The mathematics of burger flipping

TL;DR

This paper models the process of flipping food on a grill, revealing how flip timing affects cooking efficiency, and finds optimal flipping strategies that improve cooking time by about 29%.

Contribution

It introduces a mathematical model of flipping dynamics, analyzing how flip timing influences cooking rate and identifying optimal flipping intervals.

Findings

Optimal flipping intervals tend to be roughly equal in duration.

Maximum improvement over a single flip is approximately 29%.

In symmetric thermal systems, flip sequence order does not affect cooking rate.

Abstract

What is the most effective way to grill food? Timing is everything, since only one surface is exposed to heat at a given time. Should we flip only once, or many times? We present a simple model of cooking by flipping, and some interesting observations emerge. The rate of cooking depends on the spectrum of a linear operator, and on the fixed point of a map. If the system has symmetric thermal properties, the rate of cooking becomes independent of the sequence of flips, as long as the last point to be cooked is the midpoint. After numerical optimization, the flipping intervals become roughly equal in duration as their number is increased, though the final interval is significantly longer. We find that the optimal improvement in cooking time, given an arbitrary number of flips, is about 29% over a single flip. This toy problem has some characteristics reminiscent of turbulent thermal convection, such as a uniform average interior temperature with boundary layers.