COOL FOOTY MATHS: THE LONGEST KICK

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The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

MATH JOKE 6: The trigonometry of a fake tan

3. Movie Stunt MATH: The Motorbike Jump

Star Stuntman

Star Stuntman Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”

Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman

Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.

His injuries are legendary:

More Evel Knievel

Ramp Design

The angle of the kicker in ramp design can vary from 10⁰ – 70⁰ (See below)

 

Moto-X Ramp Jump Maths

The Problem? 

If the ramp angle is too high, the stunt jumper also goes high, but doesn’t travel very far.

If the ramp angle is too low, the stunt jumper doesn’t stay in the air for very long and therefore doesn’t travel far. (see below0

The stunt jumper wants the OPTIMUM RAMP ANGLE.

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METHOD 1: TRIGONOMETRY (cos we can)

 

As any bike nut knows increasing speed at ake off will increase jump distance.

Here is a graph from final gear for speed vs angle to jump 90m.

OPTIMISING RAMP ANGLE

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METHOD 2: MORE TRIGONOMETRY 

METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.

You will find a thoroughly detailed calc for STUNT JUMP MATHS here:

And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here. 

FOOTBALL MATHS: THE LONGEST KICK

………………………………………………

The following maths is suitable for Year 9+

but can be presented to lower grades just to show

maths is cool!

Hair Maths 1: The curly problem with curly hair

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More about Troy’s $million hair here. Hair statistics including how many hairs a human has on their head here.

Mathspig studied hair chemistry at uni. Tricky stuff. Put simply, hair is made of long strands of protein called keratin held together by sulphur (and some hydrogen) bonds. To curl hair, the keratin strands in the outer curve of each hair has to be stretched with curling tongs or hair curlers, heated and dried. The bonds in each hair reform with one side longer than the other … Hence, the hair curls like gift-wrap ribbon. But high humidity allows hair to reabsorb water and straightened hair just goes psycho curly again!

This excellent hair diagram comes from The Chemistry of Shampoo and Conditioner, in an article by EMMA Dux for the Royal Australian Chemical Institute

Some people are born with hair follicles that produce keratin at different rates across the follicle. They have curly hair. Hair perms chemically break and reform the sulphur bonds while the hair is held in small curlers (curly hair) or a very big curlers(relatively straight hair.) thus permanently curling the hair.

Here’s the Maths:

Curly hair looks like a 3D Helix.

More on 3D helix maths here

But, in fact, one strand of curled hair looks more like a spiral staircase.

The outer edge of the staircase is longer than the inner edge.

 

 More helix maths here.

CHALLENGE:

Mathspig doesn’t expect Middle School students to plot a 3D Helix. But if they have started TRIGONOMETRY then they can see that the maths they are studying is used in CGIs for films and computer games in this case to generate realistic curly hair!!!! That’s cool. This maths was needed to model Merida’s curly hair in  BRAVE.

SMARTY PANTS CHALLENGE:

Some middle school students could calculate some points on the helix.

Now students must be introduced to radians.

Simple EXPLANATION: Angles eg. 30⁰ are not useful in calculations but fractions are very useful.

Eg. The circumference of a circle:

C = 2πr

Now imagine if you scan with a floodlight set at a radius of 1 km. So:

C = 2π

So the circumference is 2π.

You scan ¼ of a circle, the distance the light moves is ¼(2π)

or ½ π or 1.57 km (see below)

This measurement of an angle is in RADIANS.

0⁰     = 0 circle = 0

45⁰   = 1/8 circle = 2π/ 8 = 2 (3.14) /8 = 0. 79

90⁰   = 1/4 circle = ½ π = ½ (3.14) = 1.57

135⁰   = 3/8 circle = ¾ π = ¾ (3.14) = 2.36

180⁰= 1/2 circle = π = 3.14

225⁰   = 5/8 circle = 5/4 π = 5/4(3.14) = 3.93

270⁰ = 3/4 circle = 3/2 π = 4.71

315⁰   = 7/8 circle = 7/4 π = 7/4 (3.14) = 5.50

360⁰ = 1 circle = 2π = 6.28

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You will find Cos  tables at NASA Sine tables at Mathhelp

 

Answer here: Answers- 3D Helix Table

 Advanced students may want to look at what the Uber Geek 3D Helix generating program at the free graph website PLOTLY here.

3. STUNTMAN MATHS: Motorbike Jump

Star Stuntmen

Star Stuntmen Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”

Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman

Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.

His injuries are legendary:

More Evel Knievel

Ramp Design

The angle of the kicker in ramp design can vary from 10⁰ – 70⁰ (See below)

 

Moto-X Ramp Jump Maths

 

 

 

As any bike nut knows increasing speed and angle of take off will increase jump distance.

Here is a graph from final gear for speed vs angle to jump 90m.

 

METHOD 1 is approximate (See STEP 1 & STEP 2 above), but as METHOD 2 produces the same ans (See above), it is very useful.

You will find a thoroughly detailed calc for STUNT JUMP MATHS here:

And everything you ever wanted to know about PHYSICS OF STUNT JUMPS here. 

Outdoor Maths Adventures: Middle School

 

 

Lego Man soccer fields will vary in size depending on the height of each player picked by each student. This does your head in. It is really challenging maths!

 

McGill Uni link here.

Don’t forget to throw in Mathspig’s lame protractor jokes.

You’ll find full calculations at the Maths is Fun blog.

You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.

Some students will discover their co-ordinate point is not on the grid. Students should then work out that they will need a different scale for the y-axis. You can get more inspiration at the Stand Again blog.