🚀 go-pugleaf

chris@chrism.demon.co.uk (Chris Marriott) writes:

>In article <3954@key.COM> rburns@key.COM writes:

>>
>>What are the current estimates of folks in this newsgroup of how long it 
>>will be until the world starts to see privately funded space colonization?
>>
>>I've noticed that there are some _extremely_ capital intensive schemes around
>>which might make the marginal cost of launching mass to orbit fairly cheap.
>>(I'm thinking of mechanisms like Clarke's space "elevator" or Bull's 
>>gun). I'm more interested in technologies like the Henson Sling or SSTO
>>technology that might be more useful to private citizens and less likely to
>>be shelved or monopolized by governments or mega-corps.
>>
>>
>>Thanks!
>>

>The "space elevator" - basically dropping a cable from a geosynchronous
>satellite to Earth (and, of course, another one upwards so the centre of
>mass stays still) is probably the most *lethal* device one might conceive
>of building!  Imagine the cable breaks near the mid-point.  You have 38000km
>of cable falling to earth at *orbital* velocities, enough to wrap itself
>around the entire equator of the planet!  Go figure out the kinetic energy
>involved.  How much ocean would it vaporize?  Massive medium-term climatic
>changes at best - "nuclear winter" scenarios.  A new Ice Age a distinct
>possibility.

I have to comment on the above in sequence:

1) Given my income stream, I could save $15,000 per year.  At six
percent compounded, I would have $80 million in today's dollars
in a century.  By then, it should be within that cost due to improvements
in technology.  So a century would be an upper bound.  One billionaire
could fund a private space colony out of his assets if he wanted to
and spent the money intelligently.  So the lower bound is zero time.

2) Gerald Bulls gun, or the much-improved versions of gas guns that
are being developed, would be expensive by ordinary human scale,
but cheap in relation to current space costs. The gas gun design I
am working on at Boeing is estimated to cost less than 2 Ariane IV
launches to build (<$130 million), or less than one 747-400 aircraft
to buy.

3) The Space Elevator that reaches to GEO is the limit case of
the large class of possible orbital structures.  Given today's
material strengths, it is not economic to build a full space elevator.
It is, however, resonable to build a structure several thousand
km long, whose bottom end is substantially slower than orbit
velocity (by 2-3 km/s), and using an elevator the rest of the
way.

4) Let us assume a cable with a lifting capacity of 1 million
pounds of payload has a tensile strength of 2 million psi.
This is twice the strength of today's materials, but you wouldn't
build such a thing until you have suitable materials.  If you
use a working strength of 2/3 (factor of safety = 1.5), then
the scale length of the cable is 500 km.  The cross section
must increase by a factor of e per scale length going up the
gravity well.  The earth's gravity well is equivalent to 6375
km deep, and from the surface to GEO is equivalent to 6,230 km
deep.  Thus you have 12.5 scale lengths, thus the cable is
exp(12.5)=268,000 times the cross sectional area at GEO as
at the bottom end.  Given a working strength of 1.33 million psi,
the tip cross section is 0.75 square inch.  So the GEO
cross section is 200,000 square inches, or 37 feet.  

With a cross section of 130 sqaure meters, a length of 35000
km, and a density of 1900 kg/m^3, we have a total mass opf
8.64x10^12 kg, or 8.65 million tons.  Allowing for the fact
that the thing is not the full width the whole length, and
not all of it is falling from GEO, let us reduce this to
4.3 megatons of falling stuff.  

Something falling from GEO hits the surface at close to
escape velocity, so has about 14 times the energy content of
TNT (4.2MJ/kg) to dissipate, so the equivalent energy
is 60 Megatons of TNT.  This is definitely a lot, but it
can be compared to the yield from one Trident- Class
nuclear submarine, which comes in at 87 Megatons.

5) For economy's sake, a full GEO system would not be built
as a hanging cable all the way from GEO.  Using the same
strong materials, you would build a tower up from the
ground to meet it, with the same number of scale lengths
in each structure, for minimum mass.  Compressive
towers are not as strength-efficient as cables.  They can
achieve about 40% the effective strength.  Therefore,
the span will be covered by a tower and a cable, each 9
scale lengths long each.  The maximum cross section of
the cable is then 8000 times the bottom tip, or 4 square
meters.  The impact energy is then reduced to less than
2 Megatons, still a serious matter but hardly a climate-
changing one.

6) For safety's sake and to make it manufacturable and
deliverable, the cable will probably be made in strands
about 1 cm across (ever try to wind a cable 2 meters
thick on a drum?) and no more than 10 km long.  This
produces cable reels massing about 2 tons each, which
is a manageable construction item.  The parallel strands,
all 40,000 of them, will be spread apart in space to
protect against accidental impact by spacecraft or 
space debris.  With 1 km inter-strand spacing, the
structure is 200 km wide at the GEO point, tapering
down to a set of 4 strands in a square pattern 1 km
apart at the cable-tower join point ( which will
be at a height of 1200 km).  The tower then expands
outward from there to a width of perhaps 60 km at
the base.

7) The total mass in space is on the order of 200
kilotons of cable, at a price of about $40/kg hypothesized
for large scale production of high strength carbon fiber, for
a material cost of $8 billion.  So we are talking a couple
of tens of billions total project cost.  

With a elevator capable of 30 kph, it will take
1000 hours to raise a cargo to GEO, so today's elevator
technology is not suitable for people, but okay for
bulk items.  A mono-rail type device running at
300 kph up to GEO would take 4 days to ride.  This
is more reasonable.  At 1000 tons x 90 deliveries per
year x 12 year amortization, we are talking about
an amortized cost of $20/kg to GEO.  This compares
to the present cost of $20,000/kg to GEO, a hell of
an improvement.

Dani Eder

-- 
Dani Eder/Meridian Investment Company/(205)464-2697(w)/232-7467(h)/
Rt.1, Box 188-2, Athens AL 35611/Location: 34deg 37' N 86deg 43' W +100m alt.