Is a 10,000 mph mag-lev hypertrain, running in an evacuated tunnel, a possibility?

From: Michael

Grade: 7 - 9

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Area: Physics

Message ID Number: 958706146.Ph

Ok. I have a slight understanding of the principles of magnetic levitation in passenger trains, and I have an idea.

If you took a MagLev train, placed it in a 5,000 Mile Long Tunnel, which is sealed to create a near-perfect vacuum, and use large quantities of power to propel it to 10,000 Miles per hour, wouldn't the greatest system of transportation be created?

It would have thousands of features, and hundreds of back-up emergency systems in the event of de-pressurization, or power loss, or life support failure, etc. What would a comfortable, sustained acceleration level be, to propel the train to max. speed? Is this idea even theoretically possible?

Michael

Yes, so far as I know, your concept certainly is theoretically possible. It would have some substantial engineering problems to be overcome, but the most serious objection is probably economic.

Regarding the possible acceleration, I think 2 g (ie, twice the acceleration of gravity) would probably be near the maximum for use in a commercial vehicle, available to the public. Airline passengers are occasionally subjected to accelerations in this range during non-fatal flight emergencies of various kinds, and generally do OK as long as they have their seat-belts fastened. The space shuttle has a maximum of 3 g, but this is considered mild for astronauts, who can routinely handle up to 10 g for short periods. On the other hand, we want old ladies, babies, and Little Monsters of all ages to be able to use this thing at least safely, and fairly comfortably. Two g would require the passengers to be securely strapped into good seats, for safety. It will feel like the thing is going straight up (because the apparent gravity will point almost straight backwards), and even a 10 foot fall down the aisle on the way to the restroom could easily be fatal.

How long would passengers be subjected to this situation, to reach the 10,000 mph speed you have in mind? Well, at 1g (that is, in free fall) your speed increases by 9.8 meters per second, every second the acceleration continues. This is close to 32 feet per sec per sec, or about 20 miles per hour, per second. At 2g our speed would increase by 40 mph every second. So it would take 10,000/40 = 250 sec to reach 10,000 mph at this rate; which is just over 4 minutes. All righttt!!

And most people could probably sit still for 4 min, in a comfortable seat.
It might be wise to consider a lower rate; the issue is really how to deal
with unusual situations (remember how different people are!) that might
arise if you push too close to the limit.
At 1g horizontal acceleration, it would take 500 sec, or 8 min and 20 sec,
to reach 10,000 mph, which is still not very long.
The passengers would *feel* an acceleration of 1.42g, however, since
the horizontal acceleration must be added to the normal vertical gravity,
resulting in a sensation of gravity acting at a 45 degree angle to the
rear.
(At 2g we have to consider this too, but it is relatively a smaller correction:
it would feel like 2.24g, about 27 degrees below straight backwards.
You can work these numbers out for yourself if you know Pythagora's rule
for the long side of a right triangle.)

Don't forget, you have to stop, also.
At the same g level this will take just as long as it took to get up to speed.
Now the apparent gravity is almost straight forward, so maybe the seats
better be able to swivel around to point the other way.
Even I might not like hanging by my seat-belt for 4 min.
Can you figure out how far you would travel at 2 g horizontal acceleration
for 400 sec?
(Hint: the *average* speed would be 10,000 mph divided by 2.)
Then you would travel exactly that same distance stopping.
If the tube was 5,000 miles long, how far would you have left to travel between
the acceleration and deceleration phases?
How long would that take?
So what would be the total trip time?
Not bad!!

I have no good references for this one (I recall there was a nice article in "Scientific American" maybe 20 or 25 years ago about the same idea, which you might find in your school library). However, the editor has kindly pointed me to a previous answer to a similar question, that deals with some of the other issues. As a result, I've just concentrated on the acceleration part of the subject.