Archive for the ‘10 Movie Cliches Debunked with Maths’ Category

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1. You can duck a bullet

January 15, 2019

You will find all the ballistics stats you need here:

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2.You can out run a fireball?

January 14, 2019

In nearly every Action Movie our hero possibly holding hands with his love interest will run and jump ( just in time ) out of the way of explosion. eg. Man on Fire (2004) with Denzel Washington, The Marine (2006) with John Triton, Mad MAX FURY ROAD (2015) with Charlize Theron and Predator 2 (1990) with Danny Glover .

We will use car bomb stats that come from the U.S. Bureau of Alcohol, Tobacco and Firearms. (We in Australia can only assume this bureau exists because, um , there are many exploding cigars in America.) You will find these at Car Bomb Response.

 

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3. You can out run machine gun fire

January 12, 2019


Mathspig is amazed. She didn’t think there would be any hope of survival. But if the baddies sweep the machine gun tracking you as you run then …. see calcs below.

Are you feeling lucky Punk?

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4. If you are involved in a car chase, hijacking, explosion, volcanic eruption or alien invasion, you will not go into shock.

January 10, 2019

Here are just a few of the popular disaster movies:
Avalanche (2001), Earthquake (1974), Armageddon (Involves meteors 1998), Deep Impact (More meteors 1998), 2012 (Tsunamis, earthquakes, the lot. 2009), Twister (tornadoes 1996), Backdraft (Fire. 1991) and Towering Inferno (They don’t make thunderous movie titles like that anymore. (1974)  

But what percentage of people involved in, say, an explosion suffer from SHOCK! There are many statistics about Post Traumatic Stress Disorder (PTSD) available. In one excellent study in The National Centre for PTSD Journal involved an explosion in a paint factory in Norway (1976), the 246 employees were ranked for their exposure to shock as follows:.

A. 66 Narrow escape

B. 59 Involved but not in danger

C. 121 Not present on the day.

 80% Group A suffered shock and PTSD. Both Groups A & B showed symptoms of PTSD 7 months later. If, say, a plane crashed into your school sports field and your class survived with minor injuries calculate  how many students in your maths class would go into SHOCK and how many would be left to take action using the above statistics.

These stats can also be used as a fraction or decimal exercise using 0.8 or 4/5 as the fraction of students in shock.

More information at the Health Dept WA

NOTE: Many schools in Australia today not only practise fire drills but terrorist attack lockdowns.

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5. You can jump out of an airplane that is about to crash and catch the baddie who took the last parachute.

January 10, 2019

 The names Bond, James Bond. In Moonraker  with Roger Moore (1979) 007 jumps out of a plane without a parachute to avoid an assassination attempt. He catches up with, Jaws, arch-baddie, in mid-air and takes his parachute. Jaws survives his fall by landing on a big top circus tent.

In Point Break with FBI agent Johnny Utah, Keanu Reeves, leaps from a skydiving plane after Patrick Swayzes’ characer, Bohdi, who has taken the last parachute. Utah catches Bohdi in mid-air, and after a tense confrontation with a gun, both survive using Bodhi’s chute. The remake was in 2015.

There are more movie and real life stories at the  Free Fall Maths link.

Note: We’ll assume Bhodi and Utah have equal horizontal velocities (plane exit velocity plus wind) so the following calculations only involve the vertical or falling velocity. The terminal velocities used for Bhodi and Utah are realistic estimates. 

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6. If the pilot dies the control tower can talk you down.

January 3, 2019

So mathpigs, here is a small taste of what you would need to do to land a small aircraft in an emergency if the pilot is unconscious/dead.

A = Airspeed

Find airspeed indicator on instrument panel.

Instrument Panel Piper PA-28

Check speed.

Knots or mph or kph?

Avoid red zone. Too fast.

Knots outer scale. mph inner scale. Recommended velocity between blue & red.

B = Contact nearest air traffic controllers. 

1. Call MayDay MayDay MayDay

2.  Look for plane ID. It will be on instrument panel somewhere.

3. Check fuel.

On the Piper Cherokee there are 2 fuel tanks, R & L. Check both.

Check aircraft operating handbook to see fuel consumption and remaining time in air.

Quick calc.

 

C = Checklist

Follow Emergency Landing Checklist in aircraft operating handbook for Power OFF or Power ON landing.

Keep in mind, if your air speed is too low you can drop from air, but the higher the landing speed the bigger crash.

Crash energy increases with the square of speed. It’s a parabola!!!!!

The likelihood of a passenger with

NO flying experience landing a plane safely in an emergency is

very small.

The likelihood of a passenger with

NO MATHS skills landing a plane safely in an emergency is

ZERO.

 

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7. You can safely jump from a burning skyscraper/bridge/aircraft into water.

December 13, 2018

Angels and Demons (2009) Tom Hanks character, Robert Langdon, hero of Dan Brown’s jumps from a helicopter and falls thousands of feet into Rome’s Tiber River and survives, of course.

Ahhhh! Look up. It’s raining Tom Hanks!!!!!The Hulk (2003) The Hulk hops from the Golden Gate bridge onto a jet fighter, whose pilot tries to get rid of him at high altitude. The Hulk falls off and plummets many thousands of feet into the bay. He survives.

There are 2 factors we must consider when jumping or diving from a great height:

1. Surface Impact

2.Water depth 

1. Surface Impact

According to the Free Fall website falling into water is not a good survival strategy. 

‘Someone falling without a parachute from more than 2,000 feet or so would be falling quite a bit faster than 100 miles per hour (161 kph) The folks who have survived falls into water have had streaming parachutes above them, which probably slowed their falls to the 60 mph range (97 kph). Having a streaming parachute helps in another way because it aligns the body in a position where the feet enter the water first.’

The website goes on to explain that water is an INCOMPRESSIBLE FLUID. It’s like landing on concrete. Landing in mud, on snow, on trees, on circus tents etc helps break the fall. Moreover, jumping off a bridge into turbulent sea may be safer than jumping into calm water.

On 24th Oct 1930, Vincent Kelly, 31, while working on the Sydney Harbour Bridge fell 170 ft (52 m) into Sydney Harbour and survived.

A champion diver he did several summersaults and landed feet first. He broke a couple of ribs as he did not enter the water at a perfect RIGHT ANGLE but rather a few degrees off perpendicular..

2. Water Depth

The next issue is, if you are going to dive or jump into water from a great height and, miraculously, survive the impact, how deep should the water  be?

Olympic divers often practice their dives in a bubble pools (like a spa). This reduces the impact for a bad dive but the water must be much deeper. Sports Smart Canada recommends a water depth of double the height of the drop. But is this realistic if, say, you are jumping or diving from the top of a waterfall into aerated water.

You can work out approximate depths needed if you were jumping into calm water from heights such as below:

How deep do you plunge? The answer is surprising because, in fact, you decelerate really fast in water.

See REd Bull Jump Science here

Thanks to Rod Vance  for the Fluid Engineering Calcs (done by hand … not by computer program) for calculating the depth of water when your feet stop moving. That is the minimum depth of water needed for the jump (See graph below)

NOTE: Even with this fancy maths assumptions must be made about the transition epoch-half in/half out of the water.

 Assuming you survive the impact and you breath out through your nose – to stop water going up your nostrils really fast- then you will not go any deeper than approx 4 m or 13 ft from a platform of 20 m (65 ft) or less.

If you’re diving into water from, say, a helicopter as in the Demons & Angels movie you don’t need extremely deep water. Assume Langdon was at 100m (328 ft) or the height of The Statue of Liberty(above) or a 33 story building  when he jumped, then extrapolating the graph (above), maybe, a depth of 5m (16 ft) would do.

If you want to see what looking down from a 58.8 m (193 ft) platform looks like check out thisWorld Record Jump by Laso Schaller.