2. Stuntman Math: Jumping off a Building

This is a repost of Mathspig’s very popular Stuntman/woman series.

The main concern when jumping off a building is that the airbag (cardboard boxes) cover the drop zone.

The maths calculations involved in jumping off a building are straightforward. You might like to check out How Maths Solved a real murder.

Jump Height that Kills

It doesn’t take much of a fall to cause damage. Sean Hughes, professor of surgery at Imperial College, London. Says “From a height of 3m you could fracture your spine,” he says. “At around 10m, you’re looking at very serious injuries.” (The Guardian, 20 MAY 2014)

Stunt Jump from building from standing start

As this jump – as in most base jumps – involves a standing start:

Airbagsupplies.

Stunt jump from building running

We will assume you are no Usain Bolt. His running speed, the fastest in the world, is 44.72 km/h (12.42m/s, 27.44 mph).

We’ll say your running speed on take-off is:

V_y = 15 mph = 24.1 kph = 6.7 m/sec

Don’t do this at home.

NB: Airbag dimensions: 20m x 20m x 4 m

Handstand of death

Would you jump off a 25 story building?

 

3. STUNTMAN MATH: Motorbike Jump

This is a repost of Mathspig’s very popular Stuntman/woman series.

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. 

Can you escape a FALLING TREE?

Tragically, 5 people have been killed by falling trees in Victoria, Australia, this Winter. 

In 3 separate accidents, 4 died when trees crushed the occupants in cars. One victim was a pedestrian.

So if you were walking through a park could you escape a falling tree if you either heard a cracking sound or saw the tree starting to fall?

With thanks to Physics Stack Exchange.

For an inverted pendulum near the top of its arc, there is no period, but the quantity √ℎ/𝑔 does represent a characteristic time scale for this system. The tree will take a few of these characteristic times to fall.

Mathspig hates seeing an old tree felled, but it does give us the necessary time data.

 

There are many assumptions in these calculations.

*You’d be hit by the tree trunk, not a branch which would hit you sooner.

*There is no wind pushing the tree over.

*The tree falling is an approx to a reverse pendulum.

 

Eat Red Meat and Die ….. NOT NOW! ….. Maybe, sometime.

Here we go again.

“Eating even the moderate amounts of red and processed meat sanctioned by government guidelines increases the likelihood of developing bowel cancer” according to the above article in The Guardian, UK.

The sample size was 500,000. That’s good. It is a self-selecting sample. That’s not good. They could all be health fanatics. But here is the kicker:

“The researchers found those who ate the most and least red and processed meat tended to exaggerate their consumption or lack thereof.”

That’s a shock. People lie or exaggerate. Even the researchers then suggest – despite the screaming headline – that you don’t change your diet.

Although, looking at the plate above … I would!

Real Men Eat Red Meat and Die … Sometime!

According to this headline in THE AUSTRALIAN 25th, March 2009   meat eaters are at risk of dying of cancer. The study published in  Archives of Internal Medicine involved half a million people over 10 years. So far so good. That is a good sample size. The sample consisted of people aged 50 to 71 years at baseline or, obviously, after 10 years 60 to 81years!!!!  So some deaths would be expected. Nevertheless, the article states: 

“Men whose red meat intake put them in the top 20 percent consumption band were 22 percent more likely to die of cancer in the 10 years of the study, compared to men whose intake was in the lowest 20 percent. For women, there was a 20 percent increase in risk.”

Here is the problem. Firstly and I quote from the original study: “Meat intake was estimated from a food frequency questionnaire administered at baseline.’ So they asked people once what their eating habits were then assumed they continued for the next 10 YEARS??? How likely are your eating habits to change in 10 years???

Secondly, and this was mentioned in the article without explaining the maths, big meat eaters tend also to be big drinkers, smokers, obese and the rest. This study has tried to separate out meat eating from other unhealthy lifestyle choices using the Cox Regression. Mathematical wizardry has produced these numbers but they don’t mean much. 

If the study used a control group of drinking, smoking, obese vegans then compared mortality rates over 10 years that would be interesting. But where do you find half a million of them???????? 

Finally,  the study  concluded ‘Red and processed meat intakes were associated with modest increases in total mortality, cancer mortality, and cardiovascular disease mortality.’ Not the stuff of headlines at all!!!!!!!

How They Photoshop Supermodel Pics: THE MATH

Women’s Magazines have a strange kind of logic. On the one hand they push the philosophy ‘love yourself’, ‘love who you are’ and then they provide 365 pages showing you how to change every bit of yourself including your hair, eyebrows, pubic hair, tan, weight, skin tone, fitness, nose shape, career, boobs, how-to-hook him techniques and so on. Marie Claire, Australia, is no different. Nevertheless, I adopt the policy that these magazines are a bit of frou-frou fluff that women find entertaining. If girls and women want to beat themselves up with impossible goals then that is their right. But there are limits and the January edition, 2010 of Marie Claire is a classic.

Claiming to support real women and real body sizes Marie Claire ran a survey to see which body size 6,8, 10, 12, 14 or 16 was preferred by the Australian public.

Firstly, these surveys involve meaningless maths because they use  SELF SELECTING SAMPLES.  Nevertheless, there she is, the most popular choice, Size 12 or Ms 59%.

Keep flipping through the magazine, however, and you will find a shopping guide very common in these magazines. Have a look at the model (below)???? Do alarm bells ring?? Let’s do the maths, mathspigs.

 

Look at the pictures (above). The waist to hip measurement is the same for each model namely 20mm.  I’ve scaled up the images by factor of 10 (below) so that:

Waist to hip = 200mm.

Now, look at the leg lengths!!!!!!!!

 

Who is this model? Alice in Wonderland? Her legs are 89% longer than a girl with the same waist to hip length or have her legs been digitally stretched by 89%?

Teachers, I urge you to ask girls to bring in women’s/girl’s magazines to do some similar maths. To check if a model’s legs have been digitally stretched you can use the hip to knee and knee to ankle ratio which should be close to 1:1. We have to help girls develop a visual sense of proportion. And the maths quantifies this critical thinking. Rather than girls concentrating on booster bras boosting brains makes more sense.

Sharp Shooter Maths …. METRIC

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Australia has a very strict gun laws today. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against our fridge. He pocketed the magazine.

A .22 means a bullet calibre of .22 inches.

My Dad the Sharp Shooter stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more. More on my childhood here.

cc

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Sharp Shooter Maths

One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  The MOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

As the distance away from the target increases the target zone circle area increases.

A sharp shooter would be considered very skilled if they can shoot within a target zone (circle) of 10.5 inch radius at 1000 yds. Hitting a bull’s eye at this distance is down to luck.

Medals, Meglomaniacs and Sharp Shooters…….. The Maths METRIC

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question

‘Could medals protect the wearer from a sharpshooter?’ 

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

 

The target zone (circle) had a diameter of 1.9cm. This is smaller than the diameter of an American Quarter, an Australian 10c and a UK pound all of which have a diameter of appro 2.4 cm.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.