If a train tunnel is dug on a straight line from NYC to LA, would a train fall half way without using energy?

Question

After falling downhill for half of the trip, how much further would it go uphill using its kinetic energy? (Assume magnetic suspension.) If the heat energy picked up underground could be used to charge batteries, could it make the whole trip without using external energy?

Big J
The first half of the trip is always downhill and the second half always uphill, no matter how many trains you switch to. But bring some of that liquid refreshment anyway.

Sir R.
Given: earth radius = ~4K miles, central angle a = ~PI/7 (from NYC to LA), cos a = ~0.9, we are ~400 miles under Witchita. So what is your problem?

Answer 1

It all depends on air resistance. I'm assuming that since you've specified magnatic suspension, there's no loss of kinetic energy to heat due to rail friction. So drag from air resistance would reduce the train's kinetic energy. How much depends on the drag properties of the train, how wide the tunnel is and how much air it has to force ahead of it vs. flow around it, and the density of the air.

If your train tunnel were a vacuum, then there would be no drag, and your train would leave the exit at the same speed it went into the entrance. Maybe you could use that heat along the way to run the lights and sound system. Sounds like quite a ride!

Answer 2

My brother Iggy, and I have been workin' on that idea, and we'll get back to ya as soon as we complete our Russian oil heist.
But I'll give ya a hint:---( since the earth is tilted,you would fall down in the night time, and fall up during daylight), now keep that under yer hat.
But you're startin' to use your noodle, and you might be able to join our (mine and Iggy's) scientific community.

If you unload the passengers midway, then lift them on a steam operated elevator, and board them on a second train starting on a higher elevation; then you could be going down hill again.
I really believe this could be done with a series of trains starting on a raised elevation above ground, and then transferring passengers at a certain distance below ground, then repeating these steps without tunneling too deep.---The weight of the people on the down elevator would assist in lifting the people on the elevator going up.Like a teeter-totter, or see-saw.
San Francisco has been making use of gravity with their trolley cars for many years.

EDIT No. 2:---No. You missed the part about transfering the passengers , before loosing inertia, to an elevater that takes them to an upper level to board another elevated train which continues to go down again.---It would be like skipping a stone across the water when you inner-connect the trains.
If you try to do it all with one train starting at street level, you'll end up going too deep.
The elevators can counter-balance each other to save energy.

Answer 3

Yes if it were perfectly efficient which nothing is.
This concept has been studied and it is interesting that using this system it takes the same amount of time to go anywhere on earth.

Answer 4

Interesting question.

I wish I have even a clue!