What-If 0135: "Digging Downward"

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bsaintg
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What-If 0135: "Digging Downward"

Postby bsaintg » Mon Apr 06, 2015 12:20 am UTC

http://what-if.xkcd.com/135/

If it were not april foolishness season, I would post something (only marginally interesting) about whether the limiting pressure of Oxygen being 218 feet of salt water at a limiting pressure of 1.6 atmospheres is a true limit. Many divers violate this "limit" with impunity. Fitness, water temperature, exertion, time, and other factors come into play. Of special note is the dreaded "dark nark" version of narcosis, which I've experienced myself (anecdote published elsewhere).

Nice revisions, man. Good on.

Kizarvexis
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Re: What-If 135: Digging Downward

Postby Kizarvexis » Mon Apr 06, 2015 1:26 am UTC

In Florida, depending on where you dug, the sand would cave in or you would hit the water table and drown. Either way, you would not get more than a couple hundred of feet at most.

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Re: What-If 135: Digging Downward

Postby keithl » Mon Apr 06, 2015 1:35 am UTC

I was thinking a something similar a few days ago. Not a foot per second with a shovel, but a machine-made vertical tunnel with strongest-available structural lining and water cooling. I did not know where to find the measured "ambient" temperature profile ... now I do.

Rock is a pretty good insulator, so you might not need a lot of cooling in the long term. This would make a lousy bring-your-own-water geothermal well. After temperature, the next unknown was shear fracture - the rock crushing and ejecting a wedge of rock sideways, putting extra stress on part of the structure. But as a wild guess, I would expect a very thick-walled and well-cooled carbon fiber epoxy structure (at 1GPa compression, 40% wall thickness) to survive down to 10 km or more.

Sadly, that is not deep enough for a transcontinental burrito tunnel

And I can see from my modified sig that the madness may be approaching.

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bsaintg
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Re: What-If 135: Digging Downward

Postby bsaintg » Mon Apr 06, 2015 1:46 am UTC

On the other hand, how deep would an open passage to surface (a well) have to be for the atmospheric pressure to be mesurably greater than 1 Bar? For example, the recently rescued (Andean?) miners were not at any risk of decompression sickness, no matter what the press said.

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Re: What-If 135: Digging Downward

Postby bachaddict » Mon Apr 06, 2015 1:48 am UTC

Please link to the What-If! I thought your post was trying to ask a question because I had no idea there was another what-if up.
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Sir Real
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Re: What-If 135: Digging Downward

Postby Sir Real » Mon Apr 06, 2015 5:01 am UTC

Hands up who thought "the downstairs neighbors"...

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Re: What-If 135: Digging Downward

Postby jozwa » Mon Apr 06, 2015 8:09 am UTC

Reminds me of the Donald Duсk comic where they travel down a hole to the center of the Eаrth. It's kind of a detailed what-if scenario in itself.

http://www.zocoi.com/books/177-scrooge- ... al-solvent

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Re: What-If 135: Digging Downward

Postby Rombobjörn » Mon Apr 06, 2015 12:57 pm UTC

Take care not to dig too deep in northwest Wyoming, so you don't awake the Yellowstone superbalrog.

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Re: What-If 135: Digging Downward

Postby Whizbang » Mon Apr 06, 2015 2:05 pm UTC

I call dibs on any mithril found.

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Re: What-If 135: Digging Downward

Postby SarahLawrence Scott » Mon Apr 06, 2015 2:35 pm UTC

It's not just Florida.

There aren't many places where the water table is more than a couple of hundred feet down.

So in the What-If scenario, drowning would likely kill you first, within a couple of minutes.

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Re: What-If 135: Digging Downward

Postby meithan » Mon Apr 06, 2015 4:24 pm UTC

bsaintg wrote:On the other hand, how deep would an open passage to surface (a well) have to be for the atmospheric pressure to be mesurably greater than 1 Bar? For example, the recently rescued (Andean?) miners were not at any risk of decompression sickness, no matter what the press said.


The barometric formula that gives you pressure as a function of altitude works with "negative altitudes" (i.e. depths) too:

Code: Select all

P(h) = P0 * exp(-h/H)

where P0 is atmospheric pressure at sea level (i.e. 1 atmosphere) and H is the scale height of our atmosphere, which is about 8.5 km.

So as you can see, air pressure increases exponentially if you go down a vertical well. At a depth of 1 km, it's up about 12% (this I think is on the order of the ambient pressure variations we typically encounter) and at about 5 km it's 1.8 atmospheres already (if 1.6 atmospheres is the limit at which O2 becomes toxic, then I think this is how Randall got that 5 km figure). At 10 km it's 3.2 atmospheres, probably universally lethal if breathing air directly.

Note: Of course, this formula is assuming constant temperature, and in this entry Randall is precisely exploring how temperature changes with depth, so we'd have to use a different, more general formula. But the results are similar: go down a few km and pressure will rise very quickly.

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Re: What-If 135: Going to give an elephant a nasty shock

Postby moody7277 » Mon Apr 06, 2015 10:08 pm UTC

The flames do a nice job of covering up what Randall thinks of the LOTR's ultimate question--whether a Balrog on a treadmill could take off.
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Re: What-If 135: Going to give an elephant a nasty shock

Postby Various Varieties » Tue Apr 07, 2015 11:06 am UTC

What use would Balrogs have for wings if they're buried underground!?

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Re: What-If 135: "Digging Downward"

Postby mathmannix » Tue Apr 07, 2015 7:00 pm UTC

Speaking of Balrogs... I really hopeses "Southern Methodist University Geothermal Lab" pronounces itself "Sméagol." (Hey, autocorrect added the diacritic, cool!) (And that SMU is pronounced "smoo", for that matter.)

Edit: OK, so looking at the maps from SMUGL, the 3.5-, 6.5-, and 10-km ones, it seems obvious that there is a rather strong correlation between the temperature at a given depth (according to the map) and surface elevation above sea level. You've got the rocky mountains, the Appalachian Mountains (in West Virginia especially), the central valley of California. It doesn't explain the Texas-Louisiana hot belt, but there's also probably something with latitude going on there. Anyway, it appears to me that the maps are not 3.5 km (etc.) below the surface, but below sea level, the difference of which is a kilometer or two out west.

Edit2: heh, many.lots (typed as the value of 7/2)
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Re: What-If 135: Going to give an elephant a nasty shock

Postby zjxs » Tue Apr 07, 2015 10:33 pm UTC

It really does depend on where you're digging, and the season.

{{citations needed}}

It's quite possible that before they reached the water-table heat stroke would kill this person, within several minutes. As exercise reaches 100% of aerobic capacity, muscle temperatures reach 41C. The person would be sweating at a very high rate. However, even in very cold conditions, the chemical effort exerted by digging at 1ft/s would raise the core temperature massively. This would be more than the body's capacity for heat loss. The brain's temperature would be too high and they would suffer catastrophic shutdown.

If this was performed on the top of Mt Everest, or anywhere else where there is several hundred feet above the water table and very cold temperatures, they may have a chance. Maybe. If they dug in Antarctica the ice would remain solid, even with the heat produced by digging.

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Re: What-If 135: Digging Downward

Postby kodiac » Thu Apr 09, 2015 4:57 am UTC

I thought there was impenetrable bedrock around 63 to 64 metres below sea level. :)
There's always a danger of digging into a lava lake or monster-filled cave, but at least death-by-creeper is quick.

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Re: What-If 135: Digging Downward

Postby LeChiffre » Thu Apr 09, 2015 2:51 pm UTC

When would the walls of the hole collapse?

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Re: What-If 135: Digging Downward

Postby Gavriel » Thu Apr 16, 2015 3:56 am UTC

meithan wrote:
bsaintg wrote:On the other hand, how deep would an open passage to surface (a well) have to be for the atmospheric pressure to be mesurably greater than 1 Bar? For example, the recently rescued (Andean?) miners were not at any risk of decompression sickness, no matter what the press said.

The barometric formula that gives you pressure as a function of altitude works with "negative altitudes" (i.e. depths) too:
...
So as you can see, air pressure increases exponentially if you go down a vertical well. At a depth of 1 km, it's up about 12% (this I think is on the order of the ambient pressure variations we typically encounter) and at about 5 km it's 1.8 atmospheres already (if 1.6 atmospheres is the limit at which O2 becomes toxic, then I think this is how Randall got that 5 km figure). At 10 km it's 3.2 atmospheres, probably universally lethal if breathing air directly.

I think Randall got this wrong.
The 1.6 atm toxic level is the O2 partial pressure, which is 8 times the sea-level normal 02 partial pressure of 0.2 atm.
To get 8 times the air pressure you would have to dig 35 km down.
But for sure a Balrog would have gotten you by then.

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Re: What-If 135: Going to give an elephant a nasty shock

Postby Quizatzhaderac » Wed Apr 22, 2015 5:36 pm UTC

Various Varieties wrote:What use would Balrogs have for wings if they're buried underground!?
The same reason that deep crows and Greyon does: the Earth is hollow.
The thing about recursion problems is that they tend to contain other recursion problems.


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