Flipping Burgers on an Infinite Plane

Summer is a season for hamburgers. But when it’s hot and humid out, how much time do you want to spend outside grilling hamburgers? How fast can you fully cook a hamburger patty?

That seems like a simple question, but if you want to use math and the physics of heat transfer to work out the fastest way to cook your hamburgers, it presents a lot of variables you have to take into account. Unless, that is, you simplify the problem in ways that can eliminate them.

For instance, how fast a hamburger cooks will be influenced by the shape of the patty to name just one factor. You could go for a traditional disc-shaped patty or even a Wendy’s-style square-shaped patty. But how those burgers cook will be influenced by how heat from the grill ‘wraps’ around them even as it cooks through the meat from below. It’s not hard to have the edges of a burger be the most well-done portion of it, but that may mean the inside of the burger isn’t as well-cooked as you might like. How can you ensure your burger is evenly cooked?

For a mathematician or physicist, one way to remove the patty shape as a variable is to assume the burger will be grilled on an infinite plane that only allows the meat to be exposed to heat from the grill on one side at a time. With that assumption, you can count on having the burger be cooked evenly through at all parts. When you do that, you also simplify the problem to be one in which the only variable you have to consider is how often you will flip the burger while cooking it.

That’s what one mathematician did in a paper published earlier this year. Here’s a plain English summary of what they found when they did the math:

Craving a hamburger but in a hurry? If you wish to find out the quickest way to cook a patty, mathematics can actually help you.

Jean-Luc Thiffeault, a professor of applied mathematics at the University of Wisconsin in Madison, has found that the timing between flips and the number of flips hold the key to the fastest way to cook a meat patty. Moreover, increasing the frequency of flips reduces cooking time by nearly a third.

In his study, published in Physica D on June 17, the researcher used mathematics to study how heat moves through a slab of meat, which simultaneously cooks on the bottom side and cools on the top until the meat is flipped. Eventually, his analysis showed that flipping the patty heats the meat evenly, therefore speeding up the cooking process. He also found that more flips lead to faster cooking.

According to the study, a theoretical 1-centimeter-thick patty that’s flipped just once is cooked in 80 seconds. On the other hand, flipping it 10 times at intervals ranging from six to 11 seconds results in a cooking time of only 69 seconds. A maximum decrease of 29% in cooking time is then observed when the patties are continuously flipped.

However, after a threshold is reached, the effect of the number of flips on cooking time becomes inconsequential.

“After three or four flips, the gain in time is negligible,” Thiffeault said.

But that’s for flipping a burger that fills a grill whose surface is an infinite plane. How does that compare with real-world burger flipping?

As it happens, someone has flipped enough real-world burgers to verify the math-only results:

The study’s findings resonate with the observations chef and food writer J. Kenji López-Alt shared in a 2019 article. In the said piece, López-Alt compared the time it took for a burger’s internal temperature to reach about 52° Celsius using a certain cooking method he followed. He then realized that flipping the patty every 15 seconds, compared to just once, shortened cooking time by nearly a third.

So there you have it. Flipping a patty once every 15 seconds will get your burgers cooked through about as fast as you can hope to cook it. How many flips you need will ultimately come down to how well-done you want your burgers to be cooked.

Image Credit: A person is grilling a hamburger on a grill photo by Amirhossein Shirdelan on Unsplash.