>>11780124You might be unemployed for a reason if you were serious about the idea. :D
It should be clear without even having to do the calculations that there would be no meaningful amounts of energy in human shit methane.
Let's assume the ship has food for 100 people for 100 days. Also assume daily food energy is 3000 kcal per person. And assume 10 % of that is not absorbed by people and all of it is converted into methane with 100 % efficiency.
This would give us only 30 000 000 kcal in methane. You would of course need to find some oxygen to burn it with because space and Mars don't really have it that much in a form that is combustable.
For comparison, the ship has 1.2 million kg of fuel (CH4 + LOX). That means 400 000 kg of CH4. Assuming 50 MJ/kg we get 4.78 billion kcals which is ~160 times more than what you would get from shit.
And that too is higher than what you would realistically get. Plus the problem with the oxygen.