Getting Coefficients of lift for single sail boats.

Discussion in 'Hydrodynamics and Aerodynamics' started by Tristan perry, Oct 19, 2021.

  1. Tristan perry
    Joined: Oct 2021
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    Tristan perry New Member

    Hello Everyone, I'm writing hoping to write a paper this year about sailing which explains the math behind it, but I've run into a few road blocks. First, nobody I know has used xfoil before, and therefore I'm not at all sure if I the lift coefficients I'm getting out of it are correct.
    To solve it analytically, I thought that perhaps f, in f=ma could be equal to the lift force and I could solve for it coefficient of lift this way, but I have no concrete data I could use to support my findings.
    Do my methods sound reasonably reliable (even if not perfect)?Do any of you have any resources that you could connect me to?
  2. patzefran
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    patzefran patzefran

    According to your apparent level of knowledge, I doubt you could be useful in writing anything about sailing !
    However, for your own , you can read Aero hydrodynamic of sailing from C. A. Marchaj
  3. Tiny Turnip
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    Tiny Turnip Senior Member

    Hi Tristan - welcome to the forum. Try to ignore patzefran's rudeness; I doubt they could be useful in the field of education! However, from their previous posts, I suspect they have a good knowledge of the subject area, and the recommended reference is likely to be helpful.
    There is a great deal of expertise on the forum, however you may find it is often delivered robustly, from folk who know their subject well, but perhaps not know how to help people learn. Keep a polite, cool head and a thick skin, ignore those playing alpha sh*tposter, and you should find a wealth of information here. Good luck with the paper.
  4. Erwan
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    Erwan Senior Member

    Hi Tristan,
    While XFOIL is a great freeware to study wing section, I doubt it would be usefull at your stage.

    In other words you have to settle (to write) the balance of forces and moment for the boat you are studying:
    To do so you assume the boat is sailing at constant velocity (v=constante and gamma=0) but you need a minimum of actual datas
    You need least:
    1-Boat Velocity and boat righting moment
    2-TWS and TWA

    From the datas above you can derive AWS and AWA
    As your boat has only one sail it make it easy:
    with AWS , Boat Righting Moment, Sail area, Gap between footsail and deck (Oswald ratio)
    with basic assumptions regarding the C
  5. Erwan
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    Erwan Senior Member

    with basic assumptions regarding the CoE of your sail you can derive the sail's lift necessary for the balance of forces

    And with the lift, the Oswald Coef, the AWS you have eeverything to find the required lift coef of your sail without XFOIL.

    Patzefran is an engineer who already wrote VPP on EXCEL, so your candid questions might have upset him a little bit, but dont pay attention, he is a brilliant brain, and I feel confident he will post helpfull comments in the future, but it is your responsability to go beyond of your "Total Rookie and Candid Questions" in order to trigger helpfull answers instead of "compassion" for the idiots.

    Have a look at tspeer homepage www/ check Optimum Sailplan but not only

    Good luck
    Tiny Turnip likes this.
  6. patzefran
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    patzefran patzefran

    Tristan , Sorry for my rudeness, Marchaj introduced me to physic of sailing, 40 years ago. He was controversed by some people in this Forum, but it is still the bible
    Thank you for your kindness !
    PS : Unlike Tom Speer, my VPP and other flowfield codes works on Fortran, not on EXCEL
    Tiny Turnip likes this.
  7. Dolfiman
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    Dolfiman Senior Member

    Hello Tristan, welcome on this issue. With reference to the model proposed by G.Hazen in 1980 and used in the VPP's in those days, coefficients for lift and drag were (as reported in "Principles of Yacht design - 2nd edition 2000 - Larson & Eliasson") :
    Sails coefficient, lift CLo :
    awa. Main. Jib. Spi. (awa stands for apparent wind angle) :
    27. 1,5. 1,5. 0.0
    50. 1,5. 0,5. 1,5
    80. 0,95. 0,3. 1,0
    100. 0,85. 0,0. 0,85
    180. 0,0. 0,0. 0,0

    Sails coefficients, viscous drag CDo :
    awa. Main. Jib. Spi.
    27. 0,02. 0,02. 0,0
    50. 0,15. 0,15. 0,25
    80 0,8. 0,15. 0,9
    100. 1,0. 0,0. 1,2
    180 0,9. 0,0. 0,66

    And don't forget that :
    ** Lift CL can be = CLo * Flat
    (Flat is a coefficient representative of the camber of the sail, from 1 to o,6 when upwind by breeze).
    ** Sail total drag CD = CDo + CL^2/pi/AR
    AR = Aspect ratio of the sail of area SA : AR estimation ~ (1,1*Zmast)^2/SA
  8. gonzo
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    gonzo Senior Member

    F=ma is correct. However, to calculate m and a in a dynamic system that moves in 6 axes is not easy. Whole teams of engineers with huge resources struggle to get a good approximation. Unless you are trying to do years of research, I think you are trying to bite more than you can chew. We have all done that. The more modest and realistic approach is to work on a single aspect or area of sailing. For example, I once chose for a final paper in a class to calculate the energy dissipated by a bullet that went through a 3/8" mild steel plate. As simple as it seems, the project turned into a huge amount of calculations with mediocre results.
  9. Remmlinger
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    Remmlinger engineer

  10. philSweet
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    philSweet Senior Member

    See papers on sailing vessel Dyna. Many are authored by Grabe.

    See also -

    Chesapeake Sailing Yacht Symposium archives.

    Amateur Yacht Research Society archives

    Sailing Yacht Research Foundation archives

  11. Pablo Sopelana
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    Pablo Sopelana Junior Member

    Hi Tristan,

    One approximation to the lift coefficients could be to use those of the ORC VPP ( VPP documentation 2021.pdf, section 5, page 34).

    If this is something that you think can help you out, then I have implemented based on ORC the following online calculation templates:

    => Individual sails:
    - Mainsail aerodynamic coefficients (
    - Headsail aerodynamic coefficients (Headsail aerodynamic coefficients (calculation)
    - Headsails “Set Flying” aerodynamic coefficients (Headsails “Set Flying” aerodynamic coefficients (calculation)
    - Spinnakers aerodynamic coefficients (Spinnakers aerodynamic coefficients (calculation)

    => Sail sets:
    - Sails sets: Mainsail + Headsail (
    - Sails sets: Mainsail + Flying Headsail (
    - Sails sets: Mainsail + Spinnaker (

    Each template requires some data input related to hull, sails, and rig. The results are displayed in chart and table form, for values of apparent wind angle from 0 to 180, every 1 degree. I attach some images as an example:
    Mainsail_headsail.png Mainsail_headsail_table.png

    To use the templates, you have first to register to the website ( You can do it for free, and you will have 30-day free access to all templates. And if you are a student who needs to access those templates for more than 30 days, let me know. I will be happy to help you.
  12. Sailor Al
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    Sailor Al Senior Member

    Check out Aerodynamic force on a sail and maybe we can work together using Swept Volume Theory to start to answer the "Unanswered questions" posed in that paper.

  13. rnlock
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    rnlock Senior Member


    I'm not sure that I understand your proposed method.

    Xfoil might be pretty useful for, say, an America's Cup catamaran with a high aspect ratio wing. Or a high aspect ratio sail. But if you've got a gaff sail with a 2-1/2:1 aspect ratio, or a sail that's significantly swept, the flow isn't 2D anymore and it won't be all that much help.

    If you DO want to use Xfoil, there's a program called Profili which provides a much friendlier user interface, among other things, such as drawing rib shapes. I've heard that its estimates of maximum lift coefficient might be a little rough, but that might only be for the lower Reynolds numbers we see in model airplanes. Something to check.

    If you can measure forces, say at the partners and at the base of the mast, and their direction compared to the relative wind direction, you could figure out the total force on the sail, divide it by the area of the sail, and then divide by the dynamic pressure at that wind velocity. Unfortunately, that doesn't account for the wind gradient. The top of the sail will generally see significantly stronger wind, in a different direction, than the bottom. It's a real can of worms. Maybe if you were on a clipper ship, and unfurled only the topgallants, you could ignore the wind gradient. ;-) Or you could put your boat on a trailer and tow it around on some night when the air is perfectly still, with the trailer a good long distance behind your very small and low vehicle, and the boat jacked up a few feet.

    I suppose, if you made two rigs, put them base to base, and made a glider out of that, you could get an idea of what the lift coefficient would be if there wasn't any wind gradient, but that would be a large and unwieldy project if you did it at full scale so the Reynolds numbers would be right. Maybe looking at the stall speed of single surface hang gliders, vs their loading, would get you within an order of magnitude. Probably you'd want to find a hang glider more similar to your sail, but I picked the Litesport 3, which is probably equivalent to a very good wingsail. It stalls at 16 mph, where the dynamic pressure is 0.754 lbs/ft^2. The wing loading works out to be 1.63 lbs/ft^2. So the lift coefficient is 2.16. But I bet all but the most sophisticated sails would have significantly lower lift coefficients. At lest it gives you some idea, enough to tell if you've slipped a decimal point somewhere. But not good enough for performance prediction, I'd say. And you have to keep in mind that a real sail wouldn't see the same air speed at all points.

    Maybe a sophisticated aerodynamicist with an extensively instrumented wind tunnel, with lots of wake rakes, can help you out. Maybe you could cover your sail with an array of hot bead anemometers..

    I don't know if I helped you much.

    I wonder if you have as much trouble with the TLA's* on this page as I have?

    *Three Letter Acronyms
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