Correction to Water Plane Area

Discussion in 'Boat Design' started by rehanjamshed, May 12, 2016.

  1. rehanjamshed
    Joined: Jun 2015
    Posts: 8
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    Location: Torino, Italy

    rehanjamshed Junior Member


    In my FEM structural analysis, I am employing SPRINGS attached to the wet surface as the boundary condition for a static analysis of boat in still water.

    For this I need to find the stiffness (SPRING CONSTANT) of each spring.

    Number of springs is as much as the number of nodes immersed in water.

    During the process, I found that:

    Total Spring Force/Unit deflection for all springs:
    K = Foundation modulus * Aw

    where Aw= B * L .... (Water plane area [m^2])
    B= Breadth of water plane area
    L = prismatic length of boat
    Foundation modulus = Spring constant per unit area [N/m]/m^2. Its a constant ,for water it is density*gravity.

    Initially, I chose this area Aw as the water plane area but then the answer was correct ONLY for the boats with FLAT KEEL (e.g. Rectangular sections). For arbitrary geometries such as V or Semi-Circular immersed sections, the answer was wrong.

    Then I employed the following correction to Aw:

    Draft depth, d, is known from displacement.
    From displacement volume, I found the immersed area A_i of the vertical section.

    Then B'=A_i / d ..... (breadth of a vertical rectangle having same area as A_i and draft ,d but modified geometry from original immersed section)

    Find new Aw' as ...

    Aw' = B' * L
    When I use this Aw' instead of Aw. And use the new K in my FEM model, I get the draft 100% correct.

    This means that the plane over which the Total Spring force acts is not Aw but is Aw'.

    Question is from where I can verify this idea from a published literature.

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