Backyard Brewers

Last weekend I noticed that for whatever reason one of my kegs decided it didn’t want to hold any pressure. I spent a couple of days readjusting the lid and re-pressurizing it but had no luck. Since I didn’t have any other kegs available I decided to bottle the rest of the beer. Unfortunately though, there wasn’t much carbonation left in the beer.

This was slightly problematic because I didn’t have a good feeling for how much of the beer was really left in the keg, and consequently how much priming sugar I should use to re-carbonate the beer. I whipped out the trusty volume of a cylinder equation (V = π × r ² × h) and estimated the volume of beer left in the keg by pulling the keg out of the fridge and measuring the height of the area where condensation had formed.

I took some initial measurements to find the volume of the entire keg. Since I know these kegs can hold 5 gallons I wanted to get a rough idea how close my pen and paper estimates were.

Keg measurements:

r = 4.125 in
h1 = 20 in

Unit conversion:

1 gal per 231 in3

Keg volume estimate:

⇒ V1 =  π × r2 × h
     = (π) × (4.125)2 × (20) ≈ 1069.12 in3
     = (1069.12 in3) × (1 gal ⁄ 231 in3) = 4.62 gal

⇒ What the frack = 5 – 4.62 = 0.38 gal

Somewhere in the measurements I potentially have an unaccounted 0.38 gallons. I’ll just add this on to the beer volume calculation later on…

Beer in keg measurements:

h2 = 10 in

Beer in keg volume estimate:

⇒ V2 = (π) × (4.125)2 × (10) ≈ 534.56 in3
     = (534.56 in3) × (1 gal ⁄ 231 in3) = 2.31 gal
     = 2.31 + (0.38 what the frack gal) = 2.69 gal

Alright, so looks like I’ve got ~ 2.69 gallons of beer. Fannnnnntastic. To figure out how much priming sugar I need I am using an equation I found on the Home Brew Digest mailing list. You can find the email, written by Bill Pierce, in digest #5471.

Definitions:

Vbeer      ≡ Volume of beer in US gallons
VCO2       ≡ Desired carbonation level in volumes of CO2
Tferm      ≡ Fermentation temperature of beer in °F
PS        ≡ Priming sugar weight in grams

Variables:

Vbeer     = 2.69 gal
VCO2      = 2.6 volumes of CO2
Tferm     = 58 °F

Priming sugar estimate:

⇒ PS = 15.195 × Vbeer × (VCO2 - 3.0378 + (0.050062 × Tferm) - (0.00026555 × (Tferm)2))
      = 15.195 × 2.69 × (2.6 - 3.0378 + (0.050062 × 58) - (0.00026555 × (58)2))
      ≈ 65 g

Well there you have it; 65 grams of corn sugar.  My volume estimate only ended up being off by about 11 ounces of what was actually left in the keg.   One last thing worth mentioning;  Mark Hibberd’s “A Primer on Priming“ was helpful in determining what volumes of  CO₂ is typical in different styles of beer.   Here is his table:

-------------------------------------------
Beer style                      Volumes CO2
-------------------------------------------
 British-style ales              1.5 - 2.0
 Porter, stout                   1.7 - 2.3
 Belgian ales                    1.9 - 2.4
 European lagers                 2.2 - 2.7
 American ales & lagers          2.2 - 2.7
 Lambic                          2.4 - 2.8
 Fruit lambic                    3.0 - 4.5
 German wheat beer               3.3 - 4.5
-------------------------------------------
Typical CO2 levels in bottled beers