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Outdoor meat grillers have all been there before: Hovering uncertainly over the backyard grill, squinting at the ground beef patties sizzling below, as the eternal question gnaws at our minds.

Should I flip them again?

Backyard wars have been launched over the question of the optimal number of times to flip hamburgers, steaks or zucchini on the grill—is once sufficient? Does ten flips result in a better, more quickly cooked burger?

It’s a question that also fascinated Professor of Mathematics Jean-Luc Thiffeault, who was inspired to develop a simple mathematical model to explore the issue. The upshot? Flipping your burgers more than once can provide a 29 percent optimal improvement in cooking time over flipping them only once, but there’s no advantage gained from flipping more than 3-4 times. His findings appear in an upcoming edition of Science Direct.

Professor Jean-Luc Thiffeault

Professor Jean-Luc Thiffeault

Thiffeault’s interest in the project began with potatoes, not burgers. About ten years ago he partnered with a pair of mathematician friends from Stanford to experiment with optimal cooking temperature using sliced potatoes in a pan. Thiffeault, who holds multiple degrees in physics, is deeply familiar with the parameters of thermal transfer—the way something goes from cold to hot—and has written several papers on cooling principles. Making a mathematical model for a single piece of food seemed a more focused exercise.

“As an applied mathematician, often part of the part of the charm--and part of the job--is to make a simple model of things that are complicated and then analyze them very well,” says Thiffeault. “Even if you know the answer is not necessarily going to be quantitatively correct, you'll at least learn something along the way about the process itself.”

Thiffeault approached the burger-flipping problem as if he were trying to cool a microprocessor or ventilate a room. In this case, the question was how to make the entire burger as hot as possible, as fast as possible. Rather than trying to begin with a complex framework that accounted for concepts such as the coefficient of thermal transfer, Thiffeault’s model sticks with simple constants, like assuming a single temperature under the bottom of the burger. For backyard chefs who crave a little more nuance, he also developed a computer program alongside his scientific paper to allow burger aficionados to account for different grilling temperatures.

Not surprisingly, Thiffeault’s paper started an online firestorm among grill masters that could have seared several packages of burgers in a matter of seconds.

“When I first posted this on Twitter, I got a zillion people saying, ‘Why did you account for this and not account for this?’” says Thiffeault. “Again, I'm an applied mathematician. To me, the whole point is to produce an elegant model upon which I can say something mathematical.”

Applied mathematicians appreciated the way Thiffeault’s model echoed the concept of turbulent convection, when fluid rises from a heated surface and begins to circulate, heating an object evenly from all sides. Flipping a burger several times in quick succession can create a similar scenario.

“Flipping your burger, you're overturning the air in a way,” says Thiffeault. “You're getting a very similar solution structure, which is a flat middle with something called boundary layers around the edges.”

While food scientists were somewhat less impressed with his model, Thiffeault is quick to point out that he never intended what he calls his “toy” exercise to be the final word on the subject. He is aware that his model omits certain key factors, like moisture effects—you know, the thing that happens when you flip a burger and dump all the fat that’s accumulated on the top surface onto the coals. He also did not account for the people who can’t help taking off the cover of the grill multiple times to check on the meat.

“If your goal is to get a nice burger, you might want to sear the meat a little bit at the base and get some grill marks,” he admits. “There's many other factors to cooking than just temperature.”

Caveats aside, there’s no question that Thiffeault’s exercise has added to the discussion. One of his favorite parts is the idea of what he calls the final optimal flipping interval—the best sequence of flips to get the shortest cooking time.

“The optimal solution predicts that the last flip should be twice as long as all the other flips’ intervals,” says Thiffeault. “If you pick your first two properly, then the last one should be twice as long. That is maybe the most promising thing that might affect actual grilling.”

Thiffeault is open to the possibility of exploring the burger-flipping question further, maybe getting a student interested in adding some complexity to the model, focusing on testing the limits of rapid flipping. In other words, the power-flippers who insist on turning their burgers 20 times or more could be the next subject of a theorem.

“What I created here is a mixture of relevant real-world application and interesting mathematical directions,” he says. “It's kind of fun to see math applied to burger flipping.”