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Thread: Prismatic Coefficient and getting wrapped around a wheel

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    Default Prismatic Coefficient and getting wrapped around a wheel

    Brief: Is there some way of quantifying a desirable Prismatic Coefficient as a function of (something) for speeds above hull speed????

    Details: I’ve been wrapping around a wheel… because something doesn’t make sense to me… yet.

    It all started when reading the popular thread “Do immersed transoms create less drag?”

    http://www.multihulls4us.com/forums/showpost.php?p=7974&postcount=104

    Woods Designs made a comment that doesn’t fit in with my logic of the world. Lot of other things don’t either… like some women I know, Obama’s logic and Quantum Physics to name a few. The unfortunate thing is, in this case… I really want to understand Prismatic Coefficient. The others... I've stopped trying.

    I understand the geometric definition! We don't have to beat that dead horse anymore.

    Woods Designs even prefaced it with, “Instinctively you might think that fine ends would be faster as they would “cut through the water better”. Well, I certainly did up until he dropped that bomb. I read and re-read it… pondered and re-read it again. I then read his web site.

    I found a similar comment in terhohalme’s attached document “How to dimension a sailing catamaran.pdf” found in the “Design of catamaran parameters” thread.

    http://www.multihulls4us.com/forums/showpost.php?p=302&postcount=2

    BigCat explained that it was an empirical based calculation. Sincerely, BigCat I do appreciate your reply, but that only makes me wrap tighter around that wheel. That’s like some kind of positional joke… you just have to be there.

    I’ve done several Google searches and didn’t really find anything even attempting to explain it. But I did find quite a few sailing catamarans touting prismatic coefficients in the 0.62 to 0.67 range. They all pointed to it that it was GOOD… like apple pie, but no one took at stab at why.

    Could someone comment if this sounds like a glimmer?...

    Above hull speed, I’m guessing that the bigger ends help it to be semi-planing, while the pointy end versions (~0.56) are completely displacement.

    I guess the real question is… Is there some way to quantify it?

    I’m picturing it being like a transmission on a car. That if you have it too highly geared (say Cp > 0.7) that the engine (sails) can’t get up to a good top speed. That if you put a little less gear (say Cp = 0.67) the engine can rev up and pull a higher top speed. The problem is… how to determine how much gear (Cp) one could put in based on... something (FM)… like sail size.

    … still wrapping around that wheel!

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Would it be easier if you you looked at it the other way round. I think you can agree that long thin hulls are faster than fat ones? So for a given volume if you make the ends fuller then that volume has to come from somewhere. Thus the middle gets smaller and narrower? Does that make sense?

    You are right, if you have a high Cp then you get more drag at low speeds so potentially can never get going fast enough to benefit from the higher Cp.

    That is certainly the case with, for example, kayaks which also have long thin hulls. But you (well me certainly) cannot physically paddle them fast enough to benefit from a high Cp.

    So the ideal CP will depend in part on how fast you want/can go.

    As I say on my website, changing the Cp can reduce drag by 10% at higher speeds. Or putting it another way, increase speed by 10%. To increase speed by that amount by increasing sail area would mean increasing it by about 20%, which apart from anything else (like stability, crew effort) is 20% more expensive.

    So having the right Cp is essential to having a well performing boat. Unfortunately even I cannot judge the Cp just by looking at a boat, so it is hard to compare different designs, you'll need to get data from the designer. Whereas it is easy to compare WL beam, sail areas or displacements.

    I think all agree that multihulls need a higher Cp than does a monohull (which typically will be in the .55-.56 range). But no multihull can be really considered a "planing" hull. The aspect ratio is wrong. A planing speedboat has an almost square waterplane area when planing, a multihull is like a pair of water skis. Planing boats must generate lift, same as airplane wings etc so need a wide WL beam.

    Warships have multihull like hulls, typically a length/beam ratio of 10:1 so if you want to research more you could look for tank test results on frigates etc - although obviously I doubt if you'll find any recent research on line.

    So to answer your brief.

    Yes there is: Tell me how fast you want a boat to go of a certain length and displacement and I can tell you the optimium Cp. But HOW I do it is another matter!...

    Does that confuse more, or help?

    Richard Woods of Woods Designs

    www.sailingcatamarans.com

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    Default Unwrapping the wheel...

    Quote Originally Posted by Woods Designs View Post
    Would it be easier if you you looked at it the other way round. I think you can agree that long thin hulls are faster than fat ones? So for a given volume if you make the ends fuller then that volume has to come from somewhere. Thus the middle gets smaller and narrower? Does that make sense?
    Ok, I'm starting to see some light... Whereas the low Cp hull has a gentler displacement of the water, it also has to transition it out further to create the same amount of volume (total displacement). The higher Cp hull has a more abrupt transition at the ends, but has a narrower center section for the same volume. That below hull speed finesse is needed and above the brute force method gets the job done better.

    Ok, obviously this has a limit... otherwise, we'd all be sailing around using pontoon boat hulls. So my logical (but untrained mind) says to me... you should maximize your sail plan/area for stability (most available horsepower). Keeping length and total displacement constant, you should then adjust the Cp to maximize the speed.

    Quote Originally Posted by Woods Designs View Post
    Yes there is: Tell me how fast you want a boat to go of a certain length and displacement and I can tell you the optimum Cp. But HOW I do it is another matter!...
    Sounds like that phrase, "I could tell you, but then I'd have to shoot you."

    So there is no theoretical equation or even a statistical based equation describing this behavior? And it is only through a Marine Architect's experience that they can judge this factor? I guess I can see where it would be kept a highly guarded secret. If you had a ten percent advantage in any racing circles... boat, car, plane, biking... the race is already over.

    Thank you that clears a lot up.

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    I think you have basically got it now.

    The Cp is probably the single most important factor in designing a hull. So no surprise, people don't want to give away their trade secrets by saying what Cp they use for a specific application.

    Having said that, somewhere between 0.6 and 0.65 is good. More or less than that and you should think hard about choosing that design.

    Richard Woods of Woods Designs

    www.sailingcatamarans.com

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    "Above hull speed, I’m guessing that the bigger ends help it to be semi-planing, while the pointy end versions (~0.56) are completely displacement."

    You want a theory. Well and good, but the fact of the matter is that the PC choice isn't based on theory. The history is well known to those who have studied it: it's based on tank testing and the history of yacht performance. It isn't based on theory. Even if you originate a perfectly descriptive theory that contradicts no known facts, the history of the choice of PC isn't based on your theory or anyone elses' theory - it's based on observation.
    Currently concentrating on http://earthnurture.com .

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Didn’t mean to strike a sour chord. I am trying to come to grips with a very technical subject so that I can make intelligent choices about which catamaran to build or buy. And, a day doesn’t go by that I don’t pick up something new (to me) from this forum. Albatross introduced me to a set of curves just yesterday. Although for power cats, it was the first graphs I’d seen plotting out anything above hull speed. Your thread "Formulas, rules, and Benchmarks" has been very helpful in getting me spun up. I hope you and others continue to feed it... its a great one stop resource! I was just “hoping” that there was a theory and thus, at least, empirical equations out there describing the behavior above hull speed as a function of Cp. Woods Designs explained it to me that it is probably well understood by NA’s (at least in the ranges of their expertise) but they choose to hold that proprietary. Contrary to my country’s recent flirtation with socialism, I do believe in capitalism and their right to hold that proprietary for as long as they can. More power to them!

    BTW – Most all theories are based on observation. Then, finally someone describes it with Math. Someone will someday describe the behavior above hull speed and likely Cp will be a major component of that theory. Aside - The only exceptions, that I know of, are those based on Quantum and Astrophysics where the Math was described first and it took years for someone to observe it in the real world.

    Bringing my other thread “Speed and other vices..."into context with this one. I’m a little confused. It appears to me that one thing is being said and another is being practiced. If a cruising catamaran is primarily being run under its hull speed for 90%+ of the time, wouldn’t it be wise to use Cp’s lower, say something around 0.57 seems like it would be more efficient at those speeds? Yet so many are trying to get to 0.65 or greater. Or… is something else coming into play here? Or… is that knowledge proprietary also?

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    High Cp hulls have other advantages. They make the boat pitch less and the sterns don't squat under power so much

    And also remember my last paragraph in my previous post. If you cannot go over 12 knots you are unlikely to avearge 8 knots in a multihull.

    In a monohull it's different. I raced once from Antigua to Bermuda in a 53ft monohull. 1000 miles. We did it in exactly 5 days, so 200 miles a day. Yet the boat never did more than 8 knots. It never did less either. Something that doesn't happen on a multihull

    Richard Woods of Woods Designs

    www.sailingcatamarans.com

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    In terms of resistance R, coefficent CP has secondary effect - only few % of R. Primary effect is DLR that can vary the resistance by 30%, so weights should be considered first...

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by Woods Designs View Post

    In a monohull it's different. I raced once from Antigua to Bermuda in a 53ft monohull. 1000 miles. We did it in exactly 5 days, so 200 miles a day. Yet the boat never did more than 8 knots. It never did less either. Something that doesn't happen on a multihull

    Richard Woods of Woods Designs

    www.sailingcatamarans.com
    ????? 200/24 = 8.33*

    Also: http://www.youtube.com/watch?v=XBcDXns1W28

    Don't think they went below 8 knots very often...
    Last edited by 44C; 21st September 2009 at 11:52 PM.

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Nice video...
    Gag reflex out of my mouth... Somme'bitch!

    I guess I can see what you say about DLR. Having a DLR = 2 can do that for you.

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by Albatross View Post
    In terms of resistance R, coefficent CP has secondary effect - only few % of R. Primary effect is DLR that can vary the resistance by 30%, so weights should be considered first...
    Albatross, maybe you can quantify what Sir Douglas Phillips Birt wrote - which is that a low PC is more harmful at high speeds than a high PC is at low speeds.

    Double Duty, the only genius that yacht design has ever had, AFAIK, was Nathanael Herreschoff, who introduced the catamaran to the yachting community, which promptly banned it for being too fast. A low PC makes big hull waves when a boat sails fast. A boat with a low PC has a less 'regular' shaped hull, that is, the sections are more different from each other than they are in a higher PC boat, all else being equal. I don't know who originated the phrase, but 'Water doesn't like surprises.' Water typically gets more of a surprise passing a low PC boat than a high PC boat. A practiced eye doesn't have to know any statistics at all to know that an Outremer is going to be faster than an FP of the same size. You can easily see that the hulls are leaner and that there is less stuff there-it just plain looks faster.

    There are a lot of statistics used in yacht design that are empirical. For example, the center of buoyancy at 56% aft of the center of the boat produces a faster hull than a center of buoyancy at the center of a boat's waterline (50% aft of the start of the designed waterline,) in displacement sailboats. I've never seen anyone make any effort to explain what governs these empirical findings. There are a couple of books about yacht design written by physicists that might interest you - Czeslaw A. Marchaj wrote several, and Ross Garrett wrote one. They don't say much about multihulls, though. The best book for that would be Chris White's book, 'The Cruising Multihull.' I also recommend Charles Kanter's book, 'Cruising Catamaran Communique.'

    Knowing most of these things isn't going to help you choose between, say, a St. Francis or a Fontaine Pajot catamaran, because you aren't going to have access to much of this information. Your priorities will pretty much determine how fast your boat is. If you want a boat with lots of attractive furnishings and a maximum of room, and then fill it with 20 cases of wine, a barbecue, a microwave, an electric refrigerator and a generator to run it all, your boat isn't going to be fast unless you have millions of dollars to spend on epoxy, corecell and carbon fiber to offset all of that other weight. Even so, that boat would be much faster if you left all of that stuff ashore and lived on MREs.

    The only way to have a fast livaboard boat with lots of amenities is to buy or build a long boat. Unless your needs are simple and your wants are few (and the same is true of your admiral,) you simply can't have a fast 40' livaboard boat. The reason this is true is that square root of the waterline length is the biggest determinant of hull speed. This is the BigCat philosophy, which you can read about on my website - my goal is always to get the longest boat for the buck. (In a commercial boat, though, there are powerful regulatory incentives not to build bigger than 65' / 20 meters.)
    Last edited by BigCat; 22nd September 2009 at 05:55 PM.
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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Anybody know what the CP is on my Gemini 105Mc.

    After I fill the water tanks and put on beer and the dingy on davits the whole waterline changes.

    Then my two sons (combined 500lbs) and, well...............never mind.

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by therapy View Post
    Anybody know what the CP is on my Gemini 105Mc.

    After I fill the water tanks and put on beer and the dingy on davits the whole waterline changes.

    Then my two sons (combined 500lbs) and, well...............never mind.
    Hmmmm... the beer weight falls somewhere between the water weight and the dingy weight. Well, maybe it can be shifted forward to get the transoms out of the water and reduce Cp if you have too much or put in the back to submerge them and get higher Cp. That's my vote... screw the Cp... easier to reach the beer. We must maintain a proper perspective on our priorities.

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by BigCat View Post
    There are a lot of statistics used in yacht design that are empirical. For example, the center of buoyancy at 56% aft of the center of the boat produces a faster hull than a center of buoyancy at the center of a boat's waterline (50% aft of the start of the designed waterline,) in displacement sailboats. I've never seen anyone make any effort to explain what governs these empirical findings. There are a couple of books about yacht design written by physicists that might interest you - Czeslaw A. Marchaj wrote several, and Ross Garrett wrote one. They don't say much about multihulls, though. The best book for that would be Chris White's book, 'The Cruising Multihull.' I also recommend Charles Kanter's book, 'Cruising Catamaran Communique.'
    BigCat,

    56% aft... That's a new one on me. Is this jem in one of these books you recommended? Where might I find it... is there some book or web site that might have more of these type things "rules of thumb"? It might be informative to know these when looking at designs and or talking with boat designers. May not be able to estimate them for a particular boat, but, then again... might be able to.

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    I agree with Bigcat re the position of C of B. Having the C of B aft of midships is sensible anyway, considering the fact that most weight is aft

    I also agree that the Slenderness ratio, DLR, or weight versus length, is the most important speed factor. But the original question was about Cp

    Then some time ago you asked about my pitchpoling experience in the Norseman 43.

    There were three of us on deck at the time. We were racing and sailing as fast as the boat allowed (9-10 knots) with full main and genoa. Seas weren't steep and breaking, just an average mid ocean swell from aft the beam.

    It was a squally day but nothing alarming. We got hit by a extra gust and the bows went down until the mastfoot was in the water and both rudders were right out.

    Fortunately the helmsman was experienced enough to know not to move the rudders. So when the bows resurfaced and the rudders dropped back into the water we carried on in a straight line rather than rounding up. By then we were trying to get a reef in. It was sometime after the wind dropped that before we took the reef out and hoisted a spinnaker

    Below one crew member was thrown across the galley and the owner who was asleep hit the front bulkhead as he slid forward.

    We were about 1000 miles from land at the time so it was all quite scary. And also very unexpected as I'd never sailed a catamaran that behaved like that (nor have I since). I did race on a 26ft Firebird, 40ft mast, 800kgs (known for pitchpoling) but that was easy to control by being attentive. You cannot play the sheets on a 43ft boat so are much more dependant on hull design rather than crew skill.

    Finally a personal note: I leave Canada on Sunday and fly to the UK arriving Monday. Tuesday I fly to Berlin to see builders. Back to the UK on Thursday. Then I sail on the east coast UK and then go to Millbrook about Oct 12th to 28th, when I fly to Florida and my Romany for a winter's cruising.

    So I may be too busy to write much on this forum over the next few days.

    Richard Woods of Woods Designs

    www.sailingcatamarans.com

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by DoubleDuty View Post
    BigCat,

    56% aft... That's a new one on me. Is this jem in one of these books you recommended? Where might I find it... is there some book or web site that might have more of these type things "rules of thumb"? It might be informative to know these when looking at designs and or talking with boat designers. May not be able to estimate them for a particular boat, but, then again... might be able to.
    Essentially, you have to learn monohull design and then un-learn some things that don't carry over exactly.

    Start with Ted Brewer's intro, but be aware that it is a primer to sailing monohull design: http://www.tedbrewer.com/yachtdesign.html

    Skene's Elements of Yacht Design, edited by Francis Kinney, is THE primer of yacht design. My copy is quite old, so I'm not sure what recent editions look like. This is the place to start. It doesn't say anything about multihulls, really.

    Principles of Yacht Design, by Larsson and Eliasson is much newer, but it might as well be titled, "Metric design of mid-sized racing monohull sloops." That is, it lacks breadth.

    I could name a few others, but I think Skene's is the one you want.

    There is no primer on designing multihulls. Chris White's book has some hints, but it isn't meant to teach yacht design. It's a really great book for teaching monohull sailors all about multihulls, as is Charles Kanter's book.

    I also got an enormous stack of back issues of Multihull magazine, and combed through them looking for interviews with designers. I found some very helpful hints from Alexander Simonis. Getting design information about multihulls is pretty much a treasure hunt, but you have to study basic yacht design to make use of the multihull specific info.

    I will repeat, however, if you are just trying to choose a cruising boat (that is a sailing catamaran,) I wouldn't get into details such as, "Where is the center of bouyancy?" Pretty much everybody who knows what they are doing will have put it 54 to 56 percent aft of station 0. There is an argument for putting the center of buoyancy at or just aft of the center of the waterline in sailing monohulls that doesn't apply to multihulls, because it has to do with the effects of heeling on steering.
    Currently concentrating on http://earthnurture.com .

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by Woods Designs View Post
    Then some time ago you asked about my pitchpoling experience in the Norseman 43.

    There were three of us on deck at the time. We were racing and sailing as fast as the boat allowed (9-10 knots) with full main and genoa. Seas weren't steep and breaking, just an average mid ocean swell from aft the beam.

    It was a squally day but nothing alarming. We got hit by a extra gust and the bows went down until the mastfoot was in the water and both rudders were right out.

    Fortunately the helmsman was experienced enough to know not to move the rudders. So when the bows resurfaced and the rudders dropped back into the water we carried on in a straight line rather than rounding up. By then we were trying to get a reef in. It was sometime after the wind dropped that before we took the reef out and hoisted a spinnaker

    Below one crew member was thrown across the galley and the owner who was asleep hit the front bulkhead as he slid forward.

    We were about 1000 miles from land at the time so it was all quite scary. And also very unexpected as I'd never sailed a catamaran that behaved like that (nor have I since).

    Richard Woods of Woods Designs

    www.sailingcatamarans.com
    Yow, scary story. Were you running at the time? I don't think I would have put up a spinnaker after that, due to a sheer lack of nerve. So, the moral of the story would be 'reef early, and run off if hard pressed.'

    This story illustrates what attracts me about low aspect ratio rigs, such as a biplane rig that is easily reefed - you can keep the center of effort low and reduce the lever arm that induces (wind caused) pitchpoling or capsizing.
    Currently concentrating on http://earthnurture.com .

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by BigCat View Post
    Skene's Elements of Yacht Design, edited by Francis Kinney, is THE primer of yacht design. My copy is quite old, so I'm not sure what recent editions look like. This is the place to start. It doesn't say anything about multihulls, really.
    I'm trying to get a copy of this one. But its out of print and the used ones range from $6 to $120 for some strange reasons. Also, some review said there is a newer one that is not advicable to get as it leaves stuff out the older ones had. Maybe the reason for some $6 ones. You said yours was old. Who knows... you might have a collectors item . What year do you have or do you recommend?

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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    Quote Originally Posted by DoubleDuty View Post
    I'm trying to get a copy of this one. But its out of print and the used ones range from $6 to $120 for some strange reasons. Also, some review said there is a newer one that is not advicable to get as it leaves stuff out the older ones had. Maybe the reason for some $6 ones. You said yours was old. Who knows... you might have a collectors item . What year do you have or do you recommend?
    My edition of Skene's was revised by Francis Kinny, and the latest copyright listed on it was 1973, which is the year in which I bought it.

    From Amazon.com:

    "Word of warning, although this book is probably excellent as well in the elements of yacht design, the most current edition is the 8th edition, not the reprinted 6th edition. Please note that the 8th edition contains more modern construction methods and materials. Unfortunately the 8th edition is out of print so it is kind of difficult to find. (Published in 1973 and later) Good luck and good designing."

    For some reason, the sixth edition was recently reprinted. I recommend the 8th. edition.

    http://www.macnaughtongroup.com/sken...cht_design.htm -- for remarks similar to mine from a yacht designer. Amazon.com has several of this edition available thorough contracted used book sellers for $20 to $25.


    Here's a search that will lead you to some sailing catamaran design hints:

    http://www.google.com/search?hl=en&s...&aq=f&oq=&aqi=
    Last edited by BigCat; 26th September 2009 at 09:23 PM.
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    Default Re: Prismatic Coefficient and getting wrapped around a wheel

    I'm happy to have finally found this forum and especially this thread. I have been slowly working my way through an aluminum power cat design for the past many months. One of my key focuses is ease of building. I have some questions about cp in relation to my design. On a 45ft LOA, the hulls are constant beam (BWL 40 inches) except for the forward 8ft and there is no rocker (pretty much constant draft). The bow and stern are a bit different, but the hull below the waterline isn't too different from a regular pontoon boat. The cp as it is currently, is .83, which is way higher than anyting I've seen. Does anyone know how this design might perform? My speed goals are a fuel efficient cruise slightly below hull speed on up to a top speed of maybe 14kts. Will the high cp make it slow relative to other hull shapes? Is it more prone to hobbyhorsing or other negative tendancies? Thanks for reading.

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