This isn't really geoengineering but because this is a topic that keeps
cropping up:-
The space elevator, while superficially attractive, has major flaws.
The fundamental problem is that it relies on balancing gravity and
centrifugal force. This can only happen at one height, some 36,000 km
above the earth's surface, which is of course where geostationary
satellites are placed. So the centre of gravity of the system has to be
at that height; any material below that will be hanging from that
centre of gravity, and thus in tension, and there must also be a
balancing amount of weight higher than that, which will be providing an
outward tension.
So we can then ask "How do you build it?". We have already shown that
building towers upwards from the earth to even 20 km height is
impractical, (http://www-civ.eng.cam.ac.uk/cjb/papers/cp94.pdf) and
going even higher would be impossible. So the logic is that all the
material for the elevator system would have to be taken up to
Geostationary orbit (GEO) and some automated system would then have to
extrude the tether system downwards until it reached the earth's
surface, while at the same time building the counterweight upwards. I
don't know the cost of putting material into GEO orbit but a quick
browse on the web gives figures like $US 10,000 to 15,000 per kg to Low
Earth Orbit, double that to Geostationary Transfer Orbit, and double
that again to GEO. So you would have to carry up all the material for
the tether and the factory at something like $US 50,000/kg.
Given that it would be impossible to take the tether up in one go, you
would have to build an automated factory to assemble it. This would
need power, would need to be effectively autonomous, and given that you
would be making a single tension element with no redundancy, flawless.
The question of what material to use is also pertinent. The Free Length
of a material (The length of itself that it can support) is a useful
concept. For aramids like Kevlar it is about 200 km; PBO is about
double that. Carbon nanotubes and graphene might get you to 5000 km but
that relies on being able to convert the properties of a molecule into
large rope-scale assemblies with no loss of strength. It is worth
remembering that while the stiffness of a material is governed by the
molecular bonds in the bulk material, the strength is governed by how
effectively you can get stress in and out of the molecules. So it is
the connections that matter, rather than the strength of the molecules
themselves. Consider an aramid fibre; the individual molecules are
linked together in liquid crystals; these form micro fibrils and then
single filaments (which you can see) in the spinning and stretching
process. The filaments are then assembled into yarns (which you can
handle) which are then assembled into strands, sub-ropes and finally
ropes. (I simplify considerably). So there are at least 8 levels of
structure between the molecule and something you can use on a large
scale. There is inefficiency in force transfer at every one of these
levels, so the strength of the highest level element is much lower than
the strength of the molecule. More realistic estimates of what will be
possible at the engineering scale for all known materials, including
graphene and other exotica, give free lengths <500 km, which is not far
off what you can do now with materials like PBO, and nowhere near 36,000 km.
The free length concept assumes that you have a uniform cross-section,
so all is not lost for the tether because it can be shaped, but it would
need to be a lot thicker at the top than at the bottom. Whatever is
going to crawl up the tether would have to take account of that change
in diameter. See the web page by my colleague, Hugh Hunt
(http://www2.eng.cam.ac.uk/~hemh/space_elevator.pdf). Because the
calculations depend exponentially on the ratio (density/strength), the
mass of stuff to be lofted dramatically depends on the material you can
make. If you could get a copius supply of "Unobtanium" you would "only"
need a weight of 500 Te, but at $50,000/kg to orbit that's $25 billion
just to get the stuff up there - probably double that for the factory as
well.
But then we have the problem of what do you do with the payload when you
get it up there. Only if you take the payload right to the top will it
stay there. If you let it go anywhere below the geostationary height it
would fall straight back down to earth. You would have given the payload
the height (potential energy), but not the speed (kinetic energy) needed
to maintain it in orbit. For an orbit at a height of 200 km the
potential energy is 2MJ/kg but the kinetic energy needed is 32MJ/kg. So
you will only have provided 6% of the energy and will still have to
carry up a rocket to provide the other 94%. What's the benefit?
None of this takes into account Coriolis forces, which would move the
tether sideways as weights go up and down, or the risks of satellites or
space debris hitting the tether. Since the tether would be at very high
stress (in order to keep weight down), and the space junk would be
travelling at very high velocity, the effect of an impact on the tether
would almost certainly be catastrophic. Imagine pulling a bungee cord
taut and then cutting some of the fibres (don't try this at home). Even
if the tether was not completely destroyed, cutting fibres would release
huge amounts of strain energy that would send shock waves along the
tether, almost certainly causing damage elsewhere.
I believe the space elevator concept is an interesting piece of science
fiction, and has a role in inspiring young minds to think of science for
a career, but they would learn proper physics by considering why it
wouldn't work, rather than just thinking that "they" (whoever "they"
are) have solved the world's problems.
A more relevant Wikipedia reference is
https://en.wikipedia.org/wiki/Indian_rope_trick
Chris Burgoyne
Professor of Structural Engineering
University of Cambridge
On 18/08/2015 19:19, Greg Rau wrote:
In contrast to towers, what about this?:
"A space elevator is a proposed type of space transportation system.[1] Its
main component is a ribbon-like cable (also called a tether) anchored to the surface
and extending into space. It is designed to permit vehicle transport along the cable
from a planetary surface, such as the Earth's, directly into space or orbit, without
the use of large rockets. An Earth-based space elevator would consist of a cable
with one end attached to the surface near the equator and the other end in space
beyond geostationary orbit (35,800 km altitude). The competing forces of gravity,
which is stronger at the lower end, and the outward/upward centrifugal force, which
is stronger at the upper end, would result in the cable being held up, under
tension, and stationary over a single position on Earth. Once the tether is
deployed, climbers would repeatedly climb the tether to space by mechanical means,
releasing their cargo to orbit. Climbers would also descend the tether to
return cargo to the surface from orbit.[2] "
https://en.wikipedia.org/wiki/Space_elevator
Greg
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