🍺 Top-down Brew: Documentation for Priming Carbonation Calculations

Overview

The following steps are used for determining the amount of sugar needed in priming calculations. This is a summary for documentation purposes and for people who might be interested in knowing the details. The approach is based most closely upon Kaminski (2019) but also includes additional information from several sources (see below).

In concept, the general formula is: grams of CO2 needed for target carbonation divided by grams of CO2 that can be generated from a sugar source. This determines the amount of sugar needed for carbonation.

Priming with Sugar

  1. Start by determining the amount of dissolved CO2 present in the fermented beer. This amount depends upon temperature, with colder temperatures holding a greater amount of CO2. The highest point of fermentation temperature should be used for these calculations.
    1. Fahrenheit formula: CO2measured = 3.0378-(0.050062*temperature)+(0.00026555*temperature*temperature)
    2. Comments: The formula units are volumes of dissolved CO2. It assumes no additional pressure (i.e., no spunding) during fermentation. The formula is based upon Henry's Law (Smith, 2015). This is the formula used by Brewer's Friend in their calculator.
    3. A similar calculator for metric values that includes pressure is available from Braukaiser.com. An important difference is that this formula yields CO2 in grams per liter.
  2. Determine the amount of CO2 needed in grams to achieve the desired degree of carbonation.
    1. Formula: CO2 needed (in grams) = (CO2desired-CO2measured)*1.969*LitersBeer
    2. CO2desired-CO2measured is the difference needed to reach the target level of carbonation. For example, if 2.7 volumes of CO2 are desired and .9 volumes of CO2 are already dissolved in the beer, then we will need 1.8 volumes of CO2 to come from the priming sugar to reach the target.
    3. Multiplication of this difference by the 1.969 constant converts volumes of CO2 to grams per liter. Smith (2015) has a slightly different constant of 1.926 (p. 78). Some authors simply round this constant off to 2 for simplicity.
    4. Multiplication by LitersBeer determines the amount needed for the entire batch volume.
  3. Divide the needed CO2 (in grams) by the grams of CO2 that can be produced from a gram of sugar.
    1. Each sugar molecule is split during fermentation to produce ethanol and carbon dioxide. The carbon dioxide that can be produced from each gram of sugar is of interest here for supplying the needed CO2.
    2. For glucose monohydrate (corn sugar): ((CO2desired-CO2measured)*1.969*LitersBeer)/.44
    3. For sucrose (table sugar): ((CO2desired-CO2measured)*1.969*LitersBeer)/.51
    4. For dry malt extract: ((CO2desired-CO2measured)*1.969*LitersBeer)/.375
    5. Sources: The .44 and .51 values for corn sugar and sucrose, respectively, are from McGill (2006). For corn sugar, the value is calculated as glucose monohydrate. Anhydrous glucose would be .49 grams (McGill, 2006) and would thus take less sugar. The .375 value for DME is from Kaminski (2019).
  4. Assumptions
    1. This calculator assumes that the main fermentation is 100% complete. If it's incomplete, there will be too much sugar and overcarbing.
    2. Another assumption is no extra pressure during fermentation (i.e., no spunding).
    3. No adjustment is made for CO2 that will be lost to headspace and lost during the packaging process. It may be necessary to slightly overshoot the carbonation goals to compensate for this lost carbon dioxide.

Priming with Wort

Priming with wort uses the same numerator as above for determining the needed grams of CO2. The more complicated part is the denominator, which is the grams of CO2 from wort. Worts can vary significantly in sugar content. A low gravity priming wort will need more volume than a high gravity wort to achieve the same level of carbonation. Another complication is that wort is not 100% fermentable, so the proportion of sugar that can actually be fermented is important to determine.

  1. Wort gravities must be expressed in degrees Plato for determining sugar weights.
  2. A simplifying assumption is that the same wort will be used for both the main batch and the wort added at bottling time.
  3. Real extract is a hydrometer correction for the presence of ethanol in the fermented wort.
    1. Real extract: RE = (0.1808*OG)+(0.8192*FG)
    2. OG = original gravity; FG = final gravity
  4. Real degree of fermentation is an attenuation percentage based upon real extract.
    1. Real degree of fermentation: RDF = (100*(OG-RE)/OG)*(1/(1-.001561*RE))
  5. Divide the needed CO2 (in grams) by the grams of CO2 that can be produced from a gram of wort.
    1. The following formula was published by Kaminski (2019). Unfortunately, it had an error.
    2. Original formula: LitersWort = (CO2desired-CO2measured)*1.969*LitersBeer*.5055*RDF*(OG/100)
    3. The error is that the formula must divide (not multiply) the grams of CO2 needed (numerator) by the grams of CO2 from wort (denominator). I contacted BYO about this problem. BYO and Kaminski responded with a correction in the March-April 2020 issue (Mail, p. 8, 10). I appreciate their positive and helpful feedback.
    4. Corrected formula: LitersWort = ((CO2desired-CO2measured)*1.969*LitersBeer)/(.5055*RDF*(OG/100))
    5. Interpretation: The .5055 constant is grams of CO2 from sucrose (see also the .51 constant above). It's likely that sucrose is used because the plato scale was developed from sucrose. The rest of the denominator is adjusting this value downward based on attenuation of original gravity.
    6. Kaminski prefers working in liters, but I prefer expressing this formula as grams of wort. The following modification of converting RDF from a percentage to a decimal yields the grams of wort needed to reach the target carbonation level. This modification keeps the formula consistent with grams being the units in both the numerator and the denominator.
    7. GramsWort = ((CO2desired-CO2measured)*1.969*LitersBeer)/(.5055*(RDF/100)*(OG/100))
  6. Convert the grams of wort needed to liters of wort.
    1. My original idea was grams of wort could be converted to liters by dividing by 1000 (i.e., one gram is one milliliter of water). Kaminski pointed out that this is not quite right because it does not include the weight of the sugar. The proper weight would need to include the water plus the sugar, so the needed value will certainly be more than 1000 for wort. I thank him for helping me understand this important idea.
    2. LitersWort = GramsWort/(1000+((OG/100)*1000))
      1. 1000 = Weight from water in one liter
      2. (OG/100)*1000 = Expresses OG in plato as a decimal, then multiplies by 1000 to get a sugar weight per liter

Carbonation with unfermented wort plus sugar

Ideally, it would be good to use only wort for carbonation. Sometimes though the amount of wort available might be short of the needed volume. This calculator determines the extra sugar that would be needed to supplement the available wort.

This calculator starts out the same as the wort calculator described above to determine the volume of wort needed to reach the target. The additional calculation begins by determining the percentage of sugar that can be supplied by wort, such as 90%. The decimal proportion that is left (example: 10% = .10) is multiplied by the total amount of sucrose or glucose that would be needed for carbonating the batch to get the remaining sugar.

Carbonation with fermenting wort (kraeusening)

  1. Kaminski (2019) provides the following formula. The numerator is the same as the above. The denominator is for unfermented wort that could be from a different source than the beer that is being primed.
  2. LitersKraeusen = ((CO2desired-CO2measured)*1.969*LitersBeer)/(.5055*((CG - FG)/100)) where CG = kraeusen current gravity
  3. Something uncertain about this formula is why it doesn't need real degree of fermentation like the formula for unfermented wort. Here's a possibility. This formula is for wort that may not be the same as the beer being primed. The final gravity is a bit of a guess based on past batches. Given this uncertainty a slight correction for alcohol may not make much difference. It simplifies the formula to drop this correction. Another possibility is that the alcohol present in the fermenting wort may be minor so this correction is less essential.
  4. This formula appears to yield grams of kraeusening wort needed. This makes sense because the denominator is essentially grams of CO2 produced per gram of kraeusening wort. The conversion to liters then is similar to the formula for unfermented wort.
  5. LitersWort = GramsWort/(1000+((CG/100)*1000)) where CG = kraeusen current gravity

Sources

Kaminski, C. (2019, November). Dose carbing: CO2 generation from sugar sources, Brew Your Own, 25(7), p. 98-100.

Lewis, A. (2010). Better bottling. Brew Your Own, 16(1), 16-18.

McGill, R. (2006). Priming with sugar. Brew Your Own, 12(7), 44-47.

Palmer, J.J. (2002) How to Brew. 2nd edition, Defenestrative Publishing, p. 133

Smith, B. (2015). Solve the priming puzzle. Brew Your Own, 21(3), 76-80.

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