So lets say I’m taking the Gravity Train Express from Madrid to Auckland.
The train accelerates to 17,670 miles per hour, and zooms through the center (or thereabouts) of the Earth.
Now I feel a little dizzy in a fast-moving elevator going up to the 13th floor, and airplanes make me quite sick… so I have to wonder, what would this trip feel like?
A 42-minute roller coaster ride, perhaps. And warmish, I’d say.
If you went through the center of the Earth you’d be in free fall all the way. Assuming of course that you’ve taken the normal Gravity Train precaution of stopping the Earth in its rotational tracks.
Reading articles about the Russian quest for the deepest hole ever dug killed my imagination for these types of scenarios forever even though the results itself are very interesting. Even once you get down below a scratch on the earth, the material becomes flowing plastic and then presumably more liquid the further down you go. The problem is that the earth becomes so hot, so fast as you drill down that truly deep holes are impossible and may always be. The Russians made it down almost 40,000 feet over a few decades in one giant hole and then couldn’t drill past it because the earth just flows into the hole. No one knows how to penetrate 7.5 miles into the crust let alone the thousands of miles some type of travel tunnel would require. There are no materials that could be used to build such a thing.
Assuming no friction, during the trip your weight would be equal to what it normally is times the sine of the angle between the train tunnel and vertical. Thus, as MonkeyMensch notes, if the tunnel went directly through the center of the earth, you’d be weightless for the entire trip.
If you get dizzy in an elevator, 42.2 minutes of this might not be to your taste.