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With wildfires burning across the US and Europe , Mathspig had to update this firefighter math for middle school classrooms.

Radiant Heat Stats WA Fire **Dept FACEBOOK.**

Wildfires USA 2022 Map:**NASA**

On **5 ^{th} 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.

Mark out a 30ft course. Make 3 time trials.

t_{1 }=

t_{2} =

t_{3}=

Average your time:

t_{av} = (t_{1 } + t_{2} + t_{3)}/ 3 =

Your Speed S = 30/t_{av} ft/sec

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

__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**.

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**.

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.

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.

With wildfires burning across the US and Europe , Mathspig had to update this firefighter maths post for middle school classrooms.

Radiant Heat Stats WA Fire **Dept FACEBOOK**, Australian Bushfires 14 NOV 2019 **MyFireWatch WA**

Wildfires USA 2022 Map: **NASA**

On **5 ^{th} 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.

Mark out a 10 m course. Make 3 time trials.

t_{1 }=

t_{2} =

t_{3}=

Average your time:

t_{av} = (t_{1 } + t_{2} + t_{3)}/ 3 =

Your Speed S = 10/t_{av} = ……… m/sec

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at **20kph** (up to 30 kph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 20 kph = 20 x1000/(60 x 60)

= 20 x 0.27777777 = 20 x 0.28 m/sec

= 5.6 m/sec

__Average Running Speed Boy__ 13–14 yo = 3.0 m/sec

__Average Running Speed Girl__ 13–14 yo = 2.4 m/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. 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**.

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 by the fire front 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 180 m in 1 minute. In that time the forefront has moved 2688 m or 2.7 km.

It depends how far away you are from the fire front, but it seems 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**.

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph 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 can reach 220 kph, 330kph and up to 550kph.

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.

Mathspig is in Melbourne, Australia. We’re in Lockdown. AGAIN!

And toilet paper has disappeared off the supermarket shelves. AGAIN.

So today we are doing maths based entirely on toilet paper using information from the Toilet Paper Fun Facts website. Yes! It exists **here**.

**Toilet Paper Fun Facts Website**

**Protractor Wind Speed Calculator**

**POP UP ANS Q 1 & 2 Yr 7&8 Toilet Paper fun facts**

**Pythagoras Equation Diagram here**

**Here is the Sine Rule (Watch 1.5 mins)**

**Check sine curve here:**

**Listen to sine curve here:**

More Info: **New York Times,** 5 April 2021

Also: **Which sport is more DANGEROUS to play? Cricket or baseball?**