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After seeing this answer claiming that displacing matter "In a very short time", "no matter whether the matter is solid, liquid, or gas" (even though he concludes that falling from a high altitude is fatal, independent of this).

I wondered why then is the jump itself not fatal, considering that there is a significant amount of "gas", that does need to be displaced before even hitting water.

Is it because there isn't enough mass per square inch to be fatal? And if so, at what speed would it be fatal? Or is there something else I or the guy who answered that question is missing?

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    $\begingroup$ it's not the fall that kills you; it's the sudden stop at the end. $\endgroup$
    – ratchet freak
    Apr 8, 2014 at 19:29
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    $\begingroup$ First paragraph lacks a relative clause "After seeing ..... (stuff in parentheses) ___ WHAT?" $\endgroup$
    – Kaz
    Apr 8, 2014 at 20:11
  • $\begingroup$ Shouldn't the tag experimental-physics be added here too like in the related "fatal" question? (see up-voted comment on question) $\endgroup$
    – Volker Siegel
    Apr 9, 2014 at 1:05
  • $\begingroup$ "Speed has never killed anyone, suddenly becoming stationary... That's what gets you." - Jeremy Clarkson $\endgroup$
    – aevitas
    Apr 9, 2014 at 8:31
  • $\begingroup$ The point you're asking about considers only the matter shovelled out of the way to let you move. That's not all there is to it, but it's enough to make a difference between air and water. Air is less dense than water. Therefore the mass of air that you're pushing out of the way to accommodate your body is less than the mass of water. In fact it's much, much less. $\endgroup$
    – Steve Jessop
    Apr 9, 2014 at 10:54

5 Answers 5

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It's not the falling that's fatal, it's the deceleration at the end that kills you. Something like water or concrete does this on a sub-meter distance (which requires extremely high forces). On the other hand a gas is much less dense, so it cannot decelerate a falling object nearly as quick.

Sometimes inflatable cushions are used as safety nets (think: stunts/someone jumping off a building scenario). If it is too inflated then the deceleration distance won't be great enough and it can still cause injury or even death.

It seems that a sudden deceleration of ~100g is fatal; that's about 80kN for an average male (80kg). We need the drag formula:

$F_d = \frac{1}{2}\rho v^2C_dA$.

Plugging in typical values:

$F_d = 80*10^3N$ as asserted above,

The density of air humans experience is typically $\rho = 1 \frac{kg}{m^3}$.

$A$, the frontal surface of a human seems to be hidden behind pay walls; let's go with $A = 0.5 m^2$

$C_d$, the drag coefficient, is not so straightforward, but we'll go with $1.3$ (man,ski jumper example given on the Wikipedia drag coefficient page).

$80*10^3N=\frac{1}{2}*1*v^2*1.3*0.5 $...

...results in a speed of about $500 m/s$, or 1800 km/h.

This does not mean that falling at that speed is lethal. This scenario assumes you suddenly transition form no resistance into dense air.

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    $\begingroup$ but if one were to jump from a vacuum, into a gas cloud could it be fatal? $\endgroup$
    – Math chiller
    Apr 8, 2014 at 15:17
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    $\begingroup$ no because there is no sudden transition, the gas cloud would disperse such that the transition from vacuum to dense gas would likely decelerate at a rate you could survive $\endgroup$
    – Jim
    Apr 8, 2014 at 16:29
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    $\begingroup$ @AaronNovstrup it does if you're Superman $\endgroup$
    – Jim
    Apr 8, 2014 at 18:37
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    $\begingroup$ @AaronNovstrup: Surprisingly, when objects enter an atmosphere at high speed most of the heating is due to compression of the air under the object, not due to friction from the air. $\endgroup$
    – Eric Lippert
    Apr 9, 2014 at 0:09
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    $\begingroup$ @Beta So hitting a stone wall is friction? Friction is the force resisting the sliding of two materials against each other, so on a reentry vehicle, the air rushing to the sides exchanges energy via friction, while the air in front of the vehicle does it through compression. Now both compressive heating and friction are due to electromagnetic forces, but you don't really want to do friction calculations based on first principles :)) $\endgroup$
    – Luaan
    Apr 9, 2014 at 8:07
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It depends what speed you are moving relative to the air (or water).

If you start a jump at zero velocity relative to the air, your speed will be limited to the terminal velocity of about 125 miles/hours (at least for the density of air near ground level).

An estimate of the fatal velocity relative to air is 300 miles/hour (again for the density of air near ground level), from this reference: http://www.cdc.gov/niosh/docket/archive/pdfs/NIOSH-125/125-ExplosionsandRefugeChambers.pdf

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  • $\begingroup$ The 300 mph limit from this study is not applicable to the questioner's case. The CDC study is about when "the human body may be thrown violently into objects and receive blunt force trauma". When that is avoided, here is the evidence of a person surviving a ~500 mph wind: youtu.be/IU4SDDNXuUA $\endgroup$
    – prash
    Apr 9, 2014 at 17:32
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I don't have exact statistics for any of this.

The fall is not what kills you, it is the sudden deceleration at the end. The only thing that can cause a change in speed is another force being applied to you. During the fall, the 2 forces of air resistance and gravity are acting on you constantly in opposite directions, with gravity causing more and more acceleration until you reach terminal velocity, at which the air resistance cancels the gravity out & you fall at the same speed the rest of the way.

The air you fall through, while offering resistance, lets you pass through it (almost) as easily as if you were falling through nothingness. However, the ground is not as much of a pushover; it does not let you pass through it as the molecules are too packed together. This means that, once you reach the ground, unless you break it & fall through the floor, you go from moving at tens or hundreds of miles (or km) per hour to essentially 0 in a second or 2. Because of inertia, your body does not want to slow down that fast, so it puts up a lot of resistance. What ends up happening is that some of your body continues falling while the rest of it has already stopped, and so your hands end up hitting the ground, too, your head ends up by your feet, and, if you were falling fast enough, your lungs end up hitting your kneecaps. You pretty much die by being squished to death.

The more tightly-packed the ground medium, the faster you will decelerate upon landing and the lower velocity you have to be at before you hit the ground to die. This is because a looser-packed medium lets you fall for a little longer before you stop moving, although it also means you can die before you stop moving, seemingly invalidating the premise of this answer that it's "not the fall that kills you". Even a split second of extra falling time could mean the difference between life & death. For water or lower-pressure ground, such as an airbag or loosely-packed dirt, you have to be moving at a much higher speed to die. Of course, this also depends on things like your height and how tightly-packed your insides are. A younger person would usually have to land at a higher speed to die.

Another note is that, under certain conditions not usually found on Earth, the fall can kill you before you hit the ground. If you have a sudden change in acceleration, such as going from a high-pressure air system to a sufficiently lower-pressure one or vice-versa, you could end up being squished & die. The change in speed, again, determines whether you die.

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If you were restrained, and subjected to a sufficiently powerful stream of air, it would be fatal. However, this does not happen during a jump, because you reach terminal velocity, which is typically somewhere between only 100 km/h and 200 km/h. Exposure to a wind of this velocity (which, let us say, consists of clean air that is free of debris such as sand particles) does not damage your body.

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The point you're asking about considers only the matter shovelled out of the way to let you move, ignoring the structure of the matter. That's not all there is to it, but it's enough to make a difference between air and water.

Air is less dense than water.

Therefore at a given speed the mass of air that you're pushing out of the way to accommodate your body is less than the mass of water. In fact it's much, much less. The density of air at STP is (very roughly) 1 kg per cubic meter. The density of water is very close to 1 (metric) tonne per cubic meter.

So the force of air on your body when falling through it at 50-100 m/s is much, much less than the force of water on your body when you impact it at the same speed. At terminal velocity the force of air on your body is equal to your weight. That's not harmful, but multiply by 1000 and you die.

If you were released under water and "fell" (floated) towards the surface, then you would travel much more slowly than you do in air. Partly because the difference in density between water and your body is much less than the difference in density between your body and air. Partly because water provides more resistance to your motion, which has to do with both density and the structure of water (structure affects viscosity).

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