[extropy-chat] Space elevator numbers III

[David Masten]

On Thu, 2007-02-15 at 21:27 -0500, Keith Henson wrote:
> At 04:25 PM 2/15/2007 -0800, you wrote:
> >How well does the iron process do in terms of flaws in the fiber? The
> >last presentation I saw on carbon nanotubes was that this was the crux
> >of the problem.
> 
> Who knows?  It looks good but has not been tried yet.

OK, fair enough. I was hopeful that some progress had been made.

> Ok, 200 launches a day for the SPS parts.  Ignoring mass for the tugs, 1000 
> launches, 10,000 tons will build a 5 Gw power sat.
> 
> LOX-Hydrogen for the fuel I presume? 

Not economically efficient, but I'm guessing kerosene use runs counter
to what you are doing, so sure. At any rate, the trade-offs between
LOX/LH2 performance and LOX/Kerosene energy density give approximately
equal payload to propellant ratios.

> What mass ratio?  Let me assume 95% 

With LOX/LH2 you should be able to get 91 or 92% single stage to LEO,
current two stage GEO launchers run around 90% or so as well.

> and that the payload fraction is half the dry weight. 

With current technology and the vehicle is designed for re-usability
(i.e. safety factors are dominated by fatigue rather than yield
strength) payload ends up 1/3 of dry mass. With carbon nanotubes at a
cost, availability, and strength for a space elevator you should be able
to get much better payload fraction. 

On a conservative SWAG, a doubling of strength should give about 20%
improvement in mass. Modern carbon composites can reach 2 GPa tensile,
so 5 doublings gives us the strength necessary for a tether (I think, I
have seen numbers from ~50GPa and up, though I'm not sure if this is the
nanotube strength or the strength of the composite). If we have a 30 ton
dry mass (10t payload, 20t vehicle) with current tech, then with
tether-type strength composites we should get 6.6 tons vehicle
structures mass lifting 10t.

The above is very conservative as the shift from aluminum to carbon
composite structures is 20% for a strength of material doubling, but
aluminum is isotropic, whereas carbon composites are not, so extra
layers of carbon fabric are necessary to make up for this. Since carbon
nanotube composites can reasonably be expected to have similar
anisotropic material properties as current carbon fibers we do not need
to count this again. It may be possible to get up to 40% mass savings
for each doubling. Which means a 20 ton vehicle structure would end up
as 1.6 tons to lift 10 tons. I doubt this is reasonable though. Engines
really want to be made of metals, and they will come to dominate the
mass budget.

I'd say a 25% improvement for each doubling is most reasonable. That is
4.75 tons structure per 10 tons payload.

>  So lifting ten 
> thousand tons will take 400,000 tons of propellant.  Give me real numbers 
> and I will recalculate.
> 
> Ignoring liquefying the gases,

Why? Standard industrial processes (liquefying O2 and cracking H2 from
natural gas) for making the propellants are much more efficient.

> or 1,328 Gwh or 55 Gw days.  Given various factors like electrolysis 
> efficiency it would probably take about 100 Gw days (20 days for a 5 Gw 
> power sat) to pay back the energy lift cost.
> 
> That's not actually bad, but you are up against a *one* day energy payback 
> for the space elevator.

What is the initial capital outlay required, the amortization period of
the elevator, and the maintenance/operation costs? I have found one
estimate of ~$10 billion for initial construction.

> Electrical power in to mechanical power out is typically 95 % or better for 
> large electrical motors.

Ah. Learn something new everyday.

Dave