If you fell in a tube through the earth, would you get the bends (on the upswing) or otherwise have any other ill effects from the massive pressure changes your body would be going through?
Original classic column here:
http://www.straightdope.com/classics/a1_165.html
Assuming the heat doesn’t kill you, and assuming you are falling through some sort of medium and not an evacuated tube (since you asked about pressure changes) and that the tube is large enough (or you can maintain sufficient stability) for you to complete the traverse without drifting into one of the walls and being killed on impact, and assuming the narcosis and judgement impairment from increased nitrogen pressure (assuming the medium in the tube is air) doesn’t cause you to do something stupid (like track into one of the tube walls), and assuming that the toxicity from the increased oxygen concentration doesn’t kill you (maximum typical tolerances in a gas space are somewhere in the range of 2 to 3 ATA), and assuming the rapid compression doesn’t cause high pressure nervous syndrome (HPNS), indirectly killing you, my guess is something else would probably kill you well before decompression illness has a chance.
well, since you’d have to fall (and rise?) 6000km on each leg of the journey at terminal velocity, I’d think the times would be sufficient to allow for equilibration of nitrogen partial pressures
This is as good a thread as any to clear up a misconception I must have. I was under the impression that you got the bends from breathing compressed air. True? That would explain how freedivers are able to descend to 500+ ft and rocket back to the surface with no ill effects (usually).
If so, that would mean your Earth tube traveller need not worry about the bends anyway.
this had me laughing for a while 
I guess the bends is the least of Mr. Freefall’s worries.
I guess really my question was if any deep enough decent could cause the bends (i.e. people who worked on the Brooklyn Bridge died from the bends, and I thought people who worked in diamond minds had to decompress as well?)
err… mines.
You have to descend deep enough to get sufficient dissolved gases in your system. You actually don’t have to go very deep if you’re under pressure for a sufficiently long time.
But it’s the ascent that gets you. If it’s rapid enough, the dissolved gases come out of solution and can cause severe pain in the joints and elsewhere. If the decrease in pressure is slow enough, things reach equilibrium without strange problems.
In the case of falling through the center of the earth in air, the drag of the air will limit your velocity and thus your ability to undergo a decrease in pressure. If we oversimplify things and assume you stay at 120mph all the way down, you’re not going to overshoot the center by much, and so will have to undergo only a very moderate decrease in pressure.
(As has been noted, you will have plenty of other things to worry about.)
Let’s suppose—
An insulated hole approximately 10 miles in diameter perfectly straight and going through the center of the Earth. Assume atmospheric pressure since open to atmosphere on both ends.
A person is dropped in the center of that hole.
Explain the bends and other problems that might occur.
Atmospheric pressure depends on your altitude. Who knows how to calculate what the atmospheric pressure would be at the center of the hole described by disponibilite?
I don’t know how to calculate it, however, I can tell you the pressure will not rise quite as expected, because the deeper you go beneath the Earth’s surface, the lower the gravitational force becomes, because the mass of the part of the planet “above” you begins to cancel out some of the gravity from the part “below” you, until, at the center the force of gravity is zero. I suspect the pressure will rise to a point with the rate of rise tapering off, then it will level off and not rise any further as you go deeper towards the center.
Decompression illness (the bends) arises when inert gases dissolved in the body tissues are brought out of solution by a decrease in ambient pressure. When a diver descends (or a deep mine worker, for that matter), the atmospheric pressure increases, correspondingly increasing the partial pressures of the component gases in the breathing media. When breathing air, the sea level partial pressures are 0.791 ATA for nitrogen, and 0.209 ATA for oxygen. These same partial pressures exist in the body tissues under the same conditions, and everything is in equilibrium. Upon descent, the partial pressure of both gases in the surrounding air is suddenly higher than that dissolved in the body tissues, so “ongassing” begins, and the level of these gases dissolved in the tissues increases accordingly. This is a rate limited process, however. Different tissues ongas and offgas at different rates, and also exhibit different degrees of inert gas solubility within them. For example, this happens quite quickly in blood, slowly in bone marrow, a lot of gas is dissolved in fatty tissue, not so much in lean muscle, etc. Saturation (equilibrium) is only achieved when enough time has passed at depth to allow all of the tissues to come to equilibrium. The bends, caisson disease, and decompression sickness are all the same thing. As you ascend, the tissues become supersaturated (or at least one or more does - the slowest ones may still be trying to catch up if you are not yet fully saturated) with this dissolved gas as the ambient pressure lessens, and the gas comes out of solution into bubble form. Oxygen, thankfully, is metabolized, and we usually don’t need to worry about oxygen bends. Inert gases such as the nitrogen in the air, or helium (often used when deep diving) need to be eliminated. Ordinarily this is done as the bubbles enter the bloodstream and are removed by the lungs (exchanged through respiration). Unfortunately, this only works effectively if the bubbles are below a certain critical size, and if the rate of offgassing is slow enough for the lung filter to keep up. This is why divers employ decompression stops - the deco time allows the physiological processes to come closer to equilibrium at the stop depth before proceeding, keeping the amount of supersaturation of gases within the body tissues within tolerable limits.
In your tube-through-the-earth example, the air in the tube, under the influence of gravity, will be at a higher pressure than the surface air. I don’t know how to calculate that pressure (perhaps an atmospheric science buff could step in here?), but the only way you could get “the bends” in this scenario is if the rate of ascent (and hence, decrease in ambient pressure) was great enough that the tolerable dissolved gas supersaturation in one or more body tissues was exceeded. This necessarily implies that either the pressure was great enough, or the exposure time great enough (so rate of fall is a factor) to create that level of saturation prior to passing the center and rising to a height high enough that tolerable supersaturation is exceeded.
If you are falling in air, you are going to reach a terminal velocity beyond which you will not accelerate (apart from variances in the fall rate due to your size and shape, and your body position while falling). Density of the air also plays a role, and in fact your speed will decrease as you encounter denser air
-WHOOPS- it just occurred to me that air, under the influence of gravity, will behave according to that influence, and since gravity is a function of distribution of mass, it actually decreases as you approach the center of the earth, where you would, in effect, experience weightlessness. What this means for the air pressure I’m not sure, since the pressure is dependent on the weight of the column of air above any particular point - I guess all that implies is that the rate of pressure increase will not be precisely linear with depth - whatever, I digress…
The point is that you quite likely wouldn’t be doing much more than 200 mph as you pass the center, and would then come to a halt a ways beyond that, as gravity pulled you back in, and you would oscillate back and forth across the center point until drag brought you to a stop at dead center. Also, the effect of ambient pressure change on the bubble size is proportional to absolute pressure. Closer to sea level, a given change in depth will result in a greater change in bubble size than if you changed depth by the same amount at a deeper depth. As a diver, you can ascend faster while deeper, but must slow the rate down as you approach the surface. Consequently, I wouldn’t expect the overshoot as you fly past the center of the earth to be significant, but than it depends on the absolute pressure, which as I already admitted I don’t know how to calculate for air.
Clear as mud?
Not true. Freediving can still cause DCS, although it is a bit more difficult, requiring either extreme depth and ascent rate, or cumulative exposure over a number of dives. In general, the offgassing rate for any tissue is slower than its ongassing rate (which makes sense, since when ongassing, all that is happening is that gas is being dissolved, whereas when offgassing, a bubble is growing and then being shrunk as part of it goes back to solution, but surface tension is also a rate limiter). The fact that you have only a single breath of air in the lungs during a freedive changes only the available mass, not the concentration.
I can’t speak for diamond mines, but the people who work on the pylons from bridges have to be in what’s known as a cason (hence the alternate term 'cason worker’s disease). A cason must be pressurized above atmospheric pressure so that moisture doesn’t seep in as they work. In this case it isn’t the depth but the pressure.
The air pressure in a caisson is usually the same or very slightly higher than the water pressure at that depth. A major function of pressurizing is to keep out water, if you pressurized the air to more than the depth pressure, the air (being much less viscous than water) would literally gush out throught the mud at the open bottom of the caisson. I doubt that it would even be practical to pressurize much past the (water) depth pressure. The higher the pressure, the larger the volume of escaping air that would need to be replaced. Since pressure pumps trade volume for pressure, it’s very difficult to pump a high volume at high pressure
Think of a drinking straw. If you insert it into a beverage and exert a small air pressure, you can force all the liquid out of the straw. If you try to exert more pressure, you will blow bubbles, but the pressure at the deep end of the straw will be remain very slightly higher than the depth pressure (due to the viscosity and surface tension of the beverage). You’d have to blow many, many times harder to get the pressure to, say, twice the depth pressure, and even if you succeeded, you’d exhaust your lung capacity almost instantly, even though your lungs have far more volume than the straw.
As a side note, the topic of atmospheric pressure and drag in a through-Earth hole was discussed in this thread, which was itself apropos of this column of Cecil’s.
Well, let’s see. Assuming Earth’s density is constant (which it’s not, but close enough for estimation), gravitational acceleration is linearly proportional to radial distance; in other words, local gravity g[sub]loc[/sub] = g*(1 - x/R), where
g = gravitational accel at the surface = 9.81 m/s[sup]2[/sup]
R = Earth’s radius = 6,378,000 m
x = distance below surface
At any point along the tunnel, air pressure should be equal to the weight of the air above it; in other words P[sub]loc[/sub] = P[sub]atm[/sub] + INT[sub]0->x/sub, where
[symbol]r[/symbol] = air density ([symbol]r[/symbol][sub]atm[/sub] = 1.275 kg/m[sup]3[/sup])
P[sub]atm[/sub] = 100,000
Of course, P[sub]loc[/sub], [symbol]r[/symbol][sub]loc[/sub], and g[sub]loc[/sub] are all functions of x. For an ideal gas, the density and pressure should just scale with each other, so if you know pressure, you can calculate density. Unfortunately, that makes for a nasty integral.
So I plugged that into a spreadsheet, just summing for each kilometer rather than integrating. I get about 3.2 atmospheres of pressure at 10 km depth, which doesn’t seem unreasonable. However, because the pressure increases, the local density also increases, which means the pressure increases even more quickly, etc. By the time I get to the center, I get an air pressure of 2.5 E166 atmospheres (yes, 166 decimal places). I, um, suspect that this is beyond the range where ideal gas law assumptions are reasonable.
This seems like a pretty straightforward calculation, so I’m reasonably confident I’ve done it correctly. Yet, the final answer is so enormously greater than my expectations (by, like, 164 orders of magnitude) that I hesitate to call it definitive.