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Thread: Center of Effort vs. Center of Lateral Plane

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    Default Center of Effort vs. Center of Lateral Plane

    Iím confused, for years I have believed that the distance the Center of the sail area is ahead of the Center of Lateral Plane is the positive lead, (giving weather helm). However, I was just reading a book that states that the Center of Effort should be behind of the Center of lateral Plane. Should the rudder area be included in the lateral Plane? What amount of lead is accepted for Sloops, Yawls, Ketches, cat ketches?

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    Default Re: Center of Effort vs. Center of Lateral Plane



    Others will chime in, but I believe only half the area of the rudder is used when calculating the CLR. Weather helm would be the pic on the right, where the bow tends to turn upwind. Lee helm in the center pic.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Quote Originally Posted by Bruce46 View Post
    Iím confused, for years I have believed that the distance the Center of the sail area is ahead of the Center of Lateral Plane is the positive lead, (giving weather helm). However, I was just reading a book that states that the Center of Effort should be behind of the Center of lateral Plane. Should the rudder area be included in the lateral Plane? What amount of lead is accepted for Sloops, Yawls, Ketches, cat ketches?
    You are right, the CoE leads the CLP by a % of waterline length. Skeene quotes 14 - 19% for a sloop, Yawls 15% using half of the mizzen area, Ketches 20% again half of the mizzen, Schooners 5%. Looks as though the rudder is included.

    A better way places the centre of lift at 1/4 of the chord from the leading edge. So you work out the centre for each sail based on 1/4 chord, and aggregate them. Then divide the keel from the canoe body (using a point where the garboard slopes at 45 deg to separate them. Apply the 1/4 chord rule to both hull and keel and aggregate them on area. The C o Lift of the sails is then positioned exactly over the C o Lift of the hull.
    It really is quite difficult to build an ugly wooden boat.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Lead as you first describe it is the standard setup. That is, the CE is ahead of the CLR. A simple illustration from Ted Brewer's primer on design:



    However, if boats actually sailed sitting perfectly level in the water with the sails sheeted completely in as in all the drawings that illustrate lead, the result would likely be lee helm, meaning that if you made a floating cut out of this drawing and blew on it from the side it would be blown off wind. The confusion is that no boat actually can sail in this theoretical configuration. Boats heel, changing the hull's underwater shape, creating a complex and unsymetrical combination of drag, lift, diflection of water, etc. Booms swing outboard to leeward, moving the CE both forward and outboard, causing constant changes in true CLR, CE, and lead, whether positive or negative. Foil theory also tells us that the boat will be drawn forward by the low pressure in front of a sail at an angle perpendicular to the sail. So there are many factors that produce helm balance that cannot be understood by such simple drawings and lead calculations. At least that's the way I heard it.
    Last edited by JimD; 02-10-2011 at 03:12 PM.

  5. #5

    Default Re: Center of Effort vs. Center of Lateral Plane

    This is one reason why I believe that multihull design is easier than monohull design. If you put the daggerboard directly below the rig's CoE, most of the time it will work fine.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    You need to get used to the handy fictions of science. For example, in pool simple shots (not masse or making a ball roll exactly along a rail or how you get the cue ball to either come back, follow, or go sideways from the target ball) you can pretend that the mass of the balls are in points of no particular dimension.

    So also with the relationship between center of sail area and the center of lateral resistance. The center of sail area has only a little to do with the center of effort when the sail is working - pretty obvious when you considef that sail is not a flat plane always held dead amidships and that the cumulative center of effort from whoever many little force vectors you can stand to analize has but a casual relationship to the actual sail center of effort. Even the boat's center of under water resistance is not where you draw it, since it changes with heel and with speed. For designing purposes, the NA needs a good reason not to include all of the boat that's under water - hull, keel, skeg, rudder - all of it.

    For home purposes, you can get the ficticious center of lateral resistance by cutting a profile of the boat from waterline down, no topsides or such, from nice stiff stock. Lay the cut out across a pencil that's normal to the waterline and find the balance. Simple enough and given that the whole exercise is a fiction anyway . . .

    As a first approxomation, having the center of lateral sail area a little ahead of the center of lateral static resistance is close enough that you can at least get the mast(s) in the right place and do the rest with ballasting for trim and raking the mast.

    If the sail's lead is too far ahead of the boat's lateral resistance, the boat will have a lee helm, with the bow blowing off. If the lead is not enough, the boat will have a noxious weather helm.

    There are various rules of thumb that work for different types of boat, and I hope Roger will enter this with some examples. My own pet is a literal rule of thumb. For displacement sailboats under about 5 tons if you draw the boat's hull and rig profile at a scale of 1-1/2" to 1', the lead should be about one thumbwidth. As I say, literal rule of thumb.

    Just when I started writing, my Dad called and we've had good half hour chat so I'm sure this will not be the first answering post

    G'luck

    Yep - others chimed in. They appear to believe what I do not. The center of effort for the sail is not the same as the center of sail area, and chordal "corrections" are arbitrary fictions that change with sail trim and heeling angle anyway. Same with center of resistance - not the same as geometric center of lateral plane. The point is that they are both useful fictions for a first placement. Designers who do a lot of variations on a theme develop rules of thumb that work for their theme. Just remember: Useful fiction, not science.
    Last edited by Ian McColgin; 02-10-2011 at 03:43 PM. Reason: Last remarks

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Quote Originally Posted by Peerie Maa View Post
    You are right, the CoE leads the CLP by a % of waterline length. Skeene quotes 14 - 19% for a sloop, Yawls 15% using half of the mizzen area, Ketches 20% again half of the mizzen, Schooners 5%. Looks as though the rudder is included.

    A better way places the centre of lift at 1/4 of the chord from the leading edge. So you work out the centre for each sail based on 1/4 chord, and aggregate them. Then divide the keel from the canoe body (using a point where the garboard slopes at 45 deg to separate them. Apply the 1/4 chord rule to both hull and keel and aggregate them on area. The C o Lift of the sails is then positioned exactly over the C o Lift of the hull.
    Center of lift is at the 1/4 chord for a SYMMETRIC airfoil at an angle of attack without separation. So that's a good approximation for a fin keel or centerboard with a section at least somewhat like an airfoil.

    A sail going upwind properly trimmed is closer to a thin, cambered plate with the stagnation point on the nose. In that case the center of lift is close to the mid-chord, not the 1/4 chord.

    But as Ian points out the actual center of effort of a sail when sailing is somehere to leeward, not on the centerline, and the hydrodynamic forces also need to include the forces on the hull. So the actual balance of boat is much more complicated than the fore/aft postion of the center of area of the sails on centerline relative to the center of some portion of the side-view profile of the underbody expresed as a percent of waterline.

    But the purely empirical rules can usually get a knowledgable designer close enough, particularly if there are successful, similar designs to use a reference.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Quote Originally Posted by David Cockey View Post
    Center of lift is at the 1/4 chord for a SYMMETRIC airfoil at an angle of attack without separation. So that's a good approximation for a fin keel or centerboard with a section at least somewhat like an airfoil.

    A sail going upwind properly trimmed is closer to a thin, cambered plate with the stagnation point on the nose. In that case the center of lift is close to the mid-chord, not the 1/4 chord.
    The method that I set out was proposed in a paper to the Royal Institution of Naval Architects, and was backed up by analyses of several boats known to balance well using the proposed method. They all panned out with good agreement. The benefit that I most like about it was that you did not need the guess work of "is it 10% or nearer to 20%?", you just align the two centres.
    It really is quite difficult to build an ugly wooden boat.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Quote Originally Posted by Bruce46 View Post
    I’m confused..
    Don't feel bad. Yacht designers trying to make their profession appear more scientific than it is and mindless repetition by book and magazine writers have been confusing people for decades. Almost everything you read and much of what is posted in threads whenever the subject comes up is hogwash. Confusion is the usual result of believing anything simple that is written about a complex subject.

    (Pause to let the screaming, yelling, and arm waving subside and duck various objects flying through the air.)

    All right.

    My very middle of the road boat with a semi fin keel and separate rudder on a skeg has a fairly typical lead of 16%. Helm was objectionably heavy for the first two season after which I bought a new set of sails with a slightly smaller jib. Helm balance was significantly better even though the geometric center of the sail plan was actually moved slightly aft which should increase "weather helm" according to conventional wisdom.

    When I roll up the jib to sail on main alone, the lead becomes negative (-2%) but the rudder angle and steering force are dramatically reduced even though the myth says the boat should be weathervaning up into the wind. When I sail under jib alone with the main furled, I do not have lee helm, even with a lead of 35%. The helm angle and force are actually closer to that of the full sail plan than with main alone and negative lead. You in the back with the red face still waving your arms, please explain.

    One of the first boats I ever fell in love with was the Eastport Pinky schooner in "American Sailing Craft". I calculated her C.E. and C.L.R. in high school and was shocked to discover that she has a negative 10% lead. I figured Chapelle had just recorded some incompetently designed vessel and forgot about her. Several have been built and they sail fine. You'll find negative lead on many vessels from that period if you look.

    So what is true?

    Everything else being equal (and I mean everything hull, cut of sails, sail trim, stability, wind angle, etc.) moving the sailplan as a whole forward will cause rudder angle necessary to hold a straight course to slightly decrease. Moving the sail plan aft will cause helm angle to slightly increase. There is no magic "balance point" though where the boat suddenly converts from having neutral helm to uncontrollable "weather helm". If you could mount the rig on some sort of track and move it forward and aft, you would find that huge changes in mast location were necessary to create fairly small changes in rudder angle.

    Helm force, the strain on the steering gear and how hard the helmsman has to work are the function of many factors besides helm angle. A spade rudder with some balance (area ahead of the stock) could have fingertip control and almost no strain on the tiller even though being at the same angle as a rudder with it's area entirely behind the stock. Helm force is often confused with weather helm which muddies up these net discussion considerably.

    Pressure on the rudder caused by the quarter wave pattern and other flow effects have an enormous and almost never discussed effect on steering forces. There are boats which seem to have absolutely neutral helms. You let go of the wheel or tiller and they keep going along in a straight line. You won't find that their leads or sail plan underwater profile relationships are significantly different than boat that do not have this characteristic. There is no magic amount of lead that will create this condition. It's a function of their hull shape and difficult to predict and achieve. You won't get it by balancing paper cutouts of the underbody or worrying about whether or not to include the rudder in the paper cut out.

    A bit of weather helm actually helps the boat to windward by producing side force against leeway. When I worked at Phillip L. Rhodes, I was told that they aimed for a specific angle exactly at the point where the first reef was put in. I've forgotten exactly what it was but it was 3-5 degrees. If you are designing a series of similar boats for very demanding clients who are concerned with the tiny margins the win races, the "lead" business is useful in helping to be sure that the helm angle comes out to say 4 degrees instead of 5. However, you have previous boats to draw on, you know the characteristics of the sails to be put on the boat, you know the stability and many other factors. Without this body of data, the whole lead business is rather pointless, at least on cruising boats of the kind of configuration likely to be constructed of wood. A sail plan that would make the boat "unbalanced" would just look so out of proportion that it is unlikely anyone would build it. Lee helm is almost impossible to achieve in a cruising boat.
    Roger Long

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    Default Re: Center of Effort vs. Center of Lateral Plane

    While the boat I have in mind is a cross between a B&B EC22 and a Blue Lightning http://www.bluelightning.co.uk/ts/bluelightning.shtm I like to look at things from a broader perspective and to shake off the cobwebs of being away from boat design for too long. Yes in the old days i used to make paper dolls of underwater profile, however, that method doesn't work very well on a boat with less then a foot of draft excluding the cb.

  11. #11

    Default Re: Center of Effort vs. Center of Lateral Plane

    Bruce, according to Thomas Firth Jones, you are correct. His view is that for multis and other shallow-bodied boats meant, like dinghies, to be sailed as flat as possible, that the whole rigmarole of balancing the underwater profile on a knife-edge was an anachronism. His boats sailed fine. In addition to multis, he designed a number of small unballasted sailboats, and his approach was to put the CoE directly over the CLR. As Ian says, these are very crude approximations of what is actually going on, but as Roger says, large variations don't always make a huge difference.

    I used Jones' approach in placing Slider's daggerboard, but as Roger said of other boats, dropping the jib does not perceptibly increase the rudder angle. When I was drawing Slider, I worried a lot about this stuff, but it turned out to be less critical than I'd always assumed, at least in Slider's case.
    Last edited by slidercat; 02-10-2011 at 11:51 PM.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    I suspect that the position you have your CB in at any given time will have more effect on helm balance than a percent or three of lead difference. Even the condition of your sails would be worth a percent or two.
    Steve Lewis
    Formerly Lewisboats (don't try to change your email address!)

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    Default Re: Center of Effort vs. Center of Lateral Plane

    "Aero-Hydrodynamics and the Performance of Sailing Yachts" by Fabio Fossati, 2007, has an excellent discussion on "Directional stability: balance" about the moments and forces which have to balance. It discusses the practical difficulties of determing all the force and moment characteristics. Then it goes on to say that the emperical criteria that can be used in designing a boat is the "lead" criteria. It then says "they [lead method] are only valid for producing a boat design that we can consider balanced with respect to a series of previously analysed projects; otherwise they are excessively disconnected from the fluid dynamics governing the problem, and from this point of view there is room for in-depth research, ..."

    Larsson and Eliasson in "Principles of Yacht Design" discuss the physics and where the center of effort of sails and hulls really is, but then conclude "It is obvious from the above discussion that the position of the sail plan relative to the underwater body is toocomplex to be handled entirely theoretically" and then goes on to discuss how to use the lead method.

  14. #14

    Default Re: Center of Effort vs. Center of Lateral Plane

    To amplify what Roger says above, a bit of weather helm isn't just helpful in getting to windward. I think it's essential for safety. A boat with neutral helm will sail off and leave you if you fall overboard. A boat with lee helm is actively dangerous in several ways.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    A number of different things contribute to weather (or lee ) helm. Some boats, particularly wider boats tend to develop a curved centre line??? or is is just a curved drag line as they heel. Then the boat wants to follow the curve into the wind. As any boat heels there is part of the driving force out to the side, again tending to turn the boat into the wind. Both these effects are more pronounced as the wind and speed increases. The cut of the sails and the distortion of the rigging have a profound affect. Poorly cut or bagged out sails tend to move the centre of the driving force aft, causing more weather helm. A boat more or less exclusively intended for cruising would do better with a looser cut to the sails, but of course then this needs to be compensated for in other ways. If the head-stay can sag off, the headsails should be cut differently than if it is a high tension racing boat. Cruisers do not tend to fiddle with out-haul tension and halyard tension to get the last decimal of a knot. The draft in the main changes noticeably when you do.
    I think a slight weather helm is good and effective at improving performance to windward, pretty much only for traditional boats with the rudder either on the trailing edge of the keel or at least on a skeg which joins the keel. Then it is like a flap on a wing. I do not think it helps with a fin keel and spade rudder.
    The under water shape has an effect here as well. A lot of more modern boats have a fairly fine deep bow and a flat run aft. the deep bow contributes to the lateral plane while the flat run, though pretty much the same lateral area often does not. This means the boats can sail with fore and aft imbalance between sails and lateral plane better than traditional boats. We often see them sailing with just the main or just the jib, which a lot of traditional longer keel boats could not. The flip side of this is the modern boats tend to broach more readily than the traditional form.
    there is a lot of different factors, and the old rule of thumb ( calculating lead ), spiced with some practical experience, is about as good as we can get, without very expensive tank and wind tunnel testing.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    As mentioned before, intuition and good observation of similar designs known to balance does a good job of getting a boat to balance.
    The center of effort of the sail plan, obviously isn't the geometric center and the airfoil shape (draft location, twist, fullness) have a great effect on the theoretical CE. Even with these variables, they are nothing compared to the ever changing drive force being applied from off center as the boat heels. And if it were a precise calculation, how could it be that boats can still be made to balance with a shift from a 100% to a 155% overlap headsail or going from a full main to deeply reefed?
    Balance is felt as the force (pull or push) required by the rudder to keep a boat going straight. This is usually easily adjusted by heel, sail shape and trim. None of these elememts have much to do with the calculated centers of 2D sail plans or hull shape cut outs balanced on a straight edge although they are a starting place.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Thanks for all the responses, it is comforting to know that my basic understanding of the subject is valid. I hope that others have also profited from the knowledge shared here.

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    Default Re: Center of Effort vs. Center of Lateral Plane

    Have you figured out what happened with the smaller cat you built yet?
    John Welsford

    Quote Originally Posted by slidercat View Post
    Bruce, according to Thomas Firth Jones, you are correct. His view is that for multis and other shallow-bodied boats meant, like dinghies, to be sailed as flat as possible, that the whole rigmarole of balancing the underwater profile on a knife-edge was an anachronism. His boats sailed fine. In addition to multis, he designed a number of small unballasted sailboats, and his approach was to put the CoE directly over the CLR. As Ian says, these are very crude approximations of what is actually going on, but as Roger says, large variations don't always make a huge difference.

    I used Jones' approach in placing Slider's daggerboard, but as Roger said of other boats, dropping the jib does not perceptibly increase the rudder angle. When I was drawing Slider, I worried a lot about this stuff, but it turned out to be less critical than I'd always assumed, at least in Slider's case.
    An expert is but a beginner with experience.

  19. #19

    Default Re: Center of Effort vs. Center of Lateral Plane

    Hey, John. The problems didn't have much to do with helm-- the balance was fine. The boat had modest weather helm, as it should have, but made too much leeway to be efficient to windward, and I think the lack of depth, and the lack of a decent foil section in the rudders caused the problems with tacking. It tacked about as well as a Hobie 16, but I find that inadequate. The whole backing and filling things with beach cats is terminally annoying to me. For my money, a boat that is even slightly uncertain in stays is just not good enough. I'm buying some foam sections (originally offered as model airplane wings) as the basis for some new kickup rudders.

    For folks who don't know, this is the boat John is referring to:



    It was conceived as a cartoppable cat-- each hull is about 50 lbs.

    Well, here's another, just because it's pretty:

    Last edited by slidercat; 02-12-2011 at 09:04 PM.

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