gravity~vs~sweetness

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My concern would be having the yeast stop fermenting at "X" %ABV and temperature. A mild temperature bump may be enough to reactivate some of the yeast. Your experiment may be a good case for using an alternate closure system such as swing top bottles.
 
To answer the original question: Yes. There is a loose connection.
Please note - I work only with wine.
Suppose my original sg is 1.1 then, I work on this ...
0.990 will be a dry wine. Alcohol about 12%
1.008 will be off-dry. Alcohol about 11.5%
1.015 will be medium-sweet. Alcohol about 11%
1.060 will be sweet.. Alcohol about 10%
Obviously, I can adjust the orginal sg to improve the % alcohol.

To stop fermentation early, you need to check the wine very often.
You will never get exactly what you want (partly because hydrometers are so inaccurate) but, when the sg is a bit higher than you want, then give it a really good dose of sulphite.
That will stun the yeast and (effectively) stop the fermentation fairly quickly. Adding sorbate soon after sort-of brings things to a close.
Note: Sorbate will not stop the current fermentation. It makes the yeast infertile and so it prevents fresh fermentation. So you need to use sulphite first and then sorbate.

I hate having to backsweeten wine because the sugar tastes so artificial, but as the original post was about mead .....

I hope this helps.
 
We back sweeten our wines to a particular SG, after years of going by taste. So now after so many years we know we like our meads at 1.005, our mango wines at 1.010, etc. As others have said, fruit flavor, acidity, alcohol and other factors will affect your perception of sweetness. But if you have a familiar recipe you can certainly make an educated guess using SG.

I agree with others that a very hot mead is not very tasty...maybe after many years it will mellow out, but it does taste like rocket fuel above 14% alcohol (my opinion and threshold obviously). I also agree if you want control, the only thing to do is use your OG to dictate the alcohol content and go dry, then back sweeten.

Something we do with our ports is multiple feedings until the yeast die out at about 18% to 20% alcohol. We record the measurements along the way so we know what the final alcohol content is (roughly), and we add smaller amounts near the end to keep it around 5% of what we think we'll want the sweetness to be. It's definitely not precise though (and with ports we know we'll be going fairly sweet)
 
I ferment to dryness then backsweeten if I'm looking for some residual sweetness. I've found that backsweetening to a specific SG (e.g. 1.010) doesn't reproduce consistent "sweetness" results.

Batch A may have had an SG of 1.005 and tasted semi-dry. Batch B was then backsweetened to the same SG of 1.005 but it tasted much sweeter! When I compared my notes, I had added more sugar to batch B than batch A to reach the same FSG.

I've found the most consistent results by adding the same amount of backsweetening sugar to each batch. For example, I may add 0.005 points of SG worth of sugar to each batch to reach a semi-dry wine. But in the end, taste each batch! You can always add more sugar.
 

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