# Modified Water Plane Area

Discussion in 'Hydrodynamics and Aerodynamics' started by rehanjamshed, May 12, 2016.

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### 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

2. ### compoPrevious Member

spring or a ski !

tell me what are you trying to do please I am interested but a little lost with you idea !!

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### gonzoSenior Member

Are you modelling flotation as springs?

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### TANSLSenior Member

Please, read first paragraph in post #1: "I am employing SPRINGS attached to the wet surface as the boundary condition "

5. ### compoPrevious Member

you are welcome to what ever it is you are doing but its still confusing

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### TANSLSenior Member

In the study of some phenomena, behavior of bodies or structures, you must define the contour elements (boundary elements) that limit / fix / support the object under study or bind it to other bodies. One of these elements can be springs. The difficult thing is to assign to each spring what is called the spring constant. I think this is what the OP is asking.
As it is a complicated issue and my ability to explain is not great, I'm afraid I will not be able to go deeper into the subject.

7. ### compoPrevious Member

what

Is this to do with skin friction and planning surface area ?

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### TANSLSenior Member

Compo, who's talking about skin friction or planning surface area?.
Rehanjamshed I apologize for this useless discussion with compo. As you can see we can not answer your questions because we are not even able to know what you're talking about.

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### DCockeySenior Member

For a boat at rest in still water the pressure applied to the hull is hydrostatic: density of water * g * z , where z is the distance below the surface. The pressure acts normal to the submerged surface, not in a vertical direction. This is very basic fluid mechanics.

Why are you trying to use springs to model a distributed pressure which can be calculated in advance of the FEM calculations?

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Because the applied loads need to be balanced and in equilibrium, vertically. Thus springs, via a spring constant that is directly promotional to the vessel's characteristics, are often used to support the model vertically. This is to prevent rigid body motion and an infinite number of solutions within the FEM.

This is not how I do mine, I find this too laborious.

In what way "wrong" and how do you know it is wrong..what are you comparing the reuslts with?

The springs must be aligned correctly or account for the hydrostatic pressure being normal to the plate, not just in the vertical axis of your model.

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### rehanjamshedJunior Member

I explain as follows:

The hull is supported on springs.
The spring constant of springs depend on the Water Plane Area (Aw).

For flat bottom Hulls, the Aw is same as the bottom flat area (Keel area).
For V or curved hulls, we project the slanted or curved area onto the Free Surface to get Aw.

Now, imagine two different hulls:
Hull#1: V shaped and
Hull#2 is U shaped.
Imagine both have same Aw. Then it will give same Spring Constant. Now that is wrong. The area Aw need be corrected to account for the change of section e.g. V or U should give different spring constant.

Thanks

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Static.

However, your Q above "infers" you wish to look at dynamic..which is totally different mode and method of analysis to static.

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### gonzoSenior Member

If the spring constant is the same, you could model the compression length of the spring as a relationship to pressure, which changes with depth.

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