[ExI] Lack of interest

[hkhenson]

At 11:06 PM 5/7/2008, you wrote:
> > What we really need to do is come up with a way that provides
> > renewable energy at a lower cost than coal and oil.  I think there is
> > such a way.  Anyone interested in seeing work on it should send me
> > email.  No point in sending it to the uninterested on the list.
>
>I'd say just send it to the list.  As on topic as anything else going
>on.  Tough goal, though, to compete with high-quality fuel we can just
>slurp freely out of the ground.

It's getting harder and harder to get oil out of 
the ground.  The Canadian tar sands oil 
production cost at least $13 a barrel. The could 
really use a lot of cheap electrolytic hydrogen.

I don't know the exact trade off, but dollar a 
gallon gasoline may be in the $30-40 a barrel for oil.


Dollar a Gallon: The physics and business case 
for Space Based Solar Power for vehicle fuel.

Basic numbers

Gasoline provides about 130 MJ/gal.

A kWh is 3.6MJ so the energy in a gallon of gasoline is about 40 kWh.

Given the inefficiencies of the chemical 
processes needed to make liquid fuels from water 
and air, and the need to pay for huge plants, 
dollar a gallon synthetic gasoline implies a 
penny (or less) per kWh electrical input.

If dollar a gallon gasoline is the goal, penny or 
sub penny per kWh electric power is a way to get there.

More numbers

Hydrogen has about 141 MJ/kg of energy.  It costs 
about 50 kWh/kg to make and another 15 kWh/kg to 
liquefy.  Penny a kWh power would make hydrogen 
equal to a gallon of gas for less than 50 cents.

The only long-term source of energy is the 
sun.  Solar power does not work all that well on 
earth because the earth is in the way much of the 
time.  Moving solar power collectors into high 
orbit, geosynchronous, and very modest 
concentration gets you close to a factor of ten 
more sunlight than most places on earth.  The way 
to get the energy down, low-density microwaves, 
is a 40-year-old idea, the block has been high cost to orbit.

Consider a space based solar power project big 
enough to replace all the coal-fired plants in 
the US in one year, 300 GW.  This number is 
somewhat arbitrary.  (The market for new power 
sats would go on for decades at this rate as 
fossil fuels run out.)  For reasons rooted in 
geometry and physics, power satellites have to be 
5 GW or larger.  That means constructing them at 
60 per year.  At this rate, you can ignore RDTE in a first pass analysis.

Could such a project eventually deliver power at a penny a kWh?

Take a year at 8000 hours, and the mass of a 
power sat at 2kg/kW.  The annual output from a 
power sat would be in the range of 
4000kWh/kg.  At a penny a kWh, that is $40.  If 
we allow a capital cost ten times that high 
(reasonable for long lived projects) then we can 
afford to spend about $400/kg for parts and 
transportation to reap $40 of penny a kWh power 
per year.  That is a somewhat arbitrary 
number.  At a kg/kW, we could afford $800/kg installed cost

Rectennas

There are two main parts to a power sat, the part 
in space and the rectenna on the ground.

A rectenna is microwave diodes woven into a mesh 
much like chicken wire supported by poles 
containing inverters. Pending a more detailed 
design, I am going to use the price of PC power 
supplies at about $60 a kW and estimate the 
poles, microwave diodes and plowed in wiring to bring the cost up to $100 a kW.

The assumption is that since this does not 
interfere with farming, land lease cost will not 
be a significant factor. (Maybe we give the 
farmers under the mesh free electricity.) I am 
also not including the cost of transmission lines 
and for this level of analysis am not considering 
maintenance--which should be on a par with power 
transformers on poles. (The typical one runs 50 years without being touched.)

A 5 GW rectenna is still a formidable investment. 
5 million kW at $100/kw is half a billion 
dollars. That leaves us with $300 a kW for the 
power sat parts, transport to orbit and construction

Transport to Orbit­Space Elevator

So how much is the cost to lift power satellite parts to GEO?

This breaks down into running cost, which should 
mostly be energy and capital costs. Labor should 
be a relatively small part of a mature freight operation.

Last year I calculated the absolute minimum 
energy for a space elevator carrying up 2000 tonnes per day.

<http://eugen.leitl.org/A-2000-tonne-per-day-Space-Elevator1.ppt>http://eugen.leitl.org/A-2000-tonne-per-day-Space-Elevator1.ppt 


It takes about a GW to lift about 2400 tonnes per 
day or 24 million kWh to lift 2.4 million kg. 
I.e., about 10 kWh lifts a kg to GEO. At our 
target price, that costs 10 cents. It is only a 
dollar at current consumer prices for electricity.

Can we estimate the cost to put up a space 
elevator?  If we can make nanotube cable of 
adequate strength at all, it will take about 
100,000 tonnes of it, assuming the cable weighs 
50 times the daily payload. I think we can safely 
assume that anything produced in that quantity 
will not cost more than a few dollars a kg. 100 
million kg at even $10 a kg is only a billion 
dollars. It will probably take a number of times 
that figure to clean up the flying space junk and place the seed cable.

Even if the cleanup and space elevator cost $100 
billion, and was depreciated at 10% per year, 
that is a transport capital cost of only $10 
billion a year. Taking the elevator's capacity at 
only half a million tonnes per year, the capital 
cost would be $20,000 per tonne or $20 per kg.

That is less than 10% of what we can pay for 
power sat parts delivered to GEO and still charge 
under a penny a kWh for electric power.

The problem is we don't have strong enough 
nanotube cable and might never get it.

Hauling power sat parts up by rockets

We can't yet build a space elevator. We can build rockets.

A few weeks ago, Hu Davis pointed me to a design 
for a two-stage rocket that will deliver about 
200 tons to 
GEO. 
<http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf>http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf 


(Hu was the project engineer for the Eagle as in "the Eagle has landed.")

I decided to look at building power sats using rockets.

Neptune is about 3 times the capacity of a Saturn 
5, so it is within the scale up factors engineers feel comfortable doing.

This vehicle delivers 350 mt to LEO, and 100 mt 
to lunar orbit. I am going to take it as 
delivering 200 tonnes to GEO. We would abandon 
the third stage structure at GEO or convert it to 
power sat parts. To lift 200 mt to GEO Neptune 
uses 3762-mt of propellant for the first stage 
plus 1072 mt second stage totaling 4834 mt.

O2 to H2 is 6 to 
1. 
http://www.pw.utc.com/vgn-ext-templating/v/index.jsp?vgnextrefresh=1&vgnextoid=75a0184c712de010VgnVCM100000c45a529fRCRD


I.e., 1 part in 7 of this is H. or about 690 mt 
of LH, 6900 tons to lift 2000 tons per day in ten 
launches. The launch site would make electrolytic 
hydrogen out of water (the only long term 
source). That costs about 50 kWh/kg plus another 
15 kWh to liquefy the H2. (I am ignoring the cost to liquefy the oxygen.)

That would be 65 MWh per mt, or 65 GW hours for 
1000 tons, or 448.4 GWh per day for 6900 mt. 
Since there are 24 hrs in a day, the steady flow 
of power would be about 18.7 GW.  (Close to the 
output of four 5 GW power sats.)

Considering that a straight mechanical lift to 
GEO at 100% efficiency takes .66 GW, this implies 
a lift energy efficiency of 3.5%. Constructed of 
parts lifted by elevator, a power sat repays the 
energy needed to lift it to GEO in less than a 
day. Lifted by rockets it would take 5 days 
consuming close to 20 GW/per day or 100 GW-days. 
A power sat constructed this way would repay its lift energy in 20 days.

It would also require dedicating the first four 
power sats to hydrogen production, delaying 
producing power sats for sale by a few weeks.

If these rockets flew every day like aircraft, 
the company would need ten of them active plus a 
few "in the shop." If the vehicles were good for 
200 flights and there were ten in use, then a 
replacement vehicle would be added to the fleet every 20 days.

Dry first and second stages mass 619 mt. 
Producing one set every 20 days is an annual rate of 11,300 mt.

Is that reasonable?

The Boeing 747, which massed 175 mt, was produced 
as high as 70 aircraft a year for a total of 
12,250 mt. Rockets, being mostly huge tanks, are 
less complicated than aircraft and should take a 
smaller work force. Nonetheless, it would be a huge production line.

At 40 flights per engine, 49 engines per vehicle, 
and 10 flights a day, the consumption of SSME 
would be 12 a day. That would take a lot of 
investment in plant, but the cost should come way down at that production rate.

The cost per kg would be the energy cost plus 
capital costs. 20 million kW x 24 hrs x one cent 
per kWh is $4.8 million per day. $4.8 million/2 
million kg is $2.40 per kg for fuel ($12 a kg at 5 cent per kW power)

If the rockets cost the same per ton as 747 
aircraft, they would be about $1 billion each. A 
10,000 ton power sat would take 50 flights (1/4 
of the life of one rocket) to build it, so the 
cost for used up rockets would be 250 million 
dollars / 10 million kg or $25/kg. If operation 
even doubled this cost, transport would still be 
only $50/kg of the budget of $150/kg to GEO for 
power satellite parts.  ($300/kw at 2kg/kw)

The biggest unknown in this analysis is the cost 
of the parts going into the power sats, 
particularly solar cells. Among structural mass, 
transmitter and solar cells, I am going to assume 
$100/kg or less including whatever labor it takes 
to snap the parts together. With this size of 
lift package, we could seriously consider 40% 
efficient steam turbines cooled by the 
Drexler/Henson space radiator design (expired patent).

At the end of two years following the first 
rocket off the line, with about 90 5 GW power 
sats constructed, there would have been $45 
billion of rectennas installed, and $135 billion 
spent on rocket and power sat construction. The 
revenue at a penny a kWh would 90 x 8000 hr/yr x 
5 million kW x .01 dollars/kWh or 90 x $400 
million a year, $36 billion. If the power sats 
were sold at ten times yearly income, the gross 
profit for the first two years of operation would 
be $180 billion, which should be enough to pay 
for the estimated $24 billion RDTE for the 
Neptune rocket, the electrolysis plant and the 
space port facilities.  There is probably room in 
this figure for housing the power assembly workers and their families.

Rough numbers, huge numbers, but solving the 
carbon and energy problems takes big numbers.