Saturday, April 12, 2008

The latest invention to come out of Wetzel Ind R&D Lab is a train that can travel anywhere on Earth in 42 minutes. I got the idea from damn interesting site. Let me summarize the idea, you dig a hole (Note YOU are digging this hole), between any two points on Earth, and then you pretty much drop something, and ignoring friction it'll make it from point A to B just via gravity. You'll have to overcome any loss of speed from friction, (if you made it a vacuum and kept it from hitting the sides there shouldn't be much friction). According to the site it'll take about 42 minutes regardless of how far the tunnel is (the farther it is the more straight down you'll be going and thus the greater gravity will be).

On the site it mainly deals with tunnels that go through most of the Earth. The deepest we've ever dug is about 7 miles (we as in Wetzel Ind, via our subsidiary the USSR), and that was a challenge. So instead of a tunnel which goes very deep, I thought about a tunnel which just slightly went under the Earth. Mainly one whose deepest point would be 7 miles. This would still be quite a challenge, but I'm confidant you'll work out the kinks.

So I did some calculations and if your deepest point was 7 miles your tunnel would be 470 miles long, and cover 672 miles on the surface. Traveling that distance in 42 minutes would be about 954 mph (747 cruises ~ 600mph) (note that's the equivalent speed for the surface, you'd end up going faster than that at the peak in the center). The tunnel would be 6.8 degree slope or about 12% grade.

As I said 7 miles deep would still be quite hard, but perhaps and easier way would be to put the tunnel through the ocean. I found the avg depth of the ocean is about 2.3 miles, so if your tunnel had a max depth of 3 miles the stats would be, 440 miles surface, 308 miles direct, about 625 mph equivalent speed, 4.5 degree or 8% grade.

While looking up the 747 speed, I had another thought. A 747 flies at about 6.5 miles above the Earth. That means if the plane just pointed down at say a 10% grade, and tuned off it's engines it should should be the same thing. The problem here would be air resistance. Maybe you could build a massive tube above land, although that would be really crazy.

The next thing I was thinking about was that you could make it so that right as you left a tunnel you'd enter the next tunnel and go another 600 miles. By daisy chaining tunnels you could go longer distances, without going deeper than was possible. The farthest two points can be on Earth is about 12k miles, using 670 mile tunnels that's 18 tunnels. At 42 minutes each it works out to 13 hours to go anywhere on Earth. You could do NY to LA in 4 hops, assuming the train would stop for a while at each stop that'd probably work out to 4 hours. If you are using trains (and they pretty much make the most sense for this) you could speed up the journey by accelerating at the start, say up to 200 mph, then letting gravity take over. That should make up for the loss to friction too.

In the attached picture the tunnel would run from point A to B via the straight line, as opposed to the curve. Not both circles are the same, but the second one has exaggerated angles to help illustrate.

Philly to:
NY 90 mi
Chicago 660 mi
LA 2390 mi <- Article that inspired idea <- Deepest tunnel = 7.62 miles (1989 Soviets) <- Avg depth of ocean = 2.35 miles. <- Longest tunnel = 33.5 miles (1988 Japan) <- Radius of Earth = 3960 miles (varies from 3963 - 3949) <- Circle calculator

Well I decided I wanted to redo all the calculations with out any web calculators (just using trig). I had to look up the formula for length of a arc though. It turns out that somehow in my random scribbles in paint I made an error. I wrote 308 miles, then multiplied that by 1.43 (60/42) to get mph. That gave me 440mph. Later I must have forgotten I did this, and upon seeing the two similar but different numbers assumed the larger was the surface distance. I think remultiplied that by 1.43 to get the meaningless (unless we adopt 86 minute hours) figure of 625. The surface distance traveled wouldn't be much different than the tunnel distance (less than one mile more). So in my figure the top numbers are really mph, and the bottom numbers are worthless. Also note this significantly slows down the journey. I'll leave recalculating the travel times as an exercise for the reader.

Secondly, I got the angles wrong. I didn't half the run in the rise/run (I used the full length of the tunnel as the base of the triangle when I should have been using half to make a right triangle). The new angles are 2.2, 4%, and 3.4, 6%.

Unfortunately work had already begun on the tunnel, as such the Wetzel Ind tunnel digging subsidiary (USSR) is facing bankruptcy as investors pull out. You should continue digging though.

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