About the induced drag of sails

Discussion in 'Hydrodynamics and Aerodynamics' started by Mikko Brummer, May 18, 2020.

  1. patzefran
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    patzefran patzefran

    Doug, sorry, bad reading ! you already mentioned clew height was relative to the span !

    Erwan, just a detail, you said :
    "I just compared different sailplans with same area, same span, same righting moment, just Downwash assumptions are different. Everything else equal, no twist, constant Cl along the span. "

    ---> to my knowledge, unless elliptical circulation hypothesis with constant downwash alfai , Cl cannot be constant along the span.
    According to hypothesis used to obtain the lifting line solution , it depends on the downwash distribution alfai over the span, Cl = cl0+ (dcl/dalfa)(alfa-afai) , were cl0 and dcl/dalfa is characteristic of the 2D profile (untwisted !)

    Cheers
     
  2. tspeer
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    tspeer Senior Member

    VLM would be the simplest. A panel code would be the next step up.
     
  3. Doug Halsey
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    Doug Halsey Senior Member

    There are other lifting-surface codes that might be considered as falling between VLM and the panel methods, but they might not be as easily available as VLM, and they didn't end up offering much (if any) better accuracy than VLM. In fact, one of the researchers from our department published a number of papers about how remarkably accurate VLM was: On the remarkable accuracy of the vortex lattice method - ScienceDirect

    I worked on something called the Elementary Vortex Distribution Method (EVD) in the early 1970's. Instead of horseshoe vortices (or point vortices in 2D), it used distributed vorticity that even modeled the singular behaviors at leading edges & flap hinges. These are shown nicely in this NASA figure, and proved much better for modeling the jet sheets that we were studying, even if they didn't help much for conventional wings.
    EVD_LiftingSurfaceTheory.jpg
     
  4. Erwan
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    Erwan Senior Member

    Yes I assumed Decksweeper =0 gap.
    Yes my downwash parameters are almost arbitrary, I just wanted to compare the different sailplans varying only one parameter:
    the downwash figures at the foot and the head.

    What is interesting is that the extrem case :Downwash foot :6.00 Downwash Head :-4.37
    VORTEX displays a lifting distribution with some negative lift at the top.
    As there was a debate about this point for the AC75 rig , it provides a kind of theorical confirmation in addition to quantitative data for an A-Cat rig, in the above-mentionned conditions.

    While the computed sail's chord at the foot is probably not practicable with 37% of the span (11 feet for a 29.5 feet span), it remains an interesting information for me.
    Also with more driving force, probably more boat speed, then lower AWA so the projected Lift and Induced drag would be different.
    And of course, it would be necessary to explore how such an extrem rig geometry would perform when a bit far from these design conditions.
    I am "playing" with this issue, because our rig geometry is inherited from a time where the A-Cat had much lower apparent wind than today's foiler, so it is a candid approach to explore alternative saiplans.

    I try to attach the VORTEX file for the Extrem downwash case.

    Thanks for the note Mr Speer, I know I have some homework to do.

    Very interesting this Skirt/study Doug, thanks for sharing, I guess Moth sailors will enjoy it too.

    You are perfectly right, but as mentionned, I try to change only one variable at a time, to understand better the effects of this variable. Just like exploring partial derivatives in a complex function with many variables.

    Happy Sunday and apologizes for late reply.

    Cheers
     

    Attached Files:

  5. Doug Halsey
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    Doug Halsey Senior Member

    More about the gap effect:

    Elliptical circulation produces constant downwash across the span for the case of zero gap (assuming 1/2 ellipse + reflection) or the case of very large gap (assuming full ellipse with no reflection).

    For other values of the gap, the circulation distribution is a blend between the half-ellipse and the full-ellipse, as shown below:
    GapEffects.jpg
     
  6. Erwan
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    Erwan Senior Member

    Thank Doug, it is interesting to notice little difference between 10% gap and infinite gap.

    In my former posts it should be mentionned that I used VORTEX a little bit beyond its intended domain that is why the extrem downwash slope/ negative lift at the top, comes along with negative area at the top.

    To address this point, I think I will try use negative lift coef it should make it, and see if it does not spoil the calculations.
    But unfortunatly, not today.

    Cheers
     

  7. Pablo Sopelana
    Joined: Mar 2021
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    Pablo Sopelana Junior Member

    I have implemented an online calculation template that uses Prandtl's classical Lifting-line Theory behind the scenes.

    The inputs required are:
    - b: span length of the wing or draft of the appendage
    - AR: Aspect ratio
    - Taper ratio
    - 2D lift curve slope of the root's airfoil
    - 2D lift curve slope of the tip's airfoil
    - zero-lift angle of attack of the root's airfoil
    - zero-lift angle of attack of the tip's airfoil
    - geometrical twist angle at the wingtip
    - gap: whether it is a standalone wing or on the contrary, it is an appendage attached to a surface without any gap whatsoever (unfortunately, this variable is either "1" or "0" and cannot evaluate the influence of different gap lengths as it was part of the discussion on this thread).
    - Velocity of the undisturbed fluid
    - Fluid density

    All the results are available for angles of attack from 0 to 15 degrees and are presented in chart and table formats:
    - Wing / Appendage coefficients: CL, CDi, e (Oswald's efficiency factor)
    - Wing / Appendage forcers: lift, lift-induced drag
    - Spanwise section lift coefficients (Cl)
    - Spanwise Circulation distribution
    - Lift per unit span (L')
    - Induced drag per unit span (D')
    - Spanwise induced angle of attack
    - Spanwise downwash velocity
    - Spanwise chord lengths

    If you would like to check it out, it is reachable at:
    Unswept Wings: coefficients, forces, circulation, lift per unit span, and downwash (calculation) https://navalapp.com/articles/unswept-wings-coefficients-forces-circulation-lift-per-unit-span-and-downwash-calculation/

    Please be aware that to use the template, you have first to register on the website. I have put the template behind registration to avoid bots and spammers (since it has associated computational costs). You can subscribe free and get free access to the template and any other template for 30 days. After that, some of the templates will be only available to Advance and Pro subscribers. But if interested, please give it a ride, I will be very interested in getting your feedback.
     
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