Catamaran keel area

Discussion in 'Multihulls' started by martinchaplin, Jul 17, 2008.

  1. martinchaplin
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    martinchaplin Junior Member

    Dear All,
    I have just joined the forum and have the following questions. How can I determine the keel area for a 3.5m sailing catamaran that I am designing? Second how can I determine how big the rudder area should be?

    Many thanks,

    Martin.
     
  2. bill broome
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    bill broome Senior Member

    can't answer this one, but can ask some questions:

    have you decided on a hull section? deep-v, round, square all have different requirements from a separate fin.

    have you looked at the small boats on the wood's and wharram sites? that's a good source of information, with maybe a bit of scaling.

    if you haven't seen several kinds of beach cat, make an effort to do so: 2 minutes of inspection will enlighten you more than a year of day-dreaming.
     
  3. tspeer
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    tspeer Senior Member

    Martin Schoon has an excellent writeup and documents on sizing the board and engineering the structure.

    Some things to consider:
    - The lift on the board is determined by the sail trim, and ultimately by the boat's stability, not the board design or size.

    - Sizing the board is mostly about minimizing the drag, since the lift is a given.

    - Induced drag due to lift is inversely proportional to the depth squared (not the aspect ratio) so a little deeper can be significantly less drag.

    - Area adds parasite drag, but also increases the maximum lift, making the boat less likely to stall in a tack.
     
  4. martinchaplin
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    martinchaplin Junior Member

    Dear All,
    Thanks for the replies. There has been a lot of discussion recently about the keel giving lift that I do not quite understand fully. If you can elaberate on this a little more that would help a great deal. The hulls will be round in section. I think that deep narrow daggerboards will give less drag (less surface area in the water) and fast tacking but will limit use from a beach. Longer keels less deep will give more drag, be slower to tack but will give the ability to beach safely. Not sure which way to go yet. Also in one discussion there was talk that if both keels are in the water the lift affect will be limited due to one keel canceling out the other. I really do not understand this concept. In my simple understanding the keel prevents sideways drift and two keels will be more effective than one. This is probably too simplistic and I am missing a lot of theory.

    Thanks again for all your input

    Kind regards,

    Martin
     
  5. sandy daugherty
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    sandy daugherty Senior Member

    Lift refers to how much force a keel develops to counteract the sideways push of the wind. It comes from thinking of a board like a wing. The suggestion that two boards cancel each other out is generally limited to assymetrical foils or boards that are offset, slicing outwards in stead of straight ahead. A symetrical airfoil is shaped like a long teardrop, with the same curve on both the top and bottom sides. An assymetrical airfoil is like an airplane wing, fairly flat on the bottom with more curve on the top. This shape develops more lift with less drag, but only when its flying right side up.
    You would not be happy with fixed shallow keels on a 3.5 meter boat because skin drag and induced drag are going to hurt more than on a bigger boat. To displace enough water to float you and a bag lunch, you will have a pretty boxy shape. Hobie made an eleven foot version of their 14, but it would only carry something like 120 pounds (55 kilos) and the 14 only sailed well with about 160 pounds of crew (72 kilos.)

    You want enough displacement to keep you, the rigging, and the bridgedeck above the waves! Calculate how much water each hull can carry, and try to make sure that each one will carry the total weight by itself.
     
  6. tspeer
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    tspeer Senior Member

    You are 100% right about the keel preventing sideways drift. The force on the keel will rapidly build (or decrease) until it matches the sideways force from the sail rig and windage. The force will be mostly to the side, and also pointed somewhat aft.

    It's convenient to represent the force as two forces at right angles to each other. One is parallel to the direction of travel through the water, and is called drag. The other one is perpendicular to the direction of travel through the water, and is called lift. As pointed out above, "lift" comes from aeronautical terminology. Lift is what allows a boat to sail to windward. The ratio of lift to drag is fundamental to sailing performance.

    Whether you have two boards or one, the net lift will be the same - it has to match the load from the sail rig. From a hydrodynamic point of view, the main difference is in the drag. But the main motivation for two boards usually has to do with practical matters, like how to mount the boards and what kind of interior space the trunks occupy, etc.

    If the two boards have the same depth and the same total area, they can have less drag than a single board. However, designers rarely do this. Two boards are often used to reduce the depth, in which case they sacrifice the benefit of producing the lift in two widely separated places instead of being concentrated in one place.

    Or two boards can be used to double the area when maneuvering at slow speeds by lowering the windward board before a tack, and pulling the new windward board up after the tack. This would allow a somewhat smaller board area than a single board when up to speed on each tack, for reduced drag.

    Sizing the board(s) is all about balancing three main factors:
    - Having enough area to keep the leeway angle below the stall angle when sailing at slow speeds (like when coming out of a tack)
    - Minimizing the drag due to wetted area by making the board area no larger than needed
    - Minimizing the drag due to lift by making the board as deep as practical
     
  7. martinchaplin
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    martinchaplin Junior Member

    Hi Guy's
    Things are getting clearer. It seems that dagger boards are the way to go. The bouancy should be no problem. My surf board is 3.6m x 0.63m and the hulls of the cat are 3.5m x 0.7m which supports me (82KG) easily. The design program I am using shows the water line at 125mm depth with 110Kg of load. The next question is where to place the dagger boards. I realise that the center of effort from the sail rig should be behind the dagger board but by how much. Too far aft and the weather helm will be too much, too far forward and I will have lee helm which of coarse is to be avoided at all costs. Another aspect that I am pondering, I want to keep the weight as low as possible so the plan is to use 3mm plywood glassed on both sides for the hull planking using an epoxy stitch and tape technique. There are two bulk heads that will be 9mm ply with a framework around them of 20mmx30mm. This is where the arbours will attach to the hulls. There will also be a strengthening member running the length of the hull from bow to transome as well as the dagger board case.

    Thanks for all your inputs

    Kind regards,

    Martin
     
  8. sandy daugherty
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    sandy daugherty Senior Member

    Cats are quicker when they lift one hull out of the water, suddenly reducing skin drag. To make that possible, each hull needs to support the total weight of the boat and keep everthing else out if the water, while sinking no more than its optimum depth for least resistance.

    If you can keep the beam of each hull less than one eleventh of its length, you can cheat the traditional speed limit for boats that don't plane. In your case that would be less than 5 knots. You would need something more than 6 hp to plane an inflatable of your dimensions, and a sail rig that powerful would be a handful. The Hobie 14 barely developed that much power in ten knots of wind. What is you reason for wanting to keep your vessel that short?

    Place the CLR (center of lateral resistance of your daggerboards 20% aft of the CEP (center of effective pressure of your sailplan calculated as the center of the area of sails) along the longitudinal axis of the boat. This will give you a "Weather Helm", which means that the boat will turn into the wind if you let go of the tiller. This also means that the rudders will be providing some lift into the wind, sharing a portion of the load on the daggerboards, allowing them to be smaller. Just by eyeball, I would guess that your rudders need to have about 250 sqr cms of area each, and your daggerboards need to be twice as big. You will adjust these dimensions after you start sail trials. What kind of sailplan are you considering?
     
  9. martinchaplin
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    martinchaplin Junior Member

    Hi Sandy,
    Thanks for the info. The hulls are 70cm wide each and 350cm long. The width of the cat will be between 2.0 and 2.5m, not decided this yet. The reason to keep the hulls so short is too keep the weight down making it easy for one person to transport the cat in parts on the car roof top. The idea is that the hulls should plane but from your comments the sail rig would need to be too big to achieve this? The rig I am thinking of is a 6m mast with a boom of 1.8m and the sail would then be approx 7.8 sq meters. I have a dinghy 3m long, 1.26m wide and it uses a 4.7 sq meter sail. The weight is approx 50Kg. This planes in 4 bft of wind. I am trying to keep the weight of the cat down to approx 70Kg. Do you think this is a viable concept?

    Thanks again for any comments.

    Kind regards,

    Martin
     
  10. sandy daugherty
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    sandy daugherty Senior Member

    Does this cat look like two surfboards with a trampoline and a mast?
     
  11. martinchaplin
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    martinchaplin Junior Member

    Hi Sandy,
    That sums it up quite well. The free board will be quite a lot more. The purpose is light weight, fun and easy to maneuver both on land and water. I currently have a 5m cat (also self built) but this is very heavy and really needs two especially getting it to and from the water. Plus I thought I would have a go at designing a boat as a project so I'm still in the thought stage. If it looks like I'm barking up the wrong tree I'll stop before too much money gets spent.

    Kind regards,

    Martin
     
  12. RHough
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    RHough Retro Dude

    Tom, aren't you nit-picking a bit here? ;)

    For a given lift, you state that the area must be large enough to prevent stall at low speed. At lower speeds, the AoA has to be larger to produce the same lift. If the AoA needed for the area to produce the needed lift causes the foils to stall, the solution is to add area so that a lower AoA is needed to produce the same lift. Right so far?

    For any given lift, the greater the area, the lower Cl the foil needs to produce that lift.

    When you say that span, not AR is the drag controlling dimension. It is confusing. If you increase span and do not change the AR, you are adding area. If you keep the same area and increase span, you are changing the AR.

    A greater span foil with the same area has a higher AR. Right?

    Since induced drag is greater than form drag, the easy way to increase L/D (by reducing drag since lift is fixed) is to increase AR. In sailplanes, the lift=weight, the flight speed is a function of area loading, and the L/D ratio is maximized by increasing span/AR. If span is increased along with area, the flight speed goes down. On a boat, the speed is limited by the point where drive = drag. Reducing drag by increasing foil area to reduce induced drag to the point that Cdi = Cdp should give maximum L/D.

    If the foil area is increased longitudinally (chordwise) instead of spanwise (lower AR), the induced drag will be higher than if the area is gained with greater span (higher AR).

    I got into this when I was designing RC sailplanes. The low Re at model speeds and chords showed that for the sizes range 1.5m to 3m span that higher AR did not give higher L/D past a certain point. Smaller spans had lower optimum AR than the larger spans.

    I find it very confusing when you say span not AR reduces drag. Either you mean 'added area spanwise' ie. greater span with the same chord, or you mean 'higher AR' ie. increasing span while reducing chord to maintain constant area.

    Am I just dense or are we using different words to say the same thing?
     
  13. rayaldridge
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    rayaldridge Senior Member

    Martin, you might want to lengthen your hulls while narrowing them. That way you can keep the weight down and at the same time provide more stability and use a bigger sail.

    My opinion is that planing is probably not the way to go with a multihull, especially in the smaller sizes. Fine hulls allow you to readily exceed the theoretical hull speed based on your waterline length, and they have other advantages too. You don't need as big a rig to push fine hulls past hullspeed as you do to get a boat to plane, and I feel that a planing boat is harder to control than one based on fine displacement hulls.

    You can get away with less than 11 to 1 hulls, I think. My little cat uses 10 to 1 hulls, and many trimarans have 8 to 1 hulls or even fatter.

    Ray

    http://slidercat.com
     
  14. tspeer
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    tspeer Senior Member

    Yes, a bit. All your points are valid. I would say that the various drag components have different sources and what one does to fix specific problems depends on the nature of those sources. The main idea I'm trying to get across is the common view of aspect ratio is it's a skinny-ness factor, when really it's span^2, nondimensionalized by area.

    For instance, say your boat is prone to stalling out in a tack, and you decide to add area to the board to make it less likely to stall. Given that you're adding area, there will be a parasite drag penalty to pay for it. If you change the area by making the chord larger while keeping the span the same, the aspect ratio will go down. Now if you think of induced drag as depending on how slender the board is, then you'd expect an increase in induced drag as well. But the induced drag will not be significantly affected. This is not what most people would expect, because making the board wider lowers its aspect ratio.

    You can account for it in nondimensional terms by recognizing that the lift coefficient is dropping because of the larger area, and this is offset by the decrease in aspect ratio. So both the nondimensional coefficients and the dimensional relationships are consistent. But the nondimensional coefficients tend to obscure a much more fundamental physical principle.

    The same goes for the change in induced drag with speed. Since the drag coefficient is multiplied by dynamic pressure, you'd expect both the parasite drag and the induced drag to go up with the square of the speed. But induced drag goes down with speed squared. Again, the this is because the lift coefficient is changing with speed if the dimensional lift is held constant. But that's not at all obvious from looking at the induced drag coefficient compared to looking at the dimensional form of the induced drag component.

    Physically, the board is "processing" a larger volume of water at high speed, imparting a smaller sideways velocity to it to get the same lift. Increasing the span at a given speed also results in deflecting a larger volume of water a smaller amount. It is always more efficient to move a lot of water a little than it is to move a little water a lot. This is why, for example, there's just no such thing as a really efficient shallow draft keel. You can make small gains, but for the same wetted area, it's going to be more efficient just to make the keel deeper. But having, say, two skinny surfaces of the same depth as one wide surface isn't going to provide the gain one might think from their aspect ratios. If one understands the importance of span-loading and depth on induced drag, then this makes perfect sense.
     

  15. RHough
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    RHough Retro Dude

    I agree. It makes perfect sense. Once the idea that lift always equals side force and does not change is grasped the rest comes easily.

    What bothers me is statements like, "AR has no effect on induced drag, induced drag is reduced by increasing span ... the reason that sailplanes have high L/D ratios is because the span is great, not because the AR is high."

    In my world, area loading controls speed. Glide slope is a result of planform. I KNOW that higher AR produces higher L/D ... Lift is fixed, speed range is a function of Cl needed to produce lift = weight, so with fixed lift and fixed area, the only variables are profile and AR. Reducing drag does not make a sailplane faster, it makes the glide slope flatter.

    In foils on boats, the lift is constant, but the speed is a variable not controlled by the foil's Cl, Speed is a function of drive vs drag. Reducing the drag of the foil increases the boat's speed. As you point out, the faster the boat goes, the foil can become smaller at the same Cl or the Cl and Cdi can go down with larger area.

    If I were design new foils for my old Hobie 18. I'd start with a 13 knot speed (Speed/Length ratio about 3:1 as predicted by the Texel system in 22 knots of breeze) and design the foils to have enough area and span so any increase in area to reduce Di would result in higher total drag from increased wetted surface. I'd then work backward to find the minimum stall speed for the foils and hope that it was low enough to prevent stall when tacking. If it looked like the stall speed was too high, I'd add area and live with a lower top speed for the boat. Of course with my luck I'd end up with foils that would tear the trunks out of the hulls and I'd have to buy a real boat ... :)
     
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