Displacement Question

Discussion in 'Boat Design' started by bfisher33, May 1, 2007.

  1. bfisher33
    Joined: Mar 2007
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    bfisher33 B.

    Hi-
    Does anyone know how to calculate displacement using only a lines drawing? I guess you could take the volumetric displacment in cubic feet or whatever and multiply that by the average weight of that amount of water, but that doesn't account for the wieght of the hull. In other words, I have no idea what I am doing.

    Thanks
     
  2. bfisher33
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    bfisher33 B.

    oops-weight
     
  3. Gilbert
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    Gilbert Senior Member

    The displacement is the weight of the boat, just expressed in the volume of water that the boat uses to float itself. So you are on the right track. If your boat weighs 6400 pounds it will displace 100cubic feet of water to float itself, since water weighs 64 pounds per cubic foot.
     
  4. bfisher33
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    bfisher33 B.

    thanks. what I am trying to do is determine the displacement of a boat I designed, but I don't know how much anything weighs. All I have is the lines drawing, and a model.
     
  5. bfisher33
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    bfisher33 B.

    In other words, can i find displacement without any wieghts using only a ;ines drawing and a model?
     
  6. lewisboats
    Joined: Oct 2002
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    lewisboats Obsessed Member

    Your displacement will be the total submerged volume. You should have a DWL or design waterline. The aim is to get the displacement and the DWL to cooincide when the boat is loaded to about 3/4 of its max. Your lines plan DWL is the starting point for finding the displacement. You will need to calculate the volume that is displaced when the boat is sitting where you want it. Getting the actual boat to hit that point when built is a whole 'nuther matter. Are you using any kind of design software or did you draw the boat on paper?

    Steve
     
  7. PAR
    Joined: Nov 2003
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    PAR Yacht Designer/Builder

    Unfortunately, you have to perform a center of masses calculation, for the materials you intend to use in the vessels construction and the equipment you wish to install. This is a time honored and tedious process without some CAD help, but has been done countless times the old fashioned way, using a pencil, pad and many dozens of specifications (engine location, weight and it's CG, windlass location, weight and it's CG, frames, bulkheads, planking, literally everything, etc.). Only this way can you determine where the boat will float (displaced volume).

    In small craft, the usual practice is to make a fair guess, which relies heavily on building and design experience. You get a feel for the volume necessary to float a particular design type, equipped in such and such a way. An example would be a 23' LOD, 19' 3" LWL, 7' 8" beam centerboard sailboat I recently designed. I knew, from experience that I need about a ton to float this boat, so I drew up a hull shape that would produce nice underwater areas, which roughly equaled 2,000 pounds.

    On larger vessels and weight dependant craft (racers, cargo carriers, etc.) the center of masses calculation is necessary.

    Judging by your post, you lack the experience necessary to make the rudimentary guesswork, often times necessary in yacht design efforts. When this is the case (as any design student will attest) you must rely on example. Using similar size and shape boats as a general guide, you can roughly estimate the volume you'll need. This volume will change as you refine the design and work out the actual vessel scantlings, which will provide you with masses in different locations. This is necessary to get the boat to balance as you want it, sometimes moving volume forward or aft, in the underwater areas, so centers align correctly and she'll float where you paint the waterline.
     
  8. Willallison
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    Willallison Senior Member

    What these guys are saying is that you must perform two calculations.
    One is the displacement calculation (the underwater or displaced volume x the density of the water it's to be floating in). This will give you both the 'theoretical' mass and centre of buoyancy.
    The other is the weights and moments table, which Par described, and will give you the actual mass and the centre of gravity.

    If the two masses are the same, the boat will float on its designed waterline. If the actual weight is greater than the 'theoretical' one, then it will float lower in the water, and vica versa.

    If the two centres (gravity & buoyancy) are alligned, then the boat will float level. Again, if they aren't, it will either trim up or down by the bow/stern until they do.

    I've done many of these calculations by hand - as already suggested, it's a long and tedious business (though it does give you a good understanding of the processes involved). CAD makes all this a LOT easier... with the click of a button, you will have all this info - and a whole lot more. But probably more importantly, as you make changes they are reflected in the hydrostatic calculations that the CAD program puts out.

    There's a number of good books that give a step by step guide to doing all this. Check out your local library......
     
  9. Arvy
    Joined: Jun 2005
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    Arvy Senior Member

    Hi what you are looking for is nicely describe in the book Principles of Yacht Design by Lars Larsson and Rolf Eliasson.

    I wouldn't use the method Rayk mentioned, unless your design doesn't have very much form in the underwatership (like a tube or log). The method of calculating the displacement in the book is similar but more accurate. Just check it out.

    Grtz,
    Arvy
     
  10. Raggi_Thor
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    Raggi_Thor Nav.arch/Designer/Builder

    I think you have clarified the difference and the connection between displacement and weight now :)

    Simpson's rule is very simple and much more accurate than the simple trapezoid method. Measure the area of some stations A1, A2, A3 and so on, then
    Volume ~ dL x (1/3) x (A1 + 4A2 + A3) where dL = L/2
    (Note that if A1=A3=0 this is the same as (2/3) x L x A2 or a Cp=0.67)
    or
    Volume ~ dL x (1/3) x (A1 + 4A2 + 2A3 + 4A4 + A5) where dL = L/4
    or
    Volume ~ dL x (1/3) x (A1 + 4A2 + 2A3 + 4A4 + 2A5 + 4A6 +2A7 +4A8 +2A9 + 4A10 + A11) , dL = L/10
    (usual method?)

    The only things you have to remember are
    1,4,1 or 1,4,2,4,2...4,1
    and
    constant delta L= L/2,4,6,8,10 and so on.
    See for example:
    http://www.krellinst.org/UCES/archive/modules/potential/simp/

    While I searched for a reference in English for Simpson's rule, I happened to learn a new one, Simpson's 3/8 rule:

    Volume ~ dL x (3/8) x (A1 + 3A2 + 3A3 + A4)
    or since dL = L/3 in this case,
    Volume ~ L x (1/8) x (A1 + 3A2 + 3A3 + A4)


    NOTE: I see that many start with A0 not A1, maybe a more common notification, but you get the point..

    See for example http://math.fullerton.edu/mathews/n2003/Simpson38RuleMod.html
     
  11. bfisher33
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    bfisher33 B.

    Thaks guys. I actually own the principles of yacht Design, but I didn't quite understand what they meant (mostly because i didn't know there were two calculations they were doing. That is what confused me) Also, I am pretty familiar with Simpson's rule because I am taking AP Calculus (I'm a high school Senior, which is also why I'm not that experienced in yacht design)
     
  12. Raggi_Thor
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    Raggi_Thor Nav.arch/Designer/Builder

    Then the volume/displacemtn is the easy part :)
    You will priobably make a spreadsheet for weight calculations, adding all moments in x and y direction to get the cg.
     
  13. Willallison
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    Willallison Senior Member

    ....and z direction as well....
     
  14. bfisher33
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    bfisher33 B.

    Thanks again. P.S. Does anyone know what the normal displacement for a fifty foot high performance cruising yacht is?
     

  15. gonzo
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    gonzo Senior Member

    The displacement will depend on the construction and appurtenances. You may draw a boat to float at certain lines, but unless you do all the calculations and build it accordingly it means nothing. The drawn waterline is not a magic line. It is where you decide the boat should float. To acomplish it, all the weights and volumes need to be where designed. In other words, you design the boat along with all the calculations, and then have to keep track of materials and equipment while building and fitting the boat.
     
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