We can't yet build a space elevator. We can, however, build rockets.
A few weeks ago Hu Davis of Eagle Engineering pointed me to a design for a two stage rocket that will deliver about 200 tons to GEO. (Hu was the project engineer for the Eagle as in "the Eagle has landed.")
http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf
I decided to look at building power sats using rockets.
Neptune is about 3 times the capacity of a Saturn 5, so it's 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. Third stage structure would be abandoned at GEO or converted to power sat parts. To lift 200 mt to GEO it uses.
3762-mt first stage plus 1072 mt second stage equals 4834 mt of propellant.
2/18 of this is H. or about 538 mt of LH, 5380 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. (Ignoring the cost to liquefy the oxygen.)
That would be 65 MWh per mt, or 65 GW hours for 1000 tons, or 349 GWh per day for 5380 mt. Since there are 24 hrs in a day, the steady flow of power would be about 14.6 GW.
Considering that a straight mechanical lift to GEO at 100% efficiency takes .66 GW, this implies a lift energy efficiency of 4.5%. 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 15 GW/per day or 75 GW-days. A power sat constructed this way would repay its lift energy in 75/5 or 15 days.
It would also require dedicating the first three power sats to hydrogen production, delaying producing power sats for sale by a few weeks.
How often could these vehicles could be flown? If every day, the company would need ten of them active plus perhaps a few "in the shop."
If the vehicles were good for 200 flights and there were ten in use, then a replacement vehicle would have to 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 workforce. None the less, it would be a huge production line.
At 40 flights per engine, 49 engines per vehicle, and ten 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.
So the cost per kg would be the energy cost plus capital costs. 15 million kW x 24 hrs x 1 cent per kwh is $3.6 million per day. $3.6 million/2 million kg is $1.80 per kg.
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. Of course with this size of lift package, we could seriously consider 40% efficient steam turbines cooled by the expired Drexler/Henson radiator design 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.
Rough numbers, huge numbers, but solving the carbon and energy problems takes really big numbers.
Tuesday, April 29, 2008
Monday, April 28, 2008
space elevators
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 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 10 cents. It's only a dollar at current consumer prices for electricity.
The price to put up a space elevator can be estimated. If nanotube cable of adequate strength can be made 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's a transport capital cost of only $10 billion a year. Taking the elevator's capacity at only half a million tonnes per yer, the capital cost would be $20,000 per tonne or $20 per kg.
That's 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.
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 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 10 cents. It's only a dollar at current consumer prices for electricity.
The price to put up a space elevator can be estimated. If nanotube cable of adequate strength can be made 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's a transport capital cost of only $10 billion a year. Taking the elevator's capacity at only half a million tonnes per yer, the capital cost would be $20,000 per tonne or $20 per kg.
That's 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.
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.
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.
More numbers
Hydrogen has about 141 MJ/kg of energy. It costs about 50 kWh to make and another 15 kWh to liquefy. So penny a kWh power would make hydrogen equal to a gallon of gas for less than 50 cents.
Keep 65 kWh/kg for LH2 in mind, it gets used later.
The only long term source of energy is the sun. Solar power doesn't 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, has been known for almost 40 years, 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. So the annual output from a power sat would be in the range of 4000kWh/kg. At a penny a kWh, that's $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's a somewhat arbitrary number. At a kg/kW, we could afford $800/kg installed cost.
Keep 65 kWh/kg for LH2 in mind, it gets used later.
The only long term source of energy is the sun. Solar power doesn't 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, has been known for almost 40 years, 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. So the annual output from a power sat would be in the range of 4000kWh/kg. At a penny a kWh, that's $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's a somewhat arbitrary number. At a kg/kW, we could afford $800/kg installed cost.
Friday, April 25, 2008
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.
So if dollar a gallon gasoline is the goal, penny or sub penny per kWh electric power is a way to get there.
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.
So if dollar a gallon gasoline is the goal, penny or sub penny per kWh electric power is a way to get there.
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