Advanced questions regarding CoE - CLR balance of small boats

Discussion in 'Hydrodynamics and Aerodynamics' started by laukejas, Sep 6, 2017.

  1. laukejas
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    laukejas Senior Member

    When it comes to balancing the sail plan to the hull of a sailboat, we all know the basics: Center of Effort, the force on the sail, must be in line with Center of Lateral Resistance, or be somewhat forward of it, creating the so called "lead". Boats, especially small ones that are designed to be sailed flat, usually have little or zero lead, while those that are expected to heel, have a larger lead, 5-10%, to account for the turning moment.

    For round-bottomed hulls, and hard-chine boats that are still reasonably round, the hull shape is usually neglected, and the CLR is estimated to be at the center of the area of the centerboard/daggerboard. Some say that rudder should be taken into account too, but only calculating 1/3 of it's area. I always disregarded rudder in my designs, and it worked out well.

    It is also known that for the boat to have negligible drift, the area of the board must be at least 3.5-4% of the sail area.

    -----
    These are the premises that I always took for granted, and it worked out fine for me. Correct me if you see a principal mistake there.
    -----

    However, there are some situations where I'm convinced there are more factors to account for when designing a well-balanced sailboat. I will describe each of them.

    1) In a boomless catboat, the lack of boom results in a much greater force on the sheet.
    [​IMG]

    The sheet is fixed aft. Therefore, the turning moment is greater, requiring a larger lead to compensate for it. I read about this in multiple books, and although I can't confirm it from my experience (never sailed a boomless catboat), it makes sense. I did, however, sail a gaff-rigged catamaran with a jib, and I noticed that raising or lowering the jib makes very little difference in balance, despite the fact that jib moves the CoE significantly forward. Since the jib is boomless, it also confirms the assumption that lack of boom adds weather helm.
    The question is, how much lead is needed to compensate for it, compared to the same boat with a boom? How does one estimate it?

    2) Next, the question of extra appendages, like a skeg:
    [​IMG]

    While a centerboard or a daggerboard is usually long and thin, developing lift and working like a wing, the skeg only provides brute lateral resistance due to it's low aspect ratio. And yet, it's effect is measurable, which is very evident from added directional stability when rowing.
    So, if a boat has both the skeg and a board, how does one calculate the net effect of the two? The centroid of sum of areas of the two can't be right, because a board is more effective, especially in higher speeds. So, how much does the skeg move the CLR aft? How much can it be utilized to move the CLR into the desired position?

    3) Then, what about flat-bottomed skiffs, like GIS?
    [​IMG]

    If the flare of the side panels isn't too large, they should also make some measurable influence on the lateral resistance. Obviously, if the flare is variable (steeper in bow, gradually inclining towards the transom), or the boat is short and beamy, the center of CLR might not be as simple as the center of area of submerged part of the hull.
    While it's safer to neglect it's effect on the amount of lateral resistance, relying solely on the 3.5-4% rule of the board, it might be not so safe to neglect the change of location of the lateral resistance of such a hull - it might change the balance in an unexpected way, not always correctable by sitting more forward or aft.
    So, the question is, when does the hull shape start to matter on the location of the CLR? What flare angles, how does beam curve come into play?

    EDIT: Here's one more example, more extremely representing the issue of the lateral resistance provided by a hull: National 12.

    [​IMG]

    Obviously, the bow section has very little flare, meaning it will provide a lot of lateral resistance, but as it goes aft, the profile becomes more round, offering less lateral resistance. Therefore, this kind of hull will move CLR forward - question is, how much?

    END EDIT

    I know that making a accurate, complete analysis of all these variables is next to impossible and impractical in small boats, short of performing tests in wind and water tunnels, or asking the America's Cup boat designers to "lend" their supercomputers to run these incredibly complex simulations.

    But I would not rather eyeball it either. As it happens, I am now designing a flat-bottomed skiff with a skeg and a boomless sail. While any one of these characteristics might not do too much damage on the balance of the boat, the net effect of the three might turn the boat into a steering nightmare. Therefore, I want to understand how it works.

    What I am asking here is some rules of thumb, general estimations and assumptions that would allow me to make a reasonably accurate guess of how these characteristics play together, and to build a boat that doesn't run from the wind on it's own, nor spends most of it's time in irons.

    Thank you in advance. Hopefully whatever information you can provide will prove useful to other sailors and builders as well. :)
     
    Last edited: Sep 6, 2017
  2. Angélique
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    Angélique aka Angel (only by name)

    I'm sorry, but this isn't a catboat I think, the sail looks like a boomless lug to me . . o_O
     
  3. laukejas
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    laukejas Senior Member

    Sorry, my mistake. I thought the term "catboat" refers to any single-sail boat, regardless of the rig type. I'm not sure what is the correct term, then. Anyway, I meant a small boat with any kind of single boomless sail, not just luggers.
     
  4. Angélique
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    Angélique aka Angel (only by name)

    A cat boat doesn't have any sail in front of the mast, which is called a cat rig, a boat with a lug rig is called a lugger.

    The question remains the same I understand, so I hope for some good responses.
     
  5. PAR
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    PAR Yacht Designer/Builder

    It's a cat rig, not a cat boat and any boat with a single sail, typically in the "eyes" of the boat is a cat rig. A lug cat, a gaff cat, a Bermudian cat, a leg o'mutton cat, etc., etc., etc. The boom arrangements don't matter, nor do any other sail attachment systems, though the descriptive might change a bit, such as a sprit boomed Bermudian cat. This said, there are also rigs with multiple masts that are also referred to as cat rigs, such as a cat ketch or cat schooner. The cat rig simply just doesn't use a jib, in front of the foremost mast. The SunFish is a cat rig. Columbus's Nina arguably could be a cat rig.
     
  6. laukejas
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    laukejas Senior Member

    Thank you for the correction, and sorry for not using the correct terminology... But please, let's focus on the main questions :D
     
  7. PAR
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    PAR Yacht Designer/Builder

    Lead and CLP locations can vary for many reasons, some of which you've listed. The old built down hull forms of the universal and CCA rule eras had quite different relationships, than modern canoe bodies for this reason. Once heeled over, these built down hulls lost a lot of effective lateral area, so some accommodation had to be made. As far as rules of thumb for your application some might apply, though it would be typical to simply address issues as they arise, after using fairly common practices in the design process. This would be true of a reasonably conventional design, which yours seems to fit. For example, if you use end of boom sheeting and find some weather helm, a change to mid boom sheeting might be all you need. You're correct the variables are astounding, when you start to add things up, so maybe you can post some lines and a sail plan, so we have have a look and possibly anticipate any issues you might want to address.
     
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  8. MikeDrummond
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    MikeDrummond Junior Member

    The mainsheet also has to provide the outhaul force when there is no boom.

    If the sail shape is identical with or without boom, then the centre of sail force is the same, and so the yawing moment is the same.
    With a boom there is compression due to outhaul load which is reacted by the tack tie; Without a boom there is a force in the hull, due to the mainsheet pulling forwards, which is reacted through the mast step and mast into the tack tie. A different load path, but all internal to the boat & rig - it doesn't affect the board or rudder.

    Catamarans seem fairly impervious to balance changes in general. Their higher speeds mean smaller rudder angle changes are required for yaw balance, because their higher speed generates rudder force at smaller angles. Also due to their higher speeds, the rudder blades are more balanced about the gudgeon axis, so the tiller load doesn't change much with rudder angle.

    An F-18 cat without jib has a much higher mainsheet load, but barely perceptible tiller load increase. I don't know the tiller angle change though.
     
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  9. laukejas
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    laukejas Senior Member

    Could you please elaborate on the bold-marked part? Did you mean, build the boat, and then fine-tune the balance with placement of the sail or mast rake or something? I would like to avoid that part of guesswork as much as possible, because there are hundreds of other limitations that might not permit extreme modifications once the boat is built. I know it is impossible to predict everything, but I want to account for each factor I listed as much as possible in the design phase, hoping that the final fine-tuning won't turn into a re-design.
    Thank you, but at this point, I'd rather not go into analyzing my specific design - I'm afraid the topic will be easily derailed by well-meant people pointing out other issues (ones that I intend to address later). As I'm trying to learn, I would rather analyze other designs, understand how these factors play together to determine the balance of the boat, and then choose how to utilize them in my own boat.

    As I said, I cannot really confirm or deny this based on my own experience, but multiple respected authors do say that boomless rigs have more weather helm. Let me quote one of them: Philip C. Bolger, "100 Small Boat Rigs", page 11-12:

    In the boomless rigs, all the force that drives the boat is delivered along the line of the sheet. The effect is as though the boat were being towed by a tug with a the towline attached at the sheet block. Such a towline would tend to swing the boat around. When towed by the sheet to the sail, the turning effect produces weather helm. The pull of the luff of the sail on the mast is to leeward and somewhat aft. This partly compensates for the off-center towline, but the boats setting boomless sails will normally carry more weather helm than boats with booms and should have their rigs stepped farther ahead on the hull.

    It is a shame Bolger didn't indicate how much farther ahead :( Hopefully someone here could tell.
     
  10. patzefran
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    patzefran patzefran

    "In the boomless rigs, all the force that drives the boat is delivered along the line of the sheet. The effect is as though the boat were being towed by a tug with a the towline attached at the sheet block. Such a towline would tend to swing the boat around."
    The Author seems to think tension on the aft sheet is an exterior force thet tows the boat (and forgot elementary physics). Wrong ! it is an interior force together with the other forces holding the sail to the boat i.e. forward sheet tension, and upper boom (which he omitted in is ecplanation). The sum of these three components equals the aerodynamic force and moment on the sail which iare transmitted to the boat thru attachment points and are related only to his shape and flow pressures. So the weather helm is only related to the particular equilibrium shape of the the sail related to this kind of rig, wich gives likely a center of pressur further aft than a bermudian or most other rigs !
     
  11. PAR
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    PAR Yacht Designer/Builder

    Patzefran, you obviously don't know who Bolger was. His analogy was correct, though could have been better worded. He and you are correct in that the CE seems to move aft with end of boom or boomless rigs and it's not physics, but simply geometry.

    Laukejas, I'm not sure what you're looking to prevent, but my basic point was to develop the design as you would any, given the design parameters and peculiarities. Everything from entry half angles to hull form and rig type can affect the lead/CLP relationship, my point was to stick with known norms for your design and maybe consider an adjustable step or anticipate moving a sheet block pad after the boat is built. Without knowing more precisely about the design (lines, sail plan, GA, etc.), it would be difficult to offer much more than generalities and guesses as to what you might need. I understand your reluctance to post images, fearing the discussion may degrade into off topic pursuits, but with some focus, I'll bet you'll still get the information you'd like, in spite of the occasional of topic wandering.
     
  12. laukejas
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    laukejas Senior Member

    Alright. But please keep in mind that is is a very early work-in progress. I know hull shape looks a bit weird, there's no rudder, a lot of structural elements are missing, etc. I'm left that for later, because I want to solve the balancing issue so that I can place the centerboard in the right place, and then decide on the seating arrangements.

    I'll skip the whole SOR now, because posting it would be just asking for people to re-design this thing altogether. Let's just say that this boat is built per order, for a man and his wife, for light, comfortable, very stable daysailing in a boat as small as reasonably possible. No expectations on performance.

    Displacement: 215 kg (474 lbs) with two people, 155 kg (342 lbs) with one
    Length overall: 350 cm (11' 6")
    Beam: 137cm (54')
    Transom width: 105 cm (41 1/2")
    Length on waterline: 318 cm (10' 5") with two people, 294 cm (9' 8") with one
    Flare angle: 14°
    Minimum freeboard: 18 cm (7") with two people
    Sail: boomless sprit, 5.8 m^2 (62.4 ft^2)
    Mast and sprit length: 300 cm (118")
    Lead: 7% of waterline, 23 cm (9")

    CAD sketches:

    [​IMG] [​IMG]
    [​IMG]
    [​IMG]
    [​IMG]


    Now, I want to have the centerboard as far forward as possible, because it will get in the way in such a small boat, especially with two people onboard (can't build it any longer, customer won't have it). Single sprit sail is also a must here, so no jibs. Therefore, the CoE is quite far aft, and the CLR has to be even further for a boomless sail. Keeping the centerboard forward, I added a skeg to compensate. The CLR point marked in the second sketch is just merely the centroid of the sum of two areas - centerboard and skeg. I am almost certain that the actual CLR won't be as aft as expected, and the boat will have too much weather helm. Therefore, the current lead of 7% is likely too small. I could increase the skeg size. Maybe I could even make two skegs, joined to bildge runners (not drawn yet). However, as you can see, the maximum beam is aft of the midships, and due to the low flare angle, it should present a reasonably flat surface to the lateral waterflow, giving some extra resistance - moving the CLR aft, just as I want to.

    Problem is, I'm just guessing and assuming here. I don't know how much exactly that skeg or the hull shape will influence the CLR location, which is what I need to figure out to make this work. I'm not sure if I'll be able to make the mast with an adjustable rake, because it will have to be on a tabernacle (customer will often be passing under bridges with less than 6 feet clearance). Weird, I know, but it is what it is. Swinging centerboard up a bit would allow to adjust the balance, but at the expense of loss of centerboard area, which will increase drift.
     
  13. patzefran
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    patzefran patzefran

    Another solution is to decrease the centerboard area and to use a high aspect ratio balanced rudder. So you can compute easily the COE of the two foils
    as they have similar effectiveness, and derive their respective area to get the desired COE.
     
  14. patzefran
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    patzefran patzefran

    Sorry, obviously I mean CLR, not CoE !
     

  15. laukejas
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    laukejas Senior Member

    Correct me if I'm wrong, but doesn't a part of the balanced rudder stick out beneath the hull? I plan to make a daggerboard type rudder (like here), so I don't think it will work with a balanced rudder...
     
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