VivisepultureJanuary 4, 2011 3:06 AM   Subscribe

Could a person survive for 1.5 hours in a casket, buried ~0.5-1m in desert sand?

In the 2010 movie Buried, a man is buried alive in Iraq (plot).
The estimated depth is less than 2m as he still has good quality cellphone reception, can hear the sound of a nearby mosque and the wooden casket doesn't collapse. The casket is deep enough to be filled completely once the top boards collapse; without light shining through. It appears to be possible to (barely) survive for 60 minutes in an airtight casket (Mythbusters, calculation). However, the casket used in buried is not airtight; there is a hole big enough for a snake to crawl trough and smaller gaps between the boards.

I'm wondering if diffusion of oxygen through the soil of loose sand would allow a person to survive longer and allow for additional activities and "excitement". Is there data on the O2 gradient in a soil of loose sand? How to interpret this data; would this O2 be available (through diffusion?) in a casket through the gaps of the casket-boards? At which depth could the diffusion of oxygen sustain one person for longer periods?

Bonus: What would be the influence of zippo/lighter and/or a small aclohol fire on the available oxygen?

posted by Akeem to Science & Nature (14 answers total) 4 users marked this as a favorite

Best answer: I would expect the amount of additional oxygen gained through sand to be equal to or less than the amount gained through snow when you're covered by an avalanche. Here is a chart detailing the survival times of a sample of 422 avalanche fatalities in Europe. (Staying Alive in Avalanche Terrain by Bruce Tremper, p. 11)

So I would think that the total survival time would be the survival duration in the airtight casket plus some fraction of the survival duration of avalanche victims who probably had a pocket of air in that graph. Just guesstimating it looks to me like 1.5 hours isn't impossible if you're extremely lucky (big casket, soil so loose that soil-plus-the-casket-wall is at or very near the permeability of snow, below-average consumption of oxygen by the individual) but that the vast majority of people put in this situation would die.

(One other thought - I would expect the kind of person who would carry a lighter to be a smoker and thus have less efficient lungs than average.)
posted by XMLicious at 3:37 AM on January 4, 2011

The 60-minute figure is a back-of-the-envelope calculation based on average oxygen consumption and coffin size; it's a rule of thumb, but not an absolute maximum survival time. If you performed the ghastly experiment of burying many people alive, you would find that the actual survival time distribution is a curve centered around 60, but with outliers that live for considerably longer.

Add to this the fact that not everybody breathes the same; for example, mountain climber Ed Viesturs’ physique "makes him extraordinary gifted. Tests have shown that his lung capacity is up to 40 percent greater, and his blood is able to pick up oxygen from his lungs faster than the average person.", and it's possible but unlikely that someone could live for 90 minutes even in an air-tight coffin.
posted by qxntpqbbbqxl at 4:30 AM on January 4, 2011

I'm not a soil scientist, but I would be a paycheck that there is essentially no free oxygen available in or through 2 meters of even loosely-packed soil. I think whatever you start out with in the casket is what you've got.
posted by facetious at 5:07 AM on January 4, 2011 [2 favorites]

That avalanche book, though, says that most people died of rebreathing CO2, not lack of oxygen. Can't some kinds of soil absorb CO2?
posted by mskyle at 5:15 AM on January 4, 2011

Man, we need science. My non-scientific guess is that oxygen diffusion and CO2 uptake by topsoil work at a rate that makes sense for plant metabolism, not for human respiration.
posted by facetious at 5:24 AM on January 4, 2011

Best answer: Working out how much oxygen diffuses through the soil would determine completely on the type of soil (packing, grain size, etc.). If you want to give it a go, look up Fick's law (you can skip ahead to the one-dimensional solution), but the material properties will be difficult. I found values ranging from 0.01 cm2/s to 10E-6 cm2/s (see here, I did not check if this is a good source).

However, diffusion is such a inefficient process at large scales that you would have to survive with the oxygen in the cask.
posted by swordfishtrombones at 6:41 AM on January 4, 2011

Best answer: I did some cipherin' on this (literally on the back of an envelope!) and this is what I came up with:

Assuming he was in an standard sized casket (not a six-sided coffin as seen in vampire movies and westerns) and the dimensions I found on the web (84x24x23 inches) are interior dimensions, a coffin has 54,096 cubic inches, or 886 L of volume. People are roughly the same density as water (1kg/L) so a 70 kg person would take up roughly 70 L, leaving 816 L of air to breathe. This air would be 21% oxygen so there is 171 L oxygen in the casket. Dividing by a reasonable oxygen consumption rate of 300 ml/minute, that gives a maximum of 571 minutes of oxygen in the casket. Of course as the partial pressure drops oxygen extraction becomes more difficult, and the useful amount of oxygen is a good bit less than this theoretical maximum, but as mentioned above carbon dioxide becomes a problem way before that so for the sake of this question, there is plenty of oxygen.

Now for carbon dioxide. Assuming the person had a normal diet, his respiratory quotient is about 0.8, meaning he produces 0.8 ml of carbon dioxide for every ml of oxygen he consumes, or about 240 ml/minute. People vary in their responses to carbon dioxide and with medical support can survive amazingly high levels in their blood, but in this scenario, a lower limit of 5% for toxicity seems reasonable. Plugging the 240 ml/min number into 816 L total volume of air, I get 171 minutes to get to 5% CO2 in the casket.

There are a number of factors that can change this; the 171 number is pretty much an upper limit. The person might be larger or smaller than 70 kg. If the person is agitated their metabolic rate would go up and survival time go down; their diet would affect the respiratory quotient and thus their CO2 production and survival time. The atmospheric pressure also matters; for some of the numbers I gave what really matters in terms of physiology is not the percentage of a gas, but its partial pressure. Unless they were in a hyperbaric chamber or at the top of a tall mountain, that would make relatively little difference, though. So according to my calculations, the scenario is certainly possible given my assumptions, although in the real world it might not work out so well (primarily due to agitation on the part of the victim).
posted by TedW at 7:05 AM on January 4, 2011 [2 favorites]

Oh, and my answer assumes no diffusion through sand/soil; construction workers and others suffocate very quickly when buried alive and I think it is safe to assume no air exchange by that mechanism. I will leave calculating the effect of a fire to others for now, although if no one steps up to the plate I may hae a go at it later.
posted by TedW at 7:09 AM on January 4, 2011

construction workers and others suffocate very quickly when buried alive

I'd bet a contributing factor would be being physically unable to breathe due to the soil crushing your chest and stomach.
posted by electroboy at 7:43 AM on January 4, 2011

Response by poster:
Oh, and my answer assumes no diffusion through sand/soil
Am I wrong to think there would be enough diffusion of CO2 between a 5% saturated casket and outside air with 0.04% CO2 if they are separated with 1cm of dry, porous sand (grain size 0.06mm-2mm) to keep the CO2 levels below 5%? What about 5cm of sand? 20cm?

Would a bigger surface area help? Could the entire 5m² surface area of the casket be used, only the upper 1.5m² part or only the 20cm² surface area of the gaps between the boards? My thinking is that fast diffusion in the (relatively short) neighborhood of the gaps expands the usable surface area, but the lower part of the casket can be safely neglected as diffusion slows down considerably though 60 cm of depth, the height of a casket. Just a feeling though.

diffusion is such a inefficient process at large scales
Could you elaborate?
posted by Akeem at 8:34 AM on January 4, 2011

I don't know anything specific about the diffusion rates of CO2 through sand, but I don't think this situation is comparable to being buried in an avalanche. Bear in mind that avalanche victims very often have little to no space between their face and the snow. The result is that moisture in their breath condenses and freezes in the surrounding snow, causing a layer of ice to form, effectively blocking all diffusion of CO2 away from the face (this is called an ice mask). Avalanche victims who avoid the formation of an ice mask (e.g. if they manage to make some space in front of their face before the snow becomes too hard to move) can survive for much longer (hours even) than victims who don't. This situation is not at all analogous to a casket.
posted by ssg at 10:51 AM on January 4, 2011

Could you elaborate?

First of all, sorry for the appalling spelling and grammar in my earlier post - I was doing way too much at the same time.

Diffusion is a random process: molecules (or heat, etc.) are mixed by the random walk of molecules. It is "free", it does not require work. But as it is random, the chances that molecules go in the direction that you want them to go are small. So statistically speaking, the further away you go (i.e. the deeper the cask is), the less likely it is that molecules make it from the surface to the cask. Molecules go anywhere, and end up somewhere in a (hemi-)spherical zone that increases in size with time. As an alternative illustration to illustrate this lack of directionality: if you start with a pawn at the center of a chess board and make one random step in any direction, each of the neighboring squares on the board has an 1/8 chance to receive the pawn. However, if you would now allow e.g. 5 steps, the chances of a particular square at 5 squares from the center to receive the pawn are very small (I leave out the mathematics, as I am way too tired). The latter would be what I referred to as "inefficient at large scales"

This means that you can rely on diffusion for short distances (which also have a high spatial gradient, if you want to interpret it in Fick's law terms that relates fluxes to driving forces). For larger distances, you usually want some kind of convection to assist you (i.e. a flow, which is a much more efficient transport mechanism, but this one requires work). So two neighboring cells, for instance, can rely on diffusion. Two cells in your body separated by a meter or so can wait until the end of the universe before they can communicate with each other by means of diffusion only.
posted by swordfishtrombones at 2:45 PM on January 4, 2011

Without meaning to detract from the scientific approach too much, did anyone notice how much he used the zippo in the film? It's almost constantly on. Comparing a candle to the size of flame from a zippo, I know that if you put an average sized coffee jar over said candle it'd go out in a matter of seconds. A burning zippo would use a lot of oxygen, and create a lot of toxic fumes in an enclosed space.
posted by dougrayrankin at 2:56 PM on January 4, 2011 [1 favorite]

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