[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
>
>
>
> _______________________________________________
> extropy-chat mailing list
> extropy-chat at lists.extropy.org
> http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat
>
More information about the extropy-chat
mailing list