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The wildfire equation: Math matters to Summit County firefighters

Firefighters work on containing the Buffalo Mountain Fire in June 2018. Firefighters use a lot of math while fighting flames, both in the forests and in residents’ homes.
Summit Fire & EMS/Courtesy photo

“If it burns, there’s got to be a science to it,” Red, White & Blue Fire Protection District Captain Matt Benedict said.

Fire is often thought of as a wild, unpredictable aspect of nature, but to firefighters, it follows a pattern — a pattern predicted by numbers and equations.

“We drill it right down to blades of grass,” Benedict explained. “It doesn’t go from one pine needle to another without physics.”



The patterns of wildfires have been studied since the early 1900s, Benedict said. Testing by the National Wildfire Coordinating group in Missoula, Montana, has resulted in a unique understanding of the way different fuels burn. Sagebrush burns differently than large conifers, and firefighters often differentiate between various fuel types when evaluating a wildfire.

Jackstraw — the trunks and logs strewn across the White River National Forest, largely as a result of bark beetles — is a bit of an unknown, Benedict said.



“It’s not a fuel type we’ve had for very long,” he said. “We’ve really only had this fuel type in its current state for maybe 10 years.”

Wildland firefighters have access to handheld calculating instruments made by Kestrel Instruments. The little instrument records wind speed, humidity, temperature, altitude and dew point among other statistics. That data can be paired with the land’s slope and cardinal aspect, plugged into a smartphone app and turned into important numbers like a fire’s expected speed and flame height.

Wildfire incident commanders are taught to fight fires with their backs to it, Benedict said. Looking at a fire sparks emotions, he says, but firefighters should approach a fire rationally.

“If you actually turn your back to it, your heart rate goes down, your breathing goes down. You can actually calm down a little bit more and make good calculated decisions,” he said.

During major wildfire operations, staff far from the site of the fire will often be responsible for those calculations, Benedict said. But both the Kestrel and smartphone fit in a firefighter’s pocket, as can a paper map, allowing wildland firefighters to crunch some numbers.

A map used by firefighters to determine the distance from the Ptarmigan Fire to the nearest homes shows a distance of about 1,600 feet. Wildland firefighters can use live maps like this to figure out how much time they have before a fire breaches the urban interface.
Matt Benedict/Courtesy graphic

Such numbers become important to determining what options a firefighting team can use. If an airplane carrying flame retardant slurry from Grand Junction will arrive in one hour and flames are moving southwest from Ptarmigan Peak at a speed of 20 feet per minute, where should the plane paint a line of flame retardant to prevent the fire from destroying as many homes as possible?

If that sounds like a middle school algebra problem, Benedict said that’s because it is.

During the Ptartmigan Fire, he said teams had to make that very calculation. With the fire about 5,800 feat away from homes, and a spotting distance — the distance embers can leap from a fire — of one-third of a mile, he said the fire was a safe distance from homes but had a high chance of spreading closer if the winds were right. Fortunately, fire prefers to travel uphill, and the winds didn’t shift dangerously, he said.

Math matters at home, too

Math isn’t just for wildland firefighters. Numbers matter when fighting structure fires, too.

Firefighters will scribble calculations on the back of their hand on the way to the scene of a fire. They calculate the water pressure and gear needed to reach the second floor of a 1,000-square-foot building from a hydrant 60 feet away. They even take into account that it might be a Monday morning when half of Frisco is taking a shower, for instance.

“There’s a lot of firefighters out there who say, ‘Ah, you don’t need to know math for to be a firefighter.’ Those people are steering you in the wrong direction. You do need to know a lot of math,” Red, White & Blue Captain David Rial said.

However, most calculations are done in the moment and treated more like estimates.

“I’m not getting out my tape measure and measuring the size of the building,” Rial said.

From the moment a team arrives on the scene, firefighters need to calculate how many lengths of hose it will take to reach the hydrant, fire engine and home. That, he said, falls to the firefighters on the scene.

Officers on the scene, meanwhile, calculate how much water is necessary. The square footage of a building divided by three and multiplied by the percent on fire gives you an estimate of the gallons needed per minute to put a fire out.

Crews then need to find a hydrant capable of supplying that amount of water. Hydrants are tested regularly to find out their gallons-per-minute rate by using a Pitot tube. The Pitot tube measures the pressure of the water, and someone can then determine the rate by measuring the diameter lines going to and from the hydrant.

“Of course that’s going to change throughout the day,” Rial said. “… Obviously, the gallons per minute is going to drop because of consumption.”

In those instances when calculations are uncertain, experience makes up the difference. Rial said firefighters in Summit County can memorize the grid and what to expect from certain hydrants at certain times.

And after finding a hydrant, firefighters then have to perform an equation to figure out the loss of water pressure due to friction caused by water traveling through the hose.

“When you get into aerial stuff, like our bucket trucks and our big ladders, you have to think about friction loss due to elevation, too,” Rial added.

That, he said, is where knowing the Pythagorean theorem comes in handy. If a firefighter knows the distance to a house and the length of the ladder, they can estimate the elevation off the ground.

Unfortunately, one number firefighters don’t know is the time it takes until a building is no longer safe. Rial said a structural engineer might be able to calculate that, but firefighters can’t. Knowing when to leave a building just comes down to experience, he said.

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