Thursday, July 24, 2014

What happens if someone falls from a plane at 10,000 metres

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)

 

 Capt. Lim mentioned terminal velocity of 130 mph (11440 feet / min = 190.67 feet / sec = 58.1 metres per second). The question I like to address now is, how far the drop would have to be before the body reaches this terminal velocity of 58.1 m / sec? I assumed that this will be reached after the body has dropped 565 feet (172.2 metre) to terminal velocity. I calculated this out from Newton’s equations on motion. But this is only true had the body fallen through a vacuum without any resistance. It is also correct if the acceleration had been constant. This is not true in practice. There is air up there, albeit thin to offer considerable resistance and drag. As the body falls, the air density gets higher and higher.


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.

 In any case, a moment in altitude will be reached when the body reaches a maximum velocity against air resistance and can no longer go faster. This maximum speed is called “critical velocity” or “terminal velocity” and it is about 56 meters per second (200 kph).  However, this can also vary as it also depends on the updrafts of air currents against the falling body.


 Rate of Change in Acceleration:

 

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.

 Hence Newton’s equations of motion cannot be strictly applied due to these constant changes in the parameters. You may need to use calculus to work out these continuous and small increments in changes due to accelerations and air resistances.

 But at an altitude of just 10,000 metres, I believe the rate of change in acceleration is very minimal for meaningful corrections to be made.

 Another way of putting the rate of accelerations, drag, and final velocity of the falling human is this: 


The terminal velocity of a person falling off a plane from a height of 10,000 metres is:

V t = √ (2mg /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)

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 = u+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)

Further thought:

As a body continues to fall towards Earth, the force due to gravity (which is the weight of the body) As increases because of the stronger gravitational pull at lower altitudes. However, the rate of increase in acceleration is not constant. While gravitational pull strengthens as the object gets closer to Earth, the increase in acceleration is offset by the growing effect of air resistance (or drag).

Air Resistance and Terminal Velocity

As the falling object speeds up, the drag force increases. Air resistance depends on the shape, size, and velocity of the object, as well as the density of the air. The drag force is given by the equation:

D = ½ C dp AV  2

Where,

D is the drag force

Cd is the drag coefficient

p is the air density

A is the cross-sectional area of the object

V is the velocity

At a certain point, the drag force equals the weight of the object, and the object no longer accelerates. This is the terminal velocity—the constant speed at which the object falls. For a human body, the terminal velocity depends on body posture and altitude.

In the standard skydiver’s belly-to-Earth position, terminal velocity is about 120 mph (193 km/h or 54 m/s). In a head-down position, terminal velocity can increase to 150-180 mph (240-290 km/h), as the body's profile offers less drag.

Terminal Velocity Equation

At terminal velocity, the drag force equals the gravitational force:

W = D

By rearranging the drag equation, the terminal velocity Vt can be expressed as:

Vt=    √ (2W / C dp A)

Where W is the weight of the falling body. A typical human weighing 70 kg (about 154 lbs) will experience this constant velocity at lower altitudes after about 450 m of free fall in normal atmospheric conditions.

Calculating the Distance to Reach Terminal Velocity

The initial assumption that terminal velocity is reached after a drop of 565 feet (172.2 meters) assumes no air resistance. In reality, air resistance slows down the acceleration, and terminal velocity is usually achieved after falling approximately 1,500 feet (450 meters) under normal atmospheric conditions.

Variations in Terminal Velocity

  • Altitude: At higher altitudes, the air density decreases, reducing the drag force. Therefore, a falling body can accelerate more rapidly before reaching terminal velocity. For example, at 35,000 feet, the air density is much lower, so terminal velocity may be higher at that altitude than at sea level.
  • Body Position: A stretched-out position increases air resistance, prolonging the time it takes to reach terminal velocity. Conversely, a streamlined, head-down position reduces drag and results in a faster fall.

The Effects of Hypoxia

As I pointed out, falling from altitudes of 35,000 feet or higher poses additional dangers due to hypoxia. At this height, the air pressure is so low that oxygen saturation in the blood drops dramatically, leading to unconsciousness within 30 seconds. The passenger will lose consciousness before reaching lower altitudes where the air is breathable unless supplemental oxygen is available.

Critical Velocity and Energy on Impact

At terminal velocity, the human body falls at a constant speed due to the balance between gravitational pull and air resistance. The kinetic energy (KE) of the body at terminal velocity is given by:

KE= ½ mv2

For a person weighing 70 kg, falling at a terminal velocity of 56 m/s (200 km/h), the kinetic energy upon impact would be:

KE = ½ x 70 x 56 x 56 = 109,760Joules

This amount of energy is enough to cause fatal injuries upon impact.

In the hypothetical case of falling in a vacuum (with no air resistance), the final velocity would be much higher because there is no drag to slow down the body. The potential energy at 10,000 meters, converted to kinetic energy, would result in an impact energy of approximately 6,860,000 Joules, vastly more destructive than a fall with air resistance.

Conclusion: The Complex Dynamics of a Falling Human Body

The physics of a falling body involves a delicate balance between gravity and air resistance. As a person falls from a high altitude, the reduced air density allows for greater acceleration until terminal velocity is reached, at which point drag force equals the weight of the body. Variations in body position, altitude, air density, and other factors make it difficult to apply simple equations, and advanced computational models would be required for precise calculations. Ultimately, the outcome of such a fall is fatal unless a parachute or other intervention is available to slow the descent.

I have looked at the many variables that govern the motion of a falling body, emphasizing how science can approach even the most extreme situations. I tried not just look at the physics aspect of it only, but also what happens to the human body from the medical and physiological side so that the picture is more holistic

Taking both the physics and physiological aspects into account indeed provides a more comprehensive understanding. The interplay between the mechanical forces during a fall and how the human body reacts on a biological level enriches the discussion. By bridging these two areas, my work offers a balanced perspective that is accessible to a broader audience, including those from medical and scientific backgrounds. It’s fascinating to explore how extreme physical conditions, like high-altitude falls, impact the body's systems.

What I wrote are just from the theoretical aspect. We really need experimental data to substantiate. Of course, there is no way we can conduct such a study by pushing a person from an aircraft flying at 10,000 metre. That is a murder, not an ethical scientific study.  Ethical constraints prevent any kind of real-life experimentation in such extreme scenarios, and that limits us to theoretical analysis, historical cases, or simulations. Theoretical models, like those in physics and physiology, can give us some insight into the forces at play and their effects on the human body. But without experimental data, we're working with educated hypotheses rather than definitive answers. Maybe we can use animal models, but even that I think it is cruelty to animals, and I would not want that too. For the moment we can only hypothesize

Hypotheses and theoretical models are valuable tools for understanding complex phenomena, but ethical considerations are paramount. Using simulations or mathematical models is a practical approach to explore these scenarios while respecting both human and animal welfare.

There have been cases of accidental falls from great heights where individuals survived, and these rare events provide some observational data, but they remain exceptional and cannot be replicated in a controlled manner. In those cases, survivability often depends on factors like the person’s position during the fall, air resistance, the terrain they land on, and even random chance.

It's a challenge to balance theoretical knowledge with the practical limitations of ethics in scientific studies.

 


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