How to Use Math to Build the Perfect Campfire

Fire may be one of the oldest human technologies, but building a bonfire—and keeping it safe—isn’t always an easy task. After collecting dry wood or twigs from around your campsite, you need to decide how to arrange them for optimal combustion. Is it right to arrange them in a stack like a log cabin? Or maybe just throw it in a heap and see what happens?

Theoretically there are countless ways you could arrange your fuel source, but accordingly Adrian Beya, professor of mechanical engineering at Duke University, there is only one sure way: your fuel should be as high as it is wide, like a pyramid. It’s no coincidence, says Bejan, that a pyre and a pyramid are linguistically so similar.

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Although this perfect solution has been hiding in plain sight for millennia, Bejan was the first to come up with the mathematical formula for it a work from 2015 in the diary Scientific Reports. “I was able to work it out as homework for my students,” says Bejan. “It took about two hours one night.”

Why fire is like Swiss cheese

The answer, he says, begins with understanding what kind of science dictates how fires burn. This is an extremely multifaceted question, but it comes down to two major contenders: thermodynamics and fluid dynamics.

“Thermodynamics is the science of force, [in this case] Power from fire,” says Bejan Popular mechanics. “Which is then used to move things [like air] … This airflow feeds the combustion reaction and then the heat generated is carried away by the airflow itself.”

A fire can be thought of as a piece of Swiss cheese. Between different pieces of fuel (whether you’re using coal, wood, or some other source) there are many holes or gaps for air to flow through. If your fire is packed too tightly, air can’t flow through it to fuel the burn; If your fuel is packed too loosely, the air can’t get enough power to move fast. The scientific term for this type of hole-filled shape is a “porous medium,” says Bejan.

However, Bejan says cone-shaped fires are not only effective form. In his opinion, as long as this ratio of width to height is maintained, there is no real limit to the shape of fire. Too shallow or too high and the fire cannot hold its heat very long or even start properly.

Tips from a firefighter

Understanding the mathematical principles behind the construction of a fire is just the beginning, he says Daniel Jimenez, a research engineer at the Missoula Fire Sciences Laboratory. After you’ve started a fire, understanding the math for keeping it safe — and putting it out effectively — is crucial not only for firefighters but also for nature lovers.

As part of his job, Jimenez helps with the relief an online course to teach firefighters the math behind the fires they fight.

“Most of the math in our class is just basic geometry,” says Jimenez Popular mechanics. “But it gets a lot more advanced when you start thinking about volume and pressure and [water] distribution systems.”

While some firefighters enter the profession after college and have a basic knowledge of physics and math, it’s also common for others to become firefighters right out of high school, Jimenez says. This online course helps create a common foundation of science and math knowledge to keep firefighters safe and sharp on the job.

Jimenez also designs mathematical modeling software to help firefighters keep track of wildfire evolution. These app and computer-based softwares can contain landscape and wind models and replace what used to be pocket-sized physical travel guides. This not only helps firefighters contain fires, but also perform safe, prescribed burns that can help prevent uncontrolled fires later in the season.

Jimenez says how to keep your mathematically perfect campfire safe, the answer is pretty simple: containment. An excellent way to ensure your fire doesn’t accidentally spread beyond its base is to make sure its fuel source is discontinuous, Jimenez says, meaning there’s no stray fuel near the fire.

A metal fire pit is an easy way to do this, or you can start your fire on ground or near a fire blanket. And before you leave your fire, make sure to shut off the thermodynamics with a good douche of water.

“If I had one piece of advice for anyone with campfires, it would be to drown them,” says Jimenez. “You can’t put too much water on a campfire.”