sure, balloon method would work fine.
If I were trying to make apple cider vinegar in the cheapest, simplest way possible here is how I would do it:
- get your half gallon of apple juice at room temperature (make sure it is pure apple juice, some of the storebought stuff has preservatives and things in it that will kill yeast…)
- put in maybe half a teaspoon of bread yeast, shake, and cover the bottle neck with a ballon (side note: lots of different kinds of yeasts, the main factors are the residual tastes they confer, how vigorous they are, and what percentage alcohol they can reach. Since you’re making vinegar, the residual taste will be a non-issue, and since you don’t need more than 5-7% alcohol a bread yeast will be active enough and get you to the alcohol percentage you want. If you wanted to get fancy you could get a $1 pack of champagne or cider yeast from a homebrew store, but it shouldn’t matter much for this use…)
- let the CO2 out of the balloon once in a while. When it stops filling (shouldn’t take more than a week at room temperature) then add a good dollop of apple cider vinegar. The bacteria in the vinegar should kick start the souring process in your new apple cider and that seems a lot safer than depending on whatever bacteria happen to be in the air right then.
- taste it after a week or so
Keep in mind that my vinegar has always been accidental, but the above should work to make it on purpose!
(BTW. one of my favorite books is “Wild Fermentation” and it goes into great detail on all sorts of fermentations, including some killer kimchi recipes. http://www.amazon.com/Wild-Fermentation-Flavor-Nutrition-Live-Culture/dp/1931498237/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1207724067&sr=8-1)