Unfortunately, this post will have to be broken into three parts, since I started looking into how life support worked, and the post got really long. This part will mostly be about life support, and the next one will have details on actual missions.
There are two primary ways to support humans in space with oxygen, food, and water: ecological, and chemical. Ecological uses plants to reprocess human waste, carbon dioxide, and trace nutrients into food, and humans to process food and oxygen into what the plants need, making a closed loop, as long as you have sunlight.
The largest problem with this is that the amount of plants required to support one person's oxygen needs would produce about half the required food for that person. If you have enough plants to provide enough food, half of them die off due to lack of carbon dioxide.
Chemical life support uses chemical reactors to crack carbon dioxide into oxygen, and extract usable water from sweat and urine. The problem with this is that you must pack all the food you will need.
Storage of oxygen is simple, as you can use boiloff from the main oxidizer tanks.
The air on Earth at sea level is at 101kpa. The atmosphere is 21% oxygen, so the partial pressure of oxygen is 21.21kpa.
Partial pressure, in a mix of gases, is how much pressure one of the gases would be under if all other gases were removed.
The minimum safe partial pressure of oxygen is 16kpa, and the maximum is somewhere between 50 and 100 kpa for short periods of time (a few hours). For long term breathing atmosphere, you want to stay under 50 kpa, ideally at about 21 kpa.
A high pressure pure oxygen environment is very dangerous because of fire, the Apollo 1 fire happened in a pure oxygen environment at 115kpa, this is what wood burning in a 50 kpa partial pressure environment looks like: https://youtu.be/_JkHB1hV7Hw?t=1m After that all US manned spacecraft used a 79% nitrogen/21% oxygen environment at about 101kpa.
So why was the Apollo 1 command module pressurized to 115 kpa? Because it was designed to hold pressure in, not out. During launch, the pressure would have gradually been reduced to 34 kpa. I don't know whether the ITS will use a nitrogen/oxygen mix, or pure oxygen which is always kept at safe pressures, but either way it will take about 0.85kg/day of oxygen, as nitrogen is not consumed when inhaled.
A larger problem than oxygen is carbon dioxide. Every astronaut exhales about 1 kg of it a day, and if it rises above 0.5% concentration it can become a serious danger. However, 0.273 kg of that is carbon, so most of it can be breathed again if it is cracked back into carbon and oxygen.
There are two options for dealing with carbon dioxide, cracking and scrubbing. Scrubbing uses a catalyst, which removes carbon dioxide from the air, producing water. It can be cleaned and used again by blowing hot air through it for 10 hours, however, you lose all that oxygen locked in the carbon dioxide.
A chemical reactor would use the sabatier reaction, like the ISS.
CO2 + 4H2 → CH4 + 2H2O
Exhaled CO2 would be processed with hydrogen to produce CH4 (methane) and water. The water can be electrolyzed into H2 and O2, and the CH4 can be pyrolized into C and H2. The hydrogen outputs can be fed back into the sabatier reactor, closing the loop. It would probably not be perfectly efficient, but since you only need about 180 grams of H2 for every kg or CO2 processed, even at 90% efficiency you would only need to add 18 grams of hydrogen a day.
However, every crew member exhales 1 kg of carbon dioxide/day, but only 0.727 kg of that is oxygen. That means that you have to add 108 grams of oxygen every day.
Astronauts need to drink about 3.9 kg of water every day, some mixed in with their food, if it isn't freeze-dried, and about 26 kg/day of water for personal hygiene. Most of the waste water (grey water, human waste, sweat) can be distilled and filtered. I estimate that about 0.1 kg of water would be lost in recovery every day.
Astronauts on the ISS eat about 2.5 kg of food every day, which consists of a mix of different kinds of food, mostly freeze-dried or otherwise stabilized. Some of it is fresh.
For the purposes of this, we can assume that all non-reusable waste (packaging, filters, solid human waste) is non-existent, as it can be dumped overboard between burns. If you wished to prevent the build up of trash in solar orbit you could dump it only while on a collision course with a planet, however that would likely only be a problem on trips that would be taken frequently.
Weights required:
5 tons for storage, processing equipment, etc.100 grams of water x mission length in days18 grams of H2 x mission length in days108 grams of oxygen x mission length in days x crew members2.5 kg of food x mission length in days x crew members
In a CELSS (Closed (or Controlled) ecological life support system), rather than using chemical reactors, the life support loop is fully closed, like Earth's ecosystem.
If you could get a CELSS working properly, it has the potential to be much more mass efficient than chemical life support system, with the crossover point for efficiency at around 2 years, according to Rocketpunk Manifesto. However, in their current state, they have some problems. For many plants, the amount of plants needed to provide food for astronauts is different for the amount need to provide oxygen, so the imbalance would cause an excess of oxygen, which would kill some of the plants, and then there wouldn't be enough food.
One of the most promising crops is Spirulina, a type of blue-green algae that, Marshall T. Savage claims in The Millennial Project, could close the life support loop almost fully with only 6 liters of algae per person (about 6.6 kg). (Note: I haven't read that book, this is taken from Atomic Rockets)
Even if you needed twice that much per person it would be very impressive.
For the purposes of this analysis, however, I will stick to existing methods of food production, as the goal is to use the fact that the ITS would be flying regularly to study a mission that could be much cheaper than a spacecraft designed only for the purpose of that mission.
In the next part we will finally look at the actual mission profiles.
