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> I'm trying to imagine a pathological shape that would obviously float at one size but not when scaled up. I wouldn't go that far. I know models sit at differ
by lutusp 12y ago
> I'm trying to imagine a pathological shape that would obviously float at one size but not when scaled up.
I wouldn't go that far. I know models sit at different heights for different scales, all else being equal, but I don't think you will ever see a non-pathological object sink at one scale but remain afloat at another. The reason I think this is true is that, if I take two objects having the same overall density and connect them together, this cannot change their position in the water, their buoyancy. If I think of the two objects as a single model, the same should be true.
But the difference between connecting two models, and a proportional scaled-up model, is that the ratio of surface area to volume is different for the scaled-up model compared to the two independent models. So the comparison isn't perfect.
(pause for thought ...)
For a solid object sitting on a table, making the object larger and noting the previously described square-versus-cube rule, the table loading should increase for each square unit of table area as the model's size increases, by a unit rule, meaning if you double one of the three dimensions, the table loading (per unit of area) doubles also. But because a boat model sinks into the water as its mass increases, and because that sinking is across curved surfaces, it's more like a three-dimensional area increase than a two-dimensional one, so it can't be compared to an object with a flat bottom sitting on a table.
The tl;dr: the more I think about this, the more I think I was wrong to say it the way I did -- and I say this because the shape of the boat hull means the wetted area can increase as fast as the boat's mass, i.e. as the cube of a dimensional change.
Expressed another way, even though a larger boat model sits lower in the water, with some care the waterline position on the hull can be made to stay the same.
My mistake -- sorry.
- baddox 12y agoIf the water line can be made to change when scaling the boat up, it should be trivial to make a pathological object that will sink when scaled. Just make the shape of a box without a lid, weighted so that the water line is just at the top of the walls. If scaling the shape raises the waterline, then water will flow into the box and it will sink. I still can't intuitively convince myself that the waterline would shift when the model scales.
- lutusp 12y agoI should have made clear what I meant by "sits lower in the water", and I'm responsible for the confusion. Because the boat is a three-dimensional object, and because the subsurface part contacts the water in three dimensions, if it is scaled up with all else the same, it should still have the same waterline, but (obviously) its keel is deeper in the water. > I still can't intuitively convince myself that the waterline would shift when the model scales. Your instincts are serving you well, and the answer is simple -- I wasn't sufficiently careful in how I described it, and I let an error creep into yesterday's conversation. In fact, a model whose dimensions are held constant but is scaled up, should show the same waterline at all scales. Again, I apologize for sounding so sure of myself when I wasn't.
- baddox 12y agoOkay, so you were talking about the keel of the larger model being deeper underwater in absolute terms. I suppose that would effect buoyancy, because pressure increases as depth increases. This might be significant enough to warrant adjustments, at least when scaling very large ships down to very small models.