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Could concept be applied to submarine vehicles to exponential increase their resistance to pressure at depth?
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Unfortunately it stops working when the paper gets wet. ;)

Submarines work on the principle of the arch: a spherical or cylindrical hull section transfers all the force into compression of the material so there is no net "inwards" force.

The weak points then turn out to be joints, material defects (the famous Titan failure), windows and other piercing points, and any unexpected shear forces.


Exponential in relation to what other value?

Adding 1 to _____ causes a doubling of resistance to pressure, adding 2 is a quadrupling, adding 3 is an octupling, what goes in the blank?


This is weight distribution on a flat plain. Think of Roman Arches. On a curved plain, weight distribution of THIS origami falls apart as pressure is added horizontally (not just vertically).

I've made similar tessellations before, they can be curved. You can trivially make a pre-folded tessellation into a cylinder of arbitrary diameter; to curve it like a submarine, you'd just adjust the angle of the creases. Optimize the curve so the pressure is always perpendicular and there's no problem here.

The real issue here is that there's not much point in it, as the very thing that makes this useful (the ability to fold it up) would also make it collapse easily in a pressurized environment. You'd also have to deal with preventing leaks if you wanted air inside, likely by adding an outer hull, which would then defeat the purpose.




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