# Correction to Water Plane Area

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

1. Joined: Jun 2015
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Location: Torino, Italy

### rehanjamshedJunior Member

Hi,

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.

Thanks

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