Sponson Math - Stability Deltas

Two questions regarding sponsons.

I am thinking about two factors: 1), the distance between the sponson and the centerline “a”, and ), “b” the volume of the sponson.

My hypothesis, based on posts by bajansailor and others, is that “stability” will improve at the square of the change in “a”. Is this roughly correct?

Is the effect of changes in volume on stability, assuming air-filled cylinders, roughly linear with the change in volume?

 

It would be helpful to specify the parameter you are using to define stability. If you are referring to initial stability, or metacentric height, this is calculated using the ratio Ix/V, where "Ix" is the moment of inertia of the waterplane area about the longitudinal axis passing through the centroid of that area, and "V" is the submerged volume of the hull.

Therefore:
- If we consider, to simplify the problem, a rectangular waterplane area with a length of "L" and a beam of "B", the moment of inertia would be Ix = (L*B^3)/12. That is, the metacentric height varies with the cube of the beam of the waterplane area.

- If the other factors remained constant, the metacentric height would be inversely proportional to the submerged volume.

In conclusion, I would not consider your assumptions valid.

 

Very simply - yes.
Since the inertia, Ixx is a function of the waterplane area, WPA, and the distance from the centreline of the vessel, 'a', that the outrigger/ama, is from the vessel CL.
It is simply I = ah^2.
Ergo for the same area (WPA) of hull the farther it is placed away from the hull CL (h^2) the greater the inertia, = more statical stability.
This this case h = a.

So, just to be 100% clear we are talking about statical stability - the ability of a vessel to right itself.