Air space

That depends on the size and shape of the container, and whether the wine is fermenting or still. The amount of surface area exposed is more important the depth of the air-space. Thus a (narrow-mouth) carboy with 4" of airspace is much better than a (wide-mouth) primary with 1".
While the wine is still fermenting vigorously, you can have (and often need) 30-40% headroom, and the exposed surface area is not a great concern.
When the ferment slows down, it will still produce enough CO2 to protect a red-wine in a primary, but you should probably move a white wine to a (narrow-mouth) carboy, and top up to the shoulder.
When the ferment has stopped completely, top up to ~1.5" of airspace for a 1-gallon or 4-litre jug, ~2" for a 2.8 or 3 gallon carboy, and ~3" for a 5 or 6 gallon carboy. These figures are based on my personal experience, and are the minimum amount necessary to allow for the fluid expansion with a 10ºF temperature increase (so the stopper isn't forced out and/or the wine doesn't end up in your airlock). If you can be sure that there will not be such a temperature increase (even if there is a power failure and your refrigeration system goes south for the winter), you could use 1/2-3/4" on all vessels, but the same surface area would be exposed, and there would be little difference in oxidation. If you anticipate a greater temperature increase during aging, increase the gap, or (preferably) consider installing a better refrigeration system.
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Wouldn't the amount of oxygen available is proportional to the _volume_ of the head space, and the _rate_ of transfer to the wine would be proportional to the surface area? lum
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Yes, but in the narrow "bottle-neck" of a carboy, there isn't much surface area exposed. So, I think, the rate-of-transfer is slow enough, and the volume-of-air : volume-of-wine ratio small enough, that there will not be much noticeable difference in oxidation between a 1/2-3/4" and a 2-2.5" gap, as long as the wine level is in the narrow "bottle-neck". The difference would be more significant in a wine bottle, because the air : liquid ratio is much greater. This is only a "seems logical" conclusion on my part. I have no empirical evidence to prove the theory, and I may well be incorrect.
Regardless, there must be some compromise. Ideally, there would be no air-space, and thus no worry of oxidation or acetefication. But liquid expands with significant hydraulic force upon temperature increase, and some allowance for this must be made.
I've had 3 refrigeration-system malfunctions in 2 years (and of course they occurred on the hottest days of the year). In each case, carboys that were topped up more than the levels I mentioned in my previous post either pushed the stopper out or burst. Those that were not, did not. Since I also use a layer of cling-wrap held in place with two rubber bands _over_ the stopper, all my wine was saved (except in the carboys which burst because the stopper wouldn't budge).
However, if I were ill or out of town, or didn't notice the stopper had popped, the cling-wrap might have come off too. Had I used airlocks during aging, rather than solid stoppers (as some people do), the wine would have entered the airlock, mixed with the sterilizer, which (when the temperature dropped) would have contaminated the wine.
Thus I have determined it best to leave such a large airspace in the carboy --- if I rack when the wine is at cellar temperature. If I rack when it is at room temperature, I would reduce the airspace by about 30%, since some of the thermal expansion will have already taken place. What other choice is there?
If I had a well-insulated underground cellar, where the temperature would be stable even if the refrigeration system failed (assuming one was even needed), then I would top up to 1/2-3/4", and eliminate the (hopefully) small difference that the larger gap causes.
How large an air-space do you use in your large tanks and barrels?
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The other thing that occurred to me is that, if one were to top up the carboys to 1/2" when the temperature is as warm as expected, there would be absolutely NO need to top them up when the airspace subsequently increased due to temperature drop. There would be no more air in the larger space. It will simply have "de-compressed", expanded to fill the space available, just like Boyle predicted.
I wish I had a proper cellar deep in the ground. :(
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