Falling elevator filled with water

Greetings physics superhumans!

If an adult human person is floating in a free-falling elevator, sealed and filled completely with water (no air space), that is damaged on impact in normal elevator fashion; would they experience deadly force or would being immersed in water and destruction of the elevator somehow dissapate the collision energy?

For bounding parameters, I'd be interested in how the results differ if the elevator would fall from:

1. 10 meters
2. 25 meters
3. 50 meters

Parameters:

• It lands on the concrete floor of an elevator shaft
• Is made from stainless steel
• Weighs 1000 kg
• Contains a 70 kg human who can hold their breath for the duration
• Is completely filled with 2500 kg of 20 degree C water (elevator dimensions 1 m x 1 m x 2.5 m)
• For some reason the cable has vanished, and the elevator has no safety mechanisms that would halt or slow its fall
• Gravity accelleration is normal

I don't know if position in the elevator is relevant, or if the water pressure will increase at the end of the fall and crush them against the top of the elevator, crush the air in their lungs, etc. Please assume the human starts on the water-filled elevator floor and moves according to normal forces (whatever they would be in this scenario). Also, if the breath-hold is the critical factor in survival, the human starts with full lungs but may exhale on/before impact, but only at normal human rates.

Apologies if this is ill-defined, repeated, or poorly worded. I couldn't find a similar question online and I don't know what reasonable Google terms or the relevant factors are (I'm sure this has been answered previously at some point, probably in relation to futuristic vehicle crash resistance foam etc). It's based on a dream I had about being a superhero, who's only power was to fill and empty spaces with water instantly.

• That person's internal organs are NOT anchored by the water that he is floating in, and they would experience VERY high g forces. – David White Feb 4 at 20:35
• The 10 m fall is still 50 kph on impact I think, which definitely sounds uncomfortable. The reason I picked the distances was that falls from those heights supposedly have 50%, 10%, and 'lower' survival rates. I tried to see if the forces or practical situation would make things better or worse for our hero. – Andrew Feb 5 at 15:39

I think it is tempting to assume that the sudden deceleration at the bottom will cause damage regardless of the presence or absence of the water. I will argue against that assumption.

Modeling your body as a bag of water, and supposing the elevator cab does not rupture, there is no tendency for it to deform during impact--nothing physically sets it apart from the rest of the water, so it doesn't get slammed against the bottom or unduly stretched or compressed along any axis.

During the impact, the pressure increases rapidly. The high pressure isn't necessarily an issue--the human body can survive pressures of tens of atmospheres--but the suddenness of the increase is going to cause problems. You can say goodbye to your eardrums, and the abrupt collapse of your lungs won't feel good. It would be akin to being in the water near an exploding depth charge.

In short, you might die, but your corpse will look much more presentable than it would without the water.

If you want empirical verification of this, I suggest filling a Nalgene bottle with water, inserting an egg, and dropping it from increasing heights. I think you may find you can drop it out of a second story window without breaking the egg.

• I'm not sure the bag of water assumption is a very good model. G forces kill because the body is not accelerated uniformly like in a gravitational field. The elevator and water might be able to withstand high G's, but there's no way to transmit that massive force to your internal organs without something breaking. Bones will snap, arteries will tear, your brain will slam into your skull, organs will get rearranged. The only thing holding your organs in place is a bunch of meat, which doesn't perform great under high G's. – Nuclear Hoagie Feb 4 at 21:04
• @NuclearHoagie Organs are modeled as small bags of water inside the big bag of water. I maintain the g-forces are not generally a problem. If your body was an empty shell with a few organs floating around, you'd be right. But it's basically all made up of stuff that is very similar in density and compressibility to water. If your brain was really going to smash into your skull, it would mean the fluid between the two would have to go around to the other side of the brain. But it doesn't want to go that direction any more than anything else. So brain does not smash skull. – Ben51 Feb 4 at 21:11
• You're describing coup and countrecoup injuries, which are pretty common in car accidents or other concussive blows. Some object stops the skull, and then the skull stops the brain, resulting in a bruised brain - the brain is not locked in place by a fluid cushion. I don't see how the water makes this any different from a car crash or any other sudden stop - your explanation of why the internal organs will be OK actually doesn't reference anything outside the body. – Nuclear Hoagie Feb 5 at 14:05
• @ben51 I think this is what was throwing me off. If the water completely surrounds the person, and the person is a similar density, would it still be a question of G-force shear affecting different parts of the body at different times to create a deformation and thus damage; or because water isn't compressible, would it become a question of a shockwave/energy affecting the whole person at the same/similar time and it was a pressure event. This was why I mentioned the lungs originally, big old internal airspace issue. I'll try the egg thing when I get a chance ^^ – Andrew Feb 5 at 15:03
• @NuclearHoagie If your skull was perfectly stiff, allowing no deformation (it isn't) then it's true that the brain wouldn't care about the source of the force applied to the head as long as that force produced strictly linear acceleration (which, in the reference frame of the head, is experienced as a uniform body force). But that's not what generally happens in a car crash or when you get punched in the jaw: instead, the torque produces angular acceleration, which does cause the brain to move relative to the skull. – Ben51 Feb 5 at 16:11

During impact, there would be a sudden increase in the effective weight of the water above the man. This would cause a sudden increase in the water pressure which would collapse the lungs and probably drive air into the bloodstream. There would also be an increase in the pressure gradient. This would cause a sudden increase the buoyant force, which would be like landing on a hard surface, and would be likely to cause a fatal concussion.

• This is one thought experiment that we definitely don't want to try in the real world. – David White Feb 4 at 20:37
• Thanks for the answer! So to clarify, is the 'effective weight' a function of the velocity the system is travelling at, which allows it to exert more force on the other water at the bottom of the elevator, which has become stationary again? Or have I missed the point entirely here..? Also, if you could tell me a Google-able term for this effect to help my understanding I'd be very grateful! I'd like to understand more about the relevant forces involved, why they're damaging, how the energy moves, and where it goes/disappates. – Andrew Feb 5 at 15:57
• The effective weight depends on the acceleration which could be extreme during the impact at the bottom (but would zero during free fall). – R.W. Bird Feb 5 at 18:42

I don't think this will be particularly different from the usual case of an empty elevator in free fall. When the elevator hits the bottom of the shaft, the elevator and everything inside must come to a stop over the course of a fraction of a second. Whether or not the elevator is filled with water, the person inside will experience sudden and dramatic acceleration when it hits the floor (i.e. they will go splat). From a drop of 20m, the person is traveling at 72kph when they hit the floor, and 0kph very shortly thereafter. That's going to hurt no matter what, regardless of if the person is stopped by the elevator floor or a layer of water.

Even if there are buoyant forces due to pressure gradients when the box of water hits the floor, anything that moves the person toward the ceiling of the elevator will only increase the acceleration they're experiencing, making the collision even more deadly. You might get some interesting physiological effects from the pressure shockwave traveling upward through the water, but there's nothing here that makes the situation any more survivable than your typical falling elevator.

To use this superpower to survive, the hero needs to fill the elevator shaft at the very beginning of the fall, and empty it slowly to gently bring the floating elevator to the bottom. Stopping suddenly at the bottom is going to be bad news no matter what.

• Just to check (I'm pretty naive when it comes to actual physics calculations) is the equation you used for acceleration: in freefall is 9.8 m/s^2, starting at 0 m/s, – Andrew Feb 5 at 15:10
• @Andrew Yes, although there was an error in my math (the height should have been 20m, not 10m). After 2 seconds, the person is traveling at 20m/s, or an average speed of 10m/s over those 2 seconds. They fall 20m total in the 2 seconds. – Nuclear Hoagie Feb 5 at 15:17
• Ah, sorry for the partial message - I accidentally tapped return instead of shift return, but was plugging away at the formula, and came up with 2^0.5 s, and then re-did the calculations because I assumed I'd messed up, then just saw you had already responded to the comment! – Andrew Feb 5 at 15:31

The main damage here will be caused by the incompressibility of water. (Actually, the relative incompressibility of the water compared to the human body.) The effect would be somewhat similar to a human body entering water at a high speed - the incompressibility of water means it is like concrete.

In the case of the falling water-filled elevator, a shock wave would hit the human body from all directions and compress it. Since the human body has parts of various compressibilities (lungs are very compressible, fat and muscles are somewhat compressible, bones less and teeth quite incompressible), the soft organs would likely be very damaged: they take the brunt of the compression.

The advantage compared to falling to the hard ground is that the stopping is not sudden, and $$F_t = \frac{dp}{dt}$$ what means a smaller total force.

Once hitting the ground, the water buoyancy force acts on the human body at once $$F_b = \mu Vg$$. But there is also the drag force. It depends on the final velocity and also on the position of the man. It is like the impact of diving after jumping from a great height.

It helps if the man stays vertical, if he stays close to the roof, and if the elevator cabin is tall. Otherwise it is like jumping in a shallow swimming pool.

• Thanks for the answer! The final velocity from 10 meters of free-fall would be approximately 50 kph, and from 20 meters would be 72 kph - if those numbers are helpful? Would being in free-fall affect the buoyancy, as my understanding is that the water becomes weightless whilst in fall? Also, please could you help include the terms from your equations as I'm not sure which equations they're taken from. – Andrew Feb 5 at 16:31
• The final velocities are probably smaller. The air drag can not be neglected, mainly for a elevator hole. The record of height of diving is 59m, falling in water depth of 8m. About the buoyancy it is true: it will act only after fall, just as happens when a diver hit the water surface. – Claudio Saspinski Feb 5 at 18:22