Glenn's Hop Utilization Numbers

Introduction

Some of you may know that I've been interested in hop utilization--specifically alpha acid utilization--for a while. I've been lucky enough to have access to some handy tools and knowledgable friends at the USDA hop labs and the Flavor Perception labs at Oregon State University. Over the years I've read a lot of scientific papers on the subject and had quite a few worts and beers analyzed.

Glenn's Numbers

If you would rather let a computer do the work for you, my online cgi-bin Bitterness Calculator or the JavaScript version should interest you. If not, here is an example plot using my numbers:

util vs boil time plot

As you can see, the shape of the curve is different than the curves attributed to Jackie Rager in Zymurgy or to Mark Garetz in his book. That's because I believe, backed up by the brewing literature, that alpha acid isomerization is a first order, or more likely, a pseudo first order chemical reaction. The "S" shaped curves most homebrewers are familiar with don't seem to accurately reflect what's happening in the brew kettle. What follows is a primer on how to calculate IBUs using my numbers.

To calculate IBUs, the formula is simple:

IBUs = decimal alpha acid utilization * mg/l of added alpha acids
To calculate the concentration of alpha acids you add to the wort:

mg/l of added alpha acids = decimal AA rating * grams hops * 1000
                            -------------------------------------
                              volume of finished beer in liters
or for those of you not using metric units:
mg/l of added alpha acids = decimal AA rating * ozs hops * 7490
                            -------------------------------------
                             volume of finished beer in gallons 
You can look up the decimal alpha acid utilization in the utilization table below or calculate it directly using the Bigness factor and the Boil Time factor.
decimal alpha acid utilization = Bigness factor * Boil Time factor

The Bigness factor accounts for reduced utilization due to higher wort gravities. Use an average gravity value for the entire boil to account for changes in the wort volume.

Bigness factor = 1.65 * 0.000125^(wort gravity - 1)
The Boil Time factor accounts for the change in utilization due to boil time:

Boil Time factor = 1 - e^(-0.04 * time in mins)
                   --------------------------
                             4.15
The numbers 1.65 and 0.000125 are empirically derived to fit my data. The number 0.04 controls the shape of the utilization vs. time curve. The factor 4.15 controls the maximum utilization value--make it smaller if your kettle utilization is higher than mine.

I'd suggest fiddling with 4.15 if necessary to match your system; only play with the other three if you like to muck around. I make no guarantees if you do.

The really cool thing about these new equations is that they are easily customizable. I believe the basic form is correct; by playing with the different factors, different brewers should be able to make them fit their breweries perfectly.

Utilization Table

Decimal Alpha Acid Utilization vs. Boil Time and Wort Original Gravity

Boil	Original Gravity									
Time	1.030	1.040	1.050	1.060	1.070	1.080	1.090	1.100	1.110	1.120	1.130
(min)
  0	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
  3	0.034	0.031	0.029	0.026	0.024	0.022	0.020	0.018	0.017	0.015	0.014
  6	0.065	0.059	0.054	0.049	0.045	0.041	0.038	0.035	0.032	0.029	0.026
  9	0.092	0.084	0.077	0.070	0.064	0.059	0.054	0.049	0.045	0.041	0.037
 12	0.116	0.106	0.097	0.088	0.081	0.074	0.068	0.062	0.056	0.052	0.047
 15	0.137	0.125	0.114	0.105	0.096	0.087	0.080	0.073	0.067	0.061	0.056
 18	0.156	0.142	0.130	0.119	0.109	0.099	0.091	0.083	0.076	0.069	0.063
 21	0.173	0.158	0.144	0.132	0.120	0.110	0.101	0.092	0.084	0.077	0.070
 24	0.187	0.171	0.157	0.143	0.131	0.120	0.109	0.100	0.091	0.083	0.076
 27	0.201	0.183	0.168	0.153	0.140	0.128	0.117	0.107	0.098	0.089	0.082
 30	0.212	0.194	0.177	0.162	0.148	0.135	0.124	0.113	0.103	0.094	0.086
 33	0.223	0.203	0.186	0.170	0.155	0.142	0.130	0.119	0.108	0.099	0.091
 36	0.232	0.212	0.194	0.177	0.162	0.148	0.135	0.124	0.113	0.103	0.094
 39	0.240	0.219	0.200	0.183	0.167	0.153	0.140	0.128	0.117	0.107	0.098
 42	0.247	0.226	0.206	0.189	0.172	0.158	0.144	0.132	0.120	0.110	0.101
 45	0.253	0.232	0.212	0.194	0.177	0.162	0.148	0.135	0.123	0.113	0.103
 48	0.259	0.237	0.216	0.198	0.181	0.165	0.151	0.138	0.126	0.115	0.105
 51	0.264	0.241	0.221	0.202	0.184	0.169	0.154	0.141	0.129	0.118	0.108
 54	0.269	0.246	0.224	0.205	0.188	0.171	0.157	0.143	0.131	0.120	0.109
 57	0.273	0.249	0.228	0.208	0.190	0.174	0.159	0.145	0.133	0.121	0.111
 60	0.276	0.252	0.231	0.211	0.193	0.176	0.161	0.147	0.135	0.123	0.112
 70	0.285	0.261	0.238	0.218	0.199	0.182	0.166	0.152	0.139	0.127	0.116
 80	0.291	0.266	0.243	0.222	0.203	0.186	0.170	0.155	0.142	0.130	0.119
 90	0.295	0.270	0.247	0.226	0.206	0.188	0.172	0.157	0.144	0.132	0.120
120	0.301	0.275	0.252	0.230	0.210	0.192	0.176	0.161	0.147	0.134	0.123

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