Accurately Calculating Sugar Additions for Carbonation

Accurately calculating the carbonation is a great exercise for working with apparent and actual attenuations as well as working with the extract % or Plato scale. The latter is not essential, but makes things more intuitive.

The final carbonation of bottle conditioned beer depends on the CO₂ currently present in the beer and the CO₂ that will be generated during bottle conditioning.

The amount of CO₂ already in the beer depends on the CO₂ pressure and the temperature of the beer. It can be determined by using a Carbonation Table. These tables show the equilibrium of CO₂ content that exists for a given CO₂ pressure and beer temperature.

The amount of CO>sub>2</sub> created by bottle conditioning is based on the amount of sugar that is fermented. Each gram of fermentable extract is fermented into equal parts (by weight) of alcohol and CO₂ (this is not exactly true, but close enough for this calculation).

corn sugar

The easiest way to add fermentable extract to beer is through the addition of pure sugar. This can be dextrose (corn sugar) or succrose (table sugar). Most corn sugar is actually glucose monohydrate. This means that each glucose molecule bound with a water molecule which adds to its weight but not to the potential of CO₂ that can be produced [BYO]. Glucose monohydrate contains 9% water by weight, which means that only 91% of its weight can be considered for the CO₂ calculation.

The formula for calculating the carbonation when priming with corn sugar is:

C_beer = C_flat-beer + 0.5 * 0.91 * m_corn-sugar / V_beer

• C_beer - the final carbonation of the beer (g/l)
• C_flat-beer - the CO₂ content of the beer before bottling (g/l)
• m_corn-sugar - the weight of the corn sugar (glucose monohydrate) (g)
• V_beer - beer volume (l)

table sugar

Table sugar, succrose, does not contain any water and yeast will convert half of its weight to CO₂

C_beer = C_flat-beer + 0.5 * m_table-sugar / V_beer

• m_table-sugar - the weight of the table sugar (succrose) (g)

dried malt extract

When using malt extract for priming, its fermentability needs to be taken into account. A typical aparent fermentablility (limit of attenuation) of malt extract is 80%. (a 12 Plato wort will finish at 2.4 Plato / 1.048 OG - 1.010 FG). But to determine the true fermentability the true fermentability needs to be calculated. To convert between apparent and true attenuation, the following formula can be used (see Understanding Attenuation)

A_true = A_apparent * 0.82

• A_true - true attenuation
• A_apparent - apparent attenuation

With that the carbonation that can be achieved with dried malt extract is

C_beer = C_flat-beer + 0.5 * 0.82 * 0.80 * m_DME / V_beer

• C_beer - the final carbonation of the beer (g/l)
• C_flat-beer - the CO₂ content of the beer before bottling (g/l)
• m_DME - the weight of the dried malt extract (DME) (g)
• V_beer - beer volume (l)

Speise

The carbonation calculation with Speise is similar to the calculation for malt extract with the difference that the fermentability is known and that the volume of the beer, that is going to be bottled, is increased by the Speise volume. Though water is used for the priming with sugar and DME, its contribution to the beer volume are small and have been neglected. But when using Speise or Kraeusen, the amount of volume that is added can be significant.

First, the apparent attenuation of the Speise needs to be determined. If using wort from a previously brewed batch, generally the same batch that needs to be carbonated, the original extract and final extract are known. When boiling the Speise to sanitize it before bottling, make sure you boil with a lid on to minimize evaporation loss (which changes its original extract) or compensate for it by adding water or adjusting the original extract that is used in the equations.

AA_Speise = 1 - OE_Speise / FE_Speise

• AA_Speise - apparent attenuation of the Speise wort
• OE_Speise - original extract of the Speise wort
• FE_Speise - final extract of the Speise wort. Take the final gravity reading of the beer for this.

From the apparent attenuation we can calculate the real attenuation with

RA_Speise = 0.82 * AA_Speise

The real attenuation tells how what percentage of the original extract of the Speise is actually fermentable and will contribute to the carbonation of the beer. With the Plato or percent extract scale, the amount of extract (sugars, proteins, dextrines ... everything that is dissolved in the water) in a given wort can easily be calculated with

m_extract = V_Speise * SG * OE/100

• m_extract - extract weight (g)
• V_Speise - volume of the wort (ml)
• SG - specific gravity of the wort. This can be committed for lower gravity beers as it will be close enough to 1. SG = 1 + OE/250
• OE - original extract in % or Plato

The amount of fermentable extract can be determined by scaling the extract weight with the real attenuation

m_{fermentable-extract} = m_extract * RA

• m_{fermentable-extract} - the weight of the fermentable extract

At this point the known carbonation equations can be used with the difference that the volume of the final beer is now the Volume of the beer before bottling plus the Speise volume.

C_beer = C_flat-beer + 0.5 * m_{fermentable-extract} / (V_flat-beer + V_Speise)

• C_beer - the final carbonation of the beer (g/l)
• C_flat-beer - the CO₂ content of the beer before bottling (g/l)
• V_flat-beer - beer volume before bottling (l)

sources

• [BYO] - BYO - Priming with Sugar