Space propulsion fueled by human metabolism

Impossible, right? Humans cannot propel themselves in space. Unless they exhale. Or fart. Which is, by the way, mostly composed of methane. Now that would be funny. Collect all gases from Starship inhabitants and store them in Starhip header tanks. Fart powered, indeed. 

A huge challenge for any long term human space mission is provision of consumables: breathable oxygen, water and food. NASA document Logistics Needs for Potential Deep Space MissionScenarios Post Asteroid Redirect Crewed Mission has some chilling numbers:

• 1.8 kg of food per crew per day
• 0.8 kg of oxygen per crew per day
• 2.5 kg of water per crew per day

I am not even taking into account any hygiene or medical or clothing consumables into account, which results in 5 kg of consumables per day per crew member. Round trip to and from Mars can be up to three years. Which results in 5500 kg or consumables per crew member. At least. 

Starship is supposed to transport up to hundred people to and from Mars. They might fit into the Starship. But where will 550 tons of supplies come from? Sending several supply Starships along? This is huge. Of course, there are various ways to reclaim and reuse  5 kg of consumables, so called closed loop cycle. On ISS, over 90% of water and 40% of air (essentially oxygen component of CO2) is recycled, using Sabatier reaction. This is great, since it seems it would recycle almost two thirds of the consumables (3.3 kg of 5.1 kg daily). But that is not true. Food contains over 98% of hydrogen, oxygen and carbon. Around 2% belongs to other elements, mostly nitrogen and phosphorous. 

https://www.popsci.com/how-iss-recycles-air-and-water/

So where does these 5.1 kg of consumables used daily goes to? 0.8 kg of oxygen that we inhale takes 0.3 kg of carbon from the food and ends up in the air. But on average human consumes less than 200 g of carbon per day, or 70 kg per year. So maybe oxygen consumption estimate is a little high.

2.5 kg of water ends up in the air (0.9 kg) and urine (1.5 kg). So where does 1.5 kg of remaining food ends up? In feces? Really?

This is actually quite easy to measure for yourself. Just measure your weight before and after each visit to the toilet. Actual average is around 0.5 kg. Now, poop is just dirty, and maybe it would be easier not to recycle it. But that means that 90% of daily consumables can be easily collected as water and carbon dioxide. That is roughly 500 tons of reusables and 50 tons of feces. These 50 tons can be reused for agriculture, but that part is hard. Mark Watney proved that in the Martian. But these 500 tons can be partly converted into methane and oxygen - essentially the fuel for Starship using the same process foreseen for Mars ISRU. No fancy water mining necessary. And the conversion might take place during transit flights too. If we take above 200 g as daily consumption of carbon, one crew member could provide 0.73 kg of CO2. Which could be converted into 0.26 kg of methane. With Raptor mixture ratio of 3.55 additional 0.92kg of oxygen should be stored in the tanks, so average crew member could produce or 1.2kg of Starship propellant fuel per day. Of course, there are different factors at play. Women consume less carbon than men (up to 20% less). Older people too (additional 20% less). And with less gravity, less energy should be required. Some of the carbon will end up in the poop too. And we don't want dirty technology in shiny steely Starships. So lets round this up to 1 kg of propellant fuel produced per crew member per day. 

So out of 5 kg of daily consumables, 10% (500 g) will be lost due to feces. 20% can be converted to propellant (assuming we have enough electric power onboard to power the Sabatier reaction, electrolysis of water and liquification). The rest (mostly water) can be recycled. Lets assume additional 10% conversion losses (for example, urine leftovers, misalignment of basic element ratios etc.). That means that only 40% of consumables are required. 20% will be lost and 20% will be converted into the propellant. Which means that for three year mission duration with 100 people, Starship would need just 220 tons of consumables (mostly food). And 110 tons would end up as usable propellant anyway. This makes logistics requirement feasible even with current technology.

The remaining losses can also be reused with additional technology development. Feces can be reused as part of soil generation (food growing). But they can also be converted into fuel essentially by burning it (which would convert it to mostly water, CO2 and trace gases such as NO2), and doing an ISRU all over again. In essence, human food can be used as Raptor fuel. Literarily. And thus it should not be viewed as additional mass because it can be converted into propellant using essentially the same technology that will be used for propellant manufacturing on Mars.