In the Dark

I couldn’t resist sharing a piece of fundamental research I found in an article on the arXiv withthe abstract:

This paper addresses the problem of determining the optimum shape for a beer glass that minimizes the heat transfer while the liquid is consumed, thereby keeping it cold for as long as possible. The proposed solution avoids the use of insulating materials. The glass is modeled as a body of revolution generated by a smooth curve, constructed from a material with negligible thermal resistance, but insulated at the base. The ordinary differential equation describing the problem is derived from the first law of Thermodynamics applied to a control volume encompassing the liquid. This is an inverse optimization problem, aiming to find the shape of the glass (represented by curve S) that minimizes the heat transfer rate. In contrast, the direct problem aims to determine the heat transfer rate for a given geometry. The solution obtained here is analytic, and the resulting function describing the relation between height ans radius of the glass, is in closed form, providing a family of optimal glass shapes that can be manufactured by conventional methods. Special attention is payed to the dimensions and the capacity of the resulting shapes.

arXiv:2410.12043v1

The author’s favourite shape is this:

Of course those of us who are used to proper beer don’t really want it to be cold in the first place, but I hope this doesn’t sound bitter. My main reservation about the conclusion of the paper is that it doesn’t seem to take into account how easy it is to drink from the glass. In that respect, I’m not convinced by the shape above!