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Two questions:

  1. Assuming you dive head first or fall straight with your legs first, what is the maximal height you can jump into water from and not get hurt?
    In other words, an H meter fall into water is equivalent to how many meters concrete-pavement fall, force wise? (I'm assuming the damage caused will be mainly due to amount of force and not the duration)
  2. Assume you jump head first and hold a sharp and strong long object that cuts the water before you arrive, will that make the entrance to the water more smooth and protect you?enter image description here
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Even from the high board going in head first without getting you hands in front of you is painful. From the 10 m platform it can easily result in a concussion. –  dmckee Apr 24 '11 at 14:45
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I like this style of question; the answer is complicated, but interesting and arguably useful. –  Andrew Apr 24 '11 at 15:37
    
InRe: a flag on the question. Can we have a reformulation to be more physics oriented. As it stands the answers have no physics in them, which is not a good sign. –  dmckee Apr 24 '11 at 16:14
    
dmckee It is very hard to put physics into this if one does not have access to pay wall publications. It is evident that no matter how much one tries to model the human body and behavior the data are necessary to set the scale. Here is an attempt: en.allexperts.com/q/Physics-1358/… –  anna v Apr 24 '11 at 16:39
    
Thanks for the answers so far, but I agree - they are not very physical. I'm looking for a numerical answer which will demonstrate the differences in force experienced in each type of fall, out of considerations of impulse and the density of matter you fall into. It is less important to me how many newtons are required to smash a bone. –  Uri Apr 24 '11 at 18:45
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5 Answers

up vote 4 down vote accepted

Answering your questions in reverse order:

Yes, a long pointy object (like your arms over your head, in a dive, or your pointed toes in a feet-first entry) will make a big difference. Remember the tongue-in-cheek adage, "it's not the fall that kills you; it's the sudden stop?" That is exactly what differentiates a fall onto concrete from a fall into water: how sudden is the stop. And making that stop LESS sudden (decreasing the magnitude of deceleration during the stop) is exactly how airbags save your life in a car crash. One can decrease the magnitude of deceleration by reducing the ratio --> (delta_V / delta_t). Since there is roughly a linear relationship between time and distance traveled during the instant of impact, you can achieve the same effect by reducing the ratio --> (delta_V / delta_s) where 's' = distance traveled during the deceleration event. The easiest way to do this is to lengthen 's'.

One thing to remember about the water fall statistics is that a large number of them are likely "unpracticed." These are not olympic divers working up to 250 feet. A large proportion of them are unconditioned people forced into a water "escape;" or, worse, are people TRYING to die.

Assuming you are doing the right thing, and optimizing your form for water entry, you will simultaneously be minimizing your wind resistance during the fall:

1.) A fall from 30 feet will result in a velocity of roughly 44 ft/s = 30 mph.

2.) A fall from 100 feet will result in a velocity of roughly 80 ft/s = 54 mph.

3.) A fall from 150 feet will result in a velocity of roughly 97 ft/s = 66 mph.

4.) A fall from 250 feet will result in a velocity of roughly 125 ft/s = 85 mph.

The first case is a tower jump I did for the Navy, and is trival for anyone who is HWP and doesn't belly flop. The second is an approximation of a leap from a carrier deck, which the tower jump was supposed to teach you how to survive (be able to swim after the fall). The third is only 20% faster entry speed (and force) and should be survivable by anyone in good shape and able to execute good form (pointed toe entry, knees locked, head up, arms straight up). The La Quebrada cliff divers routinely dive from 125 feet as a tourist attraction. If forced to choose, I'd pick a feet-first entry at 150 feet over a dive at 125.

So the interesting part is the stretch from 150 to 250 feet. My guess is that the limit for someone voluntarily performing repeated water dives/jumps from a height of 'x' will show 'x' to be somewhere around 225 feet +/- 25 feet.

EDIT: There are documented cases of people surviving falls from thousands of feet (failed parachute) onto LAND. These freaky cases of surviving terminal velocity falls do not answer the question practically; but they are there.

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From searching I find that the survival rate from a fall depends on the deceleration rate that the body undergoes on impact, and that depends on the surface of the fall. Water is less punishing than land.

Here is a quote, which I will not source, but can be found on the net.

Stone states that jumping from 150 feet (46 metres) or higher on land, and 250 feet (76 metres) or more on water, is 95% to 98% fatal. 150 feet/46 metres, equates to roughly 10 to 15 stories in a building, depending on the height of one story. 250 feet is the height of the Golden Gate Bridge in San Francisco.

Most publications are behind pay walls and have to do with statistics of suicide survival, not a pleasant topic.

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I suspect few if any bridge jumpers are trying to land hydrodynamically, so the odds of a professional diver surviving from the same height are probably a lot higher. –  Omega Centauri Apr 24 '11 at 15:42
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It obviously depends quite strongly on how hydrodynamic your entry is. Try doing a belly flop from 2 meters: ouch! Wheras competition divers routinely dive from 10M. Having grown up in a pool, and jumping/diving off the ten foot board I am amazed at current law, which makes it illegal to lave a 3foot dive without the water being something like 17feet deep. Ours was a mere 9feet, and thousands jumped dived in over a period of decades with noone getting smashed on the bottom. So I suspect if you get the hydrodynamics just right, you can end up pretty deep/fast. Thats the position you need to hit in, but its probably well out on the tail of the distribution. I believe I had heard about a case of someone falling into the ocean from 20,000feet and surviving (must have been a parachute failure or such), and it may have been only an urban legend, but I have no reason to doubt that a lucky landing at terminal velocity is survivable.

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I can assure you from personal experience that if you're good at it, you can hit the bottom of a 12 foot pool pretty fast from a 1 m springboard. 'Course, if you're good at it you can also pull up fast if you want to. –  dmckee Apr 24 '11 at 16:13
    
@dmckee I can believe that, I had to be careful doing an inward dive or that could happen to me. It never happened to me with any of the forward facing dives, but something about the inward dive encouraged me to enter in a very low resistance configuration. The trick is to bend once you're fully in the watre, then you won't go deep. –  Omega Centauri Apr 24 '11 at 20:45
    
Seems like the 20,000 feet story is almost true: greenharbor.com/fffolder/judkins.html –  Yakimych Apr 24 '11 at 21:08
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There are a number of factors which can influence this.

In a free fall you can reach a speed of 50 m/s. Hitting a water surface with that speed is lethal as the statistics from the other answers show nicely. In clive diving competitions they use a trick though to reduce the probability of getting hurt quite a bit. Instead of a flat water surface the athletes jump into basically a bubble bath. With either water or air pumps lots of bubbles are created below the surface and that dampens the fall quite a bit.

The cone would work in a similar way. Under ideal conditions, i.e. hitting the water with the cone exactly at the right angle you could soften the fall so that even a free fall would be survivable.

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I'm on my iPad now so I don't have it but there is a great article which covers this using suicides from structures and other known falls. It also notes that how one hits the water etc. is key and hence suicide victims are hardly thinking about that they throw it into question. Basically if you jump from a high structure say 150' and do it casually the probability of survival is like 0. Done right it may be 4%. I don't recall the number he came up with but it was something like 70 ft/s was the near ceiling. The walkway over water in my town is 212 ft high, roughly $\sqrt{212} * 8$, pretty much unsurvivable.

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Ps you can get hurt at almost ANY distance so it's really about how trained the person is doing it and sometimes luck. Head first is easy ifnu think about how much force one can take to the head before knocking themselves out etc. Holding the long pointy object may help, you need to figure out how much less force it applied to the head at heights. Still, feet first would be the best option and the cone of protection would not help you at greater heights. –  Mike q Oct 15 '11 at 11:17
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