... it is designed for wine must fermentation…
Beer seems to require an airlock to keep bacteria out of the wort. Isn't wine also a ton of sugar that needs protection against airborne bacteria? How are the bugs kept out of the 12-gallon barrel when fermenting wine?
I'm going to take you guys' advice and at least step back from using the garbage can in the near future. I like that it's rectangular and as such, will consume less area on the counter of my unused bathroom. I'm a little concerned that using a towel and a piece of plywood as a top may provide an avenue for infection. Mick Jagger was correct in the 1960s that you can't always get what you want. It's still too hot where I live to have a barrel of beer fermenting in a bathroom with a southern wall that gets blasted by the Nevada sun every day.
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i believe i see where you're coming from in a lot of your approach and intentions, but you may want to consider "what is beer?"
beer in different places and at different times in history was sour to degrees varying from slightly tart to very sour both intentionally and unintentionally. beer is/was fermented for times as short as a few hours to obviously years and years.
i mean even the term "beer" i use was preceded in many places by other terms to describe a beverage of malt and/or grains fermented with a range of fungi and bacteria.
so, its totally up to you whether you want to keep your beer covered or not with an airlock or what type of airlock. for a few years in a different country i used an improvised airlock of a plastic bag with a plastic tube taped to it (externally) and this was secured to a wide mouthed glass or PET container with a rubber band. this kept bugs out and pumped CO2 into a separate container, but probably wasnt perfectly oxygen impermeable.
you can make beer however you want, but in regards to the topic of this thread i and i believe most others indicate specific and identifiable risks with that non-good grade plastic container. it sounded like your concern was about headspace expanding beyond the volume of the beer? krausen/foam varies greatly from yeast to yeast, but overall you shouldnt be too worried about it, at most maybe you'd need another 1/6th of the wort volume in headspace and less if you just use a blowoff tube.