http://www.projectrho.com/rocket/CR-2004-208941.pdf
Astronauts on averaage
breath 0.98 kg of oxygen per day
drink 5.76 kg of water per day
eat 2.30 kg of food per day (0.60 frozen, 1.70 freeze dried)
and produce 1.35 kg of carbon-dioxide per day
To reduce carbon dioxide using the Sabatier reaction requires
hydrogen;
CO2 + 4 H2 --- CH4 + 2 H2O
So, by consuming 0.25 kg of hydrogen 1.35 kg of carbon-dioxide is
absorbed and 0.50 kg and 1.10 kg of water to eliminate all the carbon-
dioxide from the atmosphere and create water. The methane is
evaporated for temperature control. The remaining 4.66 kg of water
comes from combining 0.51kg of hydrogen with 4.15 kg of oxygen which
also produces 20.8 kWh.- which is an average power consumption of 837
watts per person.
So, oxygen is; 0.98 kg - breatheable
4.15 kg - water/energy
--------------
5.13 kg total oxygen/day/cm
hydrogen 0.25 kg - scrubbing
0.51 kg - water/energy
-------------
0.76 kg - total hydrogen per day
food 2.30 kg - total food per day
TOTAL 8.19 kg - total mass per day
90 days
737 kg per person
the water is also evaporated along with the methane for
temperature control.
A crew of 10 for 90 days (with a 1.5 day reserve) requires 7.5 tonnes
of consumables.
A small nuclear reactor would be able to take the 5.76 kg of water
each day and regenerate the hydrogen and oxygen by electrolysis -
reducing consumption rates to 2.43 kg per day allowing 2.2 metric tons
to suffice for a crew of 10 for 90 days.
However, this requires about 1 kW of electrical energy per person,
which requires about 2.5 kW of thermal energy per person. So, a crew
of 10 would need a 25 kW thermal source. But if the power source
produced less than 4.73 kW per tonne there would be no net reduction
in payload mass.
http://en.wikipedia.org/wiki/SNAP-10A
The largest space nuclear reactor was the SNAP 10A which produced 630
watts and massed 440 kg. (0.44 tonne) That's 1.43 kg per tonne which
means that a 25 kW reactor would mass 35.75 tonnes to save 5.28 tonnes
of consumables.
A 5x increase in power output per unit weight would provide a savings
for a 90 day mission, but the advantage erodes as mission lengths
decrease. Since it takes 4 days to get to the moon and 4 days to
return from the moon along minimum energy orbits, from Earth,then 40
to 90 day mission times seem reasonable.
75 tonne payload capacity means that only 10% of this total is needed
to sustain 10 astronauts for 90 days. Sustaining 4 astronauts for 900
days would require 40% of the payload mass be consumables - but would
give this vehicle the legs to traverse to Mars and stay there a full
synodic period with a crew of 4 and return home.