Understanding the relationship between CLP and CE in sailboat design.

Discussion in 'Sailboats' started by Caldera Boats, Dec 6, 2005.

  1. Guillermo
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    Guillermo Ingeniero Naval

    Some basics compiled at Gavin Atkin's pages

    Good balance can be achieved by placing the centre of gravity of the sail plan directly over the centre of lateral resistance, or perhaps an inch or two ahead of it. John F Sutton

    For balance, The lead of the centre of effort over the centre of lateral resistance should be 12-14 per cent of the waterline length in the case of a shallow hull, fin keel or centreboard craft; about 10 per cent for deeper, more traditional yachts; and about 8 per cent for cruising yachts of classic form. John Teale

    Balance: for racing machines of the scow type the lead of CE over CLR should be 5 to 15 per cent of the waterline length; for shoal, full-ended centreboarders, the lead lies between 7 and 11 per cent. For full-ended keel boats the lead is generally a little less; for cruising boats of normal form it is about 6 per cent. Norman L Skene

    To achieve balance, the correct lead of CE over CLP (=CLR?) as a percentage of LWL is 7-12 per cent for a schooner; 11-14 per cent for a ketch; 12-15 per cent for a yawl; and 13-17 per cent for a sloop or cutter. He seems to be talking about conventional designs in conventional sizes (say over 10 feet LOA).Dave Gerr (The Nature of Boats, p301)

    In flat-bottomed boats, putting the CE directly over the CLR seems to achieve good balance just about every time; however it is different in boats with a deep vee-section near the bows. Jim Michalak. Comment: a deep vee will add significant lateral resistance near the bows. Skene says that in his time designers or racing craft usually made provision for the mast to be moved to achieve optimum balance. In a rig with a boomless jib, relying on the centre of the drawn sail area to provide a guide to the lead may put the real-life centre of effort further aft because the effective centre of effort of a boomless sail is usually some way aft of the drawn position.

    L Francis Herreshoff used to place the sailplan centre of effort of a conventional sloop to produce a lead of about 7 per cent ahead of the centre of lateral resistance. However, he listed several factors that might affect a sailing craft's balance.
    (i) Hull shape. A deep, vee-shaped forefoot will obviously increase lateral resistance near the bows. However, in a yacht in particular you should also consider the lateral resistance of the heeled hull shape - it may be, for example, that at 15 or 20 degrees the bows have no grab, but the stern is beginning to put up significant lateral resistance.
    (ii) Sharpness of the bows. As a sailing boat heels, there may be a large flow of water from the lee-side to the weather side of the bows. This tends to turn the bows up to the wind - by how much depends upon the sharpness of the bows.
    (iii) Due to the shape is presents to the water, a wide shallow boat will tend to head up to the wind on heeling, while a deep narrow boat will tend to turn off the wind.
    (iv) Increasing amounts of draft in a sail will tend to move the effective centre aft. (This is especially noticeable in the case of ice yachts, apparently.)
    (v) Where the sail plan is divided into many sails, as in the case of a schooner, the effective centre of effort moves far less than when there is a single large sail, as in the case of a catboat.
    (vi) The height of the sail plan. As a boat with a high rig heels, the centre of thrust on the rig moves outboard, again tending to turn the craft up wind.
    How much allowance should be made for each of these factors? Think about each one and employ a sense of proportion, says Herreshoff, helpfully, for this is not mathematics but pure art. Comment: Thinks... now we kind-of, sort-of half-know the answer... I should add that in his book 'The Common Sense of Yacht Design' Herreshoff frequently repeats the point that mathematics is not always helpful in boat design. He also strongly dislikes the metacentric shelf theories developed by Admiral Stuart Turner and espoused by British designers of his time, including the revered Harrison Butler. They still build HB's yachts on this side of the pond, and I gather they have very light, well balanced steering in all conditions...

    Balance, againThe shape of the leading edge of the keel is one of the chief factors in determining the balance of a boat. If the edge is sharp the forward part of the boat tends to bite into the water and hold its position, whereas a a rounded or blunt leading edge will tend to slide off sideways when a boat is sailing to windward - so what we might call the true centre of resistance is further forward inn a boat with a sharp leading edge than it would be in the case of one with a blunt leading edge. In other words, we can't really know where the centre of balance is likely to be without doing tank tests. F S Kinney .
  2. RHough
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    RHough Retro Dude

    These are "The Rules" that were cited earlier.

    From Kerr:
    "Keep in mind that this is just an approximation used by designers to estimate the true center of pressure of the wind on the sails. As with the center of pressure on the hull, the actual center of pressure on the sails changes with the angle of heel, sail shape and trim, wind speed, and many other factors. The most powerful computer known wouldn't be able to reliably pinpoint it."

    Absolute bunk.

    Sails are airfoils, it is most certainly possible to predict with good accuracy what the forces are and how they act.

    If it were not possible airplanes would fall from the sky on a regular basis.

    Its the prediction of those forces that allow a designer to determine things like rate of climb, take-off and landing speeds, optimum cruise speed etc.

    They don't do it with a bit of cardboard, a ruler, pencil, a pair of scissors, and luck.

    If there were military applications for sailboats in the 1900's, we would have a NACA like volume of research to use in sailboat design.

    A simple foil with no camber has two forces that act on it. Lift and Drag. Both can be calculated easily:

    Lift = CL*Area*1/2 density*Speed^2
    Drag = CD* Area*1/2 density*Speed^2
    In 2d CL = 2*PI*angle(radians)
    This gives a lift slope of .11

    Since real sails are 3D not 2D we correct the 2D lift slope for the sail's Aspect Ratio (AR)

    AR = Span^2/Area

    tspeer posted this simple formula:
    The apparent lift curve slope of planform is closer to

    a = a0 / (1 + a0 * 57.3 / (pi * AR * e))

    a = 3D lift curve slope, per deg
    a0 = 2D lift curve slope, per deg
    AR = aspect ratio
    e = Oswald efficiency factor

    The Oswald factor is 1 for a perfect foil, less for a foil that has a body (hull or fuselage) in the span.

    I use e=.75

    If we know the angle, area, and speed we know the lift.

    Add camber to the foils and it adds one more force. Its called the Moment. A moment is a force acting on a lever, a torque.

    The only rough estimate that gets used is calculating the forces as acting through the c/4 point (1/4 chord). At the c/4 point the Moment of a cambered foil is constant so we get a third dimensionless number; CM.

    At positive angles of attack the Lift, Drag, and Moment all act through the c/4 point.

    If you know where the c/4 point is you know the forces.

    In Plan or Profile view the sails forces act on the c/4 line and in the most simple case of a square sail, anyone can see that the CE is on the c/2 line. Any calculation using CE as the point where the sails force act is automatically off by 1/4 of the chord.

    A 747 is 230 ft long, does anyone think that they used some 13-17% guess to place the centre of the wing somewhere between 30 and 40 feet in front of where a cardboard cut balanced on the head of a pin?

    Sheesh ... It AIN'T rocker science! :(
  3. RHough
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    RHough Retro Dude

    The Neutral Point

    I'm going to toss a new concept in.

    When a system is in balance there is a point that is neutral. For any simple lever with a weight at each end the neutral point is called the fulcrum.

    If the weights are equal the fulcrum is halfway between the weights.

    For a combination of Hull, Foil, and Rudder the neutral point must be the point where a force can act without turning the boat.

    When a boat sails to weather the leeway force is equal to the sail lateral force. If the sail force is in front of the neutral point the boat turns away from the wind (Lee Helm), if the force is behind the neutral point the boat turns into the wind (Weather Helm).

    The Centre of Lateral area is not the neutral point, it could be at the neutral point, but it does not define the neutral point.

    When a boat sails to weather, it has to create Lift to balance the sails. To create Lift it needs angle. This is the "Leeway Angle"

    If Lift is calculated from boat speed, leeway angle and lateral area, a map of lateral force can be made. From my last post it can be seen that if each area has a different Aspect Ratio, each area will not create equal lateral force.

    The attached graph show the difference between Lateral Area and Lateral Force. The forces are calculated using 3d lifting line theory and the force at the rudder corrected for downwash from the foil.

    I will use Lateral Neutral Point (LNP) from now on to avoid any confusion with CLA.

    The big differences on this design is that LNP is forward and below the CLA.

    Forward effects Lead calculations, lower effects heeling arm.

    Attached Files:

    • NP.gif
      File size:
      12.8 KB
  4. Guillermo
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    Guillermo Ingeniero Naval

    Yeap! I didn't say I agreed with all those gentleman.

    But be careful: Boats differ from 747's in that they move in a two medium boundary. 747's only have to fly...;)
  5. RHough
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    RHough Retro Dude

    Very true.

    I've had some success with Free Flight and RC model gliders, so I'm pretty sensitive to designs that have "good behaviour". :) Models must have good stability or they are very hard to fly.

    I'm going to crank away at this until I find a more accurate way to set lead or know the reason why. If I can get the CG right to make an airplane fly hands off, I should be able to figure out how to get a balanced helm on a boat.

    All that's required is to have the boat trimmed with a higher angle of attack on the foil than the rudder. Since the yaw moment changes with heel, there should be a range of locations that allow the rudder to go from near zero lift in the lulls and not require high rudder angles in gusts.

    I'm fairly confident that my LNP concept is sound, now I'm looking at the geometry to locate the True CE so I can place it and do some stability calculations.

    I like your comment that "airplanes only have to fly", I've found sailboats much more complex than they look at first glance!
  6. Caldera Boats
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    Caldera Boats Beer4Ballast......

    Isn't that the truth! Coming from an aerospace background, I thought sailboat design would be simple. That couldn't be much farther from the truth.

    The relationship between the aero and hydro is the complexing part ...
  7. RHough
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    RHough Retro Dude

    If you are coming at it from the aero side ... it's only mildly complex :)

    Think of the hull and foils like a semi-span view of an airplane.

    Find the NP of the "airplane" and mark it on the x-axis at the WL.

    Think of the hull and sailplan obove the WL as another semi-span view of an airplane.

    Calculate the forces and moments at the c/4 point of the sail "airplane"

    Place the sail c/4 point on the x-axis of the hull so the net force is aft of the NP of the hull ... weather helm :)

    For a skiff or dinghy that sails at near zero heel, if the sail plan c/4 point is at the NP, the profile Cmo will produce a weather yaw moment.

    You will notice that boats designed to sail flat don't have much lead.

    If the boat will sailed heeled, more lead is needed to compensate for the lateral offset of the sail drive force.

    Calculate a weather moment from the sail drive force using the lateral offset as the arm. Add the sail weather moment due to heel to the weather moment due to camber to get the total weather yaw moment.

    As you move the sail plan forward of the NP, the sail force acts to balance the yaw moment with the NP as the fulcrum in the teeter totter.

    Clear as mud no? :)
  8. Doug Lord

    Doug Lord Guest

    weather helm

    Randy, I don't see how it's possible to have weather helm(small amount ideal) and also have the angle of attack of the rudder less than the keel/daggerboard. Weather helm would have the rudder with few degrees angle of incidence to prevent the boat turning into the wind-giving it a greater angle of attack than the board. Neutral helm would have the rudder and board at the same angle of attack and lee helm would have the rudder at less angle of attack than the board(negative angle of incidence), right?
  9. RHough
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    RHough Retro Dude

    That's the way I was looking at it at first. What is important is the fact that when the rudder is in line with the hull the foil and rudder are not at the same aoa. The rudder is in downwash that makes it angle of attack lower than the foil even on center.

    The rudder is at a lower angle of attack as long as angle to the hull is lower than the hull's leeway angle.

    First calculate the 3D lift slope for the fin (depends on AR).

    Then use the 3D lift slope to calculate the foil CL at the leeway angle.

    Once the CL is known, the downwash angle behind the fin is:

    downwash angle=(36.5*CL)/AR

    Higher CL = greater downwash angle
    Higher AR = smaller downwash angle

    The design I'm working on has a downwash angle of about 4.5 degrees at a leeway angle of 5 degrees.

    When the rudder is on centre, it "sees" a aoa of .5 degree.

    If you hold total lift constant, the best trim angle will be the one that gives highest L/D for the two foils.
  10. tspeer
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    tspeer Senior Member

    Lord Brabazon of Tara (British aviation pioneer, holder of British Pilot's License No.1) said, "Compared to designing a yacht, designing aeroplanes is child's play."

    In sailing circles, he's best known for his Bembridge Redwing with an autogyro sail - rotating blades instead of a cloth sail. He's also known for the quote, "I take the view, and always have, that if you cannot say what you are going to say in twenty minutes you ought go to away and write a book about it." Perhaps he was anticipating this forum?
    1 person likes this.
  11. h_zwakenberg
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    h_zwakenberg HullDrag/32 programmer

    actually, for modern hulls (separate spade keel & rudders) you should design for some slight weather helm when sailing upwind.
    The reason for this is, that in that case both surfaces will be producing lift in the direction where it is beneficial. The overall surface span load & hence induced drag (of both keel and rudder together) will be minimized, which in turn means that the aggregate L/D is best.

    As a rough guide, shoot for some 3-5° of weather helm for best upwind performance....
  12. RHough
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    RHough Retro Dude

    I've been re-inventing the wheel.

    Marchaj, in his (c) 1990 "Sail Performance", cites a 1980 paper that uses the c/4 points rather than geometric centres to locate the CE and CLR. The method was a contribution of J Flewit to the RINA paper "Methods to Determine the Hydrodynamic Centre of Lateral Resistance and Directional Stability of Yacht Forms" by C H Williamson.

    At least its nice to know that someone else approached the problem the same way I did. :(

    They found that placing the Aerodynamic CE directly over the Hydrodynamic CLR gave acceptable balance (Zero Lead of true centres).

    RINA Publications

    Looks like the book has already been written. :D
  13. Caldera Boats
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    Caldera Boats Beer4Ballast......

    Mabey the book has already been written, but your idea for an Excell calculator has not been done yet...;)
  14. RHough
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    RHough Retro Dude

    Oh fine ...

    I've got the CLR part working pretty well ... I just started on the CE part ...

    friggin' schooners ... :mad:

  15. Stephen Ditmore
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    Stephen Ditmore Senior Member

    Don't you mean a 3-5 deg angle of incidence with the water? If the boat is making 2-3 degrees leeway, then the rudder should only be turned 1-2 degrees off boat centerline. (Skeg or keel hung rudders might be a little different, since you might take the fixed part into account in calculating the effective angle of incidence. If the boat has a jibing centerboard or keel, a trim tab, angled bilgebords, or a tandem or CBTF setup, then the leeway angle of the hull might be nearer zero, so you might be correct in those cases.)

    When you're a yacht designer and a client comes in complaining of "weather helm" it's very important to distinguish between rudder angle measured off boat centerline and issues with mechanical advantage, which can be fixed with either a change to the steering system or by adding more area on the leading edge of a balanced spade rudder.
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