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

November 16, 2009

AngelsAndDemonsTom Hanks character, Robert Langdon, hero of Dan Brown’s Angels and Demons (2009) jumps from a helicopter and falls thousands of feet into Rome’s Tiber River and survives, of course._angels1_226

Ahhhh! Look up. It’s raining Tom Hanks!!!!!

There are three factors we must consider, mathspigs, when jumping or diving from a great height:

1. Surface Impact

2.Water depth

3. How long you can hold your breath.

We’ll start with water surface impact. According to the Free Fall website falling into water is not a good survival strategy. http://www.greenharbor.com/fffolder/questions.html#anchor1234566  ‘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.

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

Sports Smart Canada (Visual Expert Website: http://www.visualexpert.com/Resources/divingaccidents.html ) recommend that the water depth should be twice the height of the dive. Olympic divers often practise their dives in a bubble pool (like a spa). This reduces the impact for a bad dive but the water must be much deeper. So a water depth of double the height of the drop is realistic if, say, you are jumping or diving from the top of a waterfall into aerated water. You can work out appropriate depths if you were diving into water from heights such as:

eiffel tower

Eiffel Tower:  300m

Note: You would need a big swimming pool!!!!

Sydney Harbour Bridge Clearance: 52.4 m    sydney harbour bridge 2

brooklyn bridge

Brooklyn Bridge NY Clearance Above Water: 41m

10 m Tower/ 4th Story Window:

dive tower






statueof liberty

Statue of Liberty Height: 93 m

Note: Assume you’re diving into water from ,say, a helicopter as in the Demons & Angels movie.



free dive Assuming you survive the impact of the jump and the water is deep enough, would you survive the journey down and then the swim to the surface on one breath???????

William Trubridge broke the world record in Unassisted Freediving with a dive to 88m (288ft) in 3 minutes 30 seconds on 2nd May 2009 which you can view on Youtube


  1. Not sure about your jumping maths. At La Quebrada, Acapulco they famously dive 48m into 6.5m depth of water. And there have been 26 survivors of attempted suicides from the Golden Gate Bridge (75m). The Sports Smart Canada numbers are nonsense – we used to jump from a 10m metre board at Reading pool into 5m of water and nobody got hurt.

    • Hi David,
      Great to have your comment. This is what it’s about. Get kids talking about maths. The statistic I need – and can’t find – is a drop or dive height/water depth chart for different ways of entering water (Dive, flat, feet first etc). If you have access to one let me know and I’ll add it to the blog. Meanwhile, here in Melbourne, Australia we call landing badly when diving off a 3 m board a ‘Belly Whacker’ and, believe me, it really hurts. Cheers Mathspig

  2. Hello I just found your blog, I like it!
    I just want to comment on the depth of water required when jumping from a height.

    There is a nice rule of thump going back to Newton himself.
    “the penetration detpht of a projectile (density a, lengt l) into a medium (dens b) will be: l x a/b”

    E.g. for a person (dens ~1 g/cm^3) falling into water the penetration depht will be ~ 1 bodylength.
    (diving or falling feet first it means ~2m and falling flat it means~.3m)
    That is the reason it is so dangerous, very fast decelration.
    for instance, it is not very efficient to shoot fish with a rifle, arrow and bow works better (long projectile). Also to penetrate the armor of a tank you need a thin and heavy projectile and that is what they use, a thin tungsten or uranium arrow.



    • Thanks Peter, I was looking for a formula for deceleration in water. I’ll check it out. But don’t forget you will need much greater depths if jumping into aerated water. Cheers Mathspig

  3. Amazing site by Katelyn Rokosz

    • Hey thanks Katelyn,
      Just been on a pig vacation. Cheer Mathspig

  4. “The statistic I need – and can’t find – is a drop or dive height/water depth chart for different ways of entering water (Dive, flat, feet first etc).”

    Exactly – I have been searching for that myself (in fact i was hoping to find an app for a smartphone to do the job.

    As for the Newton formulae: surely the velocity is missing there somewhere…

    • Hi Kai,
      Great to hear from you. The assumption is, I think, that every jumper will reach the same terminal velocity. Then each jumper would have to hit the water feet first … Risky assumptions. But better to do the maths than actually jump to test the theory. Cheers Mathspig

  5. did u ever find a table?

    • Helloooooo Jakob, Haven’t found it yet, but it would be interesting. Let me know if you stumble upon any sort of list. Cheerio Mathspig

  6. “7. You can safely jump from a burning skyscraper/bridge/aircraft into water.
    Mathspig Blog” was indeed a superb blog post and therefore I personally ended up being quite happy to
    find the article. Thanks a lot,Tasha

    • Pleasure treasure. Mathspig

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