To Everywhere in 42 Minutes
time.com
time.com
If you don't go too deep (a few thousand KM), the temperature is under 1000 degrees. We have plenty of materials than can handle that. For insulation use vacuum, or aerogel (which melts at 1,473 K) and is a phenomenal insulator. Add a large cold reservoir (liquid nitrogen) and you don't need a conventional A/C - it only has to last 42 minutes, and weight is not a problem.
The pressure is a much bigger problem. You can't bore a tunnel in the conventional sense since the rock is a liquid. You'd need some sort of wall, but I don't know if we have anything strong (and stable) enough. Most metals will oxidize and destroy themself at those temperatures.
Maybe a ceramic, or alumina coated metal. Perhaps a tungsten compound of some sort that is stable in oxygen at high temperature.
Another problem is the speed (reaching 1000 MPH), you'd need magnetic bearings (mag-lev), but magnets don't like being hot. The curie point of iron is 768 C, which is too low. Cobalt might work - but barely.
And if you survived the crash - how would you get out? The capsule is unpowered, and they don't make cables long and strong enough to pull you out.
But assuming rescue was possible, I suppose they could drop small emergency coolant refill bags down to you.
Also, I wouldn't want to build something where a single seal failure would mean the entire thing is destroyed. Plus, how would you construct it.
Anyway, it's nice to see he solved the pathfinding, but it's probably not the most challenging part of the problem!
My numerical experiments point to the latter.
Does anyone care to derive an analytic solution?
In the case where all the earth's mass is concentrated at the center, a point mass starting on the surface of the Earth would just go to the center and stay there.
In the opposite extreme where all the mass is concentrated on the surface, (that is, the Earth is a hollow shell) it actually turns out that the gravitational acceleration at any point inside the shell is zero, so it wouldn't work in that case either.
I suspect that for some reasonable class of spherically symmetric mass distributions (that is, the density only depends on the distance to the center of the Earth), tunnel systems like this are mathematically possible. But I'd be surprised to learn that there are mass distributions other than the uniform one for which the travel time doesn't depend on distance. But I'm not going to work this out because I have Real Work to do. (Now I wish I were teaching calculus so I would have an excuse to work out this problem...)
Why? That would violate conservation of energy, wouldn't it?
In a naive model of a point mass you'd get a singularity at the center. But using standard techniques (e.g. numeric pertubation, or Lebesgue integration) one gets an objects that swings back and forth like in the other scenarios.
x'' = -(x^-2)
I guess that doesn't help with the singularity, but neither does looking at energy (since you have infinite kinetic energy at the center and infinite potential energy everywhere else.)
x'' = - signum(x) * (x^-2)Would tourism explode? What would that mean for the environment?
What about international business?
Would it be the end of remote workers? Or would it encourage even more distributed workplace?
In some parts of the world you can live on $5 a day, in others it's $100 - but with cheap travel, those earning lots would buy services in the cheaper places - increasing prices.
And those earning little would seek employment elsewhere, reducing wages.
The overall result would be to flatten the income disparity about nations. (But it would have no effect on the disparity within nations, since that is caused by differences in intelligence, and that won't change.)
Some places would of course "cut themself off the grid" (like North Korea), but the majority would not, and the world (or at least the connected places) would become much more similar.
And some counties would put up barriers (like those separating the US and mexico - if not for those the wages in the US and mexico would tend to equalize, but they don't because of the barrier).
All this assumes that the travel is cheap - if it's expensive, it doesn't much matter that it's fast.
He's saying that local effects of a nation would quickly be brought up to par, whereas the distribution in nations wouldn't likely change.
With this you don't need to provide all that initial energy to get you going. You just have to handle the friction.
But an overland bullet train in a vacuum would be so much easier to build that the acceleration energy would be worth it.
You need exactly 4 times as much energy as you do accelerate to 500 MPH, which is the speed of a slow jet. Four times a small amount is still a pretty small amount.
Although that assumes you got perfect efficiency from it, which you won't.
I concede your point - and you should have gotten more mod points for it.
Based on the Beach Pneumatic Transit diameter of around 2.5 meters, a single shaped charge designed to penetrate at this width (cone diameter of around 2.5 meters) would easily penetrate between 25 or 35 meters. Although on such an industrial scale, I wouldn't doubt some military contractor would go commercial with one that could penetrate up to 50 meters.
The question would be, could such a destructive method (on the small scale) be more useful than current explosives used. There would likely be less shockwaves sent through the rock than traditional mining techniques, plus the potential glassing could help structural strength.
The use of something so easily mass produced like a shaped charge could easily be used in vac-train mining like this. Although personally, I doubt any system like this would ever be used between continental plates.
Temperatures roughly increase about 1 degree C for every hundred meters you go down. The difference could power a Stirling Engine (some of which are powered on differences of as little as .5 degrees C). It seems to me you could use a captive bolt pistol to get down just a few hundred meters, carrying a plastic tube which would have two chambers. The engine would pump the water and generate additional electricity. What do you guys think?
I guess with enough frequent zero-g points you could upgrade to the "no hurling" section.
(The not-quite-straight-through tunnels wouldn't be fully weightless, maybe we should concentrate on those. Then we just have to solve the insurmountable temperature, pressure, and vacuum problems.)
fgraham@kent.edu