That’s certainly an interesting question and one for which the short answer is “no such equation exists.” The longer answer attempts to help explain why, even though you think you should have all the parts that you need to solve for unfermented sugar. As I was considering whether to answer your question for this issue of “Wine Wizard” or not, I sent your question to WineMaker magazine Technical Editor and columnist Bob Peak. I was debating including the question in this column because I was afraid I would have to give you an unsatisfactory answer: It just can’t be done. However, as I read Bob’s response I changed my mind and realized that you and your fellow readers might be interested in why the answer is “impossible.” Before I give you my opinion, I’ll quote Bob’s response in full because it’ll help illuminate the challenge you pose above.
To quote Bob: “What an interesting question! The simple answer from me is, no, I don’t know an equation (for calculating RS based on the above given information) and I don’t think you can do it.
“In theory, a pure mixture of sucrose (simplifying from the glucose/fructose that is actually in wine) plus pure water plus pure ethanol, you might be able to do it. For instance, you know the ethanol content, so you can look up the expected density in a specific gravity/temperature chart like this www.separationprocesses.com/CourseWare/Experiments/Property01.htm. From that, you can look at the density you measured (if your hydrometer is precise enough!) and ascribe any higher density than the table as coming from dissolved sucrose. You could then look up that difference as though it were the three digits after a 1.xxx specific gravity (SG) (since you have accounted for the below-one by compensating for the ethanol) and look up the sugar content as Brix, or percent sugar by weight, in a chart like this www.winning-homebrew.com/specific-gravity-to-brix.html.
“So, for instance, if the first chart said your 13% alcohol wine at 68 °F (20 °C) should be 0.97775 SG, but you actually read 0.98175, your difference of 0.004 SG can be found at 1.004 in the second chart at 1.03 Brix, or about 1%.
“So, with all that cleverness, why do I think it can’t be done? Extract! Anyone who has ever filled out a Japan export form (government forms for selling wine in Japan), knows you have to include extract, defined as solids other than sugar in the wine. I think they require it to avoid synthetic imitation wine made from sugar, water, and ethanol. In a lab like Vinquiry (where I worked), we did the extract analysis by physically evaporating and weighing the residue from an aliquot of wine, running glu-fru (glucose plus fructose-ed) enzymatically, and subtracting to get extract. So the question as posed leaves no way to distinguish extract and sugar in the density difference (in real wine).”
Bob is absolutely right. The “extract” in wine consists of the solids left behind by minerals, tannins, and other wine components that aren’t sugar and in my experience can be significant enough, especially in tannic red wines, to throw off any attempt at getting to a residual sugar by specific gravity alone. Let’s also remember that with residual sugar in most table wines, we’re talking 0.2% (2 g/L) or less, which are small numbers. Using a hydrometer/specific gravity and the naked eye, even with a temperature correction, is a very imprecise way to get at density, especially when there are so many other things that could be contributing to that density other than sugar. This is why most winemakers, home hobbyists and otherwise, are always advised to use an alternative test like the Clinitest tablet method to check for the absence of fermentable sugars in wines that are measuring under 0.9995 by specific gravity or under -1.0 °Brix. Commercial winemakers get even more exact than the visual color-change Clinitest method, and do an enzymatic analysis at a professional wine industry laboratory.
