Posts Tagged ‘calculations’

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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

           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, practicing in a wind tunnel.

Abby Hughes, USA, in the air

          Abby Hughes, USA, in the air

Here are the X-section areas for Abby Hughes*:

Abby Hughes X-section

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.

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WINTER OLYMPICS 2022: One Rule Aerial Skiers Cannot Break

February 1, 2022


The 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

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

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.

Aerial Parabola final 2

Rocky Maloney Winter X Games Aspen

Rocky Maloney Winter X Games Aspen

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Death by Caffeine: The Math  Part 2 USA units

November 18, 2021

Death 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

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Death by Caffeine: The Maths  Part 2 METRIC

November 18, 2021

Death 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

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Sound Math 1: Good Vibrations!

October 4, 2021

There 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

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

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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

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

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Sound Math 4: Make a match Box sing like Sinatra

September 29, 2021

Other Mathspig Sound Posts:

The Curious Nature of Drummers’ Brains

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

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Maths in the Real World: 10 Attention Grabbers for Middle School

September 5, 2021

1. 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!

 

Random Music?MATHS HERE

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Ohtani vs The World ………………………. Some amazing fastball facts.

April 12, 2021

More Info: New York Times, 5 April 2021

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

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Real World Maths: Surds and all that jazz …

November 23, 2020

Eddie Woo is an Aussie Maths teacher who runs his own Youtube Channel. So popular is this channel in October 2015, Woo won the NSW Premier’s Prize for Innovation in Science and Mathematics. This youtube clip won’t tell you where you will use surds, but it does something magical.

It compares surds to different kinds of music to help students understand why mathematicians go crazy over the concept of surds. This clip tells why maths is soooooo special. There is no guesswork or fake information in this maths. Maths must be accurate. And surds demonstrate this point. (Look for the 5 min mark)

Will you use surds in real life?

Maybe. Probably, not. But surds are used in mathematical programs that demand accuracy. eg. engineering skyscrapers, building satellite dishes, and even in video games. But you won’t see them. Like so much mathematics surds will be hidden in some algorithm.

Here are two Examples:

1. The Golden Ratio:

Often written a 1:1.61 the Golden Ratio or Fibonacci Sequence appears in art and nature and has an aesthetic appeal to the eye, but the accurate ratio is:

2. The Quadratic Function

Satellite dishes, headlights, torches, and bridges all designed using the parabolic arc. The parabola is defined by the quadratic function and sometimes solving for x produces an irrational no. namely a surd. Rounding off can introduce inaccuracies that can become more dramatic when scaled up to the sie of, say, a bridge.