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How math solved the burger flipping problem

One of the sadly more neglected branches of research is the science of flipping burgers. During the barbecue months, a major conundrum for gourmets is whether a burger that has been flipped many times cooks faster than a burger that has been flipped only once. And if so, how many flips is ideal?

Today we get an answer to this important question thanks to the work of Jean-Luc Thiffeault, a mathematician at the University of Wisconsin at Madison. Thiffeault has created a mathematical model for flipping hamburgers that leads to a crucial insight that can help you cook hamburgers 29 percent faster.

Thiffeault’s model is relatively simple. It assumes a flat burger that is one centimeter thick but infinite in size (in math, dreams can come true). The model has a heating element on one side of the burger, and fresh air on the other.

Heat enters the burger through direct contact with the heating element at 200⁰C, where the contact heat transfer coefficient is 900 Watts per square meter per degree Celsius, a seemingly reasonable experimental value.

Escape from heat

Heat escapes from the burger on the side exposed to the air at 25°C, where the radiation and heat transfer coefficient is 60 Watts per square meter per degree Celsius.

The meat is considered cooked when it reaches a temperature of 70⁰C, so an important part of the calculation is determining the temperature of the meat in the center of the patty. Note that temperature history is important at every point in the burger. As Thiffeault points out, cooked meat can cool, but it cannot “uncook”.

All this allows Thiffeault to calculate how long it takes to cook a burger. He starts with the case when the burger is not turned over, a process that he says could take forever.

So what happens when the burger is flipped? One idea from famed science food author Harold McGee is that the faster a burger is flipped, the closer the cooking conditions get to a burger heated on both sides at once. So flipping a burger often, McGee suggested, should speed up the cooking process. But is this true?

Thiffeault puts this theory to the test by simulating the cooking rate for different numbers of flips, while varying the interval between flips. He then uses the math software MATLAB to optimize the process.

It turns out that for a single turn, the optimal time for the first interval is only 45 percent of the total and only 29 percent of the cooking process. The rest is done during the second break, especially towards the end, when the percentage of cooked meat suddenly increases. This is probably a result of the time it takes for the heat from both intervals to spread through the meat.

This diffusion has important implications for a greater number of flips. It turns out that for optimal cooking times, the turning intervals should be about the same length, except for the last one, which should be longer to allow for diffusion.

But as the number of turns increases, the improvements in cooking time diminish. Indeed, Thiffeault says they are approaching an asymptote that suggests that multiple flips can cook burgers at best 29% faster than a single flip. “The improvement in optimal cooking time is quite marginal after a few flips,” he says, dedicating his work to mathematician Charlie Doering, who died in 2021.

So the answer to the question “how many times should you flip a burger to optimize cooking time?” is: a few times!

Mirroring improvements

For the many people who will only turn two or three times, Thiffeault offers another piece of advice: “The shape of the cook time function for two and three turns suggests that it is better to cook a little longer than turn each time, because a shorter interval leads to a longer cooking time.”

This may seem rather esoteric, but it can have an important application. For most people, being able to cook a burger 29 percent faster probably won’t make much of a difference. But if you’re cooking 6.5 million, as a company like McDonald’s does every day, cutting cooking times by a third can save significant energy and associated carbon.

So that’s interesting work, but there are several ways in which the model can be improved. As it cooks, the burger’s moisture and fat content changes — a more sophisticated model could explain this.

Then there’s the option to enter a maximum temperature and how that would change the calculations. For many patty flippers, an unfortunate outcome to be avoided at all costs is a burger that’s burnt on the outside but raw on the inside.

Does multiple flipping help? Probably. But to be sure, Thiffeault clearly has more flipping work to do.

Ref: The Mathematics of Burger Flipping:

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