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 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.
Mark out a 10 m course. Make 3 time trials.
t1 =
t2 =
t3=
Average your time:
tav = (t1 + t2 + t3)/ 3 =
Your Speed S = 10/tav = ……… 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.
Here is the sensational pairs team from the 2018 Winter Olympics.
But why do ice skaters spin so fast?
Here is the math!
Well, mathspiggies, the girl in this video is right. Angular momentum remains constant unless external forces are applied.
L = angular momentum
v = linear velocity
r = separation of object
Louisa Barama, USA
Let’s have a look at this equation:
The fastest spin on ice skates was achieved by Natalia Kanounnikova (Russia) with a maximum rotational velocity of 308 RPM (rotations per minute) at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. See Guinness Book of Records.
Other spins include:
Mao Asada, Japan, triple Axel
……………………………………………………………………………………………..
Skaters can spin faster during a triple axel jump because there is no friction from the ice slowing their spin.
To complete a quad axel, it’s estimated that the skater would have to rotate in the air at:
…………………………………………………………………………………
More info here.
Kim Yuna, South Korea
Now, mathspiggies, you must separate Linear Velocity (v1 ) from Angular Velocity (vr ). Linear Velocity is measured in m/sec ie. it is the speed of, say, a skaters foot around the circle. Angular Velocity is measured in either RPM (Revolutions Per Minute) or degrees or Radians per minute. Ie. It is the rate of spin. We can’t judge how many m/sec a skaters foot is moving in a circle. We can only see how fast they spin. In other words, we see their Angular Velocity. When a skaters foot is in the Camel position that foot travels in a very big circle.
But when that same foot is in a Triple Axel postion it moves in a very, very small circle.
Patrick Chan, Canada, Camel Spin
Patrick Chan, Canada, Triple Axel
By halving the radius, firstly, a skater’s Linear Velocity doubles due to the conservation of angular momentum.
Then, secondly, by halving the radius the circumference of the circle moved by , say, the skaters foot is halved.
Overall, by doubling the velocity around the circle and halving the circumference a skater increases their rotational velocity by a factor of 4.
Look at the numbers:
…………………………………………………………………………………
That’s about right.
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?
Metric version here.
The Australian Open is on at the moment in Melbourne in LOCKDOWN. (We have 1 community-acquired case. Tennis players are in a bubble.)
Here are the heights of 3 top seeds in the Australian Open. (See graph below)
No. 1 Novak Djokovic 6ft 1″ (73 in)
No. 6 Alexander Zverev 6ft 6’ (78 in)
No. 8 Diego Schwartzman 5ft 7’ (67 in)
That would be an advantage. Here is a Height vs Serve Speed chart for the Top 6 seeds in the tournament:
Find serve speed data here.
There is NO CLEAR HEIGHT ADVANTAGE for serve speed.
Here is Diego Schwartzman (L) when he defeated Alexander Zverev (R ) in the 2019 US Open.
Schwartzman, the shortest player on the circuit (see graph above), tops the service returns stats. Highest 2nd serve return rate. Third highest 1st serve return rate. See data below. So agility, speed, and reaction times are also important factors in becoming a tennis star.
Go Schwartzee! Check data here.
USA units post here.
The Australian Open is on at the moment in Melbourne in LOCKDOWN. (We have 1 community-acquired case. Tennis players are in a bubble.)
Here are the heights of 3 top seeds in the Australian Open. (See graph below)
No. 1 Novak Djokovic 188cm
No. 6 Alexander Zverev 198cm
No. 8 Diego Schwartzman 170cm
That would be an advantage. Here is a Height vs Serve Speed chart for the Top 6 seeds in the tournament:
Find serve speed data here.
There is NO CLEAR HEIGHT ADVANTAGE for serve speed.
Here is Diego Schwartzman (L) when he defeated Alexander Zverev (R ) in the 2019 US Open.
Schwartzman, the shortest player on the circuit (see graph above), tops the service returns stats. Highest 2nd serve return rate. Third highest 1st serve return rate. See data below. So agility, speed, and reaction times are also important factors in becoming a tennis star.
Go Schwartzee! Check data here.
USA units post here.
The ball leaves Djokovic’s racket and hits the ground 0.31 secs later.
Go here to see why this simplified calculation works!
Mathspig tested her reaction time here. TRY IT!
Mathspig’s best, best, best reaction time = O.33 sec
METRIC post here.
The ball leaves Djokovic’s racket and hits the ground 0.30 secs later.
Go here to see why this simplified calculation works!
Mathspig tested her reaction time here. TRY IT!
Mathspig’s best, best, best reaction time = O.33 sec
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