Michel,
As I understand it, a thermal nuclear rocket such as NERVA, which I gather would be the engine of the LEO-Lunar Orbit tug you referenced, will use up its reactor core materials in just one burn, or maybe it can be stretched to several burns, but the point is, to use a whole lot of power to drive a relatively modest mass of hydrogen propellant at a high exhaust speed for high ISP. This power quickly depletes the reactor core, does it not?
So, I am guessing that while the rocket engine (the non-reactor part of it, basically the expansion nozzle) and tankage and guidance and so forth can be reused many times, the reactor core (which serves as "combustion chamber" too though there's no "combustion" going on!
) would have to be swapped out for a new one.
The mission, I suppose, would be to launch a cargo to TLI from a low earth orbit, presumably near some station, then brake itself and cargo to low Lunar orbit (or a base at L2 perhaps), then loiter around, presumably using the reactor core (largely depleted by the TLI launch) to supply power to keep the remaining hydrogen fuel liquefied. Eventually there will be a return cargo from the Moon to Earth, and when it its big enough to justify the mission, the thing blasts out of Lunar orbit (or away from L2) to put it on a return path to Earth; this requires considerably less delta-V than leaving Earth orbit did. BUT for it to be reusable, it will be necessary to then use the rocket a fourth time for a fairly heavy burn, equivalent in fact to what was needed to launch to TLI, to brake into LEO again.
Thus we have two TLI-scale burns, on the order of 3 km/sec delta V each way, near Earth, and two LOI burns, around 1500 m/sec or half TLI, around the moon--I'm hazy on how much we save by going to an L2 base instead, I think a lot; it would cost IIRC about 600, maybe 7 or 8 hundred, meters/sec for each burn.
OTOH, I think it costs somewhat more delta-V to go from L2 to the Lunar surface and back again, and a lot more time.
Assuming low Lunar orbit, we then have a total delta-V of about 9 kilometers per second. The reactor has to be able to deliver 3000 initially, power down and wait several days then power on for 1500, then wait days to months (decaying all the while but I don't think typical reactor isotopes--U-235 or plutonium--will decay much in that time frame) for another smaller burn, then finally be capable of a big burn at the end to rendezvous with the space station, or anyway a craft meant to take the cargo back down to Earth.
The ISP of NERVA-type thermal rockets was meant to be in the range of 800-1000; take it as 900 and we see we need for the launch mass from LEO to have been e times the final burnout mass when it returns--it depends on the cargo mass a bit of course, obviously the return cargo to Earth can be more or less than what was sent out, it seems reasonable to guess it would typically be a lot less. It would even be a valid mission for the thing not to carry anything back to LEO but itself, to be used again mainly to ship stuff to the Moon but with not much ever coming back from the Moon. In that case, it might not even need to brake to Lunar orbit, just eject the cargo to brake itself with on-board one-use rockets, to Lunar orbit or to a direct landing on the Moon. Then the tug can loop around the Moon on a free-return path and then we just have the two burns in close Earth orbit, which amount to 6000 meters/sec total.
Let's assume though that it does the full mission I described above, carrying back to LEO a cargo of the same mass as it hauled out to lunar orbit.
Then if the tug, with all fuel gone, plus the cargo masses 1, the hydrogen propellant at launch from LEO was 1.73. I could look up the nuclear shuttle proposal (be easier if you had offered a link or the exact name of that particular one!
) or I'll just guess here--say the cargo was 100 tonnes, and the tug masses 100 tonnes dry (including reactor core of course!) and both were launched to LEO on a standard Saturn V, whereas the propellant was launched in four Saturn V launches, along with some auxiliary mass. The tug docked at some orbiting fuel dump where the hydrogen-laden tank stages had also docked, and transferred the hydrogen in. It keeps the hydrogen liquid using the reactor in low-power mode to run active cryogenics and radiators.
Fueled, and with the cargo loaded, it masses 544 tonnes. It expelled a bit over 154.2 tonnes to send itself to the moon, leaving about 390. As it approaches the Moon some days later, it brakes using about 60 tonnes of hydrogen to wind up massing about 330. In Lunar orbit, it drops its 100 tonne cargo and takes on another one of the same mass, and then blasts back into Trans-Earth injection, using a bit under 51 tonnes, to send 279 tonnes back toward Earth. Approaching Earth, it brakes into LEO using the remaining 79 tonnes of hydrogen and arrives empty with its own 100 tonne mass and its 100 tonne cargo.
Again--my question is, what condition is the nuclear reactor core in at this point?
Each of those tonnes of hydrogen, exiting the nozzle at 10,000 meters/sec, absorbed at least 50 billion joules of heat from the reactor, so the total output of the reactor was 17.2 x 10^12 joules. Assuming the tug's rocket was initially powerful enough to shove the initial 544,000 kg mass at a full 10 m/sec acceleration (which might be more than was needed, but not a lot more considering we want TLI burn to last not more than a sixth or so of a 90 minute orbital period--we might let it go down by a factor of three or so, but not much less) and therefore put out say 5 meganewtons, with a mass flow therefore of half a tonne per second, the reactor is putting out 25 gigawatts--again, at least, that's the amount of power that is usefully thrusting the ship, but I presume there are substantial inefficiencies, in the form of heat that is not converted to useful work for instance. It has to do this for 688 seconds--actually it is acceptable for its power output and mass flow to deteriorate quite a bit as it arrives at Earth with something like 40 percent the mass it left with, so the thrust and hence power flow can be ramped down a lot--but then the burn has to last longer, so the firing lifetime for one such mission must be in the ballpark of 1000 seconds anyway.
As I said my understanding was, the NERVA and other such designs of that generation intended that the reactor core should be fully depleted by the end of one mission, and the stage discarded. I don't know how many gigajoules of heat a kilogram of reactor core material can be expected to put out before the fissionable materials in it are too dilute, too surrounded by decay products (some of which "poison" fission chain reactions by absorbing neutrons) to go on putting out useful amounts of power.
Clearly if a standard say 1970 NERVA was going to use up its core in one mission, and we want it to last not one but 10, we might simply multiply the mass of fissionable materials in the core by 10. That's not entirely satisfactory; toward the end the reactor will be sluggish and cooler, due not just to depletion of materials but due to "poisoning" by decay products. We might instead have to swap out the reactor after 5 missions or so, and then reprocess it to purge out the undesirable wastes and reconcentrate the useful isotopes, adding in supplementary ones shipped up from Earth. If we can't have a suitable reprocessing and refabrication plant in orbit, we need to ship the whole core down to Earth, recover it and haul it off to some ground-based facility, then ship the refurbished core to a launch site to ship it up to the space station where it waits to be reinstalled in another tug with an old core.
In addition to these costly investments (either building a nuclear reprocessing site in orbit, or shipping a multi-tonne reactor core down to Earth and then back up, never mind the security issues!
) of course a bigger core is more massive, taking up a bigger share of our arbitrary 100 tonne tug, leaving less for engine, tankage, guidance, etc.
In the course of considering this scenario, I went on to consider the possibility of aerocapture of the tug and its cargo to return it to Earth orbit, delivery of cargo to a station and then refurbishment and refueling in orbit for another mission; this led me to compare it to the possibility of a chemical LH-LOX version and to some interesting conclusions regarding a much smaller scale (1/8) version of the latter that seems to be a very close match to Saturn V launch capabilities; if I'm right, and it's actually feasible to aerocapture it, then such a thing (a lenticular craft about 13 meters in diameter and 3 thick in the middle) would take about one Saturn V load, just under 100 tonnes of fuel plus a payload, depending on whether the mission involves returning anything from lunar orbit or not, between 8 and 20 tonnes.
But before posting anything about that here I mean to go back and look at the exact figures for TLI and lunar orbit insertion and escape; they might be a bit better than I've been assuming which would give badly needed margin for the mass of the reusable "tug" (more like a Shuttle in that the cargo would be inside, in a bay). Or they might be worse in which case forget about it.
I just want you to clarify, how often would the nuclear cores need to be replaced with the sort of nuclear tugs NASA proposed and you seem to be endorsing here?
