Prandtl's lifting-line method for sails

Discussion in 'Hydrodynamics and Aerodynamics' started by Remmlinger, Feb 21, 2023.

  1. Mikko Brummer
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    Mikko Brummer Senior Member

    Thank you Uli for posting Ulisail. I devised a simple template to easily visualise results. Mainsail values are in black, headsail in red.

    If I understand correctly, you use interacting lifting lines to solve effective angles of attack along the span, then insert empirical Cl values at different heights, and find the corresponding camber etc. values from that?

    You mention the edge vortices and the Lamar correction but it doesn't show at the foot of the mainsail circulation?

    I assume you are using a mirror model to allow for the effect of the hull & sea surface? At what height? In my MacSail VLM program I found the best correspondence to wind tunnel & CFD results when I set the mirror surface at about half the freeboard height of the boat. At sea surface, the lift values would be too low, and at deck level exaggerated.

    Thanks again and I will run comparisons with CFD when I find the time. Your Dehler 33, by the way, is 600 kg lighter than mine, and tippier too.

    TWA 42 Leeway 4 Jib 105% HiClew.jpg TWA 42 Leeway 4 Jib 105% LowClew.jpg TWA 42 Leeway 4 Genoa.jpg
     
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  2. Remmlinger
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    Remmlinger engineer

    Thank you so much Mikko for testing my program. I really appreciate that you took the time.
    This is exactly right for the mainsail. Depending on the effective angle of attack, I get the optimal camber (best lift to drag ratio) and CL from XFOIL. The optimal camber did not work for the headsail. The sheeting point on deck, the camber, and the sheeting angle depend on each other. Also, the optimal camber would result in a sail that can not be produced. Therefore, I prescribe the camber as one of the trim parameters. The sheeting angle follows from the camber, the second trim parameter is the twist. The CL-values are not at the best L/D-ratio, but the sail is more realistic. Currently, a weak point is the part of the jib, that is below the clew. The sail shape is not smooth. I am working on an improvement and will publish an update soon.
    You are too experienced to be fooled. You are absolutely right. Lamar calculates the vortex lift as a total force for the complete wing that is added to the "normal" lift force. I first tried to distribute this additional lift near the foot of the sail, but this significantly deteriorates the convergence. One could argue that the induced velocities by this vortex are already contained in the trailing vortices, and the additional lift is only produced by the shift of the vortex to the suction side of the sail. I decided to add the vortex lift as a lumped-value to the total lift force after convergence. Since the difference is only a few percent, the error might be small.
    I also made the same tests as you did. Unfortunately, I got contradicting results from wind tunnel tests and full size tests on the water. My code uses the deck level for closed hauled upwind sailing. For larger sheeting angles, I determine the amount of foot length of the sail that is beyond the foot rail. I then use this ratio to calculate an average distance from the distance to deck and water surface.
    You are right. On the sail plan from the yard it says 3.6 tons. The righting moment for 1 degr. is given with 69 kgm. The ORC-database has even 4055 kg. I will check.
    I am looking forward to your CFD-simulation!
    Thank you,
    Uli
     
    Last edited: Feb 26, 2023
  3. Remmlinger
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    Remmlinger engineer

    Mikko, may be you can use the attached CAD-files. I exported the sail shapes as a point cloud and imported it into Rhino. It is the "light" Dehler 33 at TWA=40 deg. D33 TWA40.JPG
     

    Attached Files:

  4. Mikko Brummer
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    Mikko Brummer Senior Member

    OK, will do, I can use the IGS directly, I don't have Rhino. These are very flat.. they would not be realizable from sailcloth, due to the convex camber distribution of the mainsail - I could tell from the graphs that your model tends to produce this kind of shapes. This is a known problem for inverse design methods of sails - I recall someone (maybe Kerwin himself, or Milgram?) writing an inverse design VLM program sometimes in the 80'ies. It produced very flat sails, they even built a set for Stars but they were all too flat for real world sailing- the jib was some 6% in camber, as I recall. But it was all inviscid, your approach is on a more solid basis due to the empirical/XFoil data.

    I will still need the apparent wind speed & leeway, or true wind & boatspeed. You could perhaps add apparent wind speed into your out-file, for reference. You don't mention how your define the chord length distribution, for the headsail obviously more or less triangular, but for the mainsail?

    My standard hull model for the simulations, by the way, is your Ulilines Dehler 33, which I've then scaled to fit different boat sizes (and added a deck & coach roof) :). I have plenty of underwater with my D33 Dyna Ulilines, too, but that's another story.
     
  5. Remmlinger
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    Remmlinger engineer

    Quick answer: the missing information is in the attached file for each panel.
     

    Attached Files:

  6. Remmlinger
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    Remmlinger engineer

    I can not change the camber of the mainsail, but I can easily change it for the headsail. Before I wrote the program, I looked at measured flying shapes on the water (sailing dynamometer Fujin), in the wind tunnel (Fossati) and on your website (The Quest for the Perfect Shape). In all cases, the camber for the headsail increased linearly with height from foot to head. Therefore, I did the same in my program. Now I made a test with constant camber instead and - surprise, surprise - the driving force remained exactly the same. The optimal twist is reduced, which leads to larger angles of attack in the upper part of the sail, where the camber is reduced compared to the initial case. The lift coefficient is therefore similar. I attached the CAD-file. This sail might be easier to produce.
     

    Attached Files:

  7. Mikko Brummer
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    Mikko Brummer Senior Member

    OK, I will take a look at it. The genoa is actually OK, it was the mainsail with convex camber that would be difficult. You are right, it's the combination of camber & twist - twist is most of the time linear or very close to it, though full battens, mast bend & backwinding can make a difference.

    I did several runs already - the sails are beautiful, although at TWA 40 there would appear to be a separation vortex on the inside of the Genoa. First I ran without the hull, the added the hull, but there was little difference in the forces. I thought the sea surface at the tack of the Genoa would increase forces, but not remarkably - sails on the deck are sealed by the hull & there's a little more wind higher up.

    This is how I imagined your setup, correct? A leeway of 6, Heel 27, TWA 40 at a boatspeed 5,9 kn would give an AWA 25,4 deg in a horisontal plane at 10 m height? The wind gradient you specify appears to be very weak, normally we assume more. Which incidentally brings up that as I recall, a wind gradient/shear was a no-no in the (inviscid) lifting line theory, with the assumption of irrotational flow?

    UliD33TWA40 AWS 7,7ms AWA 25,4.jpg
     
  8. Alan Cattelliot
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    Alan Cattelliot Senior Member

    Do not want to be troublesome here, but how is it possible that sails are optimised with no mast bending and no forestay sag ?
     
  9. Remmlinger
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    Remmlinger engineer

    I define the apparent wind angle relative to the x-axis of the boat (centerline). The values at 10 meter above the water plane are:
    wind speed 10 kts
    boat speed 6.1 kts
    leeway angle 6.8 degr.
    heel angle 26.8 degr.
    true wind angle relative to x-axis TWA = 40 degr.
    true wind speed at 10 meters height Vtrue = 5.144 m/s
    x-component of boat speed VBx = 3.116 m/s
    y-component of boat speed VBy = 0.372 m/s
    x-component of apparent wind = Vtrue*COS(TWA) + VBx = Vax = 7.057 m/s
    y-component of apparent wind = Vtrue*SIN(TWA) - VBy = Vay = 2.935 m/s
    Beta apparent wind = ARCTAN(Vay/Vax) = 22.58 degr.

    I use for the wind profile the logarithmic "law of the wall". The references are given in the paper. The change in AWA due to the wind gradient has the same effect as the twist of the wing on an airplane. No reason to abandon the lifting-line method like I use it. Many cases of potential flow have a velocity gradient and are still irrotational.

    PS: your picture with the hull is impressive
    PS2: I found a typo in the code, that has a (small) impact on the results. An update is available on my website.
     
    Last edited: Mar 2, 2023
  10. Remmlinger
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    Remmlinger engineer

    This is beyond the capabilities of the lifting line method. You would have to combine the aerodynamic model with a model of a flexible rig. This rig model would have to be an interpolation of results that you might get from finite-elemente-computations. Fast optimizations are impossible with such a huge computational task. Here, I assume, that the results of the lifting-line method are the flying shape of the sail. To know the optimal flying shape is already valuable information. I hope, the sailmaker will know, how to cut the sail, to produce this flying shape.
     
  11. Alan Cattelliot
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    Alan Cattelliot Senior Member

    Here is what a sailmaker can say about FSI, in relation with his purpose of sail making :
    FSI Analysis - Elvstrøm Sails https://elvstromsails.com/technology/fsi-analysis
    "This methodology is very often used in projects within the super yacht and grand prix racing segments. For one off projects the method is a must and essential to obtain an acceptable starting point for the sail designs."​

    The starting point of a sailmaker. These are any theoretical calculations, with regards with reality on water. If your scope is to build a VPP based on a sail model, the lifting line method is surely capable of highlighting some trade-offs. Also, with less refinements, the ORC VPP method is as good. In the end, true polars will be recorded from live sessions by the skipper and its crew. I understand that your goal is to find "the ideal shape", and I wish that you can achieve that. If we take a deeper look on what's happening on the water, we can find studies like this one, that includes FSI effects :
    Experimental validation of unsteady models for fluid structure interaction: Application to yacht sails and rigs https://www.academia.edu/19001560/Experimental_validation_of_unsteady_models_for_fluid_structure_interaction_Application_to_yacht_sails_and_rigs
    "The loads are well predicted, simulated inthe right range of effort. Indeed, it is rather difficult in practice toaccurately determine the actual dimensions and mechanicalcharacteristics of each rig item. A lot of effort has been devotedto improve the accuracy of all the parameters used as inputs tothe model, but this issue remains a source of discrepanciesbetween the measured data and simulation results."
    As you can see, quite a variations in real loads. Even without taking into account the mast bending and the sag, the fabrics themselves are responsible for quite a difference between rigid and flexible calculations :
    Fluid-structure interaction analysis of deformation of sail of 30-foot yacht - ScienceDirect https://www.sciencedirect.com/science/article/pii/S209267821630396X
    "A comparison of the flow characteristics and the lift and drag forces of the deformed sail shape with those of the initial one shows that a considerable difference exists between the two and that FSI analysis is suitable for application to sail design."
    If FSI represents such an huge computational task, you may perhaps make us of more "real" 2d sections, that develop naturally in thin sheet in tension. This parametrization has been found to give a precision sufficient to be used in a VPP, at least to compare boats with similar mast (EI curves along heigh), shrouds and stays.
    upload_2023-3-2_23-10-42.png
     
  12. jehardiman
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    jehardiman Senior Member

    Ok, second aside...
    Alan, after decades of reviewing technical documents, I have learned to evaluate each technical comment I make with the following...

    1) Is the comment quantifiable...can you actually "measure" or "know" the "unknown"? There are a lot of "Known Unknowns" that are just grouped together in that 5%-15% "seaway" margin.

    2) Is the comment significant...does it make a difference above and beyond 10-20%. Is the omission significant enough to exceeded the known issues with the algorithm. I.e. stating that there is an AoA issue in a program that does not address real world pitch and roll is pedantic.

    3) Is it just Nitpicking...are you just stating "I wouldn't have done it that way....and here are 3 (carefully selected) papers to back me up." As I stated in the CFD thread, there should always be two or more methods to analyze the situation, another solution does not mean it is better, just different.

    I again return you to your regularly scheduled discussion...
     
  13. Alan Cattelliot
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    Alan Cattelliot Senior Member

    I appreciate. Thanks.

    The second link highlights the difference between actual measurements and FSI simulations. The third, the difference between elastic and rigid simulations. If you've sailed on boats equipped with load sensors, sail vision systems, multiple anemometers and multiple GPS, you know that rather accurate measurements can be done (although, it is true that leeway is always the most tedious measure). In the scope of making a VPP, you're interested in knowing the loads, right ? Of course, these data are to be processed, and their integration give rise to some approximations, that are taken into account when comparing theoritical calculations with measurements.

    Would you please accept my excuses, if my comments are to be seen as pedantic ? I only seek pushing the analysis to its bound. How significant is the comment shall be appreciate regarding the purpose of the reader. What is the definition of an optimum flying shape, when calculations differ of about 10-20% with real measurements ? Again, the answer of this question depends on the purpose, for which calculations are intended. The work done here is an excellent work, and in the end of my comment, I share my only experience on the subject, saying that, despite the difference with real world, in the scope of making a VPP, great improvements can be made following the method of Uli on rigid sails, if more parameters are introduced to define the 2D sections, on which his calculations are based.

    I've developped and tested the same approach for racing boats, working also in parallel with sailmakers and rig manufacturers. So my comment are not to be interpreted as "I wouldn't...." but as "I have done...." . Again, depending on the purpose of the calculations, these comments can be usefull or not. So I keep for me the conclusion that I've made, using this particular method, conclusions that only have a meaning in the scope of my professionnal work. (downbelow, A VPP plugin into Dassault System CATIA). Since Mikko is helping Uli with the validation of his calculations, I don't see either any need for additionnal calculations, which would only pollute the work they are doing.
    upload_2023-3-3_8-18-19.png
    Everyone has to make his own experience, and I wish to encourage Uli in pursuing his excellent work. Most of the software used by sailmakers themselves do rely on this method, to a certain point, for a specific purpose, within a certain design loop. When more confidence will be put into these calculations, Uli could eventually be interested in knowing a way to improve his approach, being compatible with his method.

    Thank you.
     
    Last edited: Mar 3, 2023
  14. Mikko Brummer
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    Mikko Brummer Senior Member

    OK. So do I in my VPP, but the general approach (like ORC) tends to be to define it relative to the direction of the motion, so they (ORC) think they can eliminate leeway from the equations that way. I can run again with your numbers, but not now, I'm in the French Alps for next week.

    Anyhow, even with my larger apparent wind angle, the genoa appears to be a bit round in the entry, with a significant separation vortex area behind the luff. The main would be perfectly at the "ideal" angle of attack. Shame you can't upload videos (?), but from the stills you can clearly distinguish foot & tip vortices. The colours are near surface velocity, the "smoke" is vorticity - legends are missing, sorry.

    Here Xflow gives without & with the hull respectively (Fz is your Fy), for AWA 25,4°
    Fx 700 N Fz 1820 N
    and with hull under the sails
    Fx 740 N Fz 1850 N
     

    Attached Files:


  15. Remmlinger
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    Remmlinger engineer

    Thank you for the interesting link. If I understand the report right, they used the following process:
    - define an initial sail shape. They do not explain, how they arrived at this shape. Is it optimal? Is it fast? The references point to experiments in the wind tunnel.
    - determine the pressure distribution, using CFD
    - use the pressure distribution and a finite-element program to calculate the stretched sail shape under load.
    - there is a difference between loaded and unloaded sail, which is trivial
    - run the CFD a second time with the loaded sail
    - there is a difference in the aerodynamic characteristics between the two runs, which is not a surprise
    - their method would require to redo the loop and iteratively determine the loaded sail shape
    - instead, they stopped the iteration after the first step. It seems that the workload was prohibitive.
    Now they have a sail shape that is not the flying shape, not the loaded shape, not the optimum – what is it good for?

    I would rather propose the following work flow:
    - use UliSail to determine the optimal flying shape, the output is the CAD-file of the sails.
    - use XFOIL to calculate the pressure-distribution on each panel from luff to leech
    - alternatively, you can use CFD to get the pressure distribution
    - this pressure-distribution will not change, and it defines all loads
    - define an unloaded sail that is in a first step close to the flying shape
    - use a finite-element program and apply the loads to the unloaded sail
    - compare the loaded sail to the flying shape. If there is a difference, improve iteratively the unloaded sail until convergence.

    I have not done this, this is only a logic modification to the method they used at the university of South Korea.
    A run of the finite-element program seems to take only 30 seconds. It should be possible to do an iteration until convergence, if no CFD is required.
    After convergence, one would have the shape of the unloaded sail, the flying shape and the aerodynamic properties.
    If I have overlooked something, please let me know.

    Based on this, I still think, getting the optimal flying shape as a first step is useful.
     
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