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New York to Los Angeles using no fuel

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In my very lengthy story in the near future, there are some great 'Modern Marvels'. The next one I'm going to introduce might not be feasible, but if it is, I'd like to attach some numbers to it.

The Secretary for Urban & Regional Development with the Federal Highway Administration have secured the funds to build a straight tunnel from New York City to Los Angeles, through the Earth. It is a near vacuum. Therefore the modernized high speed rail cars simply "fall" into the tunnel, accelerating continuously for the first half of the tunnel, then slowing down to almost a perfect stop at the other end. The only friction is that of the rolling coefficient, and perhaps what little air remains.

Simply board your pressurized rail car, and go through the airlock.

Map

(1) What is the deepest the tunnel goes? Is it in the crust still?

(2) What is the length of the tunnel? On the great arc, they're about 4,000km apart, but the tunnel will be shorter.

Bonus: Any ideas how fast a 'falling' train can get going? Should I add support from the train?

High level figures and speculation fine, of course.

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This post was sourced from https://worldbuilding.stackexchange.com/q/15353. It is licensed under CC BY-SA 3.0.

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