I do vaguely remember reading somewhere that someone in the 1930s had confidently declared that landing on the Moon was impossible because the math proved that a SSTTTMAB (Single Stage To The Moon And Back) rocket was impossible.
Don't start me on this... oh wait, too late.
Ascent to Earth orbit: 9400 m/s
+Leaving Earth: +3200 m/s
+Lunar descent: +2400 m/s
Total for a one-way trip from Earth surface to Moon surface: 15 000 m/s.
And the return ?
Once standing on the Moon solid surface: +2400 m/s to orbit, but escape from the Moon is 2700 m/s.
Now the good news: direct return hitting Earth atmosphere head-on (that's what the Apollo capsule did) is "free" once you escaped the Moon.
So: 15000+2700 = 17700 m/s. No need to make "Earth escape in reverse" if you don't want to return a low Earth orbit, otherwise it would be
2700+3200 = 5900 to be added to 15000 so 20900 m/s.
17700 m/s - it hurts.
Chemical rocket even LOX/LH2 at 465 second isp; even at the all time record of 542 seconds (lithium and fluorine on top of LOX/LH2 - scary and toxic stuff) can't make it or not with any meaningful payload.
NERVA level of isp (825 seconds) could eventually do it... but T/W is horrible, so it can't get itself out of Earth solid ground.
Orion can do it, it's own unique (and very
Wile E. Coyote) way: nuclear bombs blasting a steel plate, the plate moving like a piston engine in a cylinder; pushing a spaceship on the other side; with springs between the two, the whole thing jumping upwards in brutal hops.
Basic rocket equation
9.81*specific-impulse*ln(SSTO-mass,
prop tanks full+
PAYLOAD)/(SSTO-mass,
prop tanks empty+
PAYLOAD)
-prop tanks full
-prop tanks empty
The ratio between these two is the
propellant mass fraction.
(Let's forget payload for a moment just to ease things a little).
Propellant mass fraction for SST to Earth orbit is already horrible (9400 m/s) but for 17700 m/s ? forget it.
Let's start from 1000 metric tons.
-0.95 prop mass fraction would leave a miserable 50 mt for... the vehicle, and payload proper.
-Everything else is the tanks contains.
-465 specific impulse is the RL-10B2 all time record... in vaccuum, so bollocks.
- zero payload
9.81*465*ln(1000/50) = 13665 m/s
Ding, dong, it won't make the roundtrip to the Moon !
So what kind of goddam specific impulse should I use in that thing ? Vaccuum or not ?
Let's try NERVA 825 seconds...
9.81*825*ln(1000/50) = 24245 m/s aaaah... here we are, at least !
With zero payload however.
And NASA "Reusable nuclear shuttle" prop mass fraction was NOT 0.95 but 0.78 at best, let's round this to 0.80
0.80 out of 1000 mt is a 200 mt empty mass, still zero payload on top.
9.81*825*ln(1000/200) = 13025 m/s
Craaaap ! Back to square one. Still can't make the trip !
All right then, let's keep the goddam 0.80 mass fraction (and still zero payload, drats !) and let's see what kind of freakkin' isp is needed then.
How about 1000 seconds ? That's the best solid-core NTR can do, pushing the reactor to 3200 Kelvins rather than NERVA 2700 K (respectively: 2300°C and 2700°C... hell for materials)
9.81*1000*ln(1000/200) = 15788 m/s CRAAAP still doesn't work, and with no payload, but we are getting closer...
Ok, 1200 seconds then. 9.81*1200*ln(1200/200) = 18946 m/s
At least !
Still with zero payload, damn it.
Then add 20 mt of payload, you dummy. All right...
9.81*1200*ln((1000+20)/(200+20)) = 18057 m/s
A bit close from 17700 m/s with direct, brutal return.
And 20 metric tons is not that much payload...
Well then let's rise the specific impulse one last time !
9.81*1500*ln((1000+20)/(200+20)) = 22571 m/s
Now we are up to something... except forget NERVA, and go gas-core nuclear rocket: the mythical "light bulb".
Sure dude, now all you need is to try and contains a 20 000 Kelvins uranium plasma...
Bottom line
- better specific impulse = hotter and hotter things going out of the nozzle
- nuclear energy in theory has 20 millions times more energy than chemical
- but reactors sucks at transmitting the energy (or heat) to the damn fuel
- even if the fuel is high energy hydrogen
- clearly something is wrong between the 5000 megwatt reactor and the high energy hydrogen fuel... you guess, is it the energy "vector" between the two
- fission fragments are that vector, works by passing their energy as heat to the hydrogen
- "heat" sucks because thermodynamics sucks.
As would say Mark Watney "that fucking entropy !"
...
- now if you used neutron kinetic energy from a pulsing reactor high neutron flux...
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