[TheForge] underground house

[wmullett at bright.net]

You may kill your goats!

Because there will be manure composting in your barn as well as the animals, you should have no less ventilation than what would be required in a home ... probably a lot more. 

Most barns never have to deal with this because they have plenty of infiltration.  And that is not really a problem in a barn.  If you  

Passive ventilation takes a whole lot more area than mechanical.  Look at the number of air exchanges that are a minimum for locker rooms and that might get you close.  Not sure what that is off hand.   A mechanical contractor / engineer could give you that number.  They could also advise you as to what area it takes to accomplish that passively.