With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.
On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.
HOW FAST CAN YOU RUN?
Mark out a 30ft course. Make 3 time trials.
Average your time:
tav = (t1 + t2 + t3)/ 3 =
Your Speed S = 30/tav ft/sec
HOW FAST IS A GRASS FIRE?
This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 12mph (up to 20mph) in a gentle breeze.
Fire Front Speed Grass Fire
Fire Front Speed = 12 mph = 12 x 5280/(60 x 60)
= 17.6 ft/sec
= 18 ft/sec
CAN YOU OUT RUN A FIRE?
Average Running Speed Boy 13–14 yo = 10 ft/sec
Average Running Speed Girl 13–14 yo = 8 ft/sec
We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.
This is not looking good. See more Firefighters Need Maths here.
We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions here.
NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?
We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.
Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:
Each 10º increase in slope, the fire front speed doubles.
Now you can calculate the distance travelled up a slope at a 30º angle.
Don’t forget you can use the WEB 2.0 Calculator here
Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that you cannot out run this fire front.
Again we can do very accurate calculations using simultaneous equations.
See Firefighters Need Maths here.
Wildfire Algebra Worksheet and solutions here.
CAN YOU OUT RUN A WILD FIRE?
High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 70 mph and temperatures up to 2000 °C, which can and does melt glass and cars.
The fire front speed doubles with every 10º, so speeds for the fire front in a strong wind can reach 140 mph, 210 mph and up to 280 mph.
What happened to the Smoke Jumpers?
When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?
ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.