The Myth of Aspect Ratio

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

  1. gonzo
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    gonzo Senior Member

    I think that is the usual fallacy of comparing wings to keels as if water and air where identical fluids.
     
  2. DCockey
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    DCockey Senior Member

    What's the fallacy?

    The flow of water past an airfoil away from the surface behaves the same as the flow of air past a similar shape airfoil if the respective speed and airfoil sizes are such that Reynold's Number (Re) match and the airspeed isn't over a couple of hundred knots or so.
     
  3. gonzo
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    gonzo Senior Member

    Water does not compress so you can have, for example, cavitation and ventilation.
     
  4. DCockey
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    DCockey Senior Member

    My understanding is the concept of "leading edge suction" came about to resolve an apparent discrepency in the thin airfoil theory. Thin airfoil theory for a section at an angle of attack results in the pressure difference across the airfoil at the leading edge going to negative infinity. Close to the leading edge the pressure difference is inversely proportional to the square root of the distance from the leading edge. Integrating the pressure distribution for lift gives the expected result. But attempts at directly integrating the pressure for drag gave results higher than they should be. The explaination for this discrepency was that the "leading-edge suction" of the infinite negative pressure at the infinitely thin leading edge was not properly resolved and methods were developed to deal with it.

    A similar situation also arises with numerical methods which don't use the thin airfoil assumptions if there is not sufficient resolution of the leading edge. In that case attempts at integrating the pressure along the surface can give erroneous results.
     
  5. DCockey
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    DCockey Senior Member

    Flow of air at speeds up to a couple of hundred knots, Mach 0.3 or so and lower, is essentially incompressible.

    Water is also compressible but less so than air. The result is a much higher speed of sound which means that for any flow related to a boat compressibility can be ignored.

    Cavitation and ventilation are not the result of compressibilty. They are two-phase phenomena, liquid and gas. Cavitation results when the pressure drops low enough that the liquid turns to gas. Ventilation occurs near a free surface when the pressure drops low enough that air is sucked down into the water.
     
  6. gonzo
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    gonzo Senior Member

    I agree with your definitions. I don't understand though, how do you treat air as incompressible.
     
  7. DCockey
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    DCockey Senior Member

    Low Mach number flow of air is treated exactly the same as water is treated as incompressible. In low Mach number flows the pressure differences from atmospheric are so small that the density of air hardly changes. The density is treated as constant.
     
  8. gonzo
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    gonzo Senior Member

    The aerodynamic theory, as I read it, shows higher pressure on the bottom than the upper side of the wing.
     
  9. markdrela
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    markdrela Senior Member

    That's a serious overgeneralization. The low AR on fast airplanes is usually there for other reasons which have little relevance for a sailboat:
    - High roll rate, excess-lift capability for maneuverability (jet fighter)
    - Low supersonic wave drag due to lift (Concorde), etc.

    A more relevant example is a sailplane. It is designed for maximum speed around a course, since that's what a soaring contest is -- just like a sailing race. To make a sailplane go faster, the designer will increase AR right up to the span-rules limit, or structural limit, or cost limit, or transport constraints, or whatever other constraint is relevant. Not too different from a keel.
     
  10. gonzo
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    gonzo Senior Member

    So, you are saying that keels have to be calculated as a wing on a slow airplane? My statement is not an overgeneralization but rather an observation.
     
  11. DCockey
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    DCockey Senior Member

    Correct. Did I say otherwise? The upper surface has a higher magnitude negative pressure.
     
  12. DCockey
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    DCockey Senior Member

    Sounds like the designer increases span right up to the span-rules limit, or structural limit, or cost limit, or transport constraints, or whatever other constraint is relevant. Presumably the wing area and therefore chord and therefore AR is selected based on wing area needed for sufficient lift for takeoff and landing, thickness for structure which then results in a minium chord based on maximum section thickness, etc.
     
  13. DCockey
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    DCockey Senior Member

    But the designer may think in terms of wing area and AR.
     
  14. DCockey
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    DCockey Senior Member

    have to be calculated - no, they can be calculated by any method the designer wants to use. Of course some are more valid than others.

    The methods I'm aware of for calculating keel and rudder performance are based on methods developed for wings and subsonic aerodynamics. I can't think of a method other than perhaps a curve-fit exercise which wouldn't be. And some of the curve-fit methods start with data for wings.
     

  15. MikeJohns
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    MikeJohns Senior Member


    A long chord is much better suited to high loading at lower speeds, the foil can re-attach turbulent flow and also significantly increase Re with V constant. And increasing Re is significant in the reduction of Cdi
    Delta wings are the logical shape to reduce the tip vortex with a smaller chord length at the tip. Tip chord length is very significant for drag reduction. There are delta wings in sub mach1 highly loaded-wing aircraft that work very well.


    But back to hydro-foils, a lot of this theory is idealised aerodynamic theory outside of light air and smooth water. It needs a real dose of reality when you start applying it to boats, where suddenly you have a planform that may not even run to 4 feet on a 45 foot boat. Then foil loading becomes significant The first and foremost function of the wing is to give lift. Induced drag is just the cost of lift, not the end game in itself.

    If you actually separate out the induced foil drag and plot it against friction and form drag you might be surprised just how little it really contributes especially as the Froude number starts to rise and form drag dominates the total drag by orders of magnitude over foil lift related drag.
    In a seaway the wave encounter related drag will even double the total smooth water wave drag. Cdi from the foils becomes almost insignificant, and the real flow over the foils becomes more chaotic making idealised foil theory inapplicable. For the aerodynamicists its like designing a wing to operate not in undisturbed air but in a turbulent wake, different factors apply and a healthy chord length relative to span pays off.

    In reality on a sailboat you need to get away from LD ratios relative to angle of attack and actually relate it to polars of VMG. All factors relate in a much more synergistic way than is usually evident and you need to back off and look at the system complete, and it's not a trivial task.
     
    Last edited: Feb 23, 2011
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