How to dimension a sailing catamaran?

Discussion in 'Multihulls' started by terhohalme, Apr 27, 2008.

  1. Fanie
    Joined: Oct 2007
    Posts: 4,604
    Likes: 177, Points: 63, Legacy Rep: 2484
    Location: Colonial "Sick Africa"

    Fanie Fanie

    Hi Phil, if I read you right, then it's better to have an oversize rudder than an undersize rudder.

    If such a rudder is adjustable would one be able to trim, big for low speeds and smaller for high speeds ?

    I guess the same would apply to daggerboards then ?
     
  2. JCD
    Joined: Jul 2006
    Posts: 359
    Likes: 3, Points: 0, Legacy Rep: 36
    Location: Coney

    JCD Follow the Bubbles!

    Hello Phil,

    Sounds reasonable to me. The above explanation which I knew you or Richard would eventually provide is exactly why all aspects have to be looked at. I just wanted to point out that the lift is higher. Yes, the board is bigger as you pointed out, but as already agreed, it is a higher aspect also.

    However, if areas were the same, the higher aspect would provide more lift, although I will admit that if it isn't an extreme aspect, it is not that much more lift. Here is the information for the same area at different AR's.

    AR 1.5
    Speed = 5 mph ,
    Camber = 0.0 % chord , Thickness = 12.0 % chord ,
    Chord = 2.0 ft , Span = 3.0 ft ,
    Surface Area = 6.0 sq ft ,
    Angle of attack = 3.0 degrees ,
    Under Water
    Altitude = 0 ft , Density = 1.94slug/cu ft
    Pressure = 14.694lb/sq in, Temperature = 60F,
    Lift = 106 lbs

    AR = 6
    Speed = 5 mph ,
    Camber = 0.0 % chord , Thickness = 12.0 % chord ,
    Chord = 1.0 ft , Span = 6.0 ft ,
    Surface Area = 6.0 sq ft ,
    Angle of attack = 3.0 degrees ,
    Under Water
    Altitude = 0 ft , Density = 1.94slug/cu ft
    Pressure = 14.694lb/sq in, Temperature = 60F,
    Lift = 112 lbs

    As you can see, there is very little difference although lift is higher and, in my mind, 6 is already extreme. Conversely, I think that for the TR27B, IMO, for the same areas, it is a matter of reducing drag instead of creating lift because she is on the heavy side for her size.

    I agree 100% on the small penalty associated with the extra area, I just think that area should be placed where it creates the greatest lift and that is in the span. Not extreme...just not 1. I am very much in agreement with the low tacking speed calculation. The 5 and 10 mph used was only used as basic numbers.

    I'm not sure how it isn't the full story because I made it clear that the comparison were made with different size boards and areas. The argument that the same area would produce the same lift is not as you imply above as demonstrated by the new calculations so a higher AR does produce more lift due to better "efficiency" and, the lift induced drag is reduced for the same area. So which is the part of the story I withheld?

    Thanks
    J:cool:
     
  3. terhohalme
    Joined: Jun 2003
    Posts: 512
    Likes: 40, Points: 28, Legacy Rep: 506
    Location: Kotka, Finland

    terhohalme BEng Boat Technology

    "The reason you get more lift from the high aspect one is that it is bigger."

    Hello guys,

    There must be some misunderstanding now. Aspect ratio has a strong influence on 3d-lift coefficient (lift coefficient of real board, not the foil section). Are all the technical literature of keels and rudders rubbish? Look at my pdf page 9.
     
  4. BigCat
    Joined: Jan 2008
    Posts: 73
    Likes: 1, Points: 0, Legacy Rep: 27
    Location: near Seattle

    BigCat Junior Member

    Rudder size

    I notice that medium to large cruising catamarans seem to use smaller rudders than Richard's figures would mandate. Kelsall's KSS46MA, for example, looks like one rudder has 6 square feet or a tad more for about 860 sq. ft. of sail area. I don't think your typical catamaran with say, 1920 sq. ft. of sail area has rudders averaging 38.4 sq. ft. in area.
     
  5. Fanie
    Joined: Oct 2007
    Posts: 4,604
    Likes: 177, Points: 63, Legacy Rep: 2484
    Location: Colonial "Sick Africa"

    Fanie Fanie

    Hi BigCat,

    Could it be that the distance between the daggerboard(s) and the rudder(s) play a big roll here ?

    Taking in consideration the extremes - assuming the rudder and daggerboard are right next to one another, won't this have a smaller steering effect (the boat will want to turn in a very small circle and very little leverage) than when they are as far apart as possible (which will have a larger turning radius) ? Could be you have a bigger leaver effect when they are far apart.

    The position of the daggerboards are determined by the centre of sail force and the rudders cannot be much furter aft than the end of a hull. The only difference here is that the larger boat's rudder and daggerboards are further apart, which gives the larger leverage, and you could get away with a smaller ratio daggerboard / rudderboard.

    Right ?
     
  6. BigCat
    Joined: Jan 2008
    Posts: 73
    Likes: 1, Points: 0, Legacy Rep: 27
    Location: near Seattle

    BigCat Junior Member

    Rudder areas

    Hi, Fanie - Wouldn't everything scale up together? That is, not only would the lever arm between the pivot point and the rudders' center of effort get larger, but also the forces that it is working against, thus canceling out the longer lever arm for the separation between the rudder and the CLR? I can think of one thing that might not scale up--the disturbed and turbulent area near the water's surface. For this reason, an inboard rudder is more powerful for a given area than an outboard rudder.
     
  7. Fanie
    Joined: Oct 2007
    Posts: 4,604
    Likes: 177, Points: 63, Legacy Rep: 2484
    Location: Colonial "Sick Africa"

    Fanie Fanie

    BigCat, referring to your comparason between the smaller sail setup and the large one, there should be something fundamental that favours one in not having to use a rudder at 38.4 sq feet for the larger sail.

    Speed is one factor that has an effect on this, there should be another or more than one...
     
  8. JCD
    Joined: Jul 2006
    Posts: 359
    Likes: 3, Points: 0, Legacy Rep: 36
    Location: Coney

    JCD Follow the Bubbles!

    Hello Terho,

    I think that Phil and I could be discussing different things. I will try to lay out my thoughts in layman terms, not because I'm an expert and no one else is, but because this is extremely difficult stuff and I am a layman at it. I have read many authoritative books on the subject and absorbed very little, so I will provide the little that I did.

    Drag depends on the size and shape of the body, density, velocity, viscosity and compressibility and inclination to flow. The drag coefficient includes form, skin friction, wave, and induced drag.Lift depends on the same and flow conditions. These can be quite complex.

    In both, there is a pressure variable. The difference in these pressures = lift/drag = motion/stall respectively. That is about as simply as I understand it. All things equal, shape, flow, planform etc, the same areas will provide:
    Area A = Area B = lift/drag

    However, it is my understanding that an area that is distributed through a higher aspect ratio will produce more lift because the tip vortices are further away from the total area of the foil, thereby making the foil more "efficient" because less drag is distributed among the same area.

    So yes, the lift coefficient of the board is absolutely accurate as you mention Terho, but, if two equal foils are equal in every respect except the AR, then the higher AR will induce less drag over the entire area because the tip vortices will effect a smaller percentage of that same area. That means more lift.

    As you can see, when the second set of data was produced all variables down to planform were the same except for the AR and it reflects more lift. Also, if the lift on the first set of data is divided by the area of their respective boards, it will show that the higher AR will have more lift.

    This is all I know and I have a headache and for me it is moot, because as already agreed, unless it is a radically high AR or you're looking to bleed every little bit of lift pressure out of the area, either board will do just fine for the design that it must serve.

    Thanks
    J:cool:
     
  9. catsketcher
    Joined: Mar 2006
    Posts: 1,315
    Likes: 165, Points: 63, Legacy Rep: 790
    Location: Australia

    catsketcher Senior Member

    A little clearing up to do

    I like this thread - it means I have to clarify my own thoughts so that I can clearly state them.

    Terho - my comments on aspect were that we couldn't necessarily say that the higher aspect foils were higher lift in JCD's first case as his high aspect foil was bigger. He fixed that the second time around and we can see that high aspect foils are a bit more efficient.

    I should probably make myself really clear - because I once tried to sail a cat with extremely high aspect foils - 2m depth and 200mm chord - it really was, this is what I caution people about - 3:1 or 4:1 is great in my book.

    Fanie asks a questioon about the distance a rudder is from the longitudinal centre of resistance. He is dead right to think that this would be significant. My 9m Twiggy tri had its board about 4 metres from stern and was very twitchy and touchy to sail - I never tacked it well without a jib. Farrier tris are great to tack - they have big foils and a large distance between the rudder and CLR.

    A bloke called John Letcher (I think he had something to do with the Vacanti yacht design program) wrote a good book on self steering. One of the ideas he propounded was a concept called rudder volume. This is the area of the rudder times the distance to the CLR.

    To turn a cat we need to produce a moment - a torque. A force needs to be applied at the end of that lever to make a turning moment. You can get greater torque by increasing the lever arm or increasing the force you push the lever with. A good way to think of this is rudder volume - the area of the rudder produces the force, the distance from rudder to CLR gives the lever.

    It is probably worthwhile to consider the rudder volume rather than the rudder size on its own. The same size rudders will be subject to different loads if the distance form the CLR is changed.

    My own personal opinion, probably because I love sailing monos and feeling how they sail, is for big foils. Other people will be happiy with smaller foils - it does become a personal thing.

    cheers

    Phil Thompson
     
  10. tspeer
    Joined: Feb 2002
    Posts: 2,319
    Likes: 303, Points: 83, Legacy Rep: 1673
    Location: Port Gamble, Washington, USA

    tspeer Senior Member

    How did the designer achieve a high aspect ratio? I presume the chord was less than for comparable boards, but there are different ways to get the aspect ratio. Was the depth similar to other boats, but the area reduced to increase the aspect ratio? Or did he keep a comparable area in the foils and made them deeper?
     
  11. tspeer
    Joined: Feb 2002
    Posts: 2,319
    Likes: 303, Points: 83, Legacy Rep: 1673
    Location: Port Gamble, Washington, USA

    tspeer Senior Member

    Actually, while sailing, the lift on the two boards will be the same. The lift has to balance the side force from the sail. The leeway angle (angle of attack) will be different, however.

    This may sound like a pedantic point, but it's not. Comparing foils on the basis of equal angles of attack is quite misleading. They should be compared on the basis of equal lift. For example, if you look at constant angle of attack, you get the idea that because the induced drag coefficient is a function of aspect ratio that the induced drag will increase with the square of the speed and induced drag is a function of aspect ratio. However, that's not what happens in practice.

    Instead, because the lift on the foil is determined by the sail trim instead of the foil design, the induced drag does actually decreases with the square of the speed, and it is a function of the depth of the foil - regardless of the aspect ratio. A foil that is 900 mm deep and 500 mm wide will have essentially the same induced drag as a foil that is 900 mm deep and 300 mm wide, despite the fact that the first foil (assuming rectangular planform) has an aspect ratio of 1.8 and the second has an aspect ratio of 3. The reason is because the lift coefficient on the second foil will be 2/3 higher than the first foil's.

    In this example, the second foil will stall out much sooner than the first - not because it has a higher aspect ratio, but because it simply has less area. Had the second foil been given a depth of 1162 mm instead of 900 mm, and a chord of 387 mm instead of 300 mm, it would have had the same area and still had an aspect ratio of 3. While this higher aspect ratio foil may stall at a lower leeway angle than the lower aspect ratio foil, I'm not sure it wouldn't produce as much or more lift before it stalled.

    Instead of aspect ratio, I think it's much more productive to characterize the foil in terms of depth and area. Area addresses the contribution of the foil to parasite drag and the maximum side load from the sail that can be resisted. Depth addresses the induced drag.

    I suspect a great many boats can benefit from a simple extension of the length of the foil, with the increase in drag due to the larger area being more than offset by the reduction in induced drag. This is a case of increased aspect ratio, but increased area as well.
     
  12. JCD
    Joined: Jul 2006
    Posts: 359
    Likes: 3, Points: 0, Legacy Rep: 36
    Location: Coney

    JCD Follow the Bubbles!

    Hello Tom,

    I know this is your forte but I will not ask pardon if I appear less than knowledgeable in this because I am. But here goes anyway and it is hopeful that you will be kind when you straighten me out.

    At the same angle of attack, the lift will not be the same for the examples given. The post clearly indicated that the different boards would be checked based on 3 degrees of weather helm and the data supports that it isn't the same. Without overstating the obvious, this would mean that the different sails areas and their associated CE's would be such that 3 degrees of weather helm would be the result for their respective boards. Similar flow, section and angle of attack was the baseline for testing and not forces from sails or sail areas. The same was true for the second set of data except that areas were kept the same and the aspect was different, but still 3 degrees of helm and still the result is more lift.

    I will defer to the experts, including you, but I cannot agree that it is misleading. I have made no effort to mislead as denoted by data provided in prior posts and the criteria set to test the different boards. One of those is 3 degrees for both boards, and for a person of your caliber to say that they should be compared to lift only is IMO, and unless I'm wrong, like saying that the designer will design the board first and then let the weather or lee helm be as high or as low as it will come out to be.

    If I read you correctly, to do so, would mean a vessel designed and operating to 3 degrees weather helm with boards to provide that angle of attack efficiently and then, the same vessel operating with 45 degrees weather helm because a different set of boards are fitted and the only consideration is making sure the design operates at the lift of the initial boards regardless of angle of attack designed for the helm.

    I couldn't agree more. I believe that the board span should be based on the draft of the vessel and then incorporate further required area by way of chord. I know it isn't the "internationally" recognized way of solving for the boards based on sail area or lateral area, but the catamaran is a beast in itself with very small lateral areas and very high sail areas which would provide boards that are either too small for one or too large for the other resulting in low lift or high drag for either respectively.

    It is a sort of balancing act for the way I have come to solve for the boards, but I have realized that most times it will fall between AR's of 2.7 to 4 times the draft with 4 on the high side if the design is low in sail area. This is not an unreasonable constant.

    This is of course only my observation and not based on the generally accepted and old time tested formulas for the slow mono-hulls with small sail areas and huge lateral areas, so it is open to rebuke, but until someone can demonstrate an unequivocally unchallengeable way of acquiring perfect results, I'm sticking to it and everyone can stick to their own. For me, only the scaled demonstrator will prove if I have erred and need to re-design them.

    Again I couldn't agree more. In my mind, place the area where less drag is created by it, in the span, but chord area and enough area as a whole is imperative.

    Thanks
    J:cool:
     
  13. catsketcher
    Joined: Mar 2006
    Posts: 1,315
    Likes: 165, Points: 63, Legacy Rep: 790
    Location: Australia

    catsketcher Senior Member

    Some questions for Tom

    Hello all

    I understand what Tom is saying about lift - both rudders have to produce the same amount of torque so a larger one or a more efficient one will produce this lift at a lower angle of attack. So the drag data should be calculated at same lift - all well and good. (I hope this is correct!)

    I am really interested in stall characteristics though. I have been in a few cats that don't tack - Hobies, most simple beach cats in fact, a trailer sailer cat and one or two roomarans and would gladly give up a 1/10 of a knot for better very low speed manouvreing. I suspect that during tacking our foils come close or do change to a stall configuration - especially in waves or heavy winds. So a question to Tom - is aspect ratio or depth a factor in stall? Do low aspect foils work better when stalled? Do high or low aspect ratios re-attach flow better or is foil loading the most important variable?

    Cheers

    Phil Thompson
     
  14. catsketcher
    Joined: Mar 2006
    Posts: 1,315
    Likes: 165, Points: 63, Legacy Rep: 790
    Location: Australia

    catsketcher Senior Member

    Angle of attack

    JCD

    I think Tom thinks it is misleading to compare foils at the same angle of attack when they have really should be compared producing the same lift (force).

    Your rig will be trying to pull your boat to leeward. The vector is mostly sideways with a little bit of vector forwards. We have to counter-act the sideways (leeway) vector and minimise any drag in the forward vector. As the rig produces a pretty set force at different windspeeds you can work out the force that the boards will have to counter-act - the lift they will have to produce.

    I think this is why you can calculate drag from the lift rather than a set angle of attack. A large or more efficient foil will not get to 3 degrees angle of attack as it will produce the same force as the smaller foil at a lower AA. Or the smaller foil will have to be set at a higher angle of attack (and make more drag) to produce the larger or more efficient boards force (lift).

    Think of Mr Newton and his third law. Your boards have to produce an equal and opposite reaction to the rig to stop you accelerating sideways. They will slip sideways, increasing drag and lift until the lift they make equals the sideforce from the rig. When the two are equal and opposite the forces are balanced and the acceleration becomes zero - you will still be going sideways a bit though - that is leeway.

    cheers all

    Phil
     

  15. JCD
    Joined: Jul 2006
    Posts: 359
    Likes: 3, Points: 0, Legacy Rep: 36
    Location: Coney

    JCD Follow the Bubbles!

    Hello Tom and Phil,

    Tom, if the way Phil explained it is understood to be accurate, and it certainly makes sense to me in my own limited way, then I retract my former post and stand corrected in thinking that you meant that the boards in the example will have the same lift instead of understanding that their comparison should be to the lift and not a set variable like the angle of attack.

    Phil, thanks for giving me some more insight to this. This is really difficult to get right and the grey matter isn't a sponge anymore. I apologize to you both if I appeared to be a bit stand-offish...I've been on a short fuse since yesterday and it is still lit.

    Thanks
    J:cool:
     
Loading...
Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.