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Thread: Formulas, rules, and Benchmarks

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    Default Formulas, rules, and Benchmarks

    I think we should have a thread to gather together all the interesting and useful formulas, rules, and benchmarks that quantify issues of interest for multi-hull design and sailing, so I'm starting one.
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    Default Catamaran stability, wind speed and wind pressure

    From: http://bigcatcatamarans.com

    The theoretical stability of a catamaran is given in the formula, displacement in pounds x the distance between the centerline of the two hulls in feet x .5 = righting moment in foot pounds. To use my BigCat 65 design as an example, 45,000 x 28 x .5 =630,000 foot pounds (that is, a lever of an amount of feet times an amount of force in pounds.) If considering a capsize from wind force, the theoretical heeling force is the wind pressure x the sail area x the CE (the height from the waterline to the center of your sail area.) Wind pressure can be calculated from Martin's formula, which is windspeed in miles per hour squared x .004= pounds per square foot. So, the heeling (capsize) force for BigCat 65 that generates a theoretical force sufficient to capsize it is: 9.21 pounds x 2400 sq. ft. of sail area x 41 feet (center of sail area above waterline) =630,000 foot pounds. This wind pressure is found at 48 miles per hour, which = 41.7 knots. (One knot equals 1.15155 miles per hour, so divide the mph by 1.15155 to get the knot equivalent to the result of Martin's formula.) So, in flat water, theory predicts the BigCat 65 will capsize at 41.7 knots in calm water if the sails are up and unreefed. This theory applies rather poorly to a biplane rig, which the BigCat 65 design has, because you can't get the full effect of the wind abeam if both sails are up, but it works pretty well for a typical catamaran with a single mast. Obviously, this is all very theoretical, because a capsize is unlikely to occur in calm water, sails are rarely strapped hard amidships in high winds, etc., but it does give one a starting point for considering the forces at work. It does help explain how charter catamarans have capsized by coming out from the lee of islands in strong trade winds with the full mainsail sheeted amidships while under motor, when you consider that gusts are often equal to half again the average wind speed, and that winds will often increase as they funnel through channels between islands, or through gaps in cliffs to windward.
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    Default Slenderness of hulls and speed potential

    Also from http://bigcatcatamarans.com :

    The K factor by Bill Roberts related a hull's resistance to its beam for hull beam sizes found in catamarans. Here's a copy of his table, the original source of which is no longer online. You multiply the square root of the hull's waterline by the k factor to get a predicted maximum hull speed. So for a hull with a DWL of 64', you multiply the K factor by 8 to get the maximum predicted speed in knots.

    Bill Roberts Presentation -- The "K" Factor
    LOA / BMAX / Disp Ratio/FinenessSpeed/ MAX speed / D/L3 / K Factor
    27 16" 650 20 27 kts 30 5.2 (21.25 hull beams in the overall length)
    27 23" 1300 14.3 20 59 3.8 (14.78 hull beams in the overall length)
    27 28" 1950 11.7 17 89 3.3 (11.57 hull beams in the overall length)
    27 32" 2600 10.2 15 119 2.8 (10.13 hull beams in the overall length)
    27 72" 7500 4.0 7.3 - 1.4 (4.5 hull beams in the overall length.)

    (The square root of 27 is a bit less than 5.2.) (The displacement/L3 for a given boat can be found with the calculator at http://www.sailingusa.info/cal__hull_speed.htm ) I haven't seen any explanation given for the 'fineness speed mentioned above.)
    Last edited by BigCat; 12th August 2009 at 01:35 AM.
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    Default Yacht design links - speed, sail area, horsepower, etc.

    A primer of (monohull) yacht design:

    http://www.tedbrewer.com/yachtdesign.html

    A series of useful (monohull) online calculators, including those comparing displacement to sail area, and displacement to length:

    http://www.sailingusa.info/cal__hull_speed.htm

    Derek Kelsall has made and posted formulas for predicting speed under sail, speed under power, and stability - all designed specifically for catamarans:

    http://www.kelsall.com/images/articl...ormulas_KC.pdf

    Catamaran designer Richard Woods, a contributor to this board, has posted articles on his website. Here's an interesting one on hull shapes:

    http://www.sailingcatamarans.com/hullshapes.htm

    Catamaran designer John Shuttleworth has also posted articles he has written on his website. Here's one on seaworthiness:

    http://www.john-shuttleworth.com/Articles/NESTalk.html
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    Default Terho Halme's spreadsheets and formulas

    Terho Halme, a Finnish multihull builder and designer, has posted a couple of interesting charts and spreadsheets about the effects of factors such as hull beam, hull depth, etc. on catamaran speed at:

    http://www.boatdesign.net/forums/mul...p-22529-3.html

    http://www.boatdesign.net/forums/att...br-dr-plot.png

    http://www.boatdesign.net/forums/att...br-dr-plot.png
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    Default Re: Terho Halme's spreadsheets and formulas

    Great work Big Cat. Thank you for tracking these things down.

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    Default Hydrodynamic resistance = cubed speed

    Quote Originally Posted by Ozmultis View Post
    Great work Big Cat. Thank you for tracking these things down.
    Hi, Andrew

    Thanks, I thought of it because I saw a post in which Allan, aka Nordic Cat, mentioned that wind power increased at the square of the windspeed.

    He also said this, which I don't recall hearing before:

    "Hydrodynamic resistance increases roughly by the cube of speed, so to go twice as fast you need 8 times the power."
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    Default Bridge deck clearance

    One rule for bridgedeck clearance is 5.5% to 6% of the LOA, and some say (Melvin of Morelli and Melvin) 4% of the LOA to 6% )of the LOA.

    Some rules of thumb are published here:

    http://www.multihulldynamics.com/new...p?articleID=83

    Which offers the rule: 10% of overall beam, or more.

    IMHO, all rules are more reasonable for smaller catamarans, and tend to overstate the clearance needed in big ones. For rules that give a range, I'd say that bigger catamarans should be at the low end of the rule, and small catamarans at the high end of the rule.

    Here's another rule I just found at http://www.boatdesign.net/forums/archive/t-23889.html:

    "Hence we see the ratio of tunnel width to wing clearance expressed as around 18%."

    "39~42% BCL/LWL ratio advocated by Tarjan. (where BCL= Beam between Center Lines and LWL= Length Water Line)
    Additionally, make the bridgedeck as high as possible 14~18% of BCL, using the higher ratio for larger boats"
    Last edited by BigCat; 29th August 2009 at 06:47 AM.
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    Default Area of daggerboards and rudders

    From Richard Woods, posted on boatdesign.net . As a guide use 3-5% of sail area for the boards, about half that for the rudders.

    Use 2 to 3 x aspect ratio (length fore and aft versus height, so they should be between 2 and 3 times deeper than they are long.) (Discussion between Terho Halme and Richard Woods, same web page.)

    See: http://www.boatdesign.net/forums/mul...n-22274-2.html for source, and to get nuances.
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    Default Issues of scale - scaling and stability

    From Chris White's book:

    Doubling a multihull's size increases its stability 16 times. Increasing a multihull's size by 19% doubles its stability.

    Therefore, a 70' multihull has 16 times the capsizing resistance of a 35' multihull. I use 35' as an example because that is Richard Woods' preferred size for cruising.

    A number of people feel that catamarans under 40' aren't stable enough for offshore use, because they feel that the statistics for capsizing and pitchpoling indicates that multis under that size have a much greater incidence of capsizing. I assume that this scaling issue is why that would be the case, assuming that this contention is correct. A 67.4' multi would have 4x the stability of a 40' multi, using Chris' rule.

    (The subsequent discussion on this thread leads me to make a clarification. The stability referred to in this quote is roll moment of inertia, which Chris says is the main factor affecting capsize due to wave action. One might think of it as the 'pendulum effect.' caused by the passing of relatively regular seas.)
    Last edited by BigCat; 10th October 2009 at 10:35 PM. Reason: Clarification
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  11. #11

    Default Re: Issues of scale - scaling and stability

    Really the terms 'doubling the stability' and 'capsizing resistance' need to be explained. These are not the terms commonly used in naval architecture.

    If we say that righting moment (RM) is increasing X times - this is correct statement.

    Then, in reality it is not that simple. Say, doubling the length does not give 8 times increase of displacement; doubling the length does not give 2 times increase of beam. So, increase of RM is not 8x2=16.

    The relations are much more complicated; this is in detailed studied by Barkla for monohulls (see Larsson's 'Principles of Yacht Design').

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    Default Re: Issues of scale - scaling and stability

    Quote Originally Posted by Albatross View Post
    Really the terms 'doubling the stability' and 'capsizing resistance' need to be explained. These are not the terms commonly used in naval architecture.

    If we say that righting moment (RM) is increasing X times - this is correct statement.

    Then, in reality it is not that simple. Say, doubling the length does not give 8 times increase of displacement; doubling the length does not give 2 times increase of beam. So, increase of RM is not 8x2=16.

    The relations are much more complicated; this is in detailed studied by Barkla for monohulls (see Larsson's 'Principles of Yacht Design').
    I think Chris means scaling up both the length and beam. He's the one that says 'capsize resistance,' but then he's not writing for naval architects, but rather for sailors. The idea is pretty clearly not to substitute this rule for doing stability calculations, but rather give some idea of the consequences for building and sailing boats of different sizes.
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  13. #13

    Default Re: Issues of scale - scaling and stability

    Quote Originally Posted by BigCat View Post
    I think Chris means scaling up both the length and beam.
    If so, it is completely misleading statement from his side because it never happens in reality!

    He's the one that says 'capsize resistance,' but then he's not writing for naval architects, but rather for sailors. The idea is pretty clearly not to substitute this rule for doing stability calculations, but rather give some idea of the consequences for building and sailing boats of different sizes.
    The issue is that: does 'doubling the stability' refer to RM, to GZ, to GM, to AVS, to STIX or to any other parameter of stability? Should one trust such amateurish writings for 'non naval architects'? Does it give any 'idea of the consequences' of misunderstanding of those texts by sailor or amateur builder? Just please be careful when picking up those 'rules of thumb' - most of them work, some of them don't.

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    Default Re: Formulas, rules, and Benchmarks

    In reality, the approximation of RMmax = mLDC*BCC/2*g, where

    mLDC is fully loaded displacement (mass)
    BCC is the distance between centerlines of the hulls
    g is the acceleration of gravity

    Whatever the lenth, beam, or displacement are, the maximum righting moment is easy to find. The mass is almost proportional to L^3 and the beam is almost proportional to L. Big cruising catamarans are normally lighter and narrower than these proportions tell.

    STIX and Barkla proportions are for monohulls only.

    Terho

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    Default Re: Formulas, rules, and Benchmarks

    Quote Originally Posted by terhohalme View Post
    In reality, the approximation of RMmax = mLDC*BCC/2*g, where

    mLDC is fully loaded displacement (mass)
    BCC is the distance between centerlines of the hulls
    g is the acceleration of gravity

    Whatever the lenth, beam, or displacement are, the maximum righting moment is easy to find. The mass is almost proportional to L^3 and the beam is almost proportional to L. Big cruising catamarans are normally lighter and narrower than these proportions tell.

    STIX and Barkla proportions are for monohulls only.

    Terho
    Actually, I don't find much statistical variation in length, beam, or weight in cruising multihulls in the 38 to 65 foot range that correlates with size. Bigger boats certainly can be lighter, but they often are so loaded with amenities that you can't find any really strong trends. If we stipulate that we are discussing my main interest and Chris' main interest, which is family cruising yachts meant to be lived aboard either permanently or for fairly long cruises, I think his rule of thumb holds reasonably well.
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    Default Re: Issues of scale - scaling and stability

    Quote Originally Posted by Albatross View Post
    If so, it is completely misleading statement from his side because it never happens in reality!


    The issue is that: does 'doubling the stability' refer to RM, to GZ, to GM, to AVS, to STIX or to any other parameter of stability? Should one trust such amateurish writings for 'non naval architects'? Does it give any 'idea of the consequences' of misunderstanding of those texts by sailor or amateur builder? Just please be careful when picking up those 'rules of thumb' - most of them work, some of them don't.
    Albatross, you make me wonder if you know who Chris White is. He is a very experienced sailor and multihull designer, and he is definitely not amateurish. You may very well be qualified to design a much wider range of vessel types and sizes than Chris is, but frankly, I doubt if you know as much about midsize cruising sailing multihull yachts as he does. Please keep in mind that on this website we primarily discuss medium size multihull sailing yachts used for cruising by families and couples. This is the kind of yacht the Chris White specializes in, and the kind that I normally discuss. If you had a copy of his book, I think it would be apparent to you that his rules of thumb are meant to be valid only for this size and type of yacht.
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  17. #17

    Default Re: Formulas, rules, and Benchmarks

    Quote Originally Posted by terhohalme View Post
    In reality, the approximation of RMmax = mLDC*BCC/2*g, where
    mLDC is fully loaded displacement (mass)
    BCC is the distance between centerlines of the hulls
    g is the acceleration of gravity
    If we look at this formula, then BCC/2 gives us for lever of form. Where is lever of weight VCG*sin(Heel)? This formula works for wide catamarans where BCC/2 >> VCG*sin(Heel). It does not work for cats with limited beam or with high CG.

    Whatever the lenth, beam, or displacement are, the maximum righting moment is easy to find. The mass is almost proportional to L^3 and the beam is almost proportional to L.
    Again, this is a BIG simplfication and never happens in reality. Plot B(L) and DSPL(L) for few cats from one designer/builder and You will see that ratios mentioned by You do not work.

    STIX and Barkla proportions are for monohulls only.
    I know! But for multis we have 'multihull size factor' that is a form of stability index. Giving samples with Barkla ratios and STIX I just show that the relations are much more complicated than in rules of thumb presented above.

  18. #18

    Default Re: Issues of scale - scaling and stability

    Quote Originally Posted by BigCat View Post
    Albatross, you make me wonder if you know who Chris White is. He is a very experienced sailor and multihull designer, and he is definitely...
    I have a copy of Chris' book and I know who he is. He is experienced designer and sailor but not a professional naval architect. So when I read about 'doubling the stability' I can guess that he means RM, but average reader probably does not. Next step, You post it here without the context, and it becomes more confusing

    And of course, the statement that 'doubling the size causes 16 times increase of stability' is nonsense.
    Last edited by Albatross; 10th October 2009 at 01:13 AM. Reason: mistype

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    Default Re: Issues of scale - scaling and stability

    Quote Originally Posted by Albatross View Post
    I have a copy of Chris' book and I know who he is. He is experienced designer and sailor but not a professional naval architect. So when I read about 'doubling the stability' I can guess that he means RM, but average reader probably does not. Next step, You post it here without the context, and it becomes more confusing

    And of course, the statement that 'doubling the size causes 8 times increase of stability' is nonsense.
    The average reader on a sailing website probably does not know what RM is, and so is unlikely to be misled. I think you are asking too much of a rule of thumb, which is not meant, as I said above, to substitute for calculations, but rather to give one some understanding of the ramifications of size. Also, I think you do not sufficiently consider where you are reading and posting- we are, for the most part, a collection of folks who want to do family cruising on mid size sailing catamarans. Unless noted otherwise, I think you can safely assume that is what is being discussed on this site. That is the context.
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  20. #20

    Default Re: Issues of scale - scaling and stability

    OK, I just did a quick study taking Lagoon range as statistical base.

    Say, we have 2 boats with waterline length L0 and L1; L1=k*L0
    Then, for beam B0 and B1 of these boat, the ratios are: B1=k^0.76*B0
    For displacement D0 and D1, the ratios are: D1=k^2.26*D0
    These power factors with k are based on Lagoons, they could be slightly different for other designers/builders.

    If Chris' statements work, those power factors with k would be 1 for beam and 3 for displacement. But evidently they are not! On other side, those factors are very close to Barkla factors I mentioned before.

    Now let's estimate increase of RM if we scale length of the boat 2 times, i.e. k=2.
    We get factor for RM increase: 2^0.76*2^2.26=8.11
    Let's remember that from Chris' rule of thumb this factor should be 16, so difference is double!

    It is a good sample how a bit of theory can help to understand the basics. I can't accept such overestimation of stability - it is just dangerous!
    Last edited by Albatross; 10th October 2009 at 02:44 AM.

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