[ExI] Power sats and payload size was Small solar satellites

[Keith Henson]

On Sat, Feb 25, 2012 at 2:09 PM,  Adrian Tymes <atymes at gmail.com> wrote:

> On Sat, Feb 25, 2012 at 11:10 AM, Keith Henson <hkeithhenson at gmail.com> wrote:
>> The problem is the initial investment, $50-100 B. ?One concept is to
>> use 250 Falcon Heavy launches to put a half GW propulsion laser seed
>> in GEO and use 1/4 scale (30 tons) air launched vehicles to bootstrap
>> the rest of the 2 GW needed to support a 500,000 ton per year parts
>> pipeline to GEO. ?That only builds ~100 GW of new power per year, but
>> the profit is such it can rapidly grow by a factor of 10-20. ?There is
>> room in GEO for ten times the current total energy use of humans.
>
> Ah, right!  Keith, this is something I wanted to ask you about re: one of
> the research groups I've gotten involved with.
>
> In short, what would the economics of this look like, if you broke it into
> ~1 kg sized launches?  Specifically: 1 CubeSat launched at a time to
> LEO, to contain boosters to put a sub-kg power satellite into GEO.
> Just keep feeding more of these over time, making a cluster - both to
> easily replace any part that fails, and to let you get started for a far
> smaller investment.

Sorry, won't work.  The problem is optical.
http://en.wikipedia.org/wiki/Airy_disk

http://www.rocketdynetech.com/dataresources/WirelessPowerTransmissionOptionsForSpaceSolarPower.pdf

http://www.sspi.gatech.edu/aiaa-2009-0462_ssp_alternatives_potter.pdf
(see page 33)

If you make the target 100 GW/year, which is small compared to the
need but still significant, then the mass in GEO you need (at 5 kg/kW)
is 500,000 tons.  At 8760 hours per year it is ~60 tons per hour.  The
maximum acceleration time to get a payload into orbit is ~20 minutes
(you want the longest time for the smallest laser power).  This sets
the payload size to 3 of 20 tons per hour.  The 20 tons takes 30 tons
in LEO and that takes a 120 ton starting mass if airdropped at ten km.

There have been much smaller proposals for laser transmission from
very small power sats.  But they miss the target of making a
substantial contribution (or paying off the non recurring engineering
charges).

> Key questions:
>
> * How many satellites would you need to get any measurable output
> at ground side?  Not enough to export useful energy, but enough to
> demonstrate "ground truth" that the system works.

You are doing that right now if you have a Dish network TV.  Ever set
one up?  The energy is certainly measurable.

> This is an
> important milestone for many would-be investors - even for systems
> where there is no theoretical question as to feasibility.  (You're proving
> that whoever did this, either has or knows how to get the necessary
> resources - people, materials, regulatory approval, et cetera.)
>
> * How much energy would you get from this minimal version, and how
> would it scale by adding more satellites?  Linearly?
>
> * What's the minimum size of ground side receiving station that you
> would need?

Depends on the frequency.  10 km E/W and km 14 N/S are what you need
for 2.45 GHz.

> * Would the minimum size of ground side station scale linearly with
> the number of satellites?

No.  It scales inversely with the frequency.  But there are only a few
frequencies that get through the atmosphere well.

> * What would the initial investment to cover manufacture, assembly,
> and installation of those components (and anything else necessary
> for a minimum ground truth version)?

The power satellites and the ground station are not the hard parts.
It's the transport system that makes or breaks power satellites.  That
takes ~250 Falcon Heavy launches to set up plus the cost of the laser
hardware, power plant and heat sink (a square km).  The launch cost
alone is $25 B, but for that number of launches SpaceX might give a
substantial discount.

Keith