A Very fast way of getting from A to B
This one belongs in the "something we could do if we get a quantum leap in engineering" category.
Two places on the surface of the earth, A and B. Dig a straight tunnel from A to B. The earth is a sphere, so this tunnel will be a chord. At both ends it will slope down. Make the tunnel air-tight and remove all the air so it is a vacuum inside. Put a vehicle inside suspended from the sides by a magnetic-induction system like they use in Maglev trains.
Start the vehicle at "A" and let go. There is no friction resistance (not touching the sides) and no air resistance (vacuum). The vehicle speeds up till it reaches the middle and then slows down until it reaches "B".
This is the same as a pendulum, or a children's swing. It comes to a rest at exactly the same height as it started.
Instead of letting it swing back, catch it at "B". The vehicle is air-tight, and you need a docking mechanism at each end to let people get in and out. Then a new load of passengers get in and it swings back to "A" again. You would probably need some propulsion to overcome residual air resistance, no vacuum is ever perfect, and B might be higher above sea level than A. Or just give it a push to start it, like a child's swing.
How long would the journey take?
The answer is just over 20 minutes, regardless of the distance from A to B. I won't burden you with the maths, but it is similar to a pendulum which always takes the same time regardless of the amount it swings, it just goes faster in the middle if it starts higher up.
The occupants wouldn't feel any acceleration. Just like a child's swing, they are in free-fall in the direction of movement, but they will feel varying gravity.
Now all we need is a method of building tunnels hundreds or thousands of Km long, which are air tight and can withstand the pressures and temperatures under the earth's crust.
It's merely an engineering problem!
P.S. I had this idea years ago, I have mentioned it to a few people (usually after a few beers), but I have not seen it anywhere else.
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Many, many people had this idea many many years ago. Digging through the center of the Earth is a yet unsolved problem. Less ambitiously passages through magma presents an interesting prospect. And then, there is the instability of the Earth's crust...You might be interested inhttp://hyperphysics.phy-astr.gsu.edu/Hbase/mechanics/earthole.html
How did you find that article so quickly?
The figure they get (42 minutes each way) is twice mine. Missed a "2" out when I quickly re-did the calculations. They do not mention that you get the same time for any chord, not just the special case of a full diameter.
If it could ever be built it would put the airlines out of business!
This does not allow for the effects of a rotating earth, which would be different depending where you were falling from and too. That bit of maths is too much for me.
I know it is 100% impractical and only a bit of fun, but is there anything against that?
Sounds really amazing, but you're only going down-hill for the first half. Even if you have a vacuum to prevent wind-friction, you'll still have to overcome vehicle friction on the 'climb-out'. Unless you actually think you'll have enough momentum--which I believe is unlikely.
And you if you put a power source on the vehicle, it would have to be either electric or supply it's own oxygen, because your vehicle is running in a vacuum.
I think it would be scary to be in an electric powered vehicle dozens of miles undergroud, depending on the vacuum to assure I could get enough momentum to get out, but also scared to death that the compartment would de-pressurize and the vacuum would kill me.
hrench,
I assumed magnetic levitation, so no vehicle friction, and near perfect vacuum. I did say it was "something we could do if we get a quantum leap in engineering". The "only" propulsion you need is to overcome residual air friction, and magnetic propulsion could be used for that.
As for scariness, have you ever worked out the number of tonnes per square metre that are pressing on the tunnel walls you when you go through the channel tunnel, or a http://en.wikipedia.org/wiki/AlpTransit, or any tunnel under a major river?