User:Hkhenson/moving cable space elevator
In the summer of 2006, I was working on a chapter of a novel set beyond the singularity. In the first flashback, I explained how the world had almost lost all physical state population.
It's here if anyone wants to read it. 
In a later chapter, I went into how humanity had solved the carbon and energy crisis.
In writing that chapter I had to solve a number of engineering problems. There are very few (maybe only one) power sources large enough to replace coal, oil and nuclear power; the most promising one is solar power satellites. (Wikipedia)
Scale of the problem
To make a serious dent in the carbon problems, I assumed enough power sats were coming on line to replace all the current coal fired plants in the US in one year. That's 300 GW, or 60 5GW units. 5 GW power sats have been estimated at 2kg/kW, so a 5 GW power sat should weigh about 10,000 tons, or 600,000 tons for a year's production. Taking a year at 300 days (for some slack) you get a lift requirement of 2,000 tons per day.
GEO is 57.5 mj/kg above the earth's surface, subtract Ke because we extract that from the earth's rotation. Ke is 1/2 mv exp 2 or about 4.8 mj/kg at 3.1 km/sec. 52.7mj/kg/3.6 mj/kWh is 14.6 kWh/kg. At 10 cents a kWh this $1.46/kg. At the target price of a penny a kWh under 15 cents. Motor efficiency should be 90-95% for motors on this scale.
At 100 tonne/hr, the electric power required to drive the motor(s) would be 1.46 GW. (14.6 kWh/kg x 100,000 kg/hr = 1.46 million kW or 1.46 GW.)
For scale, the aircraft carrier Enterprise generates 0.21 Gw and could lift a few hundred tons a day to GEO.
Energy for Rockets
it takes about 43 kWh of electricity to produce 1 kg of hydrogen. 86kWh to produce 2kg of H and 16 kg of oxygen or about 100 kWh to produce 20 kg of H and O. So a kWd would produce about 5 kg of H and O, a MWd would split up 5000 kg of water, a GWd would make 5000 tons. 400/5 is 80 GW days, or 16 days from a 5 GW power sat. So the energy payback to lift the materials by rocket for a power sat would be 16 days. Not as good as a moving cable elevator, but the cost of fuel isn't the killer – it's the rocket hardware.
Energy for Climbers
Existing space elevator designs have assumed tapered cables and climbers powered by lasers. With the inefficiencies of lasers, photovoltaic cells and mass fraction, the projected overall energy efficiency is about 7%. It would require about 15 GW input to the lasers. That gives an energy payback of about the same as rockets. At least the lasers stay on the ground. Lasers with a 15 GW continuous input power are going to be expensive.
It would improve the efficiency by about 15 times if cargo went up a space elevator with mechanical rather than laser power.
It would be a lot less complicated if you didn't have to taper the cables and were able to use a constant cross sectional area cable. That can be done with one loop if the cable is strong enough (more than 63 Gpa) That looks unlikely, 15-20 Gpa look more likely. But it might be possible to get step taper from free spinning pulleys.
The thing I have in mind would take three loops, (6 strands) around the pulley at the ship end, and an increasing number of strands (8, 10, 12 etc) at transfer stations as you go up.
How many stages it requires depends on the cable strength. (And it might start with fewer than three loops at the anchor end but the “taper” is more abrupt.)
The two attached jpgs are variations; the one tied off at the top is more symmetric in the 360 loops, the one with the loop tied at the bottom has the strand on the left that goes all the way to the top through the 360s before it starts back down. (The 360 loops offload the tension in the lift strand to the other strands and the pulleys have a slight ability to adjust diameter.)
The main advantage of stringing it up like the second jpg would be low stress replication. If you just lift an identical cable by dragging it up with the upbound cable, by the time it comes back to the anchor it has doubled the capacity of the elevator.
Of course, even at 1000 mph (I don’t know how hard you could push it before air friction started to be a problem) it would take a day to get to GEO, and maybe 100 days to wind back to the ship (counting it winding out to the counterweight). (Moving the cable damage from the molecular oxygen layer would be spread over the whole cable.)
That’s still 3 doublings a year. Being near the driver wheel at the bottom would be something else—a 31-foot wheel turning 900 rpm is going to make serious noise. And even at Edward’s proposed .2 kg/km, .7 pounds per mile x 25k miles is going to be 18,000 pounds. That would take 50,000 hp if it were one g all the way out, reducing that by half is still 25,000 hp—5 really huge locomotive engines—with the hp requirements just to run up more cable doubling ever 3-4 months! 50k, 100k, 200k . . . at that point the lift capacity to geo is 80,000 pounds a day, 40 tons a day, which still isn’t in the class you need for power sats, but it’s a good start.
After a year it takes so much power that I got to thinking about nuclear powered ships.
It happens that the Enterprise is to be retired in 2013 (or 2015?). You could probably tap it for at least 200,000 hp and the flight deck would be the ideal place to build the bottom driver. You could even build it on a turntable to keep the driver wheel axel lined up North/South as you moved the ship around.
Plus the fact that doing something wild and uplifting (pun intended) like this rather than scrapping the Big E would get you a lot of political support.
Let’s see. Besides an aircraft carrier, we need the shuttles to make one last trip into space taking up parts and being used as counter weights, probably move the space station to geo as well, and the initial cable might be launched (from the deck of the Enterprise?) with the remaining 9 F1 engines. And we need several serious ion-drive and/or magnetic drive robot ships to clean up the orbital junk and lift it to geo for counterweight mass.