## Day 434

Ooops. I discovered in *Brewhouse Calculations*, to my chagrin, that I had made a boo-boo. Turns out when mixing water and grain together, you need to multiply the grain’s weight by 40%, since the grain holds back a lot of its heat during mixing. (In the formula I posted last week, I left this out.) So to calculate the resultant temperature when we mix 200 kg of grain at 20°C into 300 L of water at 69°C, the formula should be:

c = [(0.4 x Aa) + (Bb)]/(0.4A + B)

where

- A = grain weight
- a = grain temperature
- B = water weight (1 L of water = 1 kg. Yay, metric system!)
- b = water temperature
- c = resultant temperature

Plugging in all the right values:

c= [(0.4 x 200 kg x 20°C) + (300 kg x 69°C)]/(0.4 x 200) + 300 =

= [1600 + 20,700]/380 kg = 58.7°C

(Last week’s answer was 49.4°C. As I said, oops. Hope you weren’t using that blog post to study for an exam.)

Review finished, we had a real grab bag of calculations this week. First up was carbonation, which is interesting because we just learned some calculations for carbonation last week in *FCF*. Huh. Calculating when to close up the fermenter and allow CO2 being produced by fermentation to naturally carbonate the beer:

- Determine how many grams of CO2 are required (remembering that 1 g of CO2 = 0.506 volumes)
- Divide this by 0.46 to determine how much extract will be needed
- Convert grams of extract to degrees Plato
- Close up the fermenter when the gravity of the beer equals the number reached in Step 3 plus the desired final gravity.

So, if we want to naturally carbonate our beer with 2.5 volumes of CO2, and expect the yeast to attentuate the wort to 2.5°P:

Step 1: 2.5 volumes of CO2 desired/0.506 = 4.94 g/L desired

Step 2: Extract needed to produce that much CO2 = 4.94/0.46 = 10.74 g/L

Step 3: Extract needed converted to degrees Plato = (10.74/1000) x 100 [to convert to percent] = 1.1°P

Step 4: Close up fermenter when gravity reaches 2.5°P + 1.1°P = 3.6°P

OK, seems to work the same as what we learned in *FCF*. On to calculating how much wort to hold back in order to induce a secondary fermentation (i.e. krausening):

- Calculate the Apparent Degree of Fermentation (ADF): [original gravity – final gravity]/original gravity
- However, the Real Degree of Fermentation (RDF) will be lower because of the less dense alcohol in the mixture: RDF = ADF x 0.82
- Calculate the Real Final Extract (RFE) that is unfermentable: RFE = OG x (1 – RDF)
- Finally, calculate the percentage of wort that should be reserved: [(Desired g/100 mL of CO2 – existing g/100 mL of CO2)/0.46]/[OG – RFE]

Seem simple? Let’s assume we have 10 hL of 13°P wort all ready to be fermented at 20°C. We eventually want it to be carbonated with 6.5 g/L of CO2, and we believe the wort will eventually attenuate to 4°P. (We know from consulting a table that fermenting it at 20°C will cause 1.69 g/L of CO2 to be dissolved in the beer.)

Step 1: ADF = [OG – FG]/OG = (13-4)/13 = 69.2%

Step 2: RDF = ADF x 0.82 = 69.2% x 0.82 = 56.7%

Step 3: RFE = OG x (1 – RDF) = 13 x (1 – 0.567) = 5.63

Step 4: Percent of wort to be reserved = [(Desired g/100 mL of CO2 – existing g/100 mL of CO2)/0.46]/OG – RFE = [(0.65 – 0.169)/0.46]/(13 – 5.63) = 1.1/7.37 = 0.147 = 14.7%

From our 10 hL of wort, we should reserve 14.7% of it, or 147 L, to be added later in order to induce a secondary fermenttion that will produce 2.5 volumes of CO2 in the final product.

But wait, there’s more! On to balancing draught systems. In any bar’s draught system, the gas pressure needed to force beer from keg to tap is balanced by the resistance of the beer line, and can be helped or hindered by gravity, depending on whether the keg is above or below the level of the tap.

Gravity either adds or subtracts 0.5 psi per foot of rise or fall. As we saw last year in *Packaging*, various types of lines have various resistances, measured as psi/ft. I won’t go into the formulae; it is pretty basic–simply balance the pressure of the gas to the calculated resistance of the line. If there’s too much pressure, add some restrictor line near the tap to increase resistance. If there’s too much resistance, increase the gas pressure. If the gas pressure needed gets to be excessive, switch to a nitrogen/CO2 mix so that the nitrogen pushes the beer and the CO2 gas keeps the dissolved CO2 in the beer.

In *History of Beer*, some more student presentations today, including a history of the beer can. Bill White’s lecture that followed was about Beer in Art.

**Explore posts in the same categories:**Brewmaster

**Tags:** Brewhouse Calculations, History of Beer

November 13, 2012 at 12:08 am

[…] [EDIT: I discovered one week later that I have missed one factor in this formula. See the correct formula and the correct answer on Day 434.] […]

November 17, 2012 at 10:15 am

[…] [EDIT: I discovered one week later that I have missed one factor in this formula. See the correct formula and the correct answer on Day 434.] […]