Importance of a prismatic coefficient for a hull design

Discussion in 'Sailboats' started by Paulo Neueschwander, Jun 21, 2021.

  1. Paulo Neueschwander
    Joined: May 2018
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    Paulo Neueschwander New Member

    Hi everyone,

    I've been reading a lot about hull design and the number I have to keep control. According to "Principles of Yacht Design br L. Larsson and R. Eliasson", one of then is the prismatic coefficient. It's stated in the book that for every designed speed you have a optimal coefficient.
    But when you see the recent design, the sailboat become wider and the max beam shifted aft and still more or less constant towards the transom.
    I was playing with some designs I found in the manufactures websites and it turns that the prismatic coefficient is larger than what is stated for the length and speed. As far as I drew it right.
    This is easy to see if get a body plan view. The hull is becoming boxy.
    My questions here are:

    How much this high prismatic coefficient influences the design?
    What I have found is a trend or I missed something?

    I'd like to have your thoughts on that.

  2. philSweet
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    philSweet Senior Member

    Neither beam nor a dart-shaped hull directly lead to higher prismatic coefficients. But an immersed transom certainly will. Very high speed sailboats will run pretty high CPs, like 0.57.

    With sailboats, there is a lot more going on than with motorboats. The normal condition is heeled. For best pointing, you might design for 20 degrees of heel and a speed of 8 knots, with no chance of planing when sailing close hauled. But when broad reaching, you might hit 15 knots at 12 degrees of heel. The fun part is to design a hull that has the correct displacement curves and generates the correct RMs to make both those happen.

    Prismatic Coefficient is really just a checksum. If you design a hull and don't like the CP, fiddling with the hull to "improve" the CP probably won't help. You have to get the entire displacement curve correct. The CP is just a way to categorize good displacement curves. It doesn't tell you what one looks like. You can have really rotten displacement curves that evaluate to reasonable-looking CPs.

    There's also the problem of what to include in the displacement calculations. For full keel boats, normally everything is included. For strut fins with ballast bulbs, normally you just include the canoe body. For fin keel boats, you sorta have to get a feel for what the curves look like with the fin attached. The fin often has ten percent or more of the displaced volume, and it has a significant interaction with the hull on wave formation. It seems pretty common to apply some sort of draft-based attenuation factor to the fin volume, but then you have to have your own set of target displacement curves for the type of boat and the way you handle fin volumes.

    One last consideration with sailboats - the hull shape that develops the best righting moment for a given length, displacement, and wetted surface area probably doesn't have an ideal CP. At least not if you just roll about the centerline of the hull. So you have to make some compromises on displacement, wetted area, RM generation, and heeled trim in order to work towards better CPs.
    Last edited: Jun 21, 2021
  3. Ad Hoc
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    Ad Hoc Naval Architect

    Nicely put.
    bajansailor likes this.
  4. Kayakmarathon
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    Kayakmarathon Junior Member

    In Olympic sprint kayaks, the Cp played a BIG part of speed improvements. Prior to 1986 most single sprint kayak hulls had a Cp of 0.58. After Ted Vandusen introduced a fleet of modern designs funded by the US Olympic Committee, the Cp for the single jumped to 0.61. Newer designs globally are in the 0.62-0.63 area.
  5. gggGuest
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    gggGuest ...

    Some very high performance dinghies are also well into the 0.63 region.

    It seems to me human powered racing craft like Kayaks must be a bit of a special case. I assume they can be optimised for a very narrow speed range, because efficiency when not being paddled flat out is surely of minimal interest.
    DogCavalry likes this.
  6. fastsailing
    Joined: Sep 2017
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    fastsailing Senior Member

    I repeat one sentence of yours, also quoted in bold font type in context:
    "The fin often has ten percent or more of the displaced volume"

    In most common ballasted monohull sailboats, keel weight is about 30% of total weight or a little more.
    For each cubic meter of displacement, keel displacement for a steel is about 0.040 cubic meter resulting mass of 314 kg. In seawater that displacement of one cubic meter means mass of 1020kg, and therefore ballast ratio of 314kg / 1020 kg = 0.308
    Displacement volume of (fin + bulb) / total displacement volume of boat is therefore 0.040 cubicmeter / 1 cubic meter = 4%.
    For lead bulb that ratio is less with the same ballast ratio of 0.308. And with a bulb, only part of fin + bulb displacement is in the fin.
    To have 10% of more displacement volume in fin without a bulb requires either hollow fin, or aluminium solid fin, neither are common. With a bulb, the fin must be even smaller in volume, 2...3 % of total displacement volume. Or even less if made of solid carbon laminate, as those are usually made in order to minimize hydrodynamic drag, and that means minimum wetted area and cross section, resulting also minimum displacement volume for the fin.

    Can you name any common production sailboat with 10% volume in a fin keel?
    With a solid steel construction, that would mean ballast ratio of 785 kg/1020 kg = 0.7696, or even more if there is also a bulb.
    Should such extreme case exist, could you please specify materials used for such a fin?

    Easy to find a boat with 10% displacement volume in the keel for a hollow full keel design though, but that was not the claim.
  7. Paulo Neueschwander
    Joined: May 2018
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    Paulo Neueschwander New Member

    Hi @philSweet,

    I've been quite busy from the date I asked my question about the Cp. I didn't even thank you properly. Sorry about that.
    So, thanks a lot for the answer. Now I understand a little bit better how the design works. I need to study more about the displacement curves and its impact in performance/design though.

    My plan is to resume my project now in a very slow pace. Anyhow, I appreciate all the input you gave.

    Paulo Neuenschwander

  8. Tedd McHenry
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    Tedd McHenry Junior Member

    I've noticed that mentioned in various books. Is that done merely because it isn't worth the extra effort of estimating displacement for appendages, using traditional techniques? I.e., if you're using a 3D CAD method that allows fins and other appendages to be easily included in the displacement calculation, is there any reason you wouldn't do it?
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