Archimedes : Bathtub Academic par excellence

Stability and control of floating bodies is a major aspect of navigation from ancient to modern times. It is indeed remarkable that Archimedean concepts continue to guide watercraft designers even after 2200 years! Extending Euclidean concept to solids, Archimedes solved the problem of a paraboloid floating stably but with its base inclined to the water surface. Here, we revisit Archimedes and present stability maps (A-maps) for paraboloid, solid cone and a prism. For a specific combination of geometry and specific gravity, these A-maps predict whether a solid floats vertically or in a tilted fashion; or, whether it is partially submerged.