Definition: Utilization is the percentage measurement of hop's alpha acids "utilized" during the boiling process. This gives you a formulized number to measure the bitterness of a final beer known as IBU's (International Bittering units), AAU's (Alpha Acid Units), or HBU's (Homebrew Bitterness Units).
Equations for determining utilization:
If your eyes glaze over looking at IBU equations - here’s a practical guide. Hop utilization increases with boil time, so the longer you boil your hops the more bitterness and IBUs you will add. Late addition hops (boiled for 5-10 minutes) add very little bitterness, and are used primarily for aroma. Bittering hops are usually added for the full boil time (60-90 minutes).[Smith,2008]
Hop utilization also increases as you lower the gravity of your boil. If you are brewing a high gravity beer, or an extract brewer using a partial batch boil (small pot) you will get much lower utilization. This is why extract brewing requires more hops (in general) than all-grain brewing. Since different brewers use different equipment, it is important to take into account your own boil size and boil gravity when estimating the bitterness of your beer.[Smith,2008]
Three equations to estimate utilization and IBUs are most often used: Rager, Tinseth and Garetz. The equations differ in the way that they estimate the utilization percentage. Rager is most often associated with extract and partial mash brewers. The Rager equation takes original gravity of the boil into account, and tends to produce IBU estimates that are on the high side of the three equations. It’s important to understand that the three estimation methods will provide widely varying results in some cases. Each provides only an estimate of bitterness, and none are perfect or all encompassing. I would not spend too much time worrying the differences. Choose a single estimation method and stick with it.[Smith,2008]
Rager's Method:
Boiling Time(minutes)/%Utilization: 0 - 5/5.0%, 6 - 10/6.0%, 11-15/8.0%, 16-20/10.1%, 21-25/12.1%, 26-30/15.3%, 31-35/18.8%, 36-40/22.8%, 41-45/26.9%
This utilization can be reduced to a smooth function, as opposed to the table, which produces many discontinuous lines. The Rager table is represented by the following utilization equation:
%UTILIZATION = (18.11 + 13.86) * hyptan[(MINUTES - 31.32)/18.27]
According to Rager, if the gravity of the boil exceeds 1.050, there is a gravity adjustment (GA) to factor in:
GA = (BOIL_GRAVITY - 1.050)/0.2
otherwise, GA = 0
Metric Units IBU = ((GRAMS OF HOPS) * %UTILIZATION * %ALPHA * 1000)/(VOLUME(litres) * (1 + GA))
Non-metric Units IBU = ((OUNCES OF HOPS) * %UTILIZATION * %ALPHA * 7462)/(VOLUME(gallons) * (1 + GA))
Jackie Rager's numbers have been used successfully by thousands of homebrewers and provide a consistent base with which to work. Note that the figures expressed as percent should be entered as decimal values in the formula (9% = 0.09). It is apparent that his constant 7462, derived from metric to US conversion, is actually closer to 7490. The GA factor could be questioned as well, as it is intuitively obvious that a gravity of 1.049 does not affect utilization exactly the same as a gravity of 1.000 (water). It is assumed (but not verified) that the utilization table is corrected for this assumption and/or the difference is small enough that it has little effect on the final bitterness of the beer.[Pyle,1995]
Garetz Method:
It has been reported that since iso-alpha acids possess a slight electrical charge, they can be lost in many ways. Among these are absorption into the yeast cell walls (and subsequent removal of the yeast), attachment to coagulating proteins (and subsequent removal of this trub), attachment to filters, etc. It is unclear if Mr. Rager's utilization numbers have assumed these losses, but it can be assumed that Tinseth and Garetz did take them into account. The Garetz numbers below represent average yeast flocculation; he also provides tables which represent fast and slow yeast flocculation.
Boiling Time (minutes)/%Util (Avg Yeast) 0-5/0%, 6-10/0%, 11-15/2%, 16-20/5%, 21-25/8%, 26-30/11%, 31-35/14%, 36-40/16%, 41-45/18%, 46-50/19%, 51-60/20%, 61-70/21%, 71-80/22%, 81-90/23%
According to Garetz, there are several adjustment factors, that he brings together in the formula with the term "combined adjustments" (CA):
CA = GF * HF * TF
where GF is the Gravity Factor, HF is the Hopping Rate Factor, and TF is the Temperature Factor. To calculate it all, he starts with some he calls CF:
Concentration Factor: CF = Final Volume / Boil Volume,
to account for concentrated boils of extract brews. Next, calculate Boil Gravity (BG):
BG = (CF * (Starting Gravity - 1)) + 1
Then calculate GF:
GF = ((BG - 1.050)/.2)+1
HF is calculated as follows:
HF = ((CF * Desired IBUs)/260) + 1
TF is based on elevation as follows:
TF = ((Elevation in feet) / 550) * 0.02) + 1
These are all put into the following formula, along with the utilization from the table, and the IBUs are calculated. Note two things: 1) the utilization and alpha acids should be expressed as whole numbers (7% = 7), and 2) this process is iterative, since it contains a term (HF) based on your goal IBUs. You must guess at the final result, do the math, and rerun the process, each time adjusting the value downward. It takes a little practice, but can be done.
Metric Units IBU = (((%Utilization) * (%Alpha)) * Hop weight(grams)) * 0.1 / (Volume(liters) * CA)
Non-Metric Units IBU = (((%Utilization) * (%Alpha)) * Hop weight(ounces)) * 0.749 / (Volume(Gallons) * CA)
Garetz goes to allow for a yeast factor (YF), pellet factor (PF), bag factor (BF), and filter factor (FF), and comes up with:
CA = GF * HF * TF * PF * BF * FF
This allows you to adjust the formula based on your own brewery and practices.
Sources:
[Smith,2008] Brad Smith author of BeerSmith Brewing Software, BeerSmith Forum Blog
[Pyle,1995] Norm Pyle, Realbeer.com Hops FAQ's page
