[ExI] Power satellites

Keith Henson hkeithhenson at gmail.com
Wed Apr 22 20:17:27 UTC 2009

```On Wed, Apr 22, 2009 at 6:20 AM, Dan <dan_ust at yahoo.com> wrote:
>
> --- On Tue, 4/21/09, Keith Henson <hkeithhenson at gmail.com> wrote:
>> Even if moving cable space elevators are *never* built,
>> they are still
>> useful as the gold standard for space transport.
>> \$0.15 for the energy
>> and a share of the capital to put one up.
>
> I would not use a hypothetical, untested technology as my "gold standard for space transport."

"Gold standard" in this context means, "Yah can't do betta:"  I.e., it
is as the limit.

> All the numbers on their cost and efficiency are based on speculation.

No, they are based on utterly sound physics.  The orbital energy at
GEO is 57.5 MJ/kg referenced to the surface of the earth.  But a space
elevator extracts the orbital velocity from the rotation of the earth.
Since Ke = 1/2 mV^2, and the velocity at GEO is 3.1 km/s, the Ke is
4.8 MJ/kg.

52.7MJ is 52,700 kW-seconds or 14.6kWh.  Big electric
motors/generators are ~95% efficient, so call it close enough to
15kWh/kg.  In this context, I am using a penny a kWh.  Use 10 cents
per kWh if you want, it's still dirt cheap.

15kWh * 100,000kg/hr is 1.5 GW.  It would take a motor as large as the
largest power plant generators to drive a moving cable space elevator
being used to build power satellites.

Capital cost (which I didn't mention) isn't entirely speculation
either.  Because there are other ways to do it, the capital cost for a
moving cable space elevator can't go over ~\$100 billion.  The elevator
has to be constructed in single digit years and it needs to lift about
2% of it's mass per day to make it a reasonable, cost effective
project.

For 2400 t/day that's 120,000,000 kg of elevator cable.  If 60% the
cost went for cable, \$60B/0.12 Bkg is \$500/kg--which may actually be a
reasonable or even a high number in this context.

These factors force the cable speed to around 450 m/s and limit the
total cable length to around 100 times the distance to GEO.  100 x GEO
is ~3.6 x 10^9 m, 120,000,000kg/3.6 B m is 0.0333kg/m, i.e., ~33 g/m.

Nanotube cable density is ~1.1, so the cable volume would be around 30
cc/m.  From V = pi r^2 L, r^2 = V/pi L, making the cable diameter ~.62
cm or about 1/4 inch for those of us raised on such units.  (Check my
math if you are so inclined.)

Of course we don't have cable in the 40-60 GPa range and until we do
space elevators are not possible.  You might note though that the
theory for nanotubes is ~175 GPs and that single fibers have been
tested to ~40 GPa.

Climbers are a different story.  The power in to gaining potential
energy is at best 10%.   A power satellite program at ~100t/hr
delivered to GEO would take 15 GW input rather than 1.5 GW.  At 50%
efficient the lasers would put out 7.5 GW and cost ~\$75 billion.

Keith
>
> Regards,
>
> Dan
>
>
>
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```