Help me understand the Physics of foam support.

Agreed. Level flotation is best and could save lives.

I am building a larger boat, foam sandwich and it has watertight compartments. I don't believe they meet CG regs either. I have been debating putting some flotation in forward watertight compartments after we splash and see how the boat trims. If we ever hit a shipping container; we'd be a bit better off.

 

The likelihood of being certain your custom made boat will right itself on capsize is very low. The likelihood of it floating somewhat with enough foam to offset weights added like engines and batteries, etc. is very high. This is why Mertens can't go down the rabbit hole of self righting.

Is level flotation the same as self righting, or is there a middle ground where a boat that takes on water won't flip over, bit a flipped boat won't self right?

 

It's a lot easier to build it so it resists capsizing than to build it so it will self right. Foam or air compartments crossing or above the WL on both sides will do the former. My calculations were pretty simple as I have no intention to cut things close.
Hull is about 300kg, density ranges from 0.95 (hull) to 0.6(bulkheads, superstructure, transom). About 160kg of motors and batteries; 100kg equipment, gear and fish; and about 300kg of people.

I figured for level flotation I wanted to float about half the boat and pax above the water line, so figured 200L for the people and gear; 150L for the hull; and 250L for the motor, batteries etc. Then an extra for a margin. All spread through the hull, at least half above the sole. Below would be the heavier block foam, and some trapped air.

 

If you glue it, then laminate on top, it becomes a cored laminate and the moment of inertia increases, increasing stiffness. If you put foam all around like the Boston Whaler, you increase the global stiffness and decreases permeability (no water can get in).

Cored panel is calculated like an I beam. Tensile/compressive stress on skin (flange), shear stress on foam (web).

If you just wedge it, no physical connection, just friction, you are just decreasing permeability. It might shift when flooded.

Now for equilibrium. If you place it on top, the boat will not tip over when flooded. Place it on the bottom and the boat will flip when flooded.

 

Level flotation is not the same as self righting. Level flotation only means if the boat is swamped it should float relatively upright. This is so people can stay in the boat and avoid hypothermia, and they don't get thrown overboard. However, if seas are rough or a lot of weight shifts to one side it will roll over and then float nicely level upside down. Self righting is much harder to achieve and means that the boat will right itself regardless of . whatever attitude it may take in a swamping or knockdown. Inboard boats are only required to have basic flotation which means they float, usually with the bow sticking out of the water. (all that weight of the engine and drives)

As far as flotation foam adding structurally, that doesn't happen much. Generally flotation foam is 2lb density. Structural foams are usually 6 or more lb density. Typically structural foams are glassed in, such as in hat shaped stringers. Inside the glass is a dense foam. On boats like Boston Whaler the foam is sandwiched between the outer hull and the inner liner, and is a very dense foam. I suppose you could glass foam boards and achieve some structural rigidity but that is not really the purpose of flotation foam.

 

Boats have been built where the PU foam is part of the structure, but don't dally with the idea that 2lb/cu foot foam is structurally very useful or can be depended upon to make up for a deficiency elsewhere in the structure. You need heavier foam for that, and then the weight of it starts to become an issue.

 

Thanks for the comments guys. To clarify and restate, I do not believe that the structure is currently deficient in any way. The hull for example is a sandwich of 400g biaxial glass laid in epoxy both sides of a 6mm Meranti plywood core. There is more glass than that over stringers, frames, keel and chines. But I can get 4lb and 6lb block PU foam for about 1/2 of the price of 2lb pour foam, so picked some up. I am not planning to replace any engineered structure with foam, but plan to put the block foam in, and wanted some insight on how this would affect strength. For example I wasn't even sure if simply gluing it to the hull wouldn't create a stress riser. Apparently not though.

Edit: Though I don't think it deficient, I'm always interested in more strongerer. Bane of the home builder I suppose...