Landing in Water From Great Heights
Describe what will happen to the human body, when a person
jumps from a commercial airplane without a parachute and lands in the
ocean. Let us say they are 20 feet above the ocean. Is it true that
landing in ocean water at this speed is like landing on cement? My
students actually believe that a person could survive a jump from a
commercial plane flying over the ocean. I would like some scientific answer.
Maybe in a Piper Warrior single engine in slow flight (55 - 60 knts). I have
been water skiing and have fallen at about 40 mph. But that was only from 0
feet (standing on the water skis). Certainly not in a commercial 737 or the
like. I am guessing that the slowest flight speed (before stalling) of a
737 is about 160 kts (190 MPH). In other words, even with a parachute (@ 20
feet) the unfortunate person would not survive the fall since 20 feet is not
enough fall time for the parachute to fully deploy. So without the
parachute, more importantly, if a person were to hit the water at that
speed, well, without going into details, the person would really have no
chance of surviving.
Of course it is the height above the water and the position of the
"jumper" that counts -- the airplane is irrelavent. Consider a diver who
jumps off a high diving board (it is a 10 meter board or platform if I
recall correctly). A good diver enters the water almost without a splash.
However, an inexperienced diver who does a "belly flop" is going to get a
pretty hard jolt. The difference is due to the fact that it takes a finite
amount of time for the water in the path of the diver to move out of the
way of the diver and the water the diver displaces as she/he enters the
water. If the water cannot "get out of the way" it begins to behave as
though it were a solid. At 10 meters this depends upon the technique of
the diver. If the speed of the diver at the instant of entry becomes
greater (as his/her altitude becomes greater) the less time the water has
to "get out of the way" as the diver hits the water. If the water cannot
be displaced, it begins to behave as though it were a solid. The same
principles also apply if the fluid is a gas. At sufficiently high speed,
if a person jumps from an airplane even the air cannot "get out of the
way" and it is almost as though the air was "solid". This is the reason
that pilots in military aircraft flying at high speeds (e.g. greater than
the speed of sound) have to be in a protective shell. At those high speeds
even air behaves like a wall. This is also why reentry vehicles from orbit
have to skip along the atmosphere to slow down. If they do not do so the
vehicle would "crash" long before it hit solid ground.
I would say it is a little more like hitting cement at only half your
falling velocity. Or even less.
Of course, that is not any comfort, if your falling velocity is 120mph
(the usual terminal velocity for spread-eagled human body, well-known to
Perhaps you have seen high-speed movies of the jello-like wave movement as
bullets or blunt objects impact gelatin.
Or perhaps you could pat your own tummy and notice the wiggle frequency there.
For the period of time shorter than one wiggle, there is no mechanical
there is only mass, fluidity, and incompressibility.
Hitting water is about the same as hitting gelatin or hitting another
human body, during this brief time.
Imagine two human bodies going "splat", face-to-face.
If it is a perfectly symmetrical situation, right down the middle there
is a plane that neither side ever crosses.
A "virtual" concrete wall.
But each side approaches that wall at only half the closing speed of the
For periods of time longer than the slosh frequency of the flesh,
and the ability of water to flow aside starts helping.
So the later parts of the deceleration are longer and slower.
But that first slap can hit you like a giant fly swatter.
If horizontal, you would probably be decelerated to half your velocity
by passing through water mass equal to one body, roughly 1 foot thick.
120 mph is about 180 ft/sec.
Passing through 1 foot would take 1/180 = 0.006 seconds
Change in velocity would be 90 ft/sec.
acceleration = 90ft/sec / 0.006 sec = 16,000 ft/sec2
16,000 ft/sec2 / 32ft/sec2/g = 500 g's acceleration.
Maybe you can check my math, but it does not sound encouraging.
Of course that is not the way anybody imagines doing it...
Presenting a wedge, of relatively hard flesh with small forward surface
areas, is how high-diving is survived.
Can you do it accurately, after tumbling from an airplane?
Even with a controlled dive, at high speeds merely being a little out of
line might get you dislocations or a broken neck.
Acapulco high-divers never reach terminal velocity, and they need years of
If you hold a vertical orientation for long, your terminal velocity will
be higher, maybe 150 mph or even 180 mph.
That would make it much harder to survive.
So one might think to spread-eagle until the last 100-200 feet,
then quickly rotate to vertical to penetrate the surface.
(head or heels I am not going to speculate about, fantasy enough already...)
Then be straight, stiff, and almost vertical when you hit the water.
Does not sound straightforward for the inexperienced.
You can work the usual fluid drag formulas for travel in water to figure
out the frontal pressure
on your heels as you first plunge in....
Pd = shape_coeff * water_density * velocity^2
Do not hope for special treatment; your shape-factor is about 1.0,
similar to anything un-streamlined.
Water density is 1000 kg/meter^3.
Velocity is about 60 meter/sec.
Pd = 1.0 * 1000 kg/m3 * (60 m/s)^2 = 3.6e6 kg/m.s2 = 3.6 MPa million
Pascals - ( 1 atmosphere = ~ 15psi = ~ 100 KPa. )
Pd = 3.6 MPa = 36 atmospheres = 540 psi.
If your heels are considered only 10 square inches (...), that is 2.5
tons per heel, this time for ~0.05 second.
Typical bone strength can be looked up and compared with that.
I am not sure that locking your knees and tensing your muscles will be enough.
You might guess a magnitude of water turbulence curling around the impact
point and pushing on your knees.
Given the force you figure and the helpless mass of the leg, will it bend
out-of-line within 0.05 sec?
If so it may be another problem.
Balling up? Padding of a backpack? I do not know.
In principle it may be possible to survive such falls,
and I think I may have heard of rare instances when it happened.
But most of us wouldn't succeed even if we were trained to try.
I would like to see Mythbusters try it with a crash-dummy someday.
I think enough optimistic young people have carried this idea to qualify
it as a cultural myth....
My next-stage fantasy is to wonder whether a small amount of body-equipment
to keep you slower, oriented, and hardened, might make a
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Update: June 2012