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:

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.

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.

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.

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: