Hauling power sat parts up by rockets

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.