Lethal jump height?

Discussion in 'Physics & Math' started by RubiksMaster, Apr 4, 2006.

  1. RubiksMaster

    RubiksMaster Real eyes realize real lies

    Ok, so most people die when jumping from the 220 foot Golden Gate Bridge. But jumping from 20 feet is safe (into water of course). How high is too high? 80ft? 120ft? I don't know enough physics to calculate any forces or speeds, and whatnot, so I don't know the answer. (assume the person lands feet first).
  2. Pete

    Pete It's not rocket surgery

    If you plotted fall height against percentage of deaths of falls from that height, I'm guessing there'll be some sort of S curve, increase slowly at first, then more rapidly, then flattening out to 100%.

    Heights of interest would be:

    1) Minimum possibly fatal fall height (the height at which the curve leaves 0%)
    2) Minimum definitely fatal fall height (the height at which the curve reaches 100%)
    3) 50-50 fatality fall height (the height at which the curve crosses 50%)
    4) The inflection of the S. This feels interesting mathematically, but I don't know what it's meaning is in this particular case.

    Here's an example of an S-Curve.
  3. Poincare's Stepchild

    Poincare's Stepchild Inside a Klein bottle.

    I don't think there is a set answer to your question. A person can be killed by a relatively short jump. On the other hand, a few people have survived falling from a great height.

    I read about a Navy pilot during Vietnam who fell from over 1000 feet. His 'chute didn't open. He had broken bones and a ruptured spleen, but survived.
  4. Pete

    Pete It's not rocket surgery

    There's lots of research articles regarding falls from height on PubMed.
    Try this one, and click on "Related Articles": Suicidal high falls
  5. RubiksMaster

    RubiksMaster Real eyes realize real lies

    Thanks for the replies.

    Do you have any idea where I could find that data? I couldn't find it with google. I guess I'm probably interested in knowing that point where there is roughly a 50-50 chance.
  6. spidergoat

    spidergoat alien lie form

    It's not the height, it's the deceleration at the end, and the distribution of forces on the body. This data is widely collected by the auto industry. If it's a fall or a crash makes no difference.
  7. Pete

    Pete It's not rocket surgery

    Hi RubiksMaster,
    The only guaranteed way of finding the data is to do an experiment, but you might have difficulty getting ethical clearance! No, you'll definitely need to use existing data.

    So, you could scour police and hospital records looking for cases where the height of the fall, the type of landing, and list of injuries (to try to determine whether the faller landed feet first) is recorded, but this is a lot of work and requires a lot of preparation... one particularly troublesome task will be convincing the authorities to allow you access to those records at all. It can be done, but you'd to prepare a sound, well justified research proposal. This is time consuming, so you'll probably want to try finding secondary (already collected) data first...

    The last and easiest way is to find the work of people who have done this legwork for their own research. This isn't guaranteed - it is unlikely that anyone has addressed your question exactly, but it is certain that similar questions have been addressed. If this is the path you choose, then your task now is to:

    • Determine the existence of research papers which may have used the data you need. It isn't too hard to find some relevant papers, but it's damn near impossible to find all of them. You'll first need to find the right places to look. PubMed will be useful. Your University librarians might also be glad to help.
    • Locate those research papers. This can be tricky. Most research papers are not available for free download. Subscriptions to research journals are expensive, so no University will have access to all Journals. Most can be obtained through inter-library loans, but there is usually a small cost involved.
    • If the papers don't contain the data you need, but appear to have used it, you'll also need to ask the authors of the paper if you can use their raw data. This is pretty chancy - many will ignore you, just say no, or tell you that they don't have that data anymore. But you never know...

    Good luck!
  8. Raphael

    Raphael Registered Senior Member

    Fall protection and prevention is the term you should search for on the internet. There are people out there whose job is to study fall hazards, so that the world may be a safer place. Your requirement that the person lands on his feet may not be specifically addressed. But, the field does address lethality of falls from any given height. I once heard it said that any fall hazard can be lethal.
  9. Facial

    Facial Valued Senior Member

    Pete, for your sigmoid plot, what would be the units for the abscissa?
  10. Pete

    Pete It's not rocket surgery

    It's just an example S-curve - it's not supposed to directly correspond to this case.
  11. Facial

    Facial Valued Senior Member

    I would imagine that sigmoid curves would represent such a situation quite well. It would be interesting to see if there was a statistical compilation on this.
  12. Lensman

    Lensman Registered Senior Member

    It's really hard to generalize, because it depends a great deal on what you hit. People generally survive a fall from the second story of a building (12-15 ft?), but generally not from the 4th (32+ feet?). A fall from the third story approaches your 50-50 scenario. But falls from a multistory building are generally to a hard surface: sidewalk or road. Fall into water, and you have a good chance of survival at a height of 100 feet or more. Professional "cliff divers" regularly dive at heights up to 110-120 feet, and not only survive but walk away afterwards.

    "It's not the fall that kills you, it's the sudden stop at the end!" :) That's not just a joke; if the stop at the end isn't so sudden, you can survive falling a lot farther. There was a case where a Russian female pilot ejected, her parachute didn't open, but she survived (with a broken pelvis) hitting at terminal velocity, when she hit a sloping snowbank on a glacier. Updrafts and landing in haystacks have also been known to let people survive very long falls. Of course, as you might imagine, this is *extremely* rare.

    The Worst-Case Scenario Survival Handbook says "It is entirely possible to survive a high fall (five stories or more) into a dumpster, provided it is filled with the right kind of trash (empty boxes are best) and you land correctly. [Because your body will fold into a "V" upon impact, you want to land on your back. Landing on your stomach will likely break your back. Do not try this at home! :)]
    Last edited: Apr 7, 2006
  13. Flunch

    Flunch Registered Senior Member

    Anecdotally, I have experience jumping off highway bridges into water. (was a highschool pass-time). Virtually none of us ever got hurt on foot-first plunges from 40 foot bridges but whenever we attempted the 65 foot drop from the highest bridge in town about 50% of us suffered ankle sprains, bruising, etc. each time. I would not want to jump off anything higher.
  14. Facial

    Facial Valued Senior Member

    It's also known that most of the people who jump of the Golden Gate, 200+ ft, get killed even if its impact on water. I'm supposing this happens in a belly-flop acceleration upon impact?
  15. Flunch

    Flunch Registered Senior Member

    So there you have it. The LD50 is going to be somewhere between 65 and 200 feet!

    P.S. you really need to remember to keep your arms "in", and legs together when you jump from height... and it helps to wear shoes and tight-fitting clothes because they get ripped-off by the water otherwise.
  16. Asguard

    Asguard Kiss my dark side

    you would have to take into account the state of the person, the way they were falling and if they were falling into water the depth and hardness. Ie a frail elderly person who has ostioparosis and shrunken brain falling head first over a brick onto concreat could be killed where a young healthy person diving of a bridge into soft deep water might live
  17. Lensman

    Lensman Registered Senior Member

    The advantage of water is that, unlike the ground, it moves out of your way when you hit it. By stretching out the time it takes you to stop, it reduces the instant-to-instant force and stress on your body.

    But when you it the water from 200+ feet, you hit with such force that you're killed before the water has time to move far enuff to matter.
  18. Facial

    Facial Valued Senior Member

    Would it be due to the inertia or viscosity of the water? Which one would be more responsible?
  19. Flunch

    Flunch Registered Senior Member

    the viscosity and density of the water will affect the drag and thus "rate of deceleration", as would the shape of your body entering the water.

    As Lensman and others have said, it's not the fall that kills you but how quickly you slow down at the end of it. That's why belly flops hurt, even from a jump off a low height like the edge of a pool. The deceleration happens very quickly = high forces.

    I've been told that no matter how high you fall from, you will not go deeper than about 20 feet max.
  20. Facial

    Facial Valued Senior Member

    I've seen on Mythbusters once where they fired several rifles into a swimming pool.
    Only the slowest muzzle velocities got past 20 feet in the water, or something like that, when fired at an angle of (30degrees? i forgot).

    This makes a lot of sense because the water slaps back really hard. The most powerful rifles had their bullets disintegrate once they touched the water.

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