Maximum - free fall dive into water

[Ouabache]

Whenever I see footage of divers, free falling off a cliff into an deep ocean inlet, I empathize the sensation of danger they are facing.

This prompted a question in my mind, that applies to both physics and biology. If the water is plenty deep and there are no obstructions between the cliff and the water, what is the maximum height a person can make a free dive without incurring physical injury?

This could be broken down into degrees. The range could include: pain, bruising, soft-tissue damage (brain damage), broken bones, death.

Here is an http://www.reference.com/browse/wiki/Diving outside the limit: Un unobstructed free-fall dive into deep water of 66m (217ft) is lethal.

After viewing your thoughts, I will outline some assumptions.

 

[DaveC426913]

My contribution:
Feet-first impact can be lethal due to explosive rupture of the large colon. I'll leave the details to your imagination.

 

[Ouabache]

This is true (as would a http://img1.travelblog.org/Photos/1246/3735/t/12347-CANONBALL-0.jpg entry).. Perhaps you can brainstorm with me; can we determine at what height injury first occurs?

This sounds like a good time make my first assumption:
Assume the diver makes a nice streamlined hands-first entry resulting in the least sudden energy transfer and dissipation.

 

[DaveC426913]

can we determine at what height injury first occurs?

Injury always occurs at 0 feet, regardless of the initial height of the dive.

 

[Ouabache]

Okay, we probably need some physicists and biologists to help on this one.. Let's also restate the original question: What is the maximum height from which a person can make a free dive without incurring physical injury?

For the physics (calculations) let's make a few assumptions:
(whether we need them to answer the question, we shall find out)

Let the mass of the person be 70 kg. and their height 1.7m
(figures chosen to facilitate calculation, from table in http://www.brooks.af.mil/AFRL/HED/hedr/reports/handbook/tbl-54.htm )

We might also model the human body is a prolate spheroid (as described in http://medicalsciences.med.unsw.edu.au/SOMSWeb.nsf/resources/freeman01/$file/BSA.pdf )

So the person's volume based on that model is: $$V = \frac {4 \pi a^2c}{3}$$
and their surface area $$A_s = 4 \pi ac$$
(see last reference #2 for definition of variables)

Other potentially useful parameters are: kinetic energy, impact velocity (ref3 ) and impact force (ref4)

 

[Astronuc]

Well, it has to be less than 220 ft, because that is the clearance between a nearby bridge and the river its spans, and people have sustained serious injuries, in some cases fatal from that height. I have bruised myself hitting the water sideways from 20 ft.

Then there was the guy who cleared Niagra Falls and lived without significant injury.

The Falls drop about 170 feet (52 m), although the American Falls have a clear drop of only 70 feet (21 m) before reaching a jumble of fallen rocks which were deposited by a massive rock slide in 1954.

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

Height: 26 m - http://www.whdf.com/infos/event-regulations/calendar.htm

 

[Ouabache]

The http://www.reference.com/browse/wiki/Diving i gave initially, corroborates with your thoughts on diving from the top of a bridge. Though they do not give supporting references or data, it is useful food for thought. Their description makes it sound as though dives from 20-30m (65-100ft) could be accomplished without injury. The example your link describes (26m) is within this range.

Cliff jumping, a common pastime for daredevil(s)..., often takes place at heights of 20 m to 30 m. There is a limit to how high one can jump from and survive, regardless of water depth. For example, the Golden Gate Bridge is 220 feet (66 m) high and overlooks water deep enough to not hit the bottom, but the result is certain death.

 

[dav2008]

Well, it has to be less than 220 ft, because that is the clearance between a nearby bridge and the river its spans, and people have sustained serious injuries, in some cases fatal from that height. I have bruised myself hitting the water sideways from 20 ft.

Then there was the guy who cleared Niagra Falls and lived without significant injury. http://en.wikipedia.org/wiki/Niagra_Falls

Height: 26 m - http://www.whdf.com/infos/event-regulations/calendar.htm

Wouldn't there be a difference between turbulent water at the bottom of a waterfall and just a calm water surface in a swimming pool? It seems like there would be less surface tension at the bottom of a waterfall providing for a softer impact with the water. (I don't know if "less surface tension" would be the best way to describe it but I think you understand what I mean)

 

[Ouabache]

Wouldn't there be a difference between turbulent water at the bottom of a waterfall and just a calm water surface in a swimming pool?

Interesting thought about turbulence.. Well for the purposes of this thread let's make the assumption: an unobstructed free-fall dive into calm deep water

 

[Moonbear]

I'm thinking this might be better answered by physicists than biologists. We'd need some calculations on water surface tension, area of impact (hands I suppose), height of diving starting point, acceleration (or deceleration) upon impact, and then adjust the calculations for the impact of the head with the water once the surface was broken by the arms. I'd think it would be the head injury that would be fatal in a head-first dive, even if your initial impact was hands and arms first (your brain slamming into your skull when you abruptly slowed down...the cerebellum and brain stem would be most susceptible for tearing as the brain shifted forward due to the shape of the skull, and that would result in fairly sudden death, or drowning if you were still able to breathe when you couldn't swim to the surface...the most susceptible part of the brain in an impact is the area where motor control and respiratory functions are located).

You're not planning on diving off any bridges, are you?

 

[Ouabache]

I wonder if there have been any studies on "safe diving versus height"? This would be useful information for folks like Coast Guard or Navy divers jumping from helicoptors into the ocean. Moonbear has some insightful thoughts regarding the kind of injury to expect. Skilled divers will prefer the hands-first entry and they probably would be interested to learn what the upper safe-limit is, for diving height.

Regarding the physics, I think we can come up with some reasonable figures for impact forces and velocity. How that translates to degree of injury will be an interesting question. Perhaps a good place to look, is the research of G-forces on health in space travel; or rapid head acceleration as experienced on roller coasters.

I'm not planning any bridge dives.. Maybe a nice cliff dive would be fun.. Actually the last time I attempted jumping from an appreciable height, I wound up with water up my nose and my swimsuit pulled off .. Needless to say I was not tempted to repeat the performance

 

[Moonbear]

Well, I think when it comes to divers jumping into the ocean, the goal is to get as close as possible, not to push the limits of how high they can be dropped from. But, I wonder how stunt divers determine the limits of what's safe as they move the diving platforms higher and higher to impress their audiences...or is it by trial and error (i.e, if someone died diving from a particular height, nobody else goes that high again)?

 

[Marijn Blom]

With respect to rescue divers.
The main reason why they jump feet first is because a dive from say 5 meters, would result is serious damage to their face.

Divers ware masks that have a nice flat surface on the front, the impact would compress the air in the mask to an extend where bruising and damage to the eyes would be expected.

 

[Ba]

30' the highest that I've dived from, several times. It didn't cause any noticable injury that I noticed. This was a creek and not an ocean, so the tension was not as great but I could go a little bit higher.

 

[LURCH]

For example, the Golden Gate Bridge is 220 feet (66 m) high and overlooks water deep enough to not hit the bottom, but the result is certain death.

This is not entirely accerate. People have jumped from this bridge and survived. I believe there have been roughly 20 attempted suicides who have jumped from the "Golden Gate", but failed to arrive at the "Pearly".

 

[Ouabache]

can we determine at what height injury first occurs?

Injury always occurs at 0 feet, regardless of the initial height of the dive.

You're enjoy playing with semantics. You ought to consider becoming a computer

My contribution:
Feet-first impact can be lethal due to explosive rupture of the large colon. I'll leave the details to your imagination.

So with your example, at what initial height (starting point of the dive) does the lethal condition occur from a feet-first dive?

 

[Ouabache]

This is not entirely accerate. People have jumped from this bridge and survived. I believe there have been roughly 20 attempted suicides who have jumped from the "Golden Gate", but failed to arrive at the "Pearly".

That's interesting, so i also did a little digging.. This references puts the figure at 26 surviving dives from Golden Gate Bridge. However they also state that 98% of the dives are fatal. So we should specify lethal dive heights within some statistical deviation.

 

[Ouabache]

It seems the initial reference i gave in #1 is the most thorough discussion I could find on surface diving, including information regarding minor injuries.

Common injuries are bruises, which can occur on various parts of the body when entry is not streamlined. If the diver looks towards the water, there is likelihood of "bruising the face", not to mention water blasting up the nose. If the diver does not hold arms extended & hands extended over the head, they may "bruise the top of their head". If diver bends legs too much during entry, they can "bruise their thighs".

Wearing of goggles can damage the eyes due to sudden increase in pressure inside the goggle (as Marijn Blom also alluded[/i]) Competitive divers do wear goggles but they are specially designed for competitive swimming.

Interlocking the fingers during a dive can result in broken fingers.

If a diver is perfectly streamlined, they will penetrate the water to a greater depth and more likely to suffer acute barotrauma, due to exposure to a rapid increase in atmospheric pressure with depth.

The type of lethal injury that Moonbear described, the brain slamming into the skull upon abrupt deceleration, resulting in tearing cerebellum and brain stem as the brain shifts forward; sounds quite plausible. Where death has occurred from boxing (prize fights), I've heard this same type of injury described as the cause of death mechanism.

 

[bmangel716]

Ouabache:
This references puts the figure at 26 surviving dives from Golden Gate Bridge. However they also state that 98% of the dives are fatal. So we should specify lethal dive heights within some statistical deviation.This is statistic is very biased though. I have also read this, and the data claimed that 26 out of approx. 1200 jumpers survived, but those 1,200 jumpers were jumping with the intent of dying upon impact, so I doubt they hit the water in a position that would help them survive the impact, i.e., as a vertical line or in a dive.

Also, BMI is a variable to take into account. I would expect men to have a greater chance of surviving due to a more streamlined body, and also the outfit would need to be taken into account, as most of the jumpers in san francisco would be wearing several layers due to the cold weather.

If I were to guesstimate the chance of surviving this fall while trying to survive, is much higher. With proper attire, I believe a physically fit male would probably be able to increase his chances by at least 5x, if not more. I still don't give them a great chance, but its better than a measly 2% chance of survival.

While this is purely speculation, as I have not done any proper calculations, I would hope that this post at least helps someone else come to a more scientific conclusion on the matter.

 

[boomerang]

The world record dive is available on utube 4uHkyMh9FW4

Note there is not a mark on him so clearly you can survive a good deal higher than this.

My rough extimate of his entry speed is about 70 mph. (assuming no air restance).
Apparently freefall velocity is about 135mph but it is a variable depending on the body shape you adopt.
A freefall would at 135 would 3-4 times that impact of the dive shown.

 

[Jenez]

Another question would be what part of the human body is considered the weakest? It makes sense to say that whatever part that may be the weakest will sustain damage the easiest, not taking into consideration any specific position whilst hitting the surface.

My suggestion would be that the organs and the brain would take the most damage as they continue to move downwards due to sudden massive decelleration of the body when impact occurs.
Internal damage probably occurs long before any muscle injury or "bruising" and would greatly cut the distance required to sustain damage.

Would the height at which you sustain damage from when hitting for example pavement be similar to the height when hitting water? At what speed does water turn into stone?

 

[highdive]

Answer

What is the maximum height a person can make a free dive without incurring physical injury?

I believe the height is unlimited, terminal velocity can be reached and with a perfect feet first entry keep in mind you would want to transition from a flat body position 120 mph to vertical at the last possible moment to minimize acceleration which will occur.

But the most important factor here is surface tension of the water, assuming water is your choice of liquid, Diethyl ether would be a better choice when it comes to surface tension but I assume that would not be feasible.

With the proper temperature the hotter the water the less surface tension, aeration of the water to further reduce tension, and the use of Surfactants (wetting agents that lower the surface tension of a liquid) example: soap.

One thing I have not explored is mentioned in a previous post "acute barotrauma" not sure about this one and also not sure of the depth one would travel and would have to get back to the surface. You are bound to travel further because of the reduced surface tension.

If you guys can help me figure all of this out, I'm willing to take on the challenge of pulling this off from say 10,000 feet. This should sufficiently break the current record of 172 feet.

 

[davidryder]

Ok, I registered because I have been trying to figure this out.

I think something that can allow us to gauge the answer a little better is if we determined terminal velocity of a falling human.

At what distance does a 150lb human have to fall to reach terminal velocity?

 

[SpicyRamen]

Theres no definite answer for this problem is there?
I mean people vary, and in order to solve this we would need numbers, such to turn it into a word problem.
The max height would vary from person to person. A larger man would definitely sufffer from a greater impact since his surface area is greater and that he has more mass meaning the force pulling him down would be greater, acceleration equaling gravity so mass would be the only factor in this case.
Now as Ouabache put it, let's assume the water is calm, meaning the surface tension would be greater.
We could try to visualize this using silly puddy.
The Larger man hitting the water would have about the same affect as a ball of silly puddy hitting the wall. Whereas a thinner man would be like a pencil, penetrating it easier. And of course age matters too, even if a 10 year old boy is smaller and lighter there is a greater chance that he will suffer bone fractures.
It would also make a difference if the person was doing it head first or feet first where head first as Moonbear pointed out would be more susceptible to head and spine injury, this is why when the Navy(Marines? IDK) do sea rescues they always dive feet first since our legs are usually stronger than our upper body and could take the impact, and if worse comes to worse the person would only be paralyze waist down and not neck down.

 

[tokyosteve]

I'm not a physicist or a biologist, but I have jumped from 40+ metres on many occassions. My opinion is that when I hit the water (always the ocean) I'm at around half the speed of "terminal velocity". I have done this barefooted, wearing diving booties, and also wearing steel capped work boots. Barefooted was OK. One time the booties (they were very old) split and ran up my leg, and the construction boots were untouched.

I'm pretty carefull. I always go feet first (of course) and have always instinctively raised my arms straight over my head just before entry. My feeling is that if I were to enter the water at twice my current speed (which I reckon would be close to a skydiver's speed), I would be fine. It is all about "slipping in" like an arrow. There are plenty of sea birds that enter the water at absolutely astonishing speeds, but because they streamline themselves so well, it does them no harm.

In my opinion, if you do it right, you can jump from virtually any height and land in water safely.

 

[ThomasEdison]

That's interesting, so i also did a little digging.. This references puts the figure at 26 surviving dives from Golden Gate Bridge. However they also state that 98% of the dives are fatal. So we should specify lethal dive heights within some statistical deviation.

Your source is overlooking that many (I would say 100% of them but that's just me) people who die from jumping off bridges die from Hypothermia and drowning.

With the Golden Gate Bridge it's more a matter of being able to save the jumpers who've landed in water and are then paddling around in the water shocked and confused and freezing in the nick of time before they drown. Those ones that get picked up probably survive but this isn't about surviving the impact so much as not drowning in the water. It's very cold in the bay and I doubt the response time is that fast either. This is what I think the jumpers don't understand.. they are drowning themselves and they might end up treading water until they freeze to death and get exhausted and drown. that is not an easy or fast way to go. Even though a suicidal person would seem to give up many do fight for their lives after landing in water from a high drop.

My friend's roomate was seen dog paddling and attempting to swim and trying to survive for many minutes after he jumped and he eventually drown before a rescue boat could arrive. He leapt from some tall bridge in florida apparently. That scenario is common from suicide by bridge.

 

[uunter]

Glad to see other people are thinking about this! I've had this crazy idea of jumping from space into the ocean without a parachute, and I'm trying to figure out how feasible that is. I'm especially interested in tokyosteve's comment:

I'm not a physicist or a biologist, but I have jumped from 40+ metres on many occassions. My opinion is that when I hit the water (always the ocean) I'm at around half the speed of "terminal velocity".

I am a physicist, sort of, and I can tell you that your intuition is a little bit off, but not drastically. In freefall (no air resistance), your speed at impact from any height h would be the square root of h*g, where g is the acceleration of gravity near Earth's surface. In metric, that's 9.8 m/s², so from 40 m, you'd be hitting at 28 m/s, which is almost exactly half of a typical skydiver's terminal velocity of http://en.wikipedia.org/wiki/Terminal_velocity#Examples" or (insert unit conversions) 54 m/s. However, from 40 m, you're going to encounter significant air resistance on the way down, so your actual velocity on impact was somewhat less than half terminal velocity. When it's not so late, I'll make a more exact calculation of your impact velocity that takes air resistance into account.

I have done this barefooted, wearing diving booties, and also wearing steel capped work boots. Barefooted was OK. One time the booties (they were very old) split and ran up my leg, and the construction boots were untouched.
I'm pretty carefull. I always go feet first (of course) and have always instinctively raised my arms straight over my head just before entry. My feeling is that if I were to enter the water at twice my current speed (which I reckon would be close to a skydiver's speed), I would be fine...

That's very encouraging.

In my opinion, if you do it right, you can jump from virtually any height and land in water safely.

That's my conjecture too (with the caveat that "doing it right" may involve a semi-rigid full-body suit), but I'm nowhere near convinced yet. Skydivers reach terminal velocity after about 150 m, but that's in belly-down orientation (maximizing the force of the air). As tokyosteve points out, to enter the water safely, you'd want to enter feet-first (minimizing the force of the water), so you'd need a couple seconds to transition; at 54 m/s, you cover another 100+ m in that time. So if someone does it from 300 m, I'll be convinced it can be done from any height.

 

[JaredJames]

In my opinion, if you do it right, you can jump from virtually any height and land in water safely.

I assume by "do it right" you mean - "with equipment that takes the impact so your body doesn't"?

There is going to be a maximum velocity at which you could strike water before it's effects become akin to 'slapping custard'. Whether or not that speed is greater or less than terminal velocity is another issue and something I'd think would be unique to each person.

 

[Proton Soup]

seems like you could collect some useful data simply by dropping euthanized test animals (or a visit to the slaughterhouse if this is too much paperwork) from sufficient height. there would be a lot of tumbling, but you'd get an idea of worst-case breakage.

 

[uunter]

I think what tokyosteve means by "doing it right" is entering the water with proper form, i.e. feet first, toes pointed, head and arms straight up. That much would be absolutely necessary. But I suspect that yes, doing it right also includes having some sort of protective suit to distribute the impact across your body and protect against whiplash.

As for the animal tests--you might get a worst-case picture, but we already know what that is from people jumping from much lower heights. If you do it wrong, you die, from some sort of rupture or the subsequent bleeding. We're looking instead for the best case--is it possible to NOT die (or be seriously injured) entering the water at terminal velocity?

Or, the way it was originally posed: what is the maximum height one can fall into water from without serious injury or death? But if you can survive a terminal velocity entry, then there's no upper limit.