Controlled fermentation requires control of the initial sugar concentration. Assuming that fermentation is about 90 % efficient, it takes about 17grams of sucrose per liter of solution to produce 1.0 % alcohol by volume. Some fermentations will do better than this, and some worse, but it is a decent "rule of thumb" to use with pure table sugar. Glucose or Fructose require 17.9 grams per liter per percent alcohol. This is explained in Appendix 2.
Most home brewers or wine makers have a hydrometer to measure sugar content in their wort or must. Many of these hydrometers have several different scales on them. There are many possible scales for measuring the density (and hence, the sugar content) of a solution. The most common include: Specific Gravity and degrees Plato, Brix or Ballings.
The specific gravity of a solution is the ratio of its density to that of pure water. A specific gravity of 1.050, for example is 5 % denser than pure water. The Plato, Brix and Ballings scales all relate the density of the solution to the % sucrose by weight. Sucrose (common table sugar) was chosen because it is the sugar that dissolves in water to produce the greatest density. Appendix 3 includes a table that shows the relationship between sugar content and several common hydrometer scales.
Fortunately, we do not need a hydrometer to make up a correct sugar solution for fermentation. All we need to do is calculate the grams per liter of sugar we want from the % alcohol we're trying to reach using the following equation:
• % alcohol desired x 17 = grams of sugar per liter of solution
Then, calculate the weight of sugar needed based on the g/l sucrose desired, using one of these equations:
• Metric units: g/l sucrose desired x liters desired - 1000 = kg sugar
• American units: g/l sucrose desired x US gallons desired - 120 = lb. sugar
• Imperial units: g/l sucrose desired x Imperial gallons desired - 100 = lb. sugar
BE CAREFUL! You are after g/l of sugar in the final solution, so weigh out the sugar and slowly add enough water to end up at your final amount of liquid! If you add the sugar to the measured amount of water, you will end up with more liquid that is less concentrated than you expected. If you use some sugar other than sucrose, you can dissolve the proper grams into the correct final volume, but the specific gravity or degrees Plato measured with a hydrometer will mislead you.
Here are some sample calculations to show the various ways these equations can be used:
• We want to end up with 9 US gallons of 20 % alcohol. How much sugar do we need?
• We have a 25 pound sack of sugar. How much 15 % ethanol can we make?
(now, turn the equation around. Volume x g/l - factor = Weight Sugar, which means that Volume = Weight sugar - g/l sugar x factor. We'll work this all three ways.)
Metric: 11.34 kg - 255 g/l sugar x 1000 = 44.5 liters American: 25 lb - 255 g/l sugar x 120 = 11.76 US gallons Imperial: 25 lb -255 g/l sugar x 100 = 9.8 Imp. Gallons
(As a practical matter, rounding to the nearest quart or liter is just fine)
• We have 10 kg of sugar, and a 35-liter fermenter. What % alcohol will we get?
(This time we know weight of sugar and volume. Re-arrange the equation again to get g/l sugar = weight sugar - volume x factor
= 10 kg - 35 liters x 1000 = 28.6 % sugar (now, calculate % alcohol from g/l sugar, by dividing by 17) % ethanol = g/l sugar - 1.7
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