At 12:00 PM 5/16/2008, Alberto Monteiro wrote: >Keith wrote: > > > >>> There is plenty of energy around if we can figure out how to get > >>> it. For example, a solar power satellite repays the energy needed > >>> to lift it to GEO in about a day (at 100% efficiency). Five percent > >>> efficient rockets would replay the lift energy in 3 weeks. > >> > >> This is almost surely wrong. Did you do the math? > > > > Yes. > > > > Specific orbital energy is u/2r, (398,600/42,000)/2 or -4.75Mj/kg > > >Ok > > > Potential is -9.5Mk/kg and kinetic is 4.75Mj/kg > > > > Potential at the earth's surface is -62.6 MJ/kg; the > > difference is 53.1Mj/kg. > > >Ok. > > > Using a space elevator, > > >I didn't know you were invoking Magic. "If I had magical fairy >godparents I would make 2 + 2 = fish".
Restoring what you cut (I need the numbers). Using a space elevator, the rotation of the earth provides the kinetic energy. Since a joule is a watt-second; 53,100 kW-s/kg/3600kW-s/kWh is 14.75 kWh/kg A kW/kg power sat repays its lift energy 14 hour and 45 minutes after being turned on. A 2kg/kW power sat would take 29.5 hours. That is close enough to a day for back of the envelope calculations. Five per cent efficient rockets would take 20 times this long to reach payback--but try to get them! There is a heck of a lot of sunlight out there, and you don't need much structure to capture it in zero g. >Try to do the same exercise using chemical rockets :-) Sure. First we need a rocket. Here is a rocket: http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf Neptune is about 3 times the capacity of a Saturn 5, and this design was done by some of the same people so it's solid engineering. This vehicle delivers 350 mt to LEO, and 100 mt to lunar orbit or GEO. To lift 100 mt to GEO Neptune uses 3762-mt of propellant for the first stage, 1072 mt second stage and 249 mt for the third totaling 5077 mt. SSME O2 to H2 ratio 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 the propellant is LH. or about 725 mt of LH. 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. Add 5 kWh for liquefying oxygen at 6 x .8 kWh/kg. That would be 70 MWh per mt, or 70 GW hours for 1000 tons, or 50.8 GWh for 725 mt. At a kg/kW, 100 tons of satellite produces 100,000 kW, or .1 GW. Thus it would take 508 hours to pay back the lift energy or 21.2 days, 42.4 days for 2kg/kW. Rocket efficiency here would be 14.75/508 or 2.9%. A nuclear tug stage shuttling between LEO and GEO might double this efficiency raising the payload from 100 mt to 200 mt. That is the consequences of a 15 km/sec exhaust velocity. It's the high cost of rocket hardware, not lift energy payback, that makes power sats expensive. Keith PS. Don't count out a space elevator. The theoretical strength of carbon nanotubes is up in the 170 GPa range and anything over about 45 is good enough for a moving cable, step taper elevator. There are persistent accounts of 20 GPa yarn having been produced by the University of Cambridge. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
