[ExI] Power Satellite payback analysis

[Keith Henson]

On Sat, Jun 10, 2023 at 9:19 PM William Arnett <waarnett at mac.com> wrote:
>
> Yes, but how long to pay back the dollar cost of the launch?

The model to get competitive power is $200/kg or $1300 per kW.  That's
based on $100/kg to LEO and no more than a factor of 2 to GEO.  This
is speculative but looks possible with self-powering out to GEO.

The total including parts and the rectenna is $2400/kW or $2.4 B/GW or
$12 B for a 5 GW power satellite. That's about 1/4 of the cost per GW
of a nuclear plant and the power cost is about 3 cents per kWh.  The
factor from levelized cost of electricity to cents per kWh is around
80,000 to one which happens to be about the hours in ten years.

If they can last 100 flights, the cost of the rocket can be ignored as
lost in the noise.

Keith


> —
> Bill Arnett
> bill at arnett.us.com
>
> > On Jun 10, 2023, at 8:18 PM, Keith Henson <hkeithhenson at gmail.com> wrote:
> >
> > I wrote this for the blog OFW, but I thought it might amuse people here.
> >
> > Someone bitched about me saying that a power satellite would repay the
> > energy to lift it in
> >
> > “a bit over two months” with
> >
> > " Keith, I call rubbish on this. Post the study/paper documenting this
> > silly claim."
> >
> > My response:
> >
> > I can reconstruct this from a few numbers right here.
> >
> > The mass of a power satellite is around 6.5 kg/kW (my work, but it is
> > about the center for others),
> >
> > SpaceX big rocket burns about 4,600 tons of LOX and LNG to take 100
> > tons to orbit
> >
> > CH4 takes 2 O2 to burn.
> >
> > 16 and 32 so the LNG is 1/3 of 4600 or 1533 tons of LNG to lift 100
> > tons. Or 15.3 kg of LNG to lift one kg.
> >
> > So to lift enough for a kW would take 15.3 times 6.5 or 100 kg.
> > Methane is 55.5 MJ/kg or 15.4 kWh/kg. 100 kg would be 1540 kWh worth
> > of LNG. Davide by 24 hours per day and you get 64 days for the lift
> > energy to be paid back, little over two months.
> >
> > This does not account for the energy it took to make the power
> > satellite parts, but that is small compared to the lift energy, even
> > aluminum is only around 1%.
> >
> > I also left out the reaction mass to move the power satellite to GEO,
> > which might push the mass you have to lift up to 10 kg/kW.
> >
> > But if you burned the LNG for power, the best you can do in a combined
> > cycle power plant is 60%. This factor makes the payback somewhat
> > shorter.
> >
> > So using LNG for rocket fuel seems like a good idea compared with just
> > using it to make electricity.
> >
> > If you find an error in my analysis, please let me know.
> >
> >
> > Keith