How do I calculate the weight needed to ballast a centerboard?

Hello all,

I am building a centerboard and need to add ballast to overcome the buoyancy of the core material I am using.

Can someone lend me a hand with the maths to determine how placement will effect the weight of ballast needed?

The board is as follows:

8' 6" long x 2' 11" wide tapered to 2' 4"
The core material is 2" thick and tapers towards the toe and trailing edge.
The pivot axle is 11" back from leading edge and 8" down from top.
The center of mass/buoyancy is 36" down from axle.

As below (tapers not drawn):



I know the density of the core and have 3.3 cu ft of material weighing in at total of 83 lbs.

The displacement of the board is 213 lbs.

So I need to add ~ 130 lbs to make the board neutrally buoyant.
I also need some allowance to sink the board and meet the force of water wanting to kick up the board.

My question:

How does the placement of the lead added effect the required amount of lead to keep the board down, & how much weight is needed total?

Obviously, the lower the placement the longer the leverage arm acting to pivot the board down.
If greater than 130 lbs is placed at the CB 36" aft of the axle, it appears that the board should sink.
If the weight is placed further aft of the CB point, will it act in a manner so as to permit less than the 130 lbs to pivot the board down?

If I place the ballast at 2x the distance of CB from axle, can I use half the weight?

Can I use this to calculate ballast?:


http://www.engineersedge.com/calculators/levers/page_levers_3.htm

With:

X= distance of CB from axle
Weight= positive flotation at point of CB
L= location of ballast
F= weight of ballast

(the above diagram upside down as flotation floats.....

Is there a rule of thumb?:
"Thou shalt add weight to exceed the boards displaced volume by x%"?

 

Even worse, you need enough weight to "keep it down" with water flow and the occasional light bump upsetting the slightly negative buoyant object. There is also the strain on the case to consider, as the further down in the board you place the weight, the more leverage it has on the case attachments. Unless designing a racer, I like to arrange the board weight along the leading edge (just aft of it) in the lower 2/3's of the board. This places the weight at the lowest point when the board is retracted, so a substantial CG change doesn't occur. When the board is deployed the weight acts to reinforce the leading edge when it encounters an object. The amount of weight would be enough to make the board sink, but centered at 2/3' the span from the pivot, which I've found is enough to keep it down, without resisting too much in a bottom strike.

 

Thanks much PAR- that helps