# Maximum - free fall dive into water

#### Ouabache

Homework Helper
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 [Broken] 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.

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#### DaveC426913

Gold Member
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

Homework Helper
This is true (as would a http://img1.travelblog.org/Photos/1246/3735/t/12347-CANONBALL-0.jpg [Broken] 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.

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#### DaveC426913

Gold Member
Ouabache said:
can we determine at what height injury first occurs?
Injury always occurs at 0 feet, regardless of the initial height of the dive.

#### Ouabache

Homework Helper
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) lets 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 [Broken])

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 [Broken])

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)

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#### Astronuc

Staff Emeritus
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 [Broken]

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#### Ouabache

Homework Helper
The http://www.reference.com/browse/wiki/Diving [Broken] 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.

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#### dav2008

Gold Member
Astronuc said:
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 [Broken]
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)

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#### Ouabache

Homework Helper
dav2008 said:
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

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#### Moonbear

Staff Emeritus
Gold Member
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? :uhh:

#### Ouabache

Homework Helper
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.. :tongue: Actually the last time I attempted jumping from an appreciable height, I wound up with water up my nose and my swimsuit pulled off :surprised .. Needless to say I was not tempted to repeat the performance

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#### Moonbear

Staff Emeritus
Gold Member
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

Homework Helper
DaveC426913 said:
Ouabache said:
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

DaveC426913 said:
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

Homework Helper
LURCH said:
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

Homework Helper
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. :surprised 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.

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#### 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.

"Maximum - free fall dive into water"

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