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.

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.

Action heroes such as Indiana Jones or even film kids like Tom Sawyer or The Goonies who go into a cave, anabandoned house, a crypt or a catacomb light the entire place with one match, one candle, a lighter or a cellphone.

Is this real?

Now mathspigs, if you are interested in a career in stage/film lighting or even architecture you will need this maths.

60Watt light globe tells us how much power it uses. But some 60W globes are brighter than others. Light is measured with weird units.

USA uses Foot-candles. Can you imagine the pickup line ‘You brighten up my world like a footcandle’? A foot-candle is the brightness of a candle 1 foot away. Now think of a bubble around the candle. Brightness is mostly measured using one square foot or one square metre of that bubble:

1 LUMEN = 1 Footcandle/ft squared

1 LUX = 1 footcandle/m squared

Don’t get too hassled by these units. As a rough rule:

1 candle = 1 LUX

From graph you can see by 3m a Birthday Cake is not very bright even in a haunted house or crypt.

Challenge: Draw a graph of the brightness of your own Birthday Cake!

Big Challenge:Draw a graph of your Teacher’s Birthday Cake!!!!!! Ahhhh!!!!

We know:

1 candle = 1 LUX

Now compare the brightness of 1 candle to the brightness of other sources of light:

If you want sufficient light to live your everyday life you’d need:

“With enough stupidity you can get any car to roll over” (MSN AUTO)

What stuntmen and women need is maths!

Maths is essential to the process, from calculating speeds and braking distances to looking at the ratio of the amount of film shot to the length of time of the end sequence. The stunt and crash is outlined, and the co-ordinator explains how he must calculate speeds and stopping distances carefully.

So you want to be a stuntman?

First think of the pain.

Mark Eiden, 52, a professional stuntman (pictured) who is not only afraid of heights, but was once told he likely wouldn’t walk again. Eiden’s had surgery on both arms and shoulders, five knee surgeries, six nasal reconstructions, foot and hand surgery and a facial cast. He fell off the top of a stunt car at 40 mph when the tyre blew. He gaffer taped his ear and continued, despite severe concussion. Northern Express Michigan

If you still want to be a stuntman do the Maths:

Rolling a Car:

You can use quick handbrake turn, speed around a corner, fishtail into the curb or some other lunatic thing. The most controlled way to roll a car is to use a ramp.

These ramps often have a kicker at the end to add extra lift. Ramp calculations can be complicated, but the simplest way to look at the maths is to determine the angle a car will roll ie. When the Centre of Gravity moves over the base.

Centre of Gravity vs Base Width

The distance between the front wheels in cars is often called the track width.

So the Lamobgini Diablo is very hard to roll (build a higher ramp) and it therefore beats the SUV for stability every time.

Balancing on 2 Wheels

A more skilled stunt involves driving a car on two wheels. A very skilled stunt driver can lift the car onto wheels by snaking the car back and forth across the road until it balances on 2 wheels.

From the Centre of Gravity vs Base angles above you can see that the SUV is the easiest car to balance of 2 wheels.

But there is nothing quite as crazy as this SUV stunt:

The main concern when jumping out 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:

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.

A major and disasterous earthquake has just hit Indonesia. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams, power plants and even pipe lines. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.

This is intentional, as rigid structures can snap in strong winds or during earthquakes.

But the maths used to calculate SKYSCRAPER SWAY is straightforward.

Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.

Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.

The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. DetailsGoogle Books.

The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).

One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.

Earthquake Engineering

The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.

1. Base Isolation. Rubber pads or Rollers. Are used so the base does not feel the full shake or jump off foundations.

3. Active Tuned Mass Dampers use a computer controlled counter moving weight to actively move against the building sway.

The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according toWiredmagazine is highly vomit inducing (barfomatic?).

The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.

It is pushed in the opposite direction to the building sway to dampen the oscillation.

Earthquake Engineering Maths

Take 1:

Wiredmagazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):

Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.

Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?

Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.