Re: ballistic subterranean trains

From: Spike Jones (
Date: Wed Sep 26 2001 - 20:47:43 MDT

> From: Damien Broderick ( Mon Sep 24 2001
> >A year or so back, there was a brief discussion on the list of the
> >sub-orbital dynamics of a vehicle connecting distant places via an
> >evacuated tube under the ground ...
> Amara Graps wrote: The thread was titled: "Cooling technique for Jupiter brains" in early
> February 2000. (Doug Jones, Jeff Davis, Robert Bradbury, Spike Jones and I discussing).
> I remember Spike and I having a blast throwing each other junk through
> the tunnel. Our physical setup depended on a chord-tunnel through a
> constant density sphere, though, so it was only an ideal situation...

Amara's post reminded me of that exchange and some entertaining
analysis we did at the time. I recalled that if one assumes a frictionless
track in an evacuated tunnel, one can drop stuff in anywhere and
have it pop out anywhere, regardless of the shape of the tunnel. A
chord is not an ideal solution. A faster trip can be had by making
the tunnel parabolic, so the path length is actually longer but the
initial acceleration is greater. The question that I am now trying
to resolve is this: assuming no push along the frictionless track,
what is the shape of the track that makes for the shortest time
in transit? I think the shape is a catenary, but I havent proved it.

Nowthen, since we are talking about frictionless evacuated tunnels,
an acceptable solution would be to build the tunnels at a constant
depth of about 4.5 km. Such could theoretically be built. After
the car descends to that depth, regardless of the shape of the
path down there under these assumptions, it would be travelling
at about 300 meters/sec, so the trip from anywhere to anywhere
would be at speed about competitive with current airline travel.

Amara pointed out to me a year and a half ago that the solution
is path independent.

The moon would be the place for such a device, since the vacuum
is already available and the absence of plate tectonics. spike

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