Ballasted leeboards heeled effect on GZ

How does the height of a ballasted leeboard's swinging pivot point relative to the boat's VCB effect the GZ ?
Especially at 20 deg. and 30 deg. of heel when the center of each leeboard's mass is now windward of each leeboard's pivot point, and so creating greater leverage arms of their mass relative to their pivot points.

 

None; unless you calculated GZ incorrectly. Remember that GZ IS NOT the righting moment, it is only the horizontal arm between the CG and CB verticals.

If the board was modeled in the GZ curve as a fixed appendage, then the buoyancy shift is accounted for as the KG is also fixed.

If the board was modeled as a suspended weight and not a bouyant part of the hull (i.e. no change to CB as the board emerges), there is also no change since a suspended weight is always applied at the point of suspension so GZ and KG don't change in this case either. That said, if the board is modeled as rigid in the Z direction, then it will impart a righting moment, applied at the pivot, but that will not change the value of GZ, only the righting moment at that angle of heel

 

Thanks jehardiman,

So the righting moment from the windward ballast on the windward pivot arm would increase with the increase angle of heel, but NOT the GZ of CB-CG ?

 

Seems odd to me. I would think that the only two ways to increase the righting moment at a given angle of heel is to increase the weight of the boat, or lengthen the GZ (Righting Arm).

Cy Hamlin once designed a boat with what looked like lee boards, but were water filled fixed side keels, which extended all the way up to the deck. As the boat heeled, the 'board' to windward came out of the water, subtracting buoyancy on the windward side. the leeward one also went deeper, adding buoyancy to the leeward side. I would think that would lengthen the GZ, as the CG would shift slightly to windward and the CB would shift slightly to leeward.

 

Correct. In the simplest terms, GZ is the arm between CB and CG, as shown below and, baring things like swinging weights and free surfaces, is the righting moment arm.



However, things that are not calculated as part of the fixed CG and CB couple, like swinging weights and free surfaces, can add or (more usualy) subtract from the ideal righting moment. This is how some stability aids like anti-roll fins or tanks work, they aid the righting arm. Conversely, this is reason that you can flip over crane ships or capsize vessels with too much free surface.

 

Yeah Sharpii2,
that's sorta what i had been wondering, and why i started the thread.
I was thinking that the increased heel would increase the lever arm of the windward ballast on the windward swing pivot and thus increase the pivot's gravity, and then perhaps that increased gravity would move the whole center of the boat's gravity slightly to windward when heeled. But i guess all that would simply decrease the heel in the first place.