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When Area Calcs mean Big Bucks
August 25, 2022Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS
July 25, 2022
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
METRIC UNITS
Background Story
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?
METRIC UNITS
Time Trial:
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
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 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
CAN YOU OUT RUN A FIRE?
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.
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 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.
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 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.
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.
WINTER OLYMPICS: How ski Jumpers Use Math to Increase their Jump Length
February 3, 2022
While air resistance has little impact on aerial skiers it is a significant factor used by ski jumpers to increase their jump distance.
The significant maths for ski jumpers is therefore X-section area.
Here is the jump at Pyeong Chang, 2018. Just imagine going down that at top speed!!!
A ski jumper is set to jump in Pyeongchang.
Casey Larson USA Pyeong chang 2018
Ski jumpers increase their speed going down the ramp by reducing their X-section area:
Lindsey Van, USA, practicing in a wind tunnel
Once they leave the ramp, ski jumpers try to increase their X-section area like Ski Divers to slow their vertical fall. But they have to land safely so they keep their skis at a minimum angle.
Abby Hughes, USA, practicing in a wind tunnel.
Abby Hughes, USA, in the air
Here are the X-section areas for Abby Hughes*:
Here is the formula for Air Resistance of Drag:
D = ½CApv2
Where C is the drag coefficient or constant, which depends on the shape and spin of an object. It is found by testing the object in a wind tunnel.
A is the X-section Area,
p is the density of the air and
v the velocity of the object.
More here.
As Abby Hughes has tripled her X-section area in the air, she will have tripled the vertical drag during her jump. This will slow here decent.
*Mathspig calculated the X-section area by the old fashioned method of counting squares and rounding off the final count. Mathspig sized the two pics of Abby Huges so that her head was the same size in both pictures.
WINTER OLYMPICS 2022: One Rule Aerial Skiers Cannot Break
February 1, 2022The Parabola Must Be Obeyed!!!!
Aerial skiers aim for height rather than length. Their aerial flight times are much smaller than ski jumpers so air resistance has minimal impact.
In fact, there is one law the aerial skiers cannot break. It is the law of gravity.
Here is an equation for projectile motion from Wired magazine.
Screen grab from Wired Magazine
The equation for projectile motion also applies to Motorbike Jumps and Longbow Arrows.
Here is the x-y graph for different launch angles.
trajectory wired magazine
You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.
The centre of gravity of Aerial Skiers must follow a
parabolic curve.
Rocky Maloney Winter X Games Aspen
Death by Caffeine: The Math Part 2 USA units
November 18, 2021Death by Caffeine: The Math Part 2 Metric Units HERE.
Caffeine content sources Caffeine Content Data Base
On April 12 2017 16-year-old Davis Cripe collapsed at school in South Carolina and died later in hospital. In the span of two hours, Davis drank a cafe latte from McDonald’s and a large Mountain Dew, then “chugged” a 16-ounce energy drink when he got back to art class.
Here, assuming Davis drank large sized drinks, is the lethal caffeine consumption.
NOTE: Davis lived in the USA where standard drink volumes are slightly different to Australia & UK. The USA volumes are used here converted to litre and ml.
The official cause of death was “caffeine-induced cardiac event causing a probable arrhythmia,” the coroner concluded. Source: Washington Post
Caffeine can kill.
WARNING: “Mixing caffeine with alcohol is a dangerous practice because it may lead to higher levels of alcohol consumption as the person often believes and feels they are more alert,” said Dr Robert Glatter, ER doctor at Lenox Hill Hospital, NYC . “The risk of alcohol poisoning increases as people consume more alcohol because they feel the caffeine will keep them awake and alert.” Source: USA Today
Death by Caffeine: The Maths Part 2 METRIC
November 18, 2021Death by Caffeine: The Math Part 2 USA UNITS HERE.
Caffeine content sources Caffeine Content Data Base
On April 12 2017 16-year-old Davis Cripe collapsed at school in South Carolina and died later in hospital. In the span of two hours, Davis drank a cafe latte from McDonald’s and a large Mountain Dew, then “chugged” a 16-ounce energy drink when he got back to art class.
Here, assuming Davis drank large sized drinks, is the lethal caffeine consumption.
NOTE: Davis lived in the USA where standard drink volumes are slightly different to Australia & UK. The USA volumes are used here converted to litre and ml.
The official cause of death was “caffeine-induced cardiac event causing a probable arrhythmia,” the coroner concluded. Source: Washington Post
Caffeine can kill.
WARNING: “Mixing caffeine with alcohol is a dangerous practice because it may lead to higher levels of alcohol consumption as the person often believes and feels they are more alert,” said Dr Robert Glatter, ER doctor at Lenox Hill Hospital, NYC . “The risk of alcohol poisoning increases as people consume more alcohol because they feel the caffeine will keep them awake and alert.” Source: USA Today
Sound Math 1: Good Vibrations!
October 4, 2021There is so much maths around sound, but sound is simple.
Sound is made by something vibrating in air. The vibrations create waves and these pressure waves hit your ear.
The Frequency of Sound
The frequency, measured in Hertz Hz, is the no. of pressure waves per second hitting your ear.
Patterns Created by Sound Waves that add to or cancel one another
Projects Studio Handbook HARMONICS
This is a vibration plate. Sand collects in the areas which do not vibrate and create patterns. The patterns are called CHLADNI figures.
In fact, the sand collects in places where standing waves – waves that cancel each other out – form. The rest of the plate is vibrating and making the sound.
You will find more info about this violin shaped vibration plate here.
The frequency of the sound creating this Chladni pattern is shown in Hertz Hz
Other Sound Math:
Make a match Box sing like Sinatra
The Curious Nature of Drummers’ Brains
Pump Up the volume or Knock, Knock Knockin on Your skull wall!
Sound Math 3: How loud is LOUD?
September 29, 2021
The logarithmic equation for sound and the decibel calculator here
More here
Other Sound Math:
Make a match Box sing like Sinatra
The Curious Nature of Drummers’ Brains
Pump Up the volume or Knock, Knock Knockin on Your skull wall!
Sound Math 4: Make a match Box sing like Sinatra
September 29, 2021
Other Mathspig Sound Posts:
The Curious Nature of Drummers’ Brains
Pump Up the volume or Knock, Knock Knockin on Your skull wall!
Maths in the Real World: 10 Attention Grabbers for Middle School
September 5, 20211. Smoke Jumpers: The Amazing Maths of wildfires
USA UNITS HERE
METRIC UNITS HERE
2. The Rolling Coin Paradox!!
ROLLING COIN PARADOX HERE
3. How barcodes work!
Barcode MATHS HERE
4. Pop Song Beats and Jogging
Pop Song Beats and Jogging MATHS HERE
5. Linear Math and Linear Drumming. It’s a thing!
Linear Math and Linear Drumming. HERE
6. Powers and the Loudest Rock Band in the World
Powers and the Loudest Rock Band MATHS HERE
7. Alcohol Kills! Calculate how much would kill you!
Alcohol Kills! MATHS HERE
8. Tall Tales: Is height the most important factor in sport?
Height in Sport maths: USA UNITS HERE
Height in Sport maths: METRIC UNITS HERE
9. Mmmmm! Chocolate. Yes! It can kill you
Chocolate. Yes! It can kill you MATHS HERE
10. Random Music? You think!
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