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.
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.
Thanks to Rod Vancefor 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.
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.
But can the human body take this punishment?
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)
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:
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 Nyiragongolava 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.
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) 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 flowshere.
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.
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.
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.
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