**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

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.. **

**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.

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Every action hero gets into a fistfight. James Bond, Jason Bourne, Indiana Jones. Then there are all the stars known for their fight scenes. Sylvester Stallone ( Rocky), Arnold Schwarzenegger (True Lies), Jackie Chan (Any movie), Bruce Willis (Die Hard 1,2, 3 etc), Mel Gibson (Lethal Weapon I, II, III etc), Jean Claude Van Damm (Blood Sport, Street Fighter), Brad Pitt (Fight Club), Fast & Furious 1,2,3 and so on.

We can work it out. Measurements taken at The University of Manchester have shown that local boxing hero Ricky ‘The Hitman’ Hatton really does live up to his name. (DailyScience)

Ricky ‘The Hitman’ Hatton can pack a punch!!!!!

Similar results were found at Uni Manchester BBC (**Force of boxer’s punch measured)**

**So one punch is equal to being hit by a car …… if only for a split second!!!!!!!!!!! Nevertheless you can be killed by this one punch.**

You’ll find some great punching physics** here**

This is the rework of a **previous post.**

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:

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:

Every volcano disaster movie from **Volcano** (1997) with Tommy Lee Jones to **Dante’s Peak** (1997) with Pierce Brosnan someone somewhere tries to out run a lava flow. Is this possible?

The answer is maybe. You will find everything you want to know about lava flows **here**.

On January 10,1977, at **Nyiragongo** lava sprang from the sides of the volcano moving at speeds up to 40 miles per hour. About 70 people were killed.

Measuring the temperature of lava. Photograph by R.L. Christiansen, U.S. Geological Survey, January 9, 1973.

The fastest Lava flows recorded were in Hawaiiin 1950 when Mauna Loa erupted. The lava traveled at 6 miles per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 60 mph.

Speed of average sprinter = 10 – 15 mph

This is a rework of a **previous post** with full calcs.

Every volcano disaster movie from **Volcano** (1997) with Tommy Lee Jones to **Dante’s Peak** (1997) withPierce Brosnan someone somewhere tries to out run a lava flow. Is this possible?

The answer is maybe. You will find everything you want to know about lava flows **here.**

On January 10,1977, at **Nyiragongo** lava sprang from the sides of the volcano moving at speeds up to 40 miles per hour (60 km/hr). About 70 people were killed.

Measuring the temperature of lava. Photograph by R.L. Christiansen, U.S. Geological Survey, January 9, 1973.

The fastest Lava flows recorded were in Hawaiiin 1950 when Mauna Loa erupted. The lava traveled at 10 kilometers per hour through thick forest. But once the lava flows became established and good channels developed, the lava in the channels was flowing at up to 97 kph.

Speed of average sprinter = 16 – 24 kph

NOTE: Uncanny likeness of biopic actors to the real Queen!

According to **intmath** The **Sydney Opera House** is a very unusual design based on slices out of a ball. Many **differential equations** (one type of integration) were solved in the design of this building.

You will never see a better parody of Queen’s ICONIC song BOHEMIAN RHAPSODY than **Calculus Rhapsody** By Phil Kirk & Mike Gospel (below).

And if you need to be reminded of the maths you will find links to texts **here**.

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.

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:

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.

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

Table from Accident Reconstruction Website

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

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:

View full video here.

Safe Driving Info here

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

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)

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

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

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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

The angle of the kicker in ramp design can vary from 10^{0} – 70^{0} (See below)

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.

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.

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.

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