Induced drag

Discussion in 'Hydrodynamics and Aerodynamics' started by Konstanty, Aug 15, 2018.

  1. Konstanty
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    Konstanty Junior Member

    Induced drag at the ends of the sails and keel is the enemy's of the speed. What to do to reduce it ? Any drawings are welcome.
     
    Last edited: Aug 20, 2018
  2. jehardiman
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    jehardiman Senior Member

    Use infinite span?...You can make the span as great as possible, elliptically de-load the tips, or incorporate a double-duty end plate of some sort. That's about it.
     
  3. Konstanty
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    Konstanty Junior Member

    Infinite span this is low stiffness and a weak cross section of the sail. How to use the intense air flow under the boom or over the gaff ?
     
    Last edited: Aug 17, 2018
  4. sandhammaren05
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    sandhammaren05 Senior Member

    Elliptic sail with large aspect ratio. The downside is a tall mast. Keel drag is form drag. Use as thin a keel as possible.
     
  5. Konstanty
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    Konstanty Junior Member

    I am looking for solution to use as power flow through the edges.
     
    Last edited: Aug 20, 2018
  6. Doug Halsey
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    Doug Halsey Senior Member

    One factor that is often overlooked is the importance of speed.

    This is probably because everyone is familiar with the elliptic-wing formula CDi = CL^2 / (Pi * Aspect Ratio) & it isn't immediately obvious how the speed enters into that.

    But notice that CDi, CL, and Aspect Ratio are all nondimensional terms.
    CDi = Drag/(Q * Reference Area); CL = Lift/(Q * Reference Area); Q = 1/2*Density*Speed^2Aspect Ratio = Span^2/Reference Area.
    When these definitions are considered, the dimensional elliptic-wing formula becomes Drag = Lift^2 / (Pi * Q * Span^2).

    So the induced drag (in this case) is inversely proportional to the square of the speed. This means that induced drag is not always dominant; sometimes it's the viscous drag. This is illustrated in the following figure for a hypothetical case of a lifting hydrofoil, but similar arguments apply to keels, rudders, and sails, as well. DragBreakdown_HypotheticalHydrofoil.jpg
     
  7. tspeer
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    tspeer Senior Member

    There's a common misconception that induced drag is due to flow around the tips, which leads to the notion that it can be reduced with proper tip design. Instead, it's more useful to consider the flow in the wake. The trailing vortices are really just the result of the sails or keel having imparted a sideways velocity to the flow, and the flow so affected has to be replaced by new fluid. It's the same pattern you see when you draw a canoe paddle through the water. The paddle imparts a sideways velocity, displacing water ahead of it and drawing in water behind it. At the edges of the paddle, the transition between being displaced and drawn in is particularly intense, which is what we see as the core of the vortex. When you lift the paddle out of the water at the end of the stroke, the momentum of the water continues on and the vortices are left swirling where the edges of the paddle once were.

    The flow behind a sail or keel is essentially the same. Yes, modification of the edge of the paddle might change the flow picture a little bit, but it doesn't fundamentally change the fact that fluid is displaced/drawn in and vortices form at the edges. It's the same with a sail or keel.

    What's really going on is the sail is sailing in a header of its own making, owing to the velocity of the flow imparted to the wake. This tilts the lift vector back from being perpendicular to the freestream relative wind direction. When you account for the force components based on the freestream direction, the tilting of the lift vector shows up as a drag component. This is the origin of induced drag.

    For a given span (mast height, keel depth), the induced drag is a minimum when the wash velocity imparted to the wake is uniform along the span. There are lots of ways of achieving that - planform shaping, camber variation, twist. BTW, the criterion of uniform wash velocity applies even when the relative wind is not constant along the span, although the planform or twist you need to achieve the uniform wash velocity will be different for different relative wind profiles.

    If you want to minimize the induced drag for a given heeling moment, then what you want to do is to vary the wash velocity linearly along the span. Less wash at the head will lower the height of the center of effort, but there will be a drag penalty compared to a rig with the same height and uniform wash. You can use that to your advantage by making the rig taller for the same heeling moment. The increased rig height more than compensates for the drag due to the non-uniform wash velocity.

    So the short answer to your question is, "Shape them for uniform wash in the wake."
     
    tlouth7 likes this.
  8. Erwan
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    Erwan Senior Member

    I would add:

    For high performance boats like A-Cat, consider the wind gradient, and set your priorities between windward & downwind performances :

    For an A-Cat, you can see that windward you have some wind gradient, regardless of the wind shear and you have more apparent wind than downwind.

    Conversly, downwind you have almost no gradient, but some wind shear(twist) and overall for the same conditions than windward , your apparent wind will be lower downwind.

    From these observations, you can set your priorities:
    Windward= more apparent wind=quicly overpowered=lower Lift Coef= lower induced drag = Bell-Shaped lift distribution, with lower CoE might be better than Elliptical shaped (to make it short).

    Downwind almost no gradient with less apparent wind= Higher Lift Coef= Higher Induced drag
    that is why if you want to optimize your rig for both, you will choose an Elliptical Area distribution to minimize induced drag downwind, while extracting the maximum of HP from the apparent wind.

    Happy week end.
    EK
     
  9. sandhammaren05
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    sandhammaren05 Senior Member

    If you fill in the gaps in Newman's book then you will learn that only a flat wing (uncambered) has maximum lift/drag. If you add camber then L/D is reduced. This is nonintuitive, as are many results in hydrodynamics, but the vorticity distribution for an elliptic wing that is parabolically cambered wing is not elliptic, and it's only an elliptic vorticity distribution that optimizes L/D. Elliptic shape is not enough when camber is there. A sail is generally half of a cambered delta wing. The lift coeff. for half
    a flat delta wing is (pi)x(alpha)/4. For half a flat elliptic wing the lift coeff. is (pi)^2(alpha)/2. I've worked out the lift
    coeff. (and induced drag) for a cambered elliptic wing but will not write it here, it's in my book ms.
     
  10. DCockey
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    DCockey Senior Member

    Elliptical trailing vorticity distribution does not require a flat (no camber and not twist), elliptical wing. There are other combinations of planform shape, camber and twist which have elliptical trailing vorticity distribution at a certain angle of attack. It is true that only a flat elliptical wing will have elliptical trailing vorticity distribution at all angles of attack, within the limitations of inviscid thin airfoil theory.

    As tspeer described above elliptical trailing vorticity distribution results in the minimum induced drag for a given lift if the wing span is fixed, but if the wing root bending moment (heeling moment for a sail) is fixed then a linear distribution of trailing vorticity results in minimum induced drag. Note that in the latter case the wing span will vary with different trailing vorticity distributions.
     
  11. sandhammaren05
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    sandhammaren05 Senior Member

    I don't know what you mean by 'elliptic trailing vorticity'. The free vorticity from the trailing edge is drag. The bound vorticity gives the lift. So i'm talking about the bound vorticity, as in Newman. There, an elliptic distribution of bound vorticity yields L/D maximum. Now, what wing shapes and what camber satisfy the condition of elliptic vorticity. I have found exactly two: (i) an uncambered wing at finite attack angle with elliptic wing shape, and (ii) logarithmic camber at zero attack angle (the Kutta condition is violated here). I have found no other. The question is not one of minimum induced drag, the question is what yields maximum L/D. By 'trailing vorticity distibution' I can only understand the free vorticity, but it is only the bound vorticity that fixes the lift.
     
  12. DCockey
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    DCockey Senior Member

    I mean an spanwise elliptical distribution of the trailing vorticity in the wake. The trailing vorticity strength equals the spanwise derivative of the bound vorticity.
    Review pp 193-197 and figures 5.18 through 5.21 in Newman for more information.

    There is a significant difference between in individual claiming only one or two solutions exist to a problem and stating that they have only found two solutions to the problem.
     
  13. sandhammaren05
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    sandhammaren05 Senior Member

    Double integral (one singular) of circulation density and it's derivative along the wingspan, not in the wake. I've evaluated the induced drag for various cases. The elliptic density is along the wingspan, not in the wake. The vortex sheet wake is unstable, twists to form the tip vortex.

    Again, it's only the span-wise bound circulation density that's elliptic when L/D is optimal. If L/D is not optimal, which seems to include what you're considering, then the spanwise bound circulation density is not elliptic. An elliptic wing shape yields an elliptic spanwise circulation density iff. the wing is uncambered, 'flat'. Otherwise, elliptic wing shapes do not yield spanwise elliptic circulation density. I can provide you with worked-out examples. E.g., adding camber to an elliptic wing shape produces a spanwise circulation density that is not elliptic, so L/D is not optimal. The free vorticity trailing off the wing is not elliptic.

    The easiest way to minimize the drag is to shut off the wind speed.
     
    Last edited: Aug 19, 2018
  14. sandhammaren05
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    sandhammaren05 Senior Member

    PS I cut my baby teeth on Newman and Landau-Lifshitz.
     

  15. Konstanty
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    Konstanty Junior Member

    The wind blowing a round the boom or gaff has a less sharp angle. If it were to set small sails there would give a beneficial force forward. I will try to draw something. Drawing is easy. It's harder to do. :)
     
    Last edited: Aug 19, 2018
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