a N-S solver, if not for the numbers but to shed light on the flow patterns involved - that would be interesting.
     
  2. daiquiri
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    daiquiri Engineering and Design

    What for would you need to calculate the chord-based Fn of an isolated keel or rudder? Their hydrodynamic behaviour is governed by the chord-based Reynolds number, and by the distance from the free surface (as you've pointed out). The latter factor being influenced by the Fn of the hull (again, not the Fn of the keel) and by the heel angle, as you surely know.
     
  3. DCockey
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    DCockey Senior Member

    Mikko has raised several good points for discussion; perhaps worthy of their own threads on the upcoming "Hydrodynamics and Aerodynamics" forum. But I'll go ahead and start here with one or two.

    At sufficiently low Froude numbers the free surface acts like a mirror, with the deviation increasing as the Fn increases. I've also seen the claim that at sufficiently high Froude numbers the free surface acts like a "negative" mirror. In any case it will have an effect on the load distribution on a lifting surface appendage, and that effect could be considered as a change in effective depth of aspect ratio. The point I tried to make at the start of this thread is that if total "lift" is constant rather than lift coefficient, then depth is the critical factor for trailing vorticity induced drag, not aspect ratio. Span-wise load distribution shape effects are secondary to depth for trailing vorticity induced drag.

    So the question is to what extent two appendages would have different effective depths at the same speed and lift? Unless the difference in effective depth is significant the difference in trailing vorticity induced drag will be minimal. The difference in effective length might be significant for an appendage which pierces the free surface at a relatively high speed, such as a transom mounted rudder on a catamaran or the rudder on a flying Moth. For a keel/centerboard/daggerboard under a boat I'm skeptical that the free surface effects cause a significant change in effective depth unless the boat is at a large heel angle.
     
  4. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Another very important factor is the boundary layer thickness at the station where the fin, keel and/or rudder are located. For rudders there is also the velocity field induced by the propeller to consider.

    Leo.
     
  5. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Thanks for the kind comments, Mikko.

    If you really want to push your N-S code, you could try to model the flow patterns on a real Frisbee.
    See for example,
    Potts, J.R. and Crowther, W.J.,
    "Frisbee Aerodynamics",
    AIAA 2002-3150,
    20th AIAA Applied Aerodynamics Conference & Exhibit, 24 – 26 June 2002, St. Louis, Missouri, USA.
     

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  6. daiquiri
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    daiquiri Engineering and Design

    [​IMG]

    :)
     
  7. DCockey
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    DCockey Senior Member

    I've been considering starting a couple of threads along the lines of "Hydrodynamic Considerations for Keel/Centerboard/Daggerboard/Leeboard Design" and "Hydrodynamic Considerations for Rudder Design". Perhaps this thread has become the first one.
     
  8. Mikko Brummer
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    Mikko Brummer Senior Member

    If you think about an isolated foil piercing the surface, then obviously it's Fn is defined by the chord length piercing the surface. If you attach that foil into the bottom of the boat, how will the Fn-effect on its effective AR be changed? On a long keeled, deep canoe body classic style boat the LWL based Fn probably is the relevant factor, but what about a modern, high B/T type of hull with a very narrow and deep fin?
     
  9. daiquiri
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    daiquiri Engineering and Design

    But why calculate the Fn of the foil? That's what I'm wondering. Do you want to isolate the contribution of foil's wave drag to the total wave drag of the boat or what? And if yes, how do you do it, starting from the foil's Fn?
     
  10. DCockey
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    DCockey Senior Member

    Some thoughts and speculation:

    The disturbance of the water under a wave diminishes with depth proportional to the wavelength. I assume that the interaction of a moving submerged object with the free surface is proportional to the ratio of the object's length to depth.

    Interaction of a fin/keel under a hull with the free surface presumably also depends in part on the horizontal distance between the fin and the closest portion of the free suface. A given fin under a hull with 1.5 meter beam will have considerable more interaction than the same fin under a hull with the same depth but a 3 meter beam when moving at the same speed. Of course once either hull heels considerably and the fin is near the surface the situation changes. The beamier hull may raise the fin more than the narrower hull.
     
  11. tspeer
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    tspeer Senior Member

    I suspect there are two different effects at work. At zero lift, the foil is going to have wave drag due to its thickness. That would depend on the chord Froude number, because the foil would be just like a very deep draft, small waterplane area hull.

    Then there's the wave drag due to lift. If the foil is approximated as a single vortex in a lifting line, then it would be the span/depth Froude number that would be appropriate to characterize it.

    The Partnership for America's Cup Technology (PACT) did some tank tests to examine these issues. See Kuhn, John C. and Scragg, Carl A., "Analysis of Lift and Drag on a Surface Piercing Foil", Eleventh Chesapeake Sailing Yacht Symposium, January 1993.
     
  12. DCockey
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    DCockey Senior Member

    Froude number based on span/depth would be analogous to a Froude number based on beam for a planning hull in the use of a transverse length.

    What was the aspect ratio on the PACT tests? I assume very high, and wonder if the span/depth is more important than chord for a low aspect ratio lifting surface.

    An extension of thin ship theory for lifting surfaces vertical to the free surface could be a useful tool to help understand the roles of different length scales. Leo said above (Message #106) that he's working to "predict the wave resistance and wave patterns of lifting surfaces in water" but I assume it is for horizontal lifting surfaces more or less parallel to the free surface.
     
  13. Leo Lazauskas
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    Leo Lazauskas Senior Member

    It's easy to calculate the effect of a surface-piercing foil at zero AoA with Michlet. For non-zero AoA the problem is about 3 or 4 orders more difficult.
    A good reference is:
    Xu, Hongbo, "Potential flow solution for a yawed surface-piercing plate",
    J. Fluid Mech., Vol. 226, 1991, pp. 291-317.

    Of course, for keels which are fully-submerged diverging waves are very damped, and there is no hydraulic jump at the intersection of the free-surface and the trailing edge, so it is not quite as tough as the surface-piercing case.

    And, yes, the work I mentioned earlier is for pressure distributions acting on the surface from above the water.

    Leo.
     
  14. DCockey
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    DCockey Senior Member

    Non-zero angle of attack is what's needed to better understand the effects of span vs chord on wavemaking by a lifting surface.

    Can the thin ship methodology be used for vertical lifting surface "ships" which are entirely submerged below the free surface? That could be of interest as a learning tool.
     

  15. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Yes, but definitely not with Michlet. I have most of what I need in Flotilla, except the time to put it all together.

    Essentially what is needed are fast ways of calculating the derivatives of the potential (phi) of distributions of Havelock Sources. Near-field waves and squat require phi_x (i.e. the x-derivative); near-field waves made by hovercraft and travelling pressure distributions need phi_xx, phi_xy and phi_xz; and vertical lifting surfaces need phi_yy (or equivalently, phi_zz).
     
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