I like those ideas for digging a perfectly level tunnel between two distant places ignoring the earth's curvature. You roll "down"and then "up" to travel without power.
Maybe if it was a maglev and a completely evacuated tube, but if you could do that you might as well do it on the surface which would be orders of magnitude easier and travel at whatever speed you want for hardly any energy input (as you'd get it back from regenerative breaking at the other end)
Is it really true that at -150m depth that the air pressure would be 20 atmospheres? It doesn't seem like it is likely, the air pressure at +150m is scarcely different from sea level.
I think the author is trying to have it both ways where you’re both in the tunnel yet experiencing a tunnel free environment. It’s the same with the heat.
I’d like to see a reckoning that takes the rotation of the earth into account, seeing what differences come of different terminal points (pole, equator, &c.). How quickly you get turned into a crayon against the sides of the tunnel, whether the tunnel actually needs to be curved to avoid this, whether the Coriolis effect matters, &c. My intuitions are probably wildly wrong.
I do wish posts like this would include their work. There are some highly suspect claims around air pressure. Also, it's almost certainly not okay to use a constant acceleration approximation for g in this case, and I have no idea what equations you'd use for air resistance in those really exotic conditions!
Another interesting effect is if the tunnel diameter is large enough, and air is allowed to fill the tunnel, then an arbitrarily large fraction of our atmosphere will now drain into the hole. This effect not only reduces barometric pressure at seal level, but there will be ongoing gas exchange between rock and air.
Last but not least, I'd be curious if the magnetic field flux is at all interesting/dangerous to you if you're falling through the molten iron core of a planet. It would also be pretty cool to use that magnetic field as propulsion.
This article should have started with the fact that the numbers in this are made up. 150 meters below the sea level won’t get you 20 atm of pressure. More importantly, there is a precise amount of time that you can calculate for how long it’ll take you to reach the center of the earth (I calculated it in undergrad years ago and don’t remember the precise answer but I believe it is on the order of 2 hours), assuming no friction. If there is no friction, you’ll overshoot the center and go clear to the other side of the earth in about 4 hours. More interestingly, you don’t need to go through the center: any section line through the sphere will give you the same exact travel time. In other words if you dig a tunnel from Chicago to Nee York and remove all air, then put a capsule on a maglev track inside it you can travel between the two cities “for free” as far as energy costs in roughly 4 hours. Assuming of course you can manage to dig such a tunnel and keep it serviced.
I love that section-tunnel insight! I'd never thought about that before but now that you mention it it's so simple, a really tasty little bit of symmetry.
After falling about 0.15 kilometers (0.002% of the way to earth's center), you encounter about 20 atmospheres of air pressure and die from hyperoxia.
This fool is mixing up atmospheric pressure and water pressure. If you're going to speak with authority on something maybe you should spend more than five seconds thinking about it.
After falling about 1.1 kilometers (0.02% of the way to earth's center), you encounter a temperature of about 320 Kelvin
No. The temperature at 1.1km is about 36c. Uncomfortable, but not fatal. Certainly not so instantly fatal you die before passing the 2km depth on your fall.
your dried up bones and remnants of flesh encounter a temperature of about 1200 Kelvin and are completely incinerated into dust.
Burning a bone to dust requires temperatures over 1100c. He is mistaking the temperature inside a crematorium for the temperature required to incinerate bone. 1200 kelvins, like a crematorium, will produce chunks of calcified bone, not "completely incinerated into dust".
TIL that incineration in a crematorium leaves chunks of bone (bone fragments) that are then ground into the ashes we're familiar with in a device called a cremulator.
I was honestly wondering if it was a parody or joke of some kind after that first sentence. This guy is apparently a doctor? I wonder what the thought process looks like for this guy, I get that people make mistakes but also it's obvious that 150m holes don't instagib people.
There are many mines which are much deeper than that. And even some natural formations... Statement like that leads to think that they don't know very much about the world in general.
The air drag is proportional to air pressure and the square of velocity. If we assume that the air pressure grows linearly with depth, we'll get the following equation for acceleration:
F/m = a = x'' = g - px - qx•x'•x'
Here g-px accounts for linear decrease of gravity, qx is the air pressure, and x'^2 is the square of velocity.
That's a tricky equation and even wolframlpha cant solve it.
Also, if you dig a tunnel between any two points A and B on the earth's surface and jump inside -assuming no friction and that the only force is gravity- the time from A to B is the same for any point A and B [1].
Spent many hours with this 2-volume book "Physics for Entertainment" by Ya Perelman as a kid, and now I'm motivated to go back and read it all over again!
A lot of these Russian science/math/fiction books were available at very low cost during the '80s in India.
It remains one of the best posts on that platform imho, and unlike this article, is actually correct in its assertions and descriptions (to the point that human knowledge can be certain).
One thing I think is missed from these kinds of back of the napkin calculations is all the bizarre thermodynamic side-effects you'd encounter if you were somehow able to drill an actual hole through the core without it collapsing. I imagine the convection currents would be extreme.
Not to mention how the pressure in the centre of the earth is extreme because of the weight of the rock itself. When you have a hypothetical uncollapsible hole, you're explicitly removing the vast majority of that pressure. I'd be curious to know how those actual values work out for a "giant chimney" model though.
34 comments
[ 4.4 ms ] story [ 86.3 ms ] threadHm ... 6400km/(200km/h) is 32h << 2 days
(and 200km/h is reached within 10 seconds)
150 deep in a mine is about 1.02 atm. You'd need to go about 30km down to get 20 atm.
Another interesting effect is if the tunnel diameter is large enough, and air is allowed to fill the tunnel, then an arbitrarily large fraction of our atmosphere will now drain into the hole. This effect not only reduces barometric pressure at seal level, but there will be ongoing gas exchange between rock and air.
Last but not least, I'd be curious if the magnetic field flux is at all interesting/dangerous to you if you're falling through the molten iron core of a planet. It would also be pretty cool to use that magnetic field as propulsion.
This fool is mixing up atmospheric pressure and water pressure. If you're going to speak with authority on something maybe you should spend more than five seconds thinking about it.
After falling about 1.1 kilometers (0.02% of the way to earth's center), you encounter a temperature of about 320 Kelvin
No. The temperature at 1.1km is about 36c. Uncomfortable, but not fatal. Certainly not so instantly fatal you die before passing the 2km depth on your fall.
your dried up bones and remnants of flesh encounter a temperature of about 1200 Kelvin and are completely incinerated into dust.
Burning a bone to dust requires temperatures over 1100c. He is mistaking the temperature inside a crematorium for the temperature required to incinerate bone. 1200 kelvins, like a crematorium, will produce chunks of calcified bone, not "completely incinerated into dust".
God this is a lazy article.
Thank you.
It's an crazily inaccurate article, with some variables turned on and off and others like mascons/average surface height ignored.
Since gravity drives a lot of atmospheric pressure, I'm not sure that the "soup" of air at the center would be valid.
F/m = a = x'' = g - px - qx•x'•x'
Here g-px accounts for linear decrease of gravity, qx is the air pressure, and x'^2 is the square of velocity.
That's a tricky equation and even wolframlpha cant solve it.
[1] https://physics.stackexchange.com/questions/286710/period-of...
How on earth does this work? The Dead Sea is 0.4 kilometers below sea level and air pressure is about the same as it world wide.
Spent many hours with this 2-volume book "Physics for Entertainment" by Ya Perelman as a kid, and now I'm motivated to go back and read it all over again!
A lot of these Russian science/math/fiction books were available at very low cost during the '80s in India.
It remains one of the best posts on that platform imho, and unlike this article, is actually correct in its assertions and descriptions (to the point that human knowledge can be certain).
* Provided the object falling down is a spherical cow that is impervious to pressure changes and what not :)
https://en.wikipedia.org/wiki/Spherical_cow
Not to mention how the pressure in the centre of the earth is extreme because of the weight of the rock itself. When you have a hypothetical uncollapsible hole, you're explicitly removing the vast majority of that pressure. I'd be curious to know how those actual values work out for a "giant chimney" model though.
Decimal fractions and the metric system form a dangerous cocktail in the hands of West Texas A&M University people.
Someone's bound to get hurt.