Lethal jump height?

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

  1. Frencheneesz Amazing Member Registered Senior Member

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    Inertia wouldn't have anything to do with it, the only thing that matters is how the water deforms. The deformation of the water will take energy from the falling body, and the pressure is what would kill you.

    One note about the kids that jumped from 65 ft bridges: they were probably in basically dive position the whole way down - meaning that the velocity they reached at the bottom could be equivalent to the velocity reached by someone jumping at 120 feet if that person fell like a skydiver (so that they have more surface area to catch the air).

    Suicidal jumps don't often involve a person trying to save themselves by being smart about how to slow their decent before diving.
     
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  3. Fraggle Rocker Staff Member

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    Remember that after you hit the water you keep moving. If you continue in the direction of your original fall, straight down, it may be that you reach such a depth that you cannot swim back to the surface before you run out of air and lose consciousness. For most people that's not much longer than one minute, and some of that minute was already used up by the descent below the surface. Back when I was a decent swimmer I could not have swum much more than 100 feet in a minute, and surely less using an underwater stroke. And that air would not have lasted a full minute during a strenuous swim. But let's say 100 feet.

    The question now is: Once you hit the water at that speed, how far down do you go before viscosity and your own frantic paddling stop you? (Please, somebody else do the math!) If it's more than 100 feet you're probably going to float to the surface unconscious and not breathing, if you're alive at all.

    From that point on, you're at the mercy of buoyancy and currents before you finally surface. Then somebody has to spot you, get to you, and perform artificial respiration to get you breathing again.

    People who jump off the Golden Gate may die by drowning rather than impact. Let's wait for a math major to do the calculation.
     
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  5. Frencheneesz Amazing Member Registered Senior Member

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    Its gonna be a phyics major you want. with a specialty in fluid dynamics. I guarantee that you won't get even close to 50 feet down - course I have nothing to back myself up. check this out tho http://science.howstuffworks.com/question729.htm
     
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  7. Stryder Keeper of "good" ideas. Valued Senior Member

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    The method stuntmen use to overcome "High falls" into water involves using Bubbles.

    Simply the water has to be deep enough for the fall, but if you have a machine or pipe at the bottom of the target area creating bubbles it actually lessens the impact density, so you can fall from higher.
     
  8. Roman Banned Banned

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    Swimming up goes much faster than swimming down or horizontally as the human body is boyant. If you have your lungs full of air when you go under, you'll rise to the surface even faster.
     
  9. Frencheneesz Amazing Member Registered Senior Member

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    RE the bubbles: thats how barrel divers over waterfalls make it, the bubbly mist at the bottom slows them gradually. Also, I'd think stuntmen use the bubbles cause they'd rather not get sprained ankles and knees, like you'd get if you fell from a plane.
     
  10. The Evistarator Registered Member

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    Me and my room mate were just arguing about something that is kinda related to this subject and I was wondering if I might be able to get some enlightenment. Ok first off let's say that an average man (160Pounds) falls off of the Top Floor of the CN Tower (446.5m/1464.9ft). Let's suppose that the CN Tower is in the general vicinity of a large body of water (lake, ocean). This man is wearing a pair of shoes and a suit and is carrying a briefcase (15-20 pounds). If either the man falls ( panicky and flailing his arms and legs ) or ( has watched some TV and tries to spread his arms and legs out so that covers more surface), would the man hit terminal velocity before hitting the water or would the man be descending at a reasonable speed that if he was somehow able to throw his briefcase before himself into the water and break the surface so that he would be able to survive the initial impact with the water? Is it true that it takes only 14 seconds of free fall to achieve terminal velocity? I've heard that the human body because of it's natural state of buoyancy, it would not penetrate the water deeper than 45 feet? If the man takes a deep breath of air and is able to break the surface of the water with his briefcase would he be able to swim back up to the surface to be able to be saved. Thanks in advance for any help on this subject.
     
  11. iceaura Valued Senior Member

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    According to a student of mine who was injured in the Navy, the stat emergency med techs hear is that 90% of falls from over five meters are lethal in real life.

    On the other hand, several people have survived terminal velocity falls - which can be from any height. Once you're past about 150 feet it doesn't matter. If landing on land, hit splayed out level and on your back for best odds - or so they say. On water, headfirst.

    When we dove off high stuff into water, as children, we learned not to go feet first - lock your hands over your head, squeeze your ears with your arms, punch a hole for your head with your interlocked fist, and don't relax on impact.

    I never, regardless of height, went deeper than about fifteen feet.
     
  12. Frencheneesz Amazing Member Registered Senior Member

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    You do not want to dive headfirst. Your hands will be knocked away and you will be knocked out cold. Feet first is the way to go if you want to survive. Terminal velocity isn't a constant number - that number depends on your air resistance, which depends mostly on your shape. If you jackknife down to the earth, your terminal velocity will be very much higher than if you spread your arms and dive with body parallel to the ground. The problem is that if you hit the water in that position, you won't break the surface of the water - rather the water will break the surface of your skin.

    The briefcase would be useful to slow your decent, but don't expect to be able to hold onto the case when you hit the water. If you let the case get under you just before you hit the water, it'll be a brick in your side - and you probably won't survive.

    Its possible to dive into water at terminal velocity and survive, but i wouldn't try it.
     
  13. iceaura Valued Senior Member

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    Not if you interlock your fingers or cup one fist, and punch a hole for your head while squeezing your ears to slow the water hammer.

    From childhood bridge experience, feet first entry is mostly of psychological benefit - physically, you are more likely to get your head and neck whipped around violently, get water driven hard up your nose, get slammed by a tilted entry, etc.

    But to each their own. Terminal velocity diving is not something one can practice.
     
  14. draqon Banned Banned

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    "For example, The Free Fall Research Page lists the case of World War II Russian airman, Lt I M Chisov. Chisov's Ilyushin IL-4 bomber was shot down by German fighters in January, 1942. Chisov fell 22,000 feet (6,705 metres) and hit the edge of a snow-covered ravine and rolled to the bottom. Although badly injured, Chisov survived. Although this is not cliff diving into water, it shows what is possible." quoting about.com
     
  15. Facial Valued Senior Member

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    2,217
    Water is different... it is a Newtonian fluid, meaning that the viscosity increases with the rate of shear. Around terminal velocity, with body parallel to ground, that is about 120 mph.

    I cannot even slap the surface of a swimming pool half that fast, and even then, it feels (upon impact) almost like a solid surface and can result in redness after just several 'slaps'.
     
  16. quadraphonics Bloodthirsty Barbarian Valued Senior Member

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    It all depends on what you land on, what position you're in when you land, and what (if any) protective gear you're wearing.

    The world record for highest cliff skied off of is 255 feet:

    http://en.wikipedia.org/wiki/Jamie_Pierre

    But he's landing in several feet of soft snow, and wearing body armor.
     
  17. Thoreau Valued Senior Member

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    3,375
    There was a remarkable story on the news a LONG time ago in Houston about a skydiver who hit the ground at free fall speed; his chute didn't open at all. He got up and started walking. He sustained no broken bones or injury to any vital organs. Just bruising. I was hoping to find it online but I've had no luck.
     
  18. Reiku Banned Banned

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    Yes... it can happen, such as a gust of wind, breaking the fall... its not unheard of, but statistically astronomical.
     
  19. Fraggle Rocker Staff Member

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    24,690
    Since you're trying to calculate the best case, feet-first is not it. If nothing else, the pressure of the water bursting up into your nose can cause brain damage. So at least let the person do a perfect dive and enter the water in the best possible attitude. The advantage of setting the problem up this way is that it will probably generate the most interest: What is the maximum distance an Olympic diver could survive?

    We may not be able to get good data on the force of the impact. Even if we do, there is another factor that might outweigh it, so let's look into it and see what kind of a limit it provides.

    You hit the water in a perfect diving posture, which means that the both the force of the impact and the effect of the viscosity of the water once you're submerged are minimized. As a result you will continue descending very rapidly until you can turn yourself around and head back up. Do you see where I'm going with this? You might run out of oxygen and drown before you can reach the surface!

    So what you need to figure out is: at what speed can you hit the water, and reverse your descent in time to reach the surface alive? Those Acapulco cliff divers "cheat" by spreading their arms to slow their fall with wind resistance, but if they didn't their speed upon impact would be something like 75mph. They land in 12 feet of water and manage to stop and rise back out before they hit their heads on the bottom. I don't know the formulas for viscosity. If they hit the water as 150mph, how deep would the water have to be? How about at 300mph? What distance can an Olympic swimmer cover--upward, aided by buoyancy--in the 90 seconds of air he has in his lungs, or whatever the world record is for that? For the sake of argument we'll say he doesn't have to worry about delaying his inhalation till the last moment, adding another factor to the problem, because the fall will only take four or five seconds.

    Remember that there is a maximum free-fall velocity for any object due to the viscosity of air. I think for a human body it's around 400mph.

    So here's the way I would state the problem: If an Olympic athlete dives from a high enough platform that he has reached maximum free-fall velocity when he hits the water, and survives the impact, how far down will he go before he can reverse direction? How long will it take him to stop descending and swim to the surface? Can he hold his breath that long?

    If he can, then this formulation of the problem is no good. We will have proven that under ideal circumstances any dive is survivable. But if he can't, then we can work backwards to compute the maximum distance from platform to water.
    I don't know whether bullets have ideal streamlining. But in any case the fastest ones are traveling at supersonic speed. This is triple the velocity of any human diver and probably quadruple that of an untrained person who just jumps and falls.
     
  20. Pete It's not rocket surgery Moderator

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    Various not terribly reliable sources indicate that a skilled skydiver can reach maybe 140m/s in freefall.

    If our heroic diver managed that feat, then decelerated at a manageable (but ungentle) 10g, they would come to a stop in 1.4 seconds at a depth of maybe 100metres.

    If this amazing person is also an accomplished free diver, they should be able to reach the surface without difficulty if they managed to keep the breath in their lungs - the record depth for "constant weight without fins" free-diving (start at the surface, swim down, and return using no gear) is 80 metres (taking about 90 seconds each way)! So a one-way journey of 100m only a few seconds after taking a big breath should be manageable (but not comfortable!)
     
  21. Fraggle Rocker Staff Member

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    So my hypothesis is incorrect. This is not the limiting factor.

    So we've got two questions:
    • Can anyone hit the water at 300mph (sorry this is America and we're allergic to metrics

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      ) and survive the impact? I.e. not disintegrate like those bullets?
    • Could they decelerate at 10g after hitting the water, so they'd only be 300 feet down? Not sink at a much more comfortable 3g and go so deep they'd suffocate on the way up?
    If the answer to both of these questions is "yes," then in theory a properly trained athlete could survive a fall into the water from any height. In that case the only reason people die is that they're not properly trained athletes.

    Oh yeah, and also because they don't want to survive so they're not trying to do it "right."

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    Somebody please do the math: Those Acapulco cliff divers hit the water at (I guess) something around 100mph, and the water is only 12 feet deep. What is their rate of deceleration in the water?
     
  22. iceaura Valued Senior Member

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    I'd be damn surprised if anyone could get themselves more than about 20 meters down just by diving into the water, even if they tried (my real guess is more like fifteen).

    The faster you hit, the faster you decelerate - the water shear resistance rises with some large power (4?) of the shear speed.

    And the deeper you go, the more force it takes to move that water sideways and push through - it's the water pressure you are fighting, and that is increasing very rapidly with depth.

    The rate of deceleration might not be so limiting - once past the surface, the whole body is being decelerated more or less evenly, so it isn't the same as being smashed into a chair etc. The water does - and does even better, maybe - what a "g-suit" does for a pilot.

    I doubt water depth drowning is a major factor, even for the untrained.

    And a very fast rate of slowdown would be survivable.
     
  23. Fraggle Rocker Staff Member

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    So it comes down to this: Is there a maximum speed at which you can hit the water without being killed by the impact itself? 300mph is three times as fast as the cliff divers. Is the human body simply too fragile to remain intact after hitting water at that speed?
     

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