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 acidsTo calculate the concentration of alpha acids you add to the wort:
mg/l of added alpha acids = decimal AA rating * grams hops * 1000
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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
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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 factorThe 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)
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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.
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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