[ExI] Lack of interest
hkhenson at rogers.com
Thu May 8 08:08:35 UTC 2008
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.
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.
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
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.
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
(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
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.
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