[ExI] SpaceX Super Heavy and Space Solar

[Adrian Tymes]

On Mon, Oct 21, 2024 at 6:01 PM Keith Henson <hkeithhenson at gmail.com> wrote:

> On Mon, Oct 21, 2024 at 1:25 PM Adrian Tymes via extropy-chat
> <extropy-chat at lists.extropy.org> wrote:
> >
> > On Mon, Oct 21, 2024 at 3:44 PM Keith Henson <hkeithhenson at gmail.com>
> wrote:
> >>
> >> On Sun, Oct 20, 2024 at 4:12 PM Adrian Tymes via extropy-chat
> >> <extropy-chat at lists.extropy.org> wrote:
> >>
> >> > before the program is generating revenue, makes it economically
> infeasible.  No one with the requisite finances will believe that heavily
> in the revenue until after a small scale prototype is demonstrating,
> >>
> >> You can't scale a power satellite down for beans.  It is a feature of
> >> microwave optics (diffraction).
> >
> > You can.  It may be substantially less efficient, but it does work - at
> all - at smaller volumes.
>
> Adrian, if you can beat this problem, you will get nothing but praise
> from me. I worked on power satellites for ten years and made no
> progress on the scale-down problem whatsoever.
>

Caltech did it for less than $1B:
https://www.caltech.edu/about/news/in-a-first-caltechs-space-solar-power-demonstrator-wirelessly-transmits-power-in-space


> >> > even at significantly lower economic efficiency ($0.10-0.50 per kWh,
> perhaps).
> >>
> >> That would just kill the idea.
> >
> > How does the existence of limited markets that can pay higher amounts
> for the same service kill the idea?
>
> Let's put numbers on this.  What power level is a limited market?
>

How about Hawaii?  They're isolated from the grid, have a total consumption
far less than all of humanity's, and have high power prices.


> But a one km power beam from GEO at 2.45 GHz spreads out to 10 by 14
> km.  The center beam power density for 5 GW is 230 W/m^2,  Our
> imaginary one rocket power sat would supply about .46 W/m^2.  How much
> power do you propose to supply?
>

I wouldn't put it out at GEO, partly because the beam dissipates so much.
I'd put it in LEO.  Granted, the power would be intermittent from one power
satellite; for a prototype, this would be okay, but one of the first
upgrades once the prototype had proven itself would be to make a
constellation, enough that the rectenna would always have one satellite
serving it.  Meanwhile, the individual satellites store up power as they
orbit, downlinking one orbit's worth of power during one pass.  The
inefficiencies of this seem quite a bit less than the inefficiencies of
beaming all the way from GEO.

Also, running the numbers for beam divergence, even if I did start at GEO
(35,768,000 m to Earth's surface) with 2.45 GHz (about 0.1224 m
wavelength), a beam that starts 1,000 meters wide is only about 6.3 km wide
at the Earth's surface, not 10-14.

Beam divergence:
θ = 1.22 * λ / D = 1.22 * 0.1224 / 1,000 ≈ 0.00149 radians
θ = beam divergence angle
λ = wavelength
D = initial beam diameter

Beam width at Earth's surface:
Width = 100 + 2 * 35,768,000 * tan(0.00149/2) ≈ 6,341 meters

An initial beam of 2,310 m gets about 4,622.192 m at the surface, which
appears to be an optimum: increasing or decreasing the initial beam width
increases the surface area.

Getting down to 1,000 km orbit gives an optimum starting beam of 390 m, for
a received surface width of 772.89 m.  500 km orbit (avoiding the worst of
low-altitude orbital decay) gives 273 m starting beam and 546.4945 m
surface width - so that's less than 1% as much rectenna needed, whether
you're just capturing the center or the entire beam.  If the initial
rectenna did cost $1B, then this is a few tens of millions of dollars (not
straight 1%, as economies of scale work in reverse), which is far more
fundable for a prototype (not counting the cost of the satellite, granted,
though the center beam power density would be significantly higher too).


> > Your assertion that any rectenna, regardless of the power level
> involved, will cost a billion bucks is blatantly false.
>
> It's $200/kW.  I worked this out 10-15 years ago. It is fine if you
> don't like my number. What do you calculate as a rectenna cost?
>

Nonlinear.  Something that costs $200 to set up a unit that does 1 kW,
costs much less than $200,000,000 to set up a unit that does 1 GW.
Economies of scale set in.


> > For instance,
> https://www.electricchoice.com/electricity-prices-by-state/ shows that
> current electricity rates in Hawaii is above $0.30/kWh and has been for
> over a year.
>
> Consider the spread between generation cost and retail.  Most of what
> we pay in CA is for distribution.
>

True, but you were talking retail cost (what the utility using these
rectennas and satellites gets paid), right?  That $0.30/kWh is retail, so
far as I can tell.


> > That is to say: a system that could serve all of Hawaii's needs and
> charge $0.30/kWh would, right now, be commercially competitive.  Other
> sources say that Hawaii's electricity consumption is a few TWh/year.
> >
> > So, downsize a rectenna to just Hawaii's needs.  This is not the exact
> same billion dollar rectenna that would be used for larger projects.  (It
> very much wouldn't, unless Hawaii's power grid gets grid-tied to anywhere
> else.  That it isn't is part of why electricity costs so much there.)
>
> I have seen an analysis.  Don't remember the details, but we could
> regenerate them right here.
> https://en.wikipedia.org/wiki/List_of_power_stations_in_Hawaii
>
> Installed capacity is right at 3 GW and an average of around 1.07 GW.
> So whatever cost you get from the capital cost will only be generating
> revenue about 1/3rd of the time unless you can generate another
> market.  Fairly soon you need to ask where do you put the rectenna.
>

 Where do you get "an average of around 1.07 GW"?  I don't see any
discussion of base vs. peak loads in that article.

That said, in practice you wouldn't be offsetting literally everything
right away.  Base load service is far more economical than peak load, and
energy storage solutions are being investigated to take care of the
discrepancy - but investigating power storage (on the ground, anyway) gets
away from discussing the power satellite system itself.  I assume your
calculations are primarily to serve base loads, which generate around the
clock (or close to it).
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