Proofing and sweetening
Something macerated in high-proof spirit comes off the botanicals too strong and not sweet. Both of those are fixed by adding, and the two additions argue with each other, which is why we do them in one sum rather than two.
Why it is one sum
Section titled “Why it is one sum”Water lowers the strength. Sugar lowers it too, because dissolving it makes the liquid it is dissolved in bigger, and the alcohol you already had is now spread through more of it. So a strength you hit by proofing is not the strength you end up at once the sugar goes in, and a sweetness you aimed at is not the sweetness you get either.
Take a liter at 60 % and proof it to 30 %. Stir in sugar at 150 g per liter and you land near 27.4 %, carrying about 137 g per liter. Both numbers moved, and neither moved by an amount you would guess. Running a proofing calculator and then a sweetening calculator gives you that answer twice over without ever showing you it happened.
Asked as one question it has one answer: the water and the sugar that land on both targets together.
The room a sugar takes
Section titled “The room a sugar takes”A gram of sucrose in solution occupies about 0.617 mL. We do not look that figure up. Degrees Plato are grams of sucrose in a hundred grams of solution, and the fit we already use for Plato gives the density of that solution, so the volume a dissolved gram adds falls out of arithmetic this app was already doing. It runs from 0.6162 mL at 10 °Bx to 0.6249 at 60 °Bx, and the calculator evaluates it at the sweetness you asked for rather than picking one number for every case.
A syrup is the same relation read the other way. Tell us the °Bx and we know how much of what you are adding is sugar and how much is water, so the water from the tap comes down by exactly that much.
What this does not know
Section titled “What this does not know”Spirit and water pull together. Mix them and the result is a little less than the two volumes added up, by a couple of per cent at these strengths. We treat volumes as adding up, so the final volume we predict runs slightly high.
The sugar was measured in water, not in spirit. The Plato relation behind the figure above describes sucrose dissolved in water. Your amaro is sucrose dissolved in a mixture, and it behaves a little differently.
Neither is worth a table, and both point the same way: add the water a shade short of what we say, then top to volume by measuring. The strength and the sweetness are what the sum is good at; the last few milliliters are what your jug is good at.
Related
Section titled “Related”- Journal, where the calculator lives and what else a page can hold.
- Blending arithmetic, for the Pearson square and the rest of the two-lots-one-target family.
- Must, nutrients and stabilizing, for sweetening a drink that is still fermenting rather than one that never did.
The beer these numbers come from
Section titled “The beer these numbers come from”Reference pale ale — 20 L into the fermenter, a 60 minute boil.
| Grist | Amount | Color |
|---|---|---|
| Crisp Maris Otter Pale Ale Malt | 4.5 kg | 2.8 °L |
| Thomas Fawcett Caramalt | 0.35 kg | 9.9 °L |
| Hops | Amount | Alpha | Addition |
|---|---|---|---|
| Magnum | 15 g | 13.5 % | 60 min boil |
| Cascade | 30 g | 6.8 % | 10 min boil |
| Citra | 40 g | 13 % | 20 min stand at 80 °C |
| It comes out at | |
|---|---|
| Original gravity | 1.0507 |
| Final gravity | 1.0094 |
| Alcohol | 5.52 % |
| Bitterness | 35.66 IBU |
| Color | 5.14 SRM (10.12 EBC) |
| Into the fermenter | 20 L |
The numbers
Section titled “The numbers”Water to proof down and sweeten
0.815 L, from proof-and-sweeten.
water_L = final_L − spirit_L − sugar room − the syrup’s own water, with final_L = spirit_L × ABV / target ABV⇒ Water to proof down and sweeten = 0.815 L| Input | Value | Unit |
|---|---|---|
| Volume | 1 | L |
| Alcohol | 60 | % |
| Strength wanted | 30 | % |
| Sugar wanted | 150 | g/L |
| Sweetener | sugar | — |
| Final volume | 2 | L |
| Sugar | 0.3 | kg |
| Sweetness at the end | 14.21 | °Bx |
| Room a kilogram of dissolved sugar takes | 0.6169 | L/kg |
| Room this sugar takes | 0.185 | L |
| Syrup | 0 | L |
What it assumes:
- Alcohol is conserved, so the strength wanted fixes the final volume before anything else is known. Proofing and then sweetening solves the same two lines in the wrong order.
- Dissolved sucrose takes room: 0.6169 L per kilogram at 14.2 °Bx, derived from the Plato fit rather than looked up.
- Volumes are treated as adding up, and in the jar they do not quite: spirit and water pull together a little, and this sugar was measured in water rather than in spirit. Add the water a shade short and top to volume by measuring.
Sources:
- Methods of Analysis — American Society of Brewing Chemists
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