Fun idea, but didn't everyone here have to work this out in their college physics class?
Since Friday, Feb. 11, 1966 maybe ;)
Doh!
To Everywhere in 42 Minutes
31–40 of 45 posts
Re: To Everywhere in 42 Minutes
#32Re: To Everywhere in 42 Minutes
#33Earlier quoted context omitted.
Superheated magma is not really much of a problem. 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 pro…
The coolant would only need to last 42 minutes if you thought it could never get stuck.
Then you just poor a ton of liquid nitrogen down afterwards and cryonics will take care of the rest (give or take 50 years).
Re: To Everywhere in 42 Minutes
#34Earlier quoted context omitted.
> 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. 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 an…
Hmm, unless I'm going crazy here, we get the differential equation x'' = -(x^-2) x = (kt)^(2/3)(with k = (2/9)^(-3/2), not that it matters) seems to be a solution? 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.)
That differential equation only holds for positive x. Try something like the following:
x'' = - signum(x) * (x^-2)Re: To Everywhere in 42 Minutes
#35There was work done on similar things to this in the 1970s, however it all went classified. The term is "subterrene" - a tunnel boring machine that keeps the drill tip at high temperature, melting the rock and allowing a smooth glassy tunnel to be made.
Fascinating... wikipedia mentions using nuclear power to achieve the 1300-1700C temperature needed for the rock melting. (BTW, the smooth glassy tunnel is a byproduct of that). I wonder if you could achieve the same thing using plasma arcs ( http://en.wikipedia.org/wiki/Plasma_Converter ), then somehow use the pressure and heat of the earth, once you're deep enough?
I wonder how Shaped Charges would perform. They're relatively inexpensive, would easily produce the temperature needed for glassing the rock and have excellent range penetration. A single shaped charge can easily penetrate beyond 10 times its diameter.
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.
Re: To Everywhere in 42 Minutes
#36There's no such thing as a free lunch. Most of the energy required to go from A to B is needed to overcome friction, not provide kinetic energy. That remains true whether you are above or below the surface. So burrowing down buys you virtually nothing. The amount of energy you'd need to pull yourself up the other side of the tunnel would be almost exactly the same as you would need to make the same trip at (almost) t…
Not completely true. You need energy to start, and then you waste it (or try to recover it) when you stop. With this you don't need to provide all that initial energy to get you going. You just have to handle the friction.
That's why I qualified with "most" and "virtually." I haven't actually done the math, but I'd be surprised if it didn't work out to something like >90% of the total energy for a long trip going into frictional losses. Consider any vehicle: the amount of the total energy that goes into generating actual motion is roughly proportional to the time it takes to accelerate to your final cruising speed, at which point all of the energy input goes into overcoming friction.
Re: To Everywhere in 42 Minutes
#37Earlier quoted context omitted.
Superheated magma is not really much of a problem. 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 pro…
The coolant would only need to last 42 minutes if you thought it could never get stuck.
If you got stuck while moving at around 1000 MPH you have bigger problems.
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.
Re: To Everywhere in 42 Minutes
#38Earlier quoted context omitted.
Not completely true. You need energy to start, and then you waste it (or try to recover it) when you stop. With this you don't need to provide all that initial energy to get you going. You just have to handle the friction.
That's why I qualified with "most" and "virtually." I haven't actually done the math, but I'd be surprised if it didn't work out to something like >90% of the total energy for a long trip going into frictional losses. Consider any vehicle: the amount of the total energy that goes into generating actual motion is roughly proportional to the time it takes to accelerate to your final cruising speed, at which point all o…
For a car you are 100% right - it's nearly all friction. But to accelerate to over 1000 MPH you need a lot of energy just to get started, and you have little chance of recovering it.
But an overland bullet train in a vacuum would be so much easier to build that the acceleration energy would be worth it.
Re: To Everywhere in 42 Minutes
#39Earlier quoted context omitted.
The derivation in the original article (Paul W. Cooper, Through the Earth in Forty Minutes, Am. J. Phys. vol. 34 (1966) p. 68) relies on the assumption of constant density. (It's hard to say this for sure because some of the details are left out, but Cooper at least states he's making this assumption.) In the case where all the earth's mass is concentrated at the center, a point mass starting on the surface of the Ea…
> 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. 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 an…
That's a good point. I don't know what I was thinking.
Re: To Everywhere in 42 Minutes
#40I think Douglas Adams would be happy to hear this.