I don’t know if this is part 1 in an ongoing series, but seeing as I’m mostly creating my own recipes rather than brewing from kits or recipes in books, and there are plenty of equations that go into determining things like BUs, ABV, potential OG, etc., I wouldn’t be surprised to find myself writing exciting, math-based posts in the future. Hence the title.
My equations come mostly or entirely from Ray Daniels and his thoroughly wonderful Designing Great Beers. He doesn’t cover every major style, particularly now with the Belgian explosion well underway, but his coverage of the classic German and British styles is very useful, and the initial chapters on water, hops, yeast, and malt are great regardless what kind of beer you brew. He dedicates three chapters to hops alone!
But enough of book larnin’. Onto practical applications, and awesome funtime math problems.
In the IPA I just brewed (which is, by the way, the best-looking beer I’ve ever made as it sits there with a three inch thick, creamy krausen, still slowly bubbling at 70 degrees F after five days), I used two different hops in four additions. The hops are all pellets, and include Centennial at 10.4% alpha, and Amarillo at 8.9% alpha. My cheap-ass plastic scale kicked the bucket just before the last two additions, so the last two measurements are suspect. But I’m not entering any contests, so I don’t really care.
Hop additions to my new IPA:
1.25 ounces Centennial @ 60 minutes
0.75 ounces Centennial @ 30 minutes
1.00 ounces Amarillo @ 20 minutes
1.00 ounces Amarillo @ 10 minutes
I’ll be adding another couple ounces, probably of Amarillo, in the secondary, but dry hopping doesn’t extract any alpha oils according to Daniels, so they won’t enter any equations.
To determine the IBU, first I need to adjust for the gravity of the boiling wort, as gravities above 1.050 impede utilization. That’s a simple equation. Daniels calls it Cgravity (correction for gravity).
Cgravity = 1 + [(Gboil - 1.050) / 2 ]
My final gravity for five gallons was 1.055. My boiling volume was 3.5. Multiplying 1.055 * 5 gets the amount of GU (gravity units) in the wort. Dividing that by 3.5 gets the gravity of the boiling wort, 1.078.
Daniels’ equation for determining IBU is as follows:
IBU = Woz * U% * A% * 7,489 / (Vgal + Cgravity)
Woz = weight of hops in ounces
U% = utilization percentage of the hops
A% = percent alpha acids of the hops
Vgal = volume in gallons of the final wort
7,489 is a constant. I forget what for. Read the book.
Utilization percentage I determined from a table in Daniels. Here’s my math:
IBU for 60 minute hop addition:
1.25 * .3 * .104 * 7489 / 5.7 = 51.24
IBU for 30 minute hop addition:
.75 * .24 * .104 * 7489 / 5.7 = 24.60
IBU for 20 minute hop addition:
1 * .19 * .089 * 7489 / 5.7 = 22.22
IBU for 10 minute hop addition:
1 * .15 * .089 * 7489 / 5.7 = 17.54
Total IBU:
115.60
That’s a huge number! Daniels’ style guide for IPA says 40-60 IBU. Of course, that was also before the hophead explosion. Lots of explosions in US brewing lately. I have a hard time believing the numbers I came up with, but Daniels gives a simple example beer that uses a little over half an ounce less hops at only 5% alpha, and comes up with a little less than half the IBUs I did, so maybe that’s right. Of course, there’s also a saturation point, and I put all my pellets in a hop bag during the boil, which will probably impede utilization, but still, I’m expecting a very hoppy beer.
Before brew day, I was too lazy to do these equations. During brew day, I was too occupied with actually brewing the beer to do them. The only math I did that day was to figure out how much DME I needed to add to make up for the extreme inefficiency of my mash. I was worried that my mere four ounces of hops wouldn’t be enough for an IPA. Looks like my fears were a little overblown. I’m expecting a final ABV of between 4.7% (assuming 65% AA, unlikely with White Labs’ California Ale Yeast) and 5.6% (assuming 78% AA, definitely the high end, but perhaps possible with the aforementioned yeast). I will definitely be bottling this one as soon as possible (two weeks in secondary, max). I’ve had between 78% and 85% attenuation with the previous beers I brewed with this yeast (The WL website says 73% - 80%, so I guess that’s not too far off), so who knows.