Forces on sailboats (#3)

Discussion in 'Hydrodynamics and Aerodynamics' started by Sailor Al, Jun 23, 2021.

  1. Sailor Al
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    Sailor Al Senior Member

    Thanks for your work, you are obviously on the same page as me.
    I have a question, since my initial request was for experimental data, I have to be a bit picky with calculated numbers. I'm not sure you have factored a significant addition to your drag analysis and Froude based estimates.
    When a Farr40 is working upwind at 7.2 kts in 13 kts TWS, and heeling at around 20° with an AWA of around 25°, it's making leeway of around 4°. This is the AoA for the keel to develop sufficient lateral force to balance the lateral force from the wind on the sail.
    I agree with your 4000 kgm for the righting moment from the keel, (1400 kg bulb at 2.7 metres at 20° ~= 4000) but don't forget there's a further 700 Kg of crew sitting on the rail with a moment arm of 2 metres (1400 kgm).
    Doing the math with a CE of the sail at about 7 metres, the lateral force to balance that 5400 kgm is around 800 kgf
    I'm sure that generating that much lateral force from the keel comes at a significant cost in terms of drag from the keel, which would significantly increase your 126 kgf estimate.

    My apologies if you have factored this into your estimates, or if I have missed something.
    I'd be interested in your feedback.
     
  2. AJB
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    AJB Junior Member

    Sailor Al,

    My 'yacht' is not a Farr 40 - just behaves a bit like one. Some clarifications:

    1. The 5400 kg displacement includes crew weight, so the estimated RM includes this. In part, I had been fiddling around as if operating short-handed or typical beer can race; and provisionally at 12 knot TWS - i.e. just below full heel.
    2. Not sure how you have arrived at 'RM bulb' of 400o kgm... 4000/1400 = 2.85, but the transverse CB only moves to about 0.75 to leeward of the CL at full heel, so the bulb in isolation might be operating at an arm of about 1.5 metres at 20 degrees heel.
    3. The heeling couple is around 8m (using the ORC method for calculation) not the 7 metres you have suggested. (ORC uses 40 % of rig height for aero CE and 40% of draft for hydro CLR)
    4. The induced drag of the foils is less than you think. The (primary) viscous drag is already included in the 60 kg total - i.e. the foil surfaces are included in the total wetted surface of 30 m2.
    5. Around half the upwind side force is provided by the rudder, which all things optimised is operating at the helm angle of around 3 degrees plus leeway of 4 or a bit less - probably 7 degrees AOA in this example.
    6. The induced foil drag is likely to be in the range .004 - .006 of the force generated, with high grade, semi-laminar foils. So probably less than 3 kg of foil induced drag.
    7. The induced hull drag (caused by the leeway crossflow) might be about 2/3 of that, in addition. So probably there is a total for leeway induced drag of around 5 kg. This is say 80% of the 6 kg total allowed, the balance being increased resistance arising from heeled hull form asymmetry.

    Some generally accepted numbers for these foil drag coefficients are in Chapter 19 of Frank Bethwaite's first book.

    Trust this advances the cause!

    Cheers,

    AJ
     
  3. Sailor Al
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    Sailor Al Senior Member

    My apologies, I shouldn't have entered into a debate on modelling techniques, which is why I initially enquired about the availability of experimental results.
    James Conger published some experiments towing his J/32 and found its drag was around 1200 N ( ~120Kg) at 7 knots.
    upload_2021-7-13_9-27-31.png
    But that was in a direct tow, with no leeway, and in discussion with him about the effect of leeway, he responded:
    "The hull drag for my boat was measured with zero leeway (tow test). There is additional drag as the boat is pushed sideways through the water. If you know the leeway angle you can estimate the additional drag due to the keel and hull resisting leeway by estimating the lift/drag ratio of the stuff underwater to be about 5."

    I would love to get some experimental data to explore this further.
     
  4. Doug Halsey
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    Doug Halsey Senior Member

    Here's some data from Marchaj's Aero-Hydrodynamics Of Sailing that might be of interest to you. Unfortunately, there isn't any more information about the design or the source of the data than what's shown (at least I haven't been able to find any yet).
    ResitanceCurves_Marchaj.jpg
     
  5. gonzo
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    gonzo Senior Member

    The major shortcoming of all those approximations is that they treat a boat as a steady state system, which does not reflect the reality of a sailing boat. The OP is requesting actual numbers and not the usual simplification in a single plane. For example, in a short chop the leech of the sails need to be loosened so when the mast whips fore and aft it doesn't slow down the boat. A mast that "pumps" will increase and decrease the chord of the mainsail. Yawing, heaving and rolling change the angle of attack of the wind, even though the wind direction is steady.
     
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  6. Sailor Al
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    Sailor Al Senior Member

    Yes, I agree, the lack of attribution makes it hard to determine whether they are experimental or modelled numbers.
    In my view, the smoothness of the curves would argue for the latter. I suspect that much would have been made of the test design if they been derived experimentally.
    Thanks for that, you know how much I enjoy reading Marchaj!
     
  7. Sailor Al
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    Sailor Al Senior Member

    No, not at all. It's that they are approximations, not experimental results.
    I would be delighted to get any experimental results, steady state or not, but recognise that steady state would be the experimental challenge.
     
  8. AJB
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    AJB Junior Member

    Doug H and all...

    Interesting times.... but the graph from Marchaj does not make much sense, nor for that matter, his comment.

    Consider that at 6 knots, and at 0-10 degrees of heel, his yacht has around 200 lbs drag, which inevitably is about 50/50 viscous and wave/form drag.

    So let us assume that at 10 degrees heel, wave drag is also 100 lbs.

    But somehow, between 10 degrees of heel and 30 degrees, total drag increases by a factor of 2.5x, and assuming the laws of physics about viscous drag are not revoked, other drag has increased from 100 lbs to 350 lbs!!

    Exhibit A might be many designs whose drag reduces as heel increases - e.g. scows, TP 52s, Comanche etc etc.... And one even suspects that the drag of the well evolved meter boats (8s and 12s) from pre WWII also decreased as they heeled, with additional effective waterline outweighing slightly greater wetted surface.

    Exhibit B might be statements in relation to undiversifiable drag from certain designers (e.g. Farr, Peter van Oosanen, Davidson) to the effect that (in respect of sailing upwind) 'the only significant untapped source for drag reduction in heavy keelboats is from reduced crossflow on the hull' - i.e. the approach toward zero leeway. Hence the near zero leeway performance of the last 12 metres and the next generation IACC boats.

    Marchaj's comment talks about tacking, and is not reflected in the graph in any understandable way.

    In historical terms, the work (in around 1935) to establish realistic tank test methods led Olin Stephens and Ken Davidson to conduct laborious but fruitful tank to full size testing using using the 33 footer Gimcrack, measuring around 70 parameters. The resulting paper (Davidson) makes compelling reading, and formed the basis for subsequent work at MIT.... Gimcrack was evidently 25,500 lb (11.5 tonne) displacement and 33 foot LWL, with published drag figures of around 220 lbs (100 kg) at 6.5 knots.

    The most recent work to extend this knowledge in public disclosure appears to be a thorough and expensive exercise from an Italian team lead by Fossati, which included real time pressure and sail camber measurements, capable of integration with desk top aero modelling.

    Personally, I would worry less about the dynamic issues, i.e. the 'not quite steady state' problem. In a heavy displacement yacht, with good trim, equipment and steering (and not to say, relatively inelastic rig) the AWA can be kept within less than +/- 1 degree and the boat speed within about 1% of target. A heavy keelboat seems to 'iron' the flows quite effectively - a quasi equilibrium condition is readily achieved.

    Any feedback appreciated..

    AJ
     
  9. Doug Halsey
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    Doug Halsey Senior Member

    When the drag curves start looking like parabolas, it's a good bet that induced drag is involved, which means there is some amount of side force included. It might be reasonable to assume that the side force is constant at each heel angle, in which case the induced drag would be proportional to 1/Vs^2.

    When actually sailing, the smaller speeds would also have smaller side force, and the drag curves wouldn't have the parabolic shapes.
     
  10. Sailor Al
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    Sailor Al Senior Member

    I think that's because the resistance has been increased not by viscous drag, but by the hydrodynamic drag from the leeway on the keel. You can't get lift without drag.
    But please, can we move on from Marchaj's chart. As I said earlier, I'm pretty sure it's not from experimental results.
     
  11. gonzo
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    gonzo Senior Member

    Steady State is used on theoretical calculations. It assumes there are no changes, or that the change is constant. In the physical world, changes are chaotic.
     
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  12. Doug Halsey
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    Doug Halsey Senior Member

    Don't you think that steady-state predictions can be pretty realistic in steady, moderate winds and smooth water? In those conditions, I think the larger sources of errors lie in the uncertainties in the inputs (the actual sail shapes, for example), rather than the unsteadiness.

    And the more skilled the sailors, the less chaotic the changes seem.
     
  13. Doug Halsey
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    Doug Halsey Senior Member

    Davidson has published similar curves with data for a 6-Meter Class, with the curves of constant heel angle limited to only the realistic speed values.
    Davidson_6MeterData.jpg
     
  14. gonzo
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    gonzo Senior Member

    Skilled sailors are continually changing trim, heading, hiking in/out, etc. I think you will find it virtually impossible to find smooth water (no waves) and moderate winds.
     

  15. Doug Halsey
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    Doug Halsey Senior Member

    I guess all VPPs must be pointless then.
     
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