On Wed, Jul 02, 2003 at 11:07:07AM -0700, Chad Cooper wrote:
> Perhaps.... if you have in mind Kim Stanley Robinson's Mars
> Space Elevator I would agree with you. It is unrealistic, and
> unnecessary. Who needs a big fat cable, when you can build a nanotube
> ribbon a few feet wide and only microns thick. Perhaps I am a nutty
> idealist. I sometimes believe what I read.
It doesn't really matter that much whether it is round or ribbon, what
is important is the cross-sectional area, strength, density, and total
weight.
Rather than just reading, you might want to try working with the
numbers. I derived the applicable formulas for a space elevator and
posted them to Brin-L several years ago. I've appended that to my post
here if you want to try some numbers. I also included another article
that talks about space elevators and gives a few useful numbers.
> "The ribbon, the only component of the space elevator not commercially
> available, is the major hurdle in the construction of the space elevator.
Yes. And this is a huge hurdle. First someone has to make just a rope
of the stuff and measure its properties -- is it really as strong
as some people predict? (If not, no space elevator) People have to
figure out how to mass produce the stuff cheaply (it takes at least
1 million kilograms of it to make an elevator, at today's cost of
$500/g that comes out to $500B). In parallel, there would need to be
a huge, many-year study done to test the aging and reliability of the
stuff, probably culminating in putting lengths of it into orbit for
years and seeing how it ages. Then you have to get all that mass into
geosynchronous orbit, or else figure out how to get an asteroid into
orbit and make the nanotubes out of the asteroid (this might not be so
bad, at $10,000/kg for lifting the mass into orbit, it "only" comes to
$10B).
> The sheer length, 100,000 km, is considerable, but is comparable to
> what has already been constructed such as trans-oceanic ribbons and
> simple thread in textile mills.
Why would anyone make a trans-oceanic "ribbon" about 3 times the
circumference of the earth? Anyway, the problem isn't so much the length
as the fact that it is an as-yet non-existant material and that it has
to be proven extremely reliable beyond any possible doubt, no breaks
allowed (an undersea cable can tolerate a break a lot more than a space
elevator).
> The ribbon of our proposed 20,000 kg capacity elevator will have a 2
> square millimeter cross-sectional area, be 1 meter wide and microns
> thick, on average.
If it is 2 square millimeters in area, and 1 meter wide, than it must be
exactly 2 microns thick.
> It will be composed of individual fibers 10 microns in diameter lying
> side-by-side.
Huh? Unless I'm missing something, that was a big mistake there. How can
you make a 2 micron thick ribbon out of 10 micron diameter fibers?
> So my question is... are the obstacles preventing the start of a space
> elevator by 2023 technical, financial or organizational in nature?
Yes.
***
Date: Sat, 6 Feb 1999 18:38:29 -0600 (EST)
From: Erik Reuter <[EMAIL PROTECTED]>
Subject: Re: Site of Terragens Capital.
On Fri, 5 Feb 1999, Trent Shipley wrote:
> Whether or not the first fifteen-thousand feet is significant depends on
> the economics of the engineering. I know it's not a compression
> structure, but would the entire stalk be of equal diameter?
You would want it to taper. The thickest point would be at the center of
gravity (CG), then the part dropping to earth (as well as the part on
the opposite side) would taper down to a narrow width at the end. The
taper would probably be chosen so that the stress is the same at all
heights. A quick calculation I made indicates the cross-sectional area
would follow a functional form of exp(-k/r) where k is a constant and
r is the distance from the center of the earth. That formula is only
valid between the surface of the earth and the CG of the structure --
the opposite side of the structure will need a different formula.
> Also, how much stronger would the structure have to be as it gets
> longer.
>From the formula for cross-sectional area I derived as mentioned above:
strength = s = constant * (1/r - 1/r1)
where r is the radial distance (measured from earth's center) to the
bottom of the structure and r1 is the corresponding value at the CG
of the structure. The constant depends on things like the mass of the
earth and also the ratio of the cross-sectional area of the structure at
its center and the bottom, which would be chosen based on engineering
considerations. If r1 is chosen for geosynchronous orbit (GSO) then r1
is about 4.2E7 m.
The formula for strength can be manipulated to obtain
(ds/dL) * L / s = r1 / r
where the length of the structure from CG to earth end is called L = r1
- r. The surface of the earth is at about r = 6.37E6 m. If the structure
extends from GSO to the surface of the earth, a length of about 36000
km, then the ratio,
r1 / r = 6.6
so that changing the length of the structure by a small fraction x
results in a 6.6x change in the strength required of the material used
to build the structure. For example, if you raise the earth end by 10km,
0.028%, then you reduce the strength required by 6.6 * 0.028% = 0.18%
I estimated that the strength divided by the density of the material
used must exceed about 10^7 m^2/sec^2 in order to withstand the stress
(below, all units are SI). For steel, this ratio is only about 10^5
(and that is being optimistic and using 10^9 as the strength of steel,
typically steel is only loaded up to around 10^8 ). My references do
not list the strength of diamond, but its density is 2.3E3 so diamond's
strength would have to exceed 10^10 to make a space elevator to earth.
Maybe diamond or some carbon composite is that strong? I don't have a
reference for the latest super-strong material parameters. Or I could
have made a mistake (see below).
I haven't checked my work -- it could be all wrong. Beware!
define m = G M rho, where G is grav. const., M is mass earth, rho is
density of elevator material
s = strength of material in Newton per square meter
A[r] = A0 Exp[ (m / s) ( 1/r0 - 1/r ) ]
s = m ( 1/r0 - 1/r1 ) / Log[e, A1/A0 ]
( ds/dL ) / ( s/L ) = r1 / r0
G = 6.67E-11
M = 5.98E24
m / rho = 3.99E14
r_earth = 6.37E6
r_geo = ( G M / omega^2 )^(1/3) = 4.23E7
r_geo / r_earth = 6.64
r_geo - r_earth = 35,930 km
omega = 2 Pi / (24*3600) = 7.27E-5
I_earth = 0.4 M r_earth^2 = 9.71E37
KE_earth = 0.5 I omega^2 = 2.56E29
figure of merit
---------------
alpha = s / rho = 4.10E6 ( r1/r0 - 1 ) / Log[ 10, A1/A0 ]
for A1/A0 = 10, r1/r0 = 6.64:
alpha = 2.3E7
steel
-----
working stress ~ 10^8
breaking stress = 1.1E9
density = 7.8E3
alpha <= 1.4E5
diamond
-------
density = 2.3E3
shear modulus = 5E11
if alpha = 3E7 then we need
s >= 6.9E10 (this is what would be needed, actual s of diamond unknown by me)
which is about 70 times the breaking strength of steel
ARTICLE (2001 May 02)
Space Elevators Get A Lift by Karl Ziemelis London - May 2, 2001 They
say the first 100 kilometres are the best. Moments after the door
slides shut with a reassuring "ker-chunk", the acceleration takes
hold, pushing you gently but firmly into your seat. Terra firma drops
precipitously from view, and your internal organs groan in sympathy.
The base tower seems endless as it slides past the window. Then you're
in open sky, at first a seemingly infinite expanse of blue, but
gradually darkening until the Milky Way appears in all its glory. And
throughout, the shimmering blue pool that is the Earth curves away
beneath you, a sight that was once the preserve of a privileged few.
After what seems like forever -- but is actually little more than 10
minutes -- the acceleration eases. Now cruising at 2000 kilometres an
hour, at an altitude of 150 kilometres and rising, you begin to feel
uncomfortably buoyant in your seat.
Trying to keep calm, you avoid dwelling on the fact that for the next
18 hours the only thing stopping you from plummeting to Earth is little
more than a glorified piece of rope. A cable some 47,000 kilometres
long, yet no more than a few centimetres wide, stretching from the
surface of the Earth into orbit. You are taking a trip on the space
elevator. Get ready for the ride of your life.
The idea of an elevator to the heavens may sound preposterous,
like an updated version of the Tower of Babel. But it's a serious
proposition. Two independent NASA teams recently thrashed out the
technological requirements for such a project and found them to be
feasible. Extraordinarily demanding, yes, but feasible.
"You're looking at something we can seriously consider building by the
end of this century," says David Smitherman of NASA's Marshall Space
Flight Center in Huntsville, Alabama, who led one of the teams. The
space elevator -- an idea long consigned to the wastebasket of
pipe-dream technologies -- now looks like a real possibility. Just.
Why bother building one? Once such a structure is in place, it would
allow cheap and cheerful access to space. Passengers and cargo could
ride up and down the cable in a manner similar to a conventional
elevator -- or, more accurately, a cable car -- travelling at a fraction
of escape velocity.
That would cut the cost of putting payloads into orbit to as little as
$1.48 a kilogram, compared with $22,000 a kilogram on a rocket. And you
wouldn't have to be a super-fit astronaut to make the trip, which would
open up space to the (modestly wealthy) masses.
The idea of the space elevator was first raised in 1960 by Russian
engineer Yuri Artsutanov, and rehashed several times in the years that
followed. But the idea went largely unnoticed until 1979, when Arthur
C. Clarke used it as the centrepiece for his novel The Fountains of
Paradise.
So how does it work? The best way to get a handle on the concept is to
use that traditional tool of physics, the thought experiment. Start
by imagining a satellite. The time it takes to orbit the Earth is
determined by the strength of gravity, and this varies with distance:
low-flying satellites orbit quickly, distant ones much more slowly.
In between is a special distance -- 35,786 kilometres -- at which a
satellite takes exactly one day to orbit. If its orbit is aligned with
the equator, a satellite at this distance will hover over the same point
on the Earth's surface as the two turn in celestial tandem. Satellites
parked in such an orbit are termed "geostationary".
To continue the thought experiment, imagine elongating the satellite
inwards towards the Earth, and at the same time outwards into space, so
that its centre of mass remains in geostationary orbit. Those parts of
the satellite closer to Earth will be moving more slowly than necessary
to maintain a stable orbit, and so will start to feel gravity's pull. In
contrast, the parts further away will be moving too quickly for their
distance and so, like a stone in a sling, will try to move further
afield. The result: tension. The satellite becomes a taut cable in
orbit.
Tower of power
It is then trivial to carry the thought experiment to its logical
conclusion, where the satellite's innermost point strikes ground zero --
or, more likely, connects to a tall tower.
The result is a continuous structure stretching all the way from the
equator into space. At the Earth end is the base station, a massive
complex with all the trappings of a major international airport --
hotels, restaurants, duty-free shops and the like.
Looming above the complex is the launch structure, something like
the Eiffel Tower but tens of kilometres tall. Then comes the cable:
47,000 kilometres long, uninterrupted except for a space station at the
geostationary point. This would serve as the structure's centre of mass
as well as housing labs, a business park and a zero-gravity resort.
Further out lies a counterweight, possibly a minor asteroid tethered to
the end of the cable (see Diagram, p 27) [NOTE: Not available here -
A.Y.]. So much for thought experiments. Could we actually build such a
thing? The answer, according to NASA, is a cautious yes -- once we've
overcome a few technological hurdles.
By far the greatest challenge is the cable itself. The sheer weight
of the structure dangling from geostationary orbit would place
extraordinary demands on the material used to make it. What sort of
stuff has the tensile strength needed to support its own weight over
such a length? Surprisingly, almost anything would work in principle,
provided it was appropriately tapered: widest at geostationary orbit,
where tension is highest, and narrowest at the extremities.
But possible is not the same as practical. A steel cable 1 millimetre
across at ground level would have to be 40 billion kilometres in
diameter at geostationary orbit -- equivalent to building an upside-down
mountain bigger than the Solar System. Even Kevlar, which is stronger
and lighter than steel, would need to widen to 16 metres, so you'd need
2 gigatonnes of the stuff.
To make matters worse, the cable would need a minimum diameter more like
10 centimetres, not 1 millimetre. For a cable of practical dimensions,
you need a material with enormous tensile strength. NASA's estimates
suggest a magic number of 62.5 gigapascals -- that's 30 times stronger
than steel and 17 times stronger than Kevlar.
[Erik note: that means the strength of steel is 2.1E9, and kevlar is
3.7E9]
Until recently, the lack of such a material has denied the space
elevator even a modicum of credence. Enthusiasts have been forced to
make wildly exotic suggestions: fibres of crystalline hydrogen or even
antimatter. But now it turns out that an element as down-to-earth as
carbon might hold the key to the heavens.
It comes as no real surprise that carbon has been elevated to the
material of choice. In the form of diamond, it shows record-breaking
mechanical properties. Diamond can't be spun into filaments, but there
is a form of carbon that combines strength with length: nanotubes. These
tiny, hollow cylinders made from sheets of hexagonally arranged carbon
atoms exceed the tensile strength of steel by at least a factor
of 100. Even conservative estimates place their strength at 130
gigapascals, which surpasses the magic number by a comfortable margin.
So what's the catch? (And there's always a catch ...) For a start,
they're extremely expensive, clocking in at a cool $500 per gram.
They're also a little short at present, with even the best synthesis
methods yielding tubes no longer than a few micrometres. Bradley
Edwards of Los Alamos National Laboratory in New Mexico, who led the
other NASA team, has worked out how long nanotubes would need to be to
form a viable composite material. The figure he has come up with is 4
millimetres.
But there is hope. According to Dan Colbert of Carbon Nanotechnologies,
a spin-off from Rice University in Houston, Texas, the cost of making
nanotubes is set to tumble. At the moment they are produced by laser
vaporisation of graphite, a process that yields small batches of pure
product perfect for laboratory use but far too expensive for the
construction industry -- let alone anyone building a space elevator.
But Carbon Nanotechnologies has a new production process called "high
pressure carbon monoxide deposition", or HiPCO, which promises to be
scalable, so production plants could be as big as you like -- and bigger
means cheaper. Colbert reckons that within seven years HiPCO will have
cut the cost of nanotubes to just a few cents a gram, though he won't
give details of how it works.
What about the problem of length? Things might not be too bad as they
stand. Nanotubes have a tendency to "rope up", or stick together side by
side, and the cohesive forces between them seem strong. Good news. But
on the downside, roped-up nanotubes also slip and slide erratically
against one another in a way we don't fully understand. Nobody has yet
measured the strength of a nanotube rope, but early indications are that
the tensile strength is reduced by at least a factor of 3, putting it
"right on the ragged edge" of what is needed for an elevator, Colbert
says.
And when a multibillion-dollar project is at stake, what engineer
would work on the ragged edge? Perhaps the simplest solution is to
find a way of incorporating nanotubes into a composite material like
fibreglass. The downside of this approach is that whatever material is
used to bind the nanotubes together will dilute their strength.
The most elegant solution would be to produce continuous nanotubes
extending the full length of the cable. There's no doubt that such a
material would be strong enough, but is it a realistic prospect? At
present no one knows how to join individual nanotubes together to make
longer molecules. But researchers are working on the problem, and
Colbert believes there's a very good chance of success.
Getting attached
So now that we have a cable dangling from a distant point in space, we
need something to attach it to. We could, of course, extend it all the
way down to sea level and tie it in place. But recall the taper problem:
the cable needs to widen as it gets higher in order to support its own
weight. And the lowest section must have a certain minimum thickness
which, in turn, determines the cable's girth at geostationary orbit
-- and hence the mass and cost of the structure as a whole. Raise the
bottom of the cable and you'll save an awful lot of material at the
top. Ideally we need to attach it to something very tall.
A well-placed mountain near the equator would be a good start, but there
are safety concerns with this. Should the unthinkable happen and the
cable snap, a large amount of debris would fall on land. Little wonder,
then, that the preferred option is a gigantic tower built on a platform
out at sea. The tower would have to be tens of kilometres tall, but
compared with dangling a cable from orbit, building one would be child's
play.
The tallest self-supporting building in the world today is the 553-metre
CN Tower in Toronto, nowhere near the theoretical limit. With existing
construction methods you could raise a tower 20 kilometres tall, more
than enough for the base station. With the cable and tower in place, we
have the skeleton of a space elevator.
All that is lacking is a means of climbing it. Traditional mechanical
means -- cables, wheels and pulleys -- wouldn't do. Given the stupendous
distances involved, a viable transport system must satisfy two basic
requirements: very low maintenance and extremely high speeds. Magnetic
levitation and propulsion holds the key to both.
By using repulsive magnetic forces to keep the vehicle out of direct
contact with the cable, maglev eliminates the wear and tear that plagues
most transport systems. And in the absence of friction, the vehicle
can rapidly accelerate to several thousand kilometres an hour. Another
advantage of the system is that you can use the braking and descending
phases of the journey to generate electricity. This makes running the
elevator very energy efficient.
Is that everything covered? Not quite: space is a hazardous place. The
near-Earth environment is fizzing with energetic particles, all waiting
to etch, sputter and generally erode any material they come across. Then
there are potentially cable-cutting projectiles, including meteoroids
and space debris. But such hurdles are surmountable. Just look at the
success of the Moon shots, interplanetary probes and, most recently, the
International Space Station, all of which had to contend with similar
problems.
There's also the small matter of economics. There's no doubt that an
elevator would slash the cost of getting into space, but would this
justify the phenomenal expense of building one in the first place? On
this point Smitherman is optimistic. He says the trick is to start
generating revenues early on, perhaps by using the first nanotube
strands to deliver solar power from space. Then the project becomes
comparable in scale to building a road or rail network.
Some four decades after the space elevator was first dreamed up, there
are still plenty of reasons to be sceptical about it, even allowing for
the tremendous technological advances that have been made during this
period.
What if nanotubes prove too weak or can't be made long enough? What if
the near-Earth environment is too hostile for such a structure? What if
it's too expensive after all? Well, as Mr Wonka said in Roald Dahl's
Charlie and the Great Glass Elevator, "Bunkum and tummyrot! You'll never
get anywhere if you go about what-iffing like that."
So if all goes well, when can we expect such a structure to be
built? Arthur C. Clarke was once asked this question and came up with
the answer: "The space elevator will be built about 50 years after
everyone stops laughing". They just stopped.
Karl Ziemelis is physical sciences editor at Nature
--
"Erik Reuter" <[EMAIL PROTECTED]> http://www.erikreuter.net/
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