CMC fnord!
A big bag of foam peanuts can of course protect you from a very high fall. You could even do it with the peanuts staying on the ground-- That’s not too different from what stuntmen use to jump off of tall buildings. If you’re surrounded by the peanuts so they slow down your terminal velocity, so much the better.
And yes, all of that energy is going to have to go to heat. But some of that heat is going to be dissipated into the surrounding air, and some is going to be absorbed by the peanuts. Just because there’s a lot of heat involved doesn’t mean it’s going to cook you.
Tomatoes and cucumbers? 
So what is the correct answer here? Are you dead or nor not in a big ball of water?
The fruit is puréed - the entire internal structure is broken down into liquid goop by the shock wave. But the outer skin doesn’t rupture. Assume the same fate for your internal organs.
But, as I wrote - and even in the XKCD example - the water drop hits too slowly to generate a shock wave. It does however produce a pressure wave that could cause harm. Calculating what the peak pressure would be would not be trivial.
A lot would depend on the heigth, but under any given circumstances, I sure would rather jump into a big pool of water than onto rock or concrete. Wouldn’t you?
I imagine bringing the water with me instead of having it sitting there beneath me wouldn’t make much of a difference…
Since we’re dealing with hydrostatic pressure, you wouldn’t be crushed to death in the same manner as you would if a concrete slab fell on top of you. Your body would be subjected to enormous pressure, but that pressure would be fairly uniform over your entire body
The problem that I see would be air spaces in your respiratory tract, ears, and gut. sudden compression from ~14.7 psi to hundreds of psi would result in a huge temperature increase. This is, afterall, how diesel engines create temperatures high enough to ignite fuel. Each of those pockets of gas would reach a very high temperature. The squeezing/heating of air pockets in your gut and ears would result in painful burns, but the burns in your lungs would wreck the alveoli, and you’d soon die of asphyxiation. A fall of 500 feet is enough to generate temperatures as high as 700F.
Anecdata time: in a college physics lab we were trying to time the fall of a steel ball bearing from a known height (this was to demonstrate problems with measurement error, cause it’s very hard to do ‘by eye’). We did this by dropping the ball out of a window onto the lawn. Looking out the window, it was hard to see when the ball hit the ground. I had the idea of putting my down jacket on the ground, with the notion that the jacket would twitch when the ball hit it, making the contact easier to see. We did this for three or four drops, and it seemed to work well. When I went out to pick up the coat, I found that the impacts had melted holes in the synthetic material of the coat - even more impressive, they had actually melted and fused the inside and outside layers together, so my coat now had a number of grommet like sealed holes punched in it, and didn’t leak any down. This was for a fall from a third story window, with all the energy focused on a small point of contact.
If Cecil and Randall keep going, we will be able to answer all SDMB General Questions with links to SD columns and What-ifs.
I saw that before posting. It’s positing a 600 million ton sphere of water a kilometer across. Much larger than I had in mind, though maybe it doesn’t matter. I’d think smaller would be better since the water below you would have somewhere to go as opposed to be blocked by hundreds of feet of more water.
That was my optimistic logic in the OP. You’re a physicist of some stripe, right? Most people seem to agree the pressure wave would kill you. Do you agree?
People have survived falling out of airplanes. Do you think the water sphere idea would be about the same risk, or even more lethal?
I guess if you’re a falling wizard you should poof in some big time airbags, like the kind used in the Mars probes.
Given that fact, it’s not going to make any difference if you fall into the water, or hit the ground surrounded by the water.
People have survived jumping off the Golden Gate Bridge, which is 220 feet high, although not commonly, whereas I am not aware of anyone who has fallen 220 feet onto flat ground and lived. There are freak cases of falling out of airplanes from thousands of feet, but they landed on slanting mountainsides with cushioning trees and such. Let’s assume landing on a flat surface, either of dirt or water, and say arbitrarily that 250 feet is the maximum one can fall into water and live. Ergo, falling at the center of a raindrop, of whatever size, is going to cushion your landing as much as falling into a pool of water of the same depth as the radius of the raindrop. So ISTM that “the height from which you are going to die if you hit earth” = “the height from you are going to die if you hit water” + 250 feet.
It isn’t a question of the water having someplace to go - it can’t move fast enough to go there even if it had the room. Thus it has to compress, and water doesn’t compress easily - not as easily (so to speak) as the human body.
On a related note, I seem to remember an emergency room doctor saying that four stories is the 50/50 for falls - if you fall from the fifith floor or above, you don’t live, most of the time.
When I was in college, someone jumped off the top of a ten story building and landed on concrete. He moved a little after he landed, but not for long. He was pre-med and had gotten a C on a chemistry exam.
Regards,
Shodan
The human body is made mostly of liquids and solids, which are pretty much as incompressible as water. The problem with falling through the air and hitting a body of water is that the force is all applied to the down-facing surfaces of your body, and zero force is applied to the sideways-facing surfaces of your body. The result is that large uniaxial compressive and shear stresses are generated in your body tissues, stresses that are beyond the strengths of those tissues.
If you are cocooned in a ball of water such that the water decelerates along with you, then the water applies pressure to the sides of your body as well as to the bottom. You experience something close to hydrostatic pressure for as long as the deceleration continues. Hydrostatic compression is not the same as uniaxial compression: the strength of your body’s tissues is not a factor here. If pressures rise to ridiculous levels there may be momentary effects on body chemistry (ISTR some proteins behave differently at very high pressures), but one would not expect physical damage to the body due to mechanical stress.
But your lungs would be toasted.
What exactly are you referring to with the last sentence?
Anyway, I don’t think this compressive heating is necessarily the biggest issue. Sure if you compress all the air in your ear it will heat up, but mass-wise there’s not much air there. A fraction of a gram of gas --even really hot gas-- won’t give you much of a burn. A very tiny patch of skin might be affected, but it’s not going to do third degree burns over the entire ear canal.
Water falling from a height of 500 feet will develop a pressure, at impact, sufficient to adiabatically raise the temperature of an air pocket from 70F to 700F.
700F is pretty dang hot. Fire pistons don’t get quite this hot.
If it happened slowly, then the heat would have time to dissipate into tissues, cooling the air down before an injury could occur. But in an impact event, it’s going to happen pretty fast, sorta like that fire piston. So you’ll get really high temperatures that damage the surface layers of tissue before enough heat is dissipated to cool things down. As you’ve noted, it this won’t do much damage to your ears or gut, but that thin layer of skin in your lungs is all-important. Damage that, and you lose the ability to oxygenate your blood.
I think that, for any given height, the fall encased in water will be at least as survivable as the naked fall, and if the naked fall has nonzero survivability, the survivability encased in water will be strictly greater. I do not take a position on whether there is a height sufficient that the water-encased fall will be lethal. I’m a physicist, which means I can calculate things like the speed the water will be traveling, and if I look up a few details, the maximum pressure that would be generated. But I’m not an anatomist, a physiologist, or a physician, and so I lack sufficient knowledge to say what effects those pressures would have on the human body.
Too subtle? I was trying to balance the over the top response from pizzaguy.
700F is very hot, but the issue isn’t temperature, it’s heat. A very small amount of stuff doesn’t have much heat in it, even if it’s very very hot.
If I did my rough calculations right, the whole six liters of air in an person’s lungs has about the same heat capacity as 1/3 teaspoon of water (assuming dry air).
Yeah, 1/3 teaspoon of 700F water all in one place could damage some tissue, but it’s not enough to destroy the entire lungs. And of course, it won’t be all in one place; that heat will be spread over a big area of the lungs, probably doing no damage at all.
And of course, if your lungs have been squeezed down sufficiently to heat the air to 700F, I think you’re going to have much bigger problems than very slight extra amounts of heat in your lungs…
The reason water would help you is the same reason cushioning helps you: it lengthens the deceleration process, which means less energy is being applied to your body at any given moment.
The Space Shuttle (when it was in service) entered the atmosphere at over 10x the speed of sound (Cite), but because it spread it’s deceleration over 30 minutes (and a few thousand miles) was able to touch down without killing it’s crew
Are you sure about that ? Wouldn’t plastic deformation or breaking of the peanuts account for some of the energy ?
I am not a physicist but an engineer - and in my experience with crushing minerals (or rocks) with impactors - a significant amount of energy shows up as heat but not an insignificant amount is related to the surface area being created due to the crushing. We used empirical formulas to associate the surface area before and after grinding/crushing operations (function of plastic deformation) to calculate grinding/crushing power requirements.
God forgive me, but that made me think of our great grandfathers and theirs depth charging each other.