maximal-tipping-angles-of-nonempty-bottles

Imagine a bottle that is filled with air and water and placed on an even surface that is inclined by a certain angle. Depending on the geometry and material of the bottle, the amount of water inside and the inclination angle the bottle might tip. The aim of this project is to model the above setting and to determine the maximal inclination angle and the corresponding fill quantity for various existing bottles. Note that for a general geometry of the bottle it is not possible to model this problem in 2D due to the horizontal surface of the water. What is the angle maximizing geometry of a radially symmetric bottle that is half full (under reasonable restrictions)?

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