I did what I could to verify your numbers. Its difficult because there isn't much data available on the Internet (for free) giving the thermal characteristics of LH2. That leaves me to guess at the specific heats. I ended up using 28.836 kJ/kg-K. Best I could come up with is 77.8528746 M J/kg or 0.076412418 M BTU/kg to raise the temperature of LH2 from 14 K to 3000 K. I had to assume that chamber pressure was high enough, pumped of course. (Assume a configuration like used for the SSME hydrogen pumps where energy extracted to cool the nozzle drives the pumps.) I chose 3000 K temperature because hydrogen starts to dissociate at that point. More heat starts to increase the engine ISP from 1251.083382 seconds to 1771.053473 fully dissociated, but it takes a lot of energy to dissociate hence your mass flow drops, reducing thrust. 3000 K LH2 temperature and the energy available from your 6 GW engine gives power limited mass flow of 74.42 kg/sec and a thrust of 791 (not 913.41 as I first wrote) tonnes with a burn time of 8061.94 seconds. That will get you into space with a lot of reaction mass left over.MSimon wrote:Doesn't engine power required depend on the mass?
I was thinking of reducing the mass. First off - no LOX (except for minor amounts) second off LH2 for reaction mass.
I did some BOE a while back an IIRC 50 ton 6 GW engine. 600 tons of reaction mass. 100 tons of payload.
I didn't run the acceleration profile, but use something like 9.7 km/sec for delta V required to LEO. That accounts for LEO orbital velocity and the extra aerodynamic drag of the HUGE hydrogen tank, and gravity drag. Of course, with this low acceleration and a near vertical climb-out, aerodynamic drag might not be so bad. However, with the low acceleration, gravity losses will operate for a longer time so the delta V required might be higher.
Again, the big uncertainty is in the specific heat of LH2 at the required pressure, throughout the temperature profile.
Edit: I originally used 4000 K to calculate ISP, using a separate spread sheet. Using 3000 K reduces ISP hence thrust to 791 tonnes.