
To Everywhere in 42 Minutes - mariorz
http://www.time.com/time/printout/0,8816,842469,00.html
======
anigbrowl
It sounds like great fun until your rapid transit pod plunges into a bath of
superheated magma. Vomitous fellow passengers would not be my primary anxiety
about this mode of travel.

~~~
ars
Superheated magma is not really much of a problem.

If you don't go too deep (a few thousand KM), the temperature is under 1000
degrees. We have plenty of materials than can handle that. For insulation use
vacuum, or aerogel (which melts at 1,473 K) and is a phenomenal insulator. Add
a large cold reservoir (liquid nitrogen) and you don't need a conventional A/C
- it only has to last 42 minutes, and weight is not a problem.

The pressure is a much bigger problem. You can't bore a tunnel in the
conventional sense since the rock is a liquid. You'd need some sort of wall,
but I don't know if we have anything strong (and stable) enough. Most metals
will oxidize and destroy themself at those temperatures.

Maybe a ceramic, or alumina coated metal. Perhaps a tungsten compound of some
sort that is stable in oxygen at high temperature.

Another problem is the speed (reaching 1000 MPH), you'd need magnetic bearings
(mag-lev), but magnets don't like being hot. The curie point of iron is 768 C,
which is too low. Cobalt might work - but barely.

~~~
reconbot
The coolant would only need to last 42 minutes if you thought it could never
get stuck.

~~~
ars
If you got stuck while moving at around 1000 MPH you have bigger problems.

And if you survived the crash - how would you get out? The capsule is
unpowered, and they don't make cables long and strong enough to pull you out.

But assuming rescue was possible, I suppose they could drop small emergency
coolant refill bags down to you.

------
te_platt
Fun idea, but didn't everyone here have to work this out in their college
physics class?

~~~
scorxn
Since Friday, Feb. 11, 1966 maybe ;)

~~~
eru
I just wrote a simple python script to test whether this holds only when all
of earth's mass is concentrated at its center, or in the slightly more
realistic case of constant density.

My numerical experiments point to the latter.

Does anyone care to derive an analytic solution?

~~~
madcaptenor
The derivation in the original article (Paul W. Cooper, Through the Earth in
Forty Minutes, Am. J. Phys. vol. 34 (1966) p. 68) relies on the assumption of
constant density. (It's hard to say this for sure because some of the details
are left out, but Cooper at least states he's making this assumption.)

In the case where all the earth's mass is concentrated at the center, a point
mass starting on the surface of the Earth would just go to the center and stay
there.

In the opposite extreme where all the mass is concentrated on the surface,
(that is, the Earth is a hollow shell) it actually turns out that the
gravitational acceleration at any point inside the shell is zero, so it
wouldn't work in that case either.

I suspect that for some reasonable class of spherically symmetric mass
distributions (that is, the density only depends on the distance to the center
of the Earth), tunnel systems like this are mathematically possible. But I'd
be surprised to learn that there are mass distributions other than the uniform
one for which the travel time doesn't depend on distance. But I'm not going to
work this out because I have Real Work to do. (Now I wish I were teaching
calculus so I would have an excuse to work out this problem...)

~~~
eru
> In the case where all the earth's mass is concentrated at the center, a
> point mass starting on the surface of the Earth would just go to the center
> and stay there.

Why? That would violate conservation of energy, wouldn't it?

In a naive model of a point mass you'd get a singularity at the center. But
using standard techniques (e.g. numeric pertubation, or Lebesgue integration)
one gets an objects that swings back and forth like in the other scenarios.

~~~
jibiki
Hmm, unless I'm going crazy here, we get the differential equation

    
    
      x'' =  -(x^-2)
    

x = (kt)^(2/3)(with k = (2/9)^(-3/2), not that it matters) seems to be a
solution?

I guess that doesn't help with the singularity, but neither does looking at
energy (since you have infinite kinetic energy at the center and infinite
potential energy everywhere else.)

~~~
eru
That differential equation only holds for positive x. Try something like the
following:

    
    
      x'' =  - signum(x) * (x^-2)

------
d1rge
Putting practical considerations aside, what might the effect on society be if
we could be at any other place on earth in less than an hour?

Would tourism explode? What would that mean for the environment?

What about international business?

Would it be the end of remote workers? Or would it encourage even more
distributed workplace?

~~~
ars
It would more or less mean the end of nations.

In some parts of the world you can live on $5 a day, in others it's $100 - but
with cheap travel, those earning lots would buy services in the cheaper places
- increasing prices.

And those earning little would seek employment elsewhere, reducing wages.

The overall result would be to flatten the income disparity about nations.
(But it would have no effect on the disparity _within_ nations, since that is
caused by differences in intelligence, and that won't change.)

Some places would of course "cut themself off the grid" (like North Korea),
but the majority would not, and the world (or at least the connected places)
would become much more similar.

And some counties would put up barriers (like those separating the US and
mexico - if not for those the wages in the US and mexico would tend to
equalize, but they don't because of the barrier).

All this assumes that the travel is cheap - if it's expensive, it doesn't much
matter that it's fast.

~~~
gtufano
I find interesting that you assume that disparity within nations is caused by
differences in intelligence. While this is true (i.e.: differences in
intelligence make a difference, sorry for the joke) there are many, many,
other causes for differences: geographics (easy), social (not all the
countries are permeable to social status changes) and so on... I feel this
"all is caused by the intelligence" a bit ingenuous. But may be it is only my
european culture speaking...

~~~
dantheman
You misread his statement: > The overall result would be to flatten the income
disparity about nations. (But it would have no effect on the disparity within
nations, since that is caused by differences in intelligence, and that won't
change.)

He's saying that local effects of a nation would quickly be brought up to par,
whereas the distribution in nations wouldn't likely change.

~~~
bocajuniors
I think the misreading was you misreading gtufano.He disputed the unsupported
statement that income differences within a nation are mainly because of
intelligence differences

------
lisper
There's no such thing as a free lunch. Most of the energy required to go from
A to B is needed to overcome friction, not provide kinetic energy. That
remains true whether you are above or below the surface. So burrowing down
buys you virtually nothing. The amount of energy you'd need to pull yourself
up the other side of the tunnel would be almost exactly the same as you would
need to make the same trip at (almost) the same speed on the surface.

~~~
ars
Not completely true. You need energy to start, and then you waste it (or try
to recover it) when you stop.

With this you don't need to provide all that initial energy to get you going.
You just have to handle the friction.

~~~
lisper
That's why I qualified with "most" and "virtually." I haven't actually done
the math, but I'd be surprised if it didn't work out to something like >90% of
the total energy for a long trip going into frictional losses. Consider any
vehicle: the amount of the total energy that goes into generating actual
motion is roughly proportional to the time it takes to accelerate to your
final cruising speed, at which point all of the energy input goes into
overcoming friction.

~~~
ars
For a car you are 100% right - it's nearly all friction. But to accelerate to
over 1000 MPH you need a lot of energy just to get started, and you have
little chance of recovering it.

But an overland bullet train in a vacuum would be so much easier to build that
the acceleration energy would be worth it.

~~~
lisper
> But to accelerate to over 1000 MPH you need a lot of energy

You need exactly 4 times as much energy as you do accelerate to 500 MPH, which
is the speed of a slow jet. Four times a small amount is still a pretty small
amount.

~~~
lisper
BTW, the math in this case is really easy. Kinetic energy is 1/2 _m_ v^2. 1000
MPH is 444m/s. So to accelerate a one metric ton vehicle to 1000 MPH requires
1/2 _1000_ 444^2 = ~100MJ, which is less than the energy in one gallon of
gasoline.

~~~
ars
Any vehicle would probably by much heavier than 1 ton. A 747 weighs about 400
metric tons. But still 400 gallons of gas (in bulk) only costs about $750
which is nothing.

Although that assumes you got perfect efficiency from it, which you won't.

I concede your point - and you should have gotten more mod points for it.

------
patrickg-zill
There was work done on similar things to this in the 1970s, however it all
went classified. The term is "subterrene" - a tunnel boring machine that keeps
the drill tip at high temperature, melting the rock and allowing a smooth
glassy tunnel to be made.

~~~
ph0rque
Fascinating... wikipedia mentions using nuclear power to achieve the
1300-1700C temperature needed for the rock melting. (BTW, the smooth glassy
tunnel is a byproduct of that). I wonder if you could achieve the same thing
using plasma arcs (<http://en.wikipedia.org/wiki/Plasma_Converter>), then
somehow use the pressure and heat of the earth, once you're deep enough?

~~~
electromagnetic
I wonder how Shaped Charges would perform. They're relatively inexpensive,
would easily produce the temperature needed for glassing the rock and have
excellent range penetration. A single shaped charge can easily penetrate
beyond 10 times its diameter.

Based on the Beach Pneumatic Transit diameter of around 2.5 meters, a single
shaped charge designed to penetrate at this width (cone diameter of around 2.5
meters) would easily penetrate between 25 or 35 meters. Although on such an
industrial scale, I wouldn't doubt some military contractor would go
commercial with one that could penetrate up to 50 meters.

The question would be, could such a destructive method (on the small scale) be
more useful than current explosives used. There would likely be less
shockwaves sent through the rock than traditional mining techniques, plus the
potential glassing could help structural strength.

The use of something so easily mass produced like a shaped charge could easily
be used in vac-train mining like this. Although personally, I doubt any system
like this would ever be used between continental plates.

------
david927
Silly. It took us 24 years to get 12km straight down, and that's the best
we've ever done.

<http://www.damninteresting.com/?p=567>

~~~
david927
Actually, screw traveling -- if we could just drill a few hundred meters
easily and cheaply, we could solve all our energy problems.

Temperatures roughly increase about 1 degree C for every hundred meters you go
down. The difference could power a Stirling Engine (some of which are powered
on differences of as little as .5 degrees C). It seems to me you could use a
captive bolt pistol to get down just a few hundred meters, carrying a plastic
tube which would have two chambers. The engine would pump the water and
generate additional electricity. What do you guys think?

------
jws
This and atmosphere hopping space planes both have the same drawback: a
significant number of people vomit on their first weightless trips. Do you
really want to ride packed into coach in that kind of environment?

I guess with enough frequent zero-g points you could upgrade to the "no
hurling" section.

(The not-quite-straight-through tunnels wouldn't be fully weightless, maybe we
should concentrate on those. Then we just have to solve the insurmountable
temperature, pressure, and vacuum problems.)

------
kokofoo
I would guess somebody or something need to catch the passengers from the
other side of the hole; otherwise, it would fall back and forth forever like
gigantic pendulums..

------
viggity
I think Douglas Adams would be happy to hear this.

------
fgraham
Does anyone know where Paul W Cooper, the author of Anywhere in 42 Minutes, is
today?

fgraham@kent.edu

