What Happens When a Human Falls
from 10,000 metres?
The Physics and Physiology of Falling
by
lim ju boo
A Scientific Poser:
I read a very interesting answer the other day from Captain KH Lim on his
website (Google Search: ‘KH Lim Boeing 777’) when someone wrote to him
inquiring what happens when a passenger is thrown out from a plane flying at
35,000 feet? I believe Capt. Lim gave a very accurate answer to that question.
The question was so interesting that I could not help thinking of the possible
physics and physiology occurring to a human body falling from such a tremendous
height. Allow me to fill in the details where Capt. Lim left out.
Before I start elaborating on the answer Captain KH Lim gave, let me straight
away tell you I do not know the answer with absolute certainty. The reason is
very simple. I have never seen a person falling off an aircraft before, let
alone has a study or a scientific experiment been done to study him as he falls
to his death. Neither do I do not know of any sane person who would conduct
such a bizarre experiment either. In the absence of any account documented in
the literature, whatever discussed here is entirely, and personally my own. I
conjure up a scientific hypothesis, based on other indirect existing
observations, and established facts. Knowledge can only come from studying. All
scientific experiments on humans are governed by professional ethics, and
scientists do not go round murdering people just to gather some scientific
facts.
No Study Done:
Hence I do not know of any experiment being done where a person is being pushed
out of a plane at 35,000 feet just to observe what happens to him during the
fall. I do not think they have done this even to an animal. The only other way
to study such an effect is through controlled experiments using a parachute.
But the psychological and physiological effects on a parachutist who knows he
is undergoing an experiment, and who knows he is safe, and will land safely, is
entirely different from one who accidentally fell off from a plane without a
parachute.
Furthermore, it is from a height more than three times higher than those
attempted by a parachutist. The scenarios are totally, and entirely different.
There is just no comparison. As I am not a parachutist, I do not know if there
had been anyone attempting to jump from a height of over 10 km, where the air
is so thin, and where the temperature is a forbidden – 55 0 C. I do not think a
parachute could open effectively at such great heights where the air is very
thin. A parachute can only work when air rushes into it to unfold it. When the
air is so rarified at that attitude, one can hardly breathe. The parachutist
will be knocked unconscious within 30 seconds before he could even open his
parachute.
So what I am attempting here is to construct a scenario using intelligent
guesses based on existing knowledge, and observations in physics, medicine and
physiology. Some indirect experiments may already have been conducted by NASA
scientists but some of the results are kept in very tight wrap, and the rest of
the scientific world is kept in the dark.
The Scenario :
Now, let us imagine a picture of a human passenger falling off a jetliner
flying at 35,000 feet. That’s 10,668 metres or 10.67 km up in a hostile
environment where the temperatures are down to the tune of – 55 0 C. The
atmospheric pressure there registers only 8.89 inches of mercury, whereas the
normal atmospheric pressure at sea level is 29.9 inch of mercury. What happens
then? Thanks to Capt KH Lim who assures us that, that will never happen as the
aircraft doors are shut tight by air pressures within the cabin, and it can
never be opened unless the pressure is released by the captain on landing.
That's enough! But let us examine a hypothetical situation where the plane
burst open due to an onboard explosion. Hopefully this will not be another
Satanic act by another madman onboard. Let us assume the passengers are all
thrown out. What happens?
Let us look at the haemodynamic first. This means its effects on the physics
and dynamics of blood circulation. We assume the passengers were not killed or
injured by the explosion, but were merely falling down, and began to accelerate
downwards. It will continue to accelerate until air resistance, and drag brake
it to a maximum velocity. This is called the terminal velocity.
Once the terminal velocity is reached, no matter how fast that speed is, it
will have no effect on the haemodynamic. The danger lies not because of the
maximum (terminal) velocity, but from the acceleration as the body plunges
faster and faster towards the ground. As I said, I have not seen or studied the
effects of a human body plunging downwards to earth before, let alone from such
great height, so the scenarios I construct here are only based on theoretical
scientific principles.
Circulatory Dynamics :
First of all, I do not anticipate much changes to the haemodynamic since the
acceleration is only 1 G (one unit of gravitation force). This is from the
natural pull of the Earth’s gravity. During the fall, the casualty, if
conscious, will only experience the feeling of weightlessness and free
floating, and this may not have a very profound effect on the circulatory
system. This feeling of weightlessness will soon disappear the moment the
terminal speed is reached, and there is no more acceleration. The victim will
feel as if he was riding on a very fast roller coaster, or in a very fast car.
But suppose now we imagine a situation where the passenger didn’t fall out of
the plane but was actually diving downwards together with the plane at a
tremendous acceleration of let’s say 4-5 G (4-5 times greater than the pull of
natural Earth’s gravity). This probably is achievable by a very fast plane
accelerating downwards at a rate greater than the natural gravity of Earth.
What happened then? Ah! That makes a great difference.
Physiology of Fall:
Suppose now he plunges downwards headfirst, and legs up. The acceleration that
mimics tremendous gravitation pull downwards will act like a centrifugal force,
similar to the water being spun outwards from wet clothes against the drum in a
washing machine. This will cause all the blood to pool towards the legs,
leaving no or little blood going to the head (brain).
The casualty will immediately suffer a syncopal event (faints) or a ‘black out’
due to low cerebral perfusion of blood and oxygen. This gives rise to an event
called transient cerebral ischaemia leading to a “black out”. The black out is
similar to one caused by hypoxia (lack of oxygen), but not exactly the same as
the cabin partial oxygen pressure is still maintained. But both are due to lack
of sufficient oxygen perfusion into the brain, although the mechanism causing
it is different.
Of course a number of other factors can also cause faints (syncope). It is not
just from falling off a plane into a hostile environment where the oxygen
tension is very low. In fact, anything that causes the blood flow to the brain
to be compromised, will result in a faint. For instance, if the vague nerve
(the 10th cranial nerve – the longest and the principal component of the
parasympathetic division of the autonomic nervous system) is over-stimulated,
it will cause the heart to slow down, thus reducing the blood flow to the
brain. In medicine, we call this phenomenon “(vaso) vagal attack” brought about
by factors such as fear, pain, stress, and shock as Capt. Lim pointed out.
This event results in vaso- dilation, and a corresponding drop in blood
pressure. This event temporarily de-stabilizes blood pressure, affects
circulatory dynamics, and the blood supply to the brain. I have quite a number
of patients (predominantly females) who come to me complaining about their
frequent ‘blackouts’ Most of these are young patients who are tall, and have
low haemoglobin (Hb) levels, a feature among young menstruating women.
Their frequent momentary faints were due to sudden change in their positions
from lying down to standing up. That sudden change in the position, coupled
with their low Hb which carries vital oxygen to the tissues, causes a sudden
drop in blood pressure as the heart pumping ability (cardiac efficiency and
output) is unable to cope with the sudden change in position against gravity.
This phenomenon is called postural hypotension.
This affects sufficient blood going to the brain. On a number of other occasions,
I have elderly patients with the same problem. But they were normotensive
(normal blood pressures), meaning they were also not hypotensive (low blood
pressure). On further investigations, I found they were diabetic, a disease
that damages the nerves (neuropathy), which in turn controls blood pressure
among other functions. Some of them with frequent faints were also taking
antihypertensive, or vasodilator drugs, all of which may affect blood flow to
the brain (cerebral insufficiency).
Medical Aspects of Fall: Syncope & Heart Irregularities:
Other cases though I have not come across, were those with vertebrobasilar
insufficiency or those with Stokes-Adams Syndrome. They affect cerebral
perfusion because of cardiac arrhythmia (irregularities in the heartbeat),
which in turn is caused by heart block (interruption to electrical impulses to
the heart muscles to contract rhythmically). Heart block or auriculoventricular
block, is a medical term to mean an interruption to the transmission of
electrical impulses from the sinoatrial nodes (SA node or “pacemaker”) onwards
to the atrioventricular (AV) nodes. Ultimately, the electrical impulses enter
the muscles of ventricles to contract rhythmically (alternately) with the
auricles via specialized conducting systems (AV bundle, or the Bundle of His) before
distribution to a network of fibres in the ventricles. If there is any
interruption to this electrical transmission it will cause the heart to beat
irregularly (arrhythmia). The P-R interval in the ECG tracing is prolonged.
There are many types of ‘heart block - branch bundle block, etc, and the
severity (degrees) of heart block, but we will not go into that.
Heart block here does not mean that the coronary vessels were blocked by
cholesterol e.g. atherosclerosis, although heart block may be an indirect
result of “hardening” (sclerosis) of the Bundle of His caused by interference
of blood supply to the heart. This affects subsequent electrical transmission
through the network of ventricular fibres (Purkinje fibres) through the damaged
myocardium (heart muscles). The Bundle of His is a sheath of insulating
connective tissues, also called the atrioventricular bundle, which extends from
the atrioventricular node from the atrium across the fibrous skeleton of the
heart to the ventricles. It acts as the main transmission wire to conduct
electrical impulse across the heart from the atrium to the ventricles.
However, these are separate pathologies, and have no relationships to ‘faints’
caused by hypoxia in an environment where the oxygen tension is very low. We
are not discussing a subject on medicine or physiology here, although it is
good to know that there are many other factors that can cause a person to
faint, and not just the fright of falling off a plane. But Capt. KH Lim has
correctly pointed out that a person can be unconscious from sudden (nervous / emotional)
shock of falling.
But as I said earlier, the likelihood of a casualty fainting due to a
mechanical cause (not emotional shock) such as blood being pulled away from the
head (if he accelerates head first) is unlikely as the acceleration is only 1
G. This is just not great enough to destabilize haemodynamic or induce any
profound physiological changes. In fact, a person falling from a great height
merely feels the sensation of weightlessness (I guess) during the initial
stages of acceleration, but once the terminal velocity is reached, he probably
feels he is riding on a fast vehicle. This is my guess, as I have not
experienced it myself.
Acceleration & Shifting Parameters :
In the event of a tremendous acceleration experienced by a falling (human) body
such as a pilot in a plane nose diving down at a fantastic speed with the
victim inside, and if the position of the body is such that the legs go first
and head last towards the direction of the dive. A lot of blood will start to
pull towards the head causing tremendous cerebral congestion due to pooling of
blood towards the brain This also results in lesser venous return from the
brain.
The result can be even more disastrous than a mere faint. The casualty instead,
may run the very heavy risk of suffering a haemorrhage in the brain – a CVA
(Cerebral Vascular Accident) or stroke. One of the vessels may burst open due
to increased intracranial / intravascular pressures. In the actual situation of
a body falling off a plane, it is very unlikely that he will black out (head
downward first) due to this particular mechanical reason or run a risk of a CVA
event (legs downward first) as the acceleration is too small, and the time too
short to elicit an effect. He would by then achieve terminal velocity.
In fact with the air drag and air resistance, the acceleration due to earth’s
gravity is even less than the standard 9.81 metres per second per second. The
rate of acceleration is less at very high altitudes since the force of
attraction between the body and the Earth’s gravitational pull falls off
inversely as the square of their distance.
As the body falls nearer and nearer towards Earth, the pull (force) becomes
greater and greater , and thus the acceleration will no longer be constant at
9.81 m / sec /sec. Acceleration (a) is directly proportion to pull or force
(F). . F = ma, where m (mass) is constant. In truth this is not so. Remember
air is always there. It will slow down all the acceleration until a terminal
velocity is reached. The very slightly greater acceleration achieved nearer
Earth will be cancelled out by the vastly increased in air drag due to higher
air density at lower heights. In fact (I guess) the air resistance will be a
much greater factor in slowing down the speed of fall than the mild increase in
speed due to a change in acceleration as the body plunges down towards Earth.
Equations to a Critical or Terminal
Velocity:
An object which is falling through
the atmosphere is subjected to two external forces. One force is the
gravitational force, expressed as the weight of the object. The other force is
the air resistance or drag of the object. If the mass of an falling human body
remains constant, the motion of the object can be described by Newton's second
law of motion, force F equals mass m times acceleration a:
F = m * a
which can be solved for the
acceleration of the object in terms of the net external force and the mass of
the object:
a = F / m
Weight and drag are forces which
are vector quantities. The net external force F is then equal to the difference
of the weight W and the drag D
F = W - D
The acceleration of a falling
object then becomes:
a = (W - D) / m
The magnitude of the drag is given
by the drag equation. Drag D depends on a drag coefficient Cd, the atmospheric
density r, the square of the air velocity V, and some reference area A of the
object.
D = Cd * r * V ^2 * A / 2
Drag increases with the square of
the speed. So as the human body or any object falls, the drag becomes equal to
the weight, if the weight is small. When drag is equal to weight, there is no
net external force on the object and the vertical acceleration goes to zero.
With no acceleration, the object
falls at a constant velocity as described by Newton's first law of motion. The
constant vertical velocity is called the terminal velocity.
Using algebra, we can determine the
value of the terminal velocity. At terminal velocity:
D = W
Cd * r * V ^2 * A / 2 = W
Solving for the vertical velocity
V, we obtain the equation.
V = sqrt ( (2 * W) / (Cd * r * A)
The density of the air affects the drag. But density will also depend on the
humidity and the temperature. Hence the drag will depend on all these factors.
To add to the difficulty of calculating acceleration, drag and final speed
these parameters keep on changing at varying altitudes, in fact every second,
and a fraction of a second.
The denser air at lower heights may even have a mild braking effect on the
terminal velocity, and the braking effect is even greater if the body drops
into the sea where the density of salt water is even higher than fresh water.
It is very hard to determine what these changes would be, as the parameters are
continuously shifting. With variables changing all the time, it is almost
impossible to apply standard equations to come with some conclusion. It is of
course possible to apply calculus to evaluate small increments over time, but
how are we to know what the values would be to enable them to be substituted
into the equations.
Then again, the drag will also depend on the shape and size of the falling
body. If a passenger stretches out his legs and arms the drag will be greater
against the air resistance. He will take a longer time, and greater distance to
fall before he arrives at the terminal velocity. But if the passenger /victim
curls up like a ball or puts his arms and legs by his sides and drops
vertically down, the effect is the other way round – faster. All these
parameters are very difficult to determine and calculate.
I suppose one way is to use a super-computer to simulate these changes in order
for us to arrive at the correct distance travelled before the body arrives at
the terminal velocity of 130 mph (58.1 metres per second). So, I have assumed
the air up at 35,000 feet (10.668 km) is almost ‘vacuum’ and then applying
Newton equations to arrive at a drop of 565 feet before reaching terminal
velocity of 130 mph. I guess it should not differ very much from the actual
figure since the air density up there is near “vacuum”. This means the drop is
from 35,000 - 565 feet = 34,435 feet (10,495.8 metres) before terminal
velocity.
Hypoxia & Oxygen Saturation:
Then as Capt Lim correctly said, the passenger will be unconscious after 30
seconds. In other words, at 10,700 metres (about 35,000 feet) where the air
pressure is only 260 hPa (normal at sea-level = 1013 hPa), and a density of
only 0.41 kg / m3, the oxygen partial pressure will drop to 21/100 X 260 = 54.6
hPa. At that partial pressure of oxygen, the oxyhaemoglobin dissociation curve
showed that the haemoglobin is only about 82 % saturated with oxygen.
This is well below the safe level of at least 95 % saturation recommended by
the American College of Chest Physicians and the National Heart, Lung and Blood
Institute for a person to stay conscious. Oxygen saturation (SaO2) level below
90 % will result in hypoxaemia (hypoxia), and unconsciousness. A SaO2 level of
82 % at that height (35,000 feet), the “useful consciousness” lasts only 30
seconds from severe hypoxia as rightly pointed out by Capt. Lim.
If he is a parachutist at that height (God-forbids), he better get his
parachute opened before 30 seconds, or else…….? He will remain unconscious
until he reaches 10,000 feet when there is sufficient air. The time taken at
130 mph, or 11440 feet / min = 190.67 feet / sec will be 128.15 seconds (2
minutes 8 sec) before he reaches that height. He will probably have another
52.5 seconds more to go before he crashes into the ground towards a certain
death, provided there is no updraft of air currents to delay the death. All in,
he will take 180 seconds – exactly 3 minutes since achieving a terminal
velocity of 130 mph at a height of 34,435 feet.
Critical Velocity:
Once again, I need to
repeat it is not as easy as that.
Many factors need to be considered
if a human body falls from a great height like those from a plane at an
altitude of 10,000 meters.
Firstly, the air is extremely
rarified at that altitude. Thus, there is very high air resistance to cushion
the rate of fall. The fall is faster there in a rarefied atmosphere.
Secondly, the speed of
fall also depends on the contour of the body, meaning the
body’s shape and surface area. It also depends on whether or not the
arms and legs are stretched out or the body curled up like a ball.
In short, the speed of the fall depends greatly on the shape and aerodynamics of the falling body against air resistance. Initially the speed becomes more and more as the body descends to a lower altitude until where the density of air becomes more and more dense. It will then slow down to reach a terminal or critical velocity.
Another factor we need to consider is that, at extremely great heights further away from the centre of the Earth, the acceleration of fall due to gravity is less than 9.8 metres per sec per sec. As a falling body gets nearer and nearer to the Earth’s surface, the pull due to gravity becomes greater and greater.
Hence the acceleration becomes
faster and faster assuming it was in a vacuum. In short, there is not just a
change of velocity, but also a change in the rate of acceleration due to the
stronger and stronger pull of gravity as it descends.
Even the latitude where the fall
was, determines the rate of acceleration. It is about 9.780 m/s2 at
the Equator to about 9.832 m/s2 at the poles. All these
need to be considered.
The terminal velocity of a person falling off a plane from a height of
10,000 metres is:
V t = √ (2mg /p ACd)
where:
Vt = terminal
velocity
M = mass of falling body or the
human body. (example a 70 kg man with a body surface area of 1.75 m2)
P = density of the fluid through
which the body is falling (example in the air).
A = projected area of the body
(example: position of falling human body)
C d =
coefficient of drag (example, air)
The speed achieved by a human body
in freefall is slowed down by air resistance and body orientation. In a stable,
belly-to-earth position, terminal velocity of the human body is about 200
km/h (about 120mph). A stable, free fly, head-down position produces a speed of
around 240-290 km/h (around 150-180 mph), averaging about 56 metre / sec or 200
km / hr.
The drag coefficient of a human
body depends on the size of the human body and the position or orientation of
the body in the air from which he drops, and on the altitude where the density
of air varies.
An adult human body in an
upright position, the drag coefficient (cd) would be
1.0 – 1.3 whereas the drag coefficient for a 70 kg skydiver descending through
air, head on first that has a body area of approximately 0.18 m2,
the drag coefficient from an altitude of 4,000 meters is approximately 0.7. A
typical free fall time from an altitude of 4,000 meters is between 55 – 60
seconds.
When falling in the standard
belly-to-Earth position, an average estimate of terminal velocity for skydivers
is 200 km / hr (120 mph), and a falling person will reach terminal velocity
after about 12 seconds after falling some 450 m (1,500 ft) in that
time.
But the most popular type of sky
jump for beginners is usually from a height of 2500-4000
meters before opening the parachute at a height of 1000-1500 meters.
Please note that there is sufficient air at this altitude to breathe and where
the air drag is also greater to slow down the acceleration than at 10,000
metres where commercial jet planes fly if he falls down from that height.
At 10,000 meters it is even higher
than Mount Everest standing at an elevation of 8,849 metres where bottled
oxygen is needed for climbers above 7,000 metres.
Let’s have a look at the
motion of a falling body with air resistance “a” called “drag”.
a = (W -D) / m
When drag is equal to weight of the
falling body, acceleration becomes zero, and the falling body reaches its final
terminal velocity which is normally about 200 kph for a human body.
W = D = Cd (r V^2 / 2). A
Terminal Velocity: V = sqrt (2 W
/Cd r A)
Where:
W = weight of the body
D = drag
V = velocity
A = frontal area
Cd = drag coefficient
The drag
coefficient Cd is equal to the drag D divided by the
quantity: density r times half the velocity V squared times
the reference area A, namely:
Cd = D / (A * .5 * r * V^2)
In simple lay language without
going into all this mathematics, a person falling from a jet plane flying at
10,000 meters will accelerate over a longer time than at lower altitude, say at
3,000 meters for a skydiver due to lesser drag at higher, than at lower
altitude.
But finally, when he reaches the
lower altitude where drag of air becomes equal to his weight, acceleration
finally stops, and he reaches an average terminal velocity of about 56 metre /
sec or 200 km / hr.
At that velocity the kinetic energy
he developed on landing is:
½ mv 2
Let’s say he weighs 70 kg.
The kinetic energy on impact on the
ground during landing would be a whooping:
½ x 70 x 56^2 = 109,760
Joules
Sufficient to break all his bones
in his body – instant death.
But suppose he fell from 10,000
metres in a vacuum where there is no air or drag to break the acceleration of
his fall, then the energy dissipated on his body is:
mass x acceleration x height
= 70 kg x 9.8 meters per second per
second x 10,000 m = 6,860,000 Joules
This is 62.5 times more poweful than if he had an atmosphere to buffer his fall.
This is equivalent to the power of
1.6 kg of TNT scattering his body.
(1 tonne of TNT = 4.184e x 10 9 Joules)
Suppose we imagine again he was falling in a vacuum from 10,000 m where there was no atmosphere to slow down his acceleration due to drag, then we can apply Isaac Newton 2 out of his 3 equations of motion to determine the final velocity, the time taken and the force of fall on the ground instead of the terminal velocity of about 200 kph when there is an atmosphere.
Here are Newton's 3 equations of motion.
v = u + at
s = ut + ½ at2
v2 = u2 +2as
where:
v = final velocity
u = initial velocity (0)
s = height or distance of the fall
t = time taken
s = acceleration due to gravity (9.80665 m /s /s)
We need to determine the final velocity first since we only know the height of the fall (10,000 meters)
Final velocity v2 = u2 + 2as
v = √ (u2 + 2as)
= √ (0 + 2 x 9.80665 x 10,000 m) = 442.87 metre per second
Next, the time taken:
v = u + at
at = v -u
t = v-u /a
= 442.87 – 0 / 9.80665
= 45.16 seconds
We can verify the height of the fall:
s = ut + ½ at2
= 0 + (9.80665 x 45.16 x 45.16) / 2
= 10,000 meters (QED)
Since the acceleration assumed to be constant at 9.80665 m per sec per sec in a vacuum from a short height of 10,000 m, and if a person weighs 70 kg falls, then the force (F) of his impact on the ground would be:
Mass x acceleration
= 70 kg x (9.80665 m /s /s)
= 686.5 Newton
(5,059 words)
