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Thread: Formulas, rules, and Benchmarks

  1. #41

    Default Re: Formulas, rules, and Benchmarks

    Quote Originally Posted by BigCat View Post
    I don't think flat water is what he had in mind. He is referring to the famous Fastnet race where lots of (monohull) boats rolled over more easily after losing their masts, and points out that their decreased roll moment of inertia due to mast loss made them more vulnerable to rolling again.
    Case on flat water is simplified example. You want it on wave, underway? Add few other components to the formula... Then significance of Ixx will be even less.

    As to Fastnet race investigation, it is a well known publication by Stephens O., Kirkman K., Peterson R. 'Sailing Yacht Capsizing'. The Fifth Chesepeake Sailing Yacht Symposium. 1981. p.37-58. and covers monohulls. For catamarans, the order of hydrostatic component is much higher.

    Whether you agree with him, I will leave between him and you - I am satisfied to feel sure that I have correctly understood and reported what he said and meant.
    Sorry to say, I feel that he has written a nonsense, and You are trying to find explaination for that. I think CW is great designer but he is not a scientist in the field of ship/boat dynamics.

    I can't make anything out of your formula, because it references other formulas (or measurements,) without giving them; Kxx, for example.
    Yes, theory of ship motions is a complicated subject. I just show a sample of that, without going into details. If You are interested in differential equations of roll, You can get PNA book and study it in Volume III.

  2. #42
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    Default Re: Formulas, rules, and Benchmarks

    Ross Garrett of the Physics Department of the University of Auckland takes the same view as Chris White, regarding the effects of the roll moment of inertia on capsizing due to breaking waves, in his book, "The Symmetry of Sailing," published in 1987, on page 179. He also states that a doubling in size of the vessel increases its roll moment of inertia 16 times.
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  3. #43

    Default Re: Formulas, rules, and Benchmarks

    Quote Originally Posted by BigCat View Post
    Ross Garrett... ...also states that a doubling in size of the vessel increases its roll moment of inertia 16 times.
    But this about to be is correct if we talking about increase of moment of inertia!

    Moment of inertia is approximately: Ixx=f*DISPL*B^2 where f is coefficient depending on type of boat;
    If we increase length L of boat by k=2, then beam B will be increased by k^0.76=2^0.76=1.69 times and displacement DISPL in k^2.26=2^2.26=4.79 times. Then, moment of inertia Ixx will be increased by 4.79*1.69^2=13.7 times. Height of rig needs also to be considered, but result will be similar.

    Unfortunately in CW's book he says that stability is increasing 16 times, not moment of inertia! And anyway moment of inertia is not a direct measure of stability, it is only a part of equation describing roll, along with other more significant factors (inertial, damping and hydrostatic). See equation I posted before.

    So we are coming back from what I have started: 'stability is increasing 16 times' - is amteurish statement and it is sad that it appears in such valuable book.
    Last edited by Albatross; 13th October 2009 at 05:14 AM.

  4. #44

    Default Re: Formulas, rules, and Benchmarks

    Now we come to point: what is a measure of stability for wave/wind induced capsize of multihull (and any other ship)? The answer is: area under stability diagram. Area under stability diagram is a measure of work required to capsize the boat. This approach is used everywhere, starting from ISO12217 for small craft to... IMO Intact Stabiltiy Code and Rules of Classification Societies for commercial vessels. If we look at ISO12217 criteria for wave and wind stiffness, we can clearly notice that areas under stability curve are used there. No consideration is given to moment of inertia, though I agree that there is some effect, but not first order of significance.

    I can expalin in more detail if someone is interested.

  5. #45
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    Default Re: Formulas, rules, and Benchmarks

    Quote Originally Posted by Albatross View Post
    But this about to be is correct if we talking about increase of moment of inertia!

    Moment of inertia is approximately: Ixx=f*DISPL*B^2 where f is coefficient depending on type of boat;
    If we increase length L of boat by k=2, then beam B will be increased by k^0.76=2^0.76=1.69 times and displacement DISPL in k^2.26=2^2.26=4.79 times. Then, moment of inertia Ixx will be increased by 4.79*1.69^2=13.7 times. Height of rig needs also to be considered, but result will be similar.

    Unfortunately in CW's book he says that stability is increasing 16 times, not moment of inertia! And anyway moment of inertia is not a direct measure of stability, it is only a part of equation describing roll, along with other more significant factors (inertial, damping and hydrostatic). See equation I posted before.

    So we are coming back from what I have started: 'stability is increasing 16 times' - is amteurish statement and it is sad that it appears in such valuable book.
    Well, I agree that CW didn't write very clearly. You have to look at the context in his book to get the idea that he might be speaking of the roll moment of inertia. I don't know if the idea that roll moment of inertia is the major factor in capsizing due to breaking waves is true, but I find it interesting that both CW and RG think so.

    I actually think that 'rogue waves' capsize boats due to their extreme steepness, and if a really bit wave breaks under the boat, which is what happens when waves get really steep, it hardly matters what the characteristics of the boat are - like driving off a cliff, it doesn't matter if you are on a motorcycle, in a car, or a bus. However, common sense tells us that the bigger the boat, the bigger a wave has to be to be 'big.'

    In really big storms, however, even huge ships are damaged or lost, if they find one of these very tall, very steep waves. So, being in a large yacht versus a small one probably only matters in marginal situations. The BBC had a couple of shows (which you can see on YouTube,) about this, showing oceanographers changing their conclusions to acknowledge these huge waves. You can also find lots of videos on YouTube showing ones that were impressive, but that didn't smash the ships from which they were filmed, because the ships were really large.

    (I sailed across the Pacific, and also I sailed to Hawaii and back from the US mainland, encountering huge waves in the fall in the North Pacific's Westerlies. I was also nearly capsized between New Zealand and the Kermadecs a few years later - but it was very dark and I couldn't see the sea state. My wife woke me up and said, "Tim, I was just standing on the side of the pilot house!" We decided to run at that point, and worry about hitting the Kermadecs later.)
    Last edited by BigCat; 13th October 2009 at 05:50 AM.
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  6. #46

    Default Re: Formulas, rules, and Benchmarks

    2BigCat
    OK, one more point I want to show You is Marchaj's 'Seaworthiness'. On p.235 he is referencing results of tests in breaking waves and the conclusion is: beam is most significant parameter in its effect on capsize, than any other design parameter as displacement, inertia, freeboard, appendages. So hydrostatic stability effected by beam has priority - see diagrams on p.234.

    Also on p.215 there is a diagram expaining the equation of roll I posted before, in simple words.
    Last edited by Albatross; 13th October 2009 at 11:26 AM.

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    Smile Wave capsize resistance

    Quote Originally Posted by Albatross View Post
    2BigCat
    OK, one more point I want to show You is Marchaj's 'Seaworthiness'. On p.235 he is referencing results of tests in breaking waves and the conclusion is: beam is most significant parameter in its effect on capsize, than any other design parameter as displacement, inertia, freeboard, appendages. So hydrostatic stability effected by beam has priority - see diagrams on p.234.

    Also on p.215 there is a diagram expaining the equation of roll I posted before, in simple words.
    That's one book I don't have-I have his 'Sailing Theory and Practice," only. The good news is that if there's one thing a sailing multihull has a lot of, it's beam. And in a cruising catamaran, it's usually well distributed throughout the boat, leading to a lot of roll moment of inertia. There is also plenty of freeboard, and not so much in the way of appendages to be had on multihulls.
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  8. #48

    Default Re: Wave capsize resistance

    Quote Originally Posted by BigCat View Post
    That's one book I don't have-I have his 'Sailing Theory and Practice," only.
    That is really excellent book, actually I like all of them from Marchaj - in simple language but with strong experimental science behind. The first one I have read when I was a student was 1963 Russian edition.

    The good news is that if there's one thing a sailing multihull has a lot of, it's beam. And in a cruising catamaran, it's usually well distributed throughout the boat, leading to a lot of roll moment of inertia. There is also plenty of freeboard, and not so much in the way of appendages to be had on multihulls.
    We'll carry some experiments with catamaran roll/pitch soon using acceleration gauges, at small inclination angles. Will check it and share the results on inertia effect.

  9. #49
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    Default Re: Formulas, rules, and Benchmarks

    Some people may find my three articles on stability useful in understanding this thread. Start by looking here

    http://sailingcatamarans.com/stability1.htm

    Early days yet on defining the "uncapsizeable multihull", but basically it is a boat that is extremly unlikely to capsize if sailed in its design category. We are thinking about the very heavy, underrigged big chartercats and similar boats.

    They won't need to be unsinkable, nor need escape hatches.

    We have a meeting in a couple of weeks when we discuss it further, then another one at METS. I won't be at METS though, I'll be sailing - yippee!

    Richard Woods of Woods Designs

    www.sailingcatamarans.com

  10. #50
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    Default Re: Formulas, rules, and Benchmarks

    "Previous tank testing had shown that the factors worth paying particular attention to are, length to beam ratio, wetted surface area, block coefficient, hull draft, length to draft ratio, and prismatic coefficient. (Block coefficient is the ratio of the hull volume to a volume equal to the maximum waterline beam x the maximum draft x the waterline length.) (Prismatic coefficient is the ratio of the hull volume to a volume equal to the maximum cross sectional area x the waterline length.)."

    "I have shown in a previous article (ref. 4) that if the length to beam ratio is under 8 the hull starts to create noticeable wave making drag. The effect of this is that there will be a "hump" of performance where the speed will "stick" until there is considerably more input of power. This occurs at a speed of 1.34 multiplied by the square root of the waterline length. Further tank testing that I have done on catamaran hull forms close to the waterline length and weight expected in this design show that there is an optimum relationship between length to beam ratio, prismatic coefficient, length to draft and wetted surface area. For instance decreasing length to beam ratio by increasing the length to draft ration (sic) does not necessarily result in a faster design."

    "Traditionally the prismatic coefficient has been assumed to be crucial, but my results show that changes in length to beam ratio, length to draft ratio, and wetted surface area cause the greatest changes in hull drag. " Above, John Shuttleworth, http://shuttleworthdesign.com

    "But wave making resistance is proportional to BWL cubed, so unless you plane you're better with a finer hull. If you go too fine, say over 15:1 then the WSA will be a major factor at low speeds.

    As proof. My 24ft Strider has a L/B ratio of about 12:1. The Firebird and Gwahir about 16:1. The Strider is the fastest boat in winds/boatspeed under 10 knots. (In our first race in our Strider Turbo we beat all 6 racing Firebirds boat for boat) But in stronger winds the finer hulls are a lot faster, the Strider hull is not competitive. It seems to peak in flat water at about 18 knots, the others in the mid 20's" - Richard Woods, http://www.boatdesign.net/forums/mul...p-50329-5.html


    "The upshot of all that is that I think it is unwise for a cruising catamaran to have too fine a hull. 12:1 seems optimum, 10:1 is the minimum and only racing boats sailing in strong winds should have finer hulls.

    Of course a fine hull limits interior room and load carrying, which are obvious drawbacks for cruising boats. As i said, cruising boats should have Veed sections forward, which means a hull is usually proportionately deeper rather than wider." -Richard Woods, http://www.boatdesign.net/forums/mul...-50329-10.html
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  11. #51
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    Default Re: Formulas, rules, and Benchmarks

    "The biggest factors affecting performance are the built in washing machine and the granite countertops.....

    After that its the length, weight (which implies a certain slenderness ratio)and sailarea. Then the wetted surface area, prismatic coefficient, angle of entry and the depth/BWL ratio. Wavemaking is proportional to BWL cubed, but go too narrow and you have to go deeper for the same displ, which increase WSA. So the ideal is a semicircle, thus depth is half BWL. But that's only good in flat water, which is why you don't necessarily want to have a day racing hull shape on an offshore cruiser, even if its faster

    A cruising boat will probably have a more Veed forefoot to reduce slamming. Which means less rocker which usually means its harder to manouver, but pitches less." -Richard Woods, http://www.boatdesign.net/forums/mul...nce-49947.html
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  12. #52
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    Default Re: Formulas, rules, and Benchmarks

    It turns out, after some 150 years or so of analysis, that performance is closely related
    to Cp. That is, there is an optimum range of Cp for various speeds of the boat traveling
    through the water. You can see a table of speed/length ratios versus optimum Cp in
    Skene’s Elements of Yacht Design (by Francis Kinney, 5 th ed.) pg.284,
    which I repeat below:

    Speed/Length ratio Cp
    1.0 0.52
    1.1 0.54
    1.2
    0.58
    1.3 0.62
    1.4 0.64
    1.5 0.66
    1.6 0.68
    1.7 0.69
    1.8 0.69
    1.9
    0.70
    2.0 0.70

    -http://www.sponbergyachtdesign.com/the%20design%20ratios.pdf
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  13. #53
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    Default Re: Formulas, rules, and Benchmarks

    Bruce Number (BN = SA^0.5/Displ^0.333 Where:SA = Sail Area in square feet
    Displ = displacement in pounds,) has a few significant drawbacks that prevent it from being more
    comprehensive than you may think. In addition to sail area and weight, a sailing
    multihull derives power from the distance between the hulls (wider hull-to
    -hull beam more stability = more power) and from the length
    -to-beam ratio (higher length-to-beam ratio = less wave making drag = more power).


    But these factors do not appear in the Bruce Number equation.
    So if you are comparing two multihulls of the same length and
    weight so that they have the same Bruce Number, the boat with the wider spread
    between the hulls will have more power and potentially faster speed. Likewise, a boat
    with narrower hulls compared to a sister generally will have less hull drag and,
    therefore, more speed. Therefore, Bruce Number has to be used judiciously in order to
    make valid comparisons. -http://www.sponbergyachtdesign.com/the%20design%20ratios.pdf
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  14. #54
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    Default Re: Formulas, rules, and Benchmarks

    Near as I can tell this thread has been dead for 6 years. Who were you replying to?

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    Default Re: Formulas, rules, and Benchmarks

    I established this thread to post yacht design rules of thumb, so I suppose I am replying to myself.
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    Default Re: Formulas, rules, and Benchmarks

    Early on, Hatfield recognized that speed and energy efficiency of hulls were highly dependent on hull length-to-beam ratios. For his early trimarans, he employed ratios of 9:1 or greater. But, especially for catamarans, “I don’t like to go below 12:1,” he says. His faster sailboats employ 14:1 or more, as do his wave piercers. - http://www.proboat.com/gold-coast-yachts.html
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  17. #57
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    Default Re: Formulas, rules, and Benchmarks

    "My thoughts on rudder shafts are that the fattest, thickest tube that will fit easily into a 13% section, with the top bearing about at the same distance from rudder top as from the center of effort, will be right for sailing multis. It will also meet ABS ORY. The one exception is sailing cats with big engines. A pair of caterpillar 500 hp diesels bent anything this side of a solid shaft some years ago and took us to school." -Kurt Hughes, http://multihullblog.com/page/56/

    Please note, this is a rule of thumb, NOT a substitute for the calculations which should ALWAYS be used to size rudder shafts. - BigCat
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  18. #58

    Default Re: Issues of scale - scaling and stability

    Can anybody translate some of this stuff, like righting moment, for trimarans? Or offer links?

  19. #59

    Default Re: Issues of scale - scaling and stability


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