don't kill me this is going to be a long one
#1- no protein rest for well modified grains though a protein rest may aid in head retention
#2- that ratio is fine though i like 1.25 qt / 1 lbratio as it loosens the mash up a bit and still allows for step mashing or temp corrections.
#3- 1/2 a gallon is way to little , figure your mash/sparge something like this. assuming you want to coolect 6 gallons of wort and you have 7 lbs of grain. step 1, assume a .15 absorbtion from the 7lbs of grain so that is 1.05 gallons step 2 assume 1.25 qts/lbs so that is a ratio of 8.75 qts or 2 3/4 gallons so now knowing you have a loss of 1.05 gallons from that 2.75 mash you will end up with 1.7 gallons from your mash after losses which tells you do a slow running and you need to sparge with 4.3 gallons of water using this example.
#4- here's the long calcs sorry there are all 3 forms here .
Estimating Beer Bitterness
The simplest way to describe the bittering potential of a given hop sample is to use Alpha Acid Units (AAU) or Homebrew Bittering Units (HBU) (they're the same). For the sake of discussion we will use the term AAU, which is calculated as follows:
AAU = AA * W
where:
• AA = alpha acid % provided with the hops
• W = weight of the hops in ounces
AAU's are literally hundredths of an ounce, so the units would be ounces. This is a bit awkward, and they are usually discussed as if they are "unit-less". It is generally assumed that, when using AAU or HBU, the batch size is the standard homebrewing unit of 5 gallons. If a beer is said to have 10 AAU's of bitterness in it, and it is a 5 gallon batch, there would probably be no confusion. On the other hand, if it is a 10 gallon batch, there is actually half the AAU's per gallon when compared to the 5 gallon batch and the beer would be quite different. Another drawback to using AAU's is that they don't consider the utilization obtained from long, intermediate, or short boil times. Fudge factors are sometimes added but at best they offer a rough approximation.
To help solve these problems, the International Bittering Unit (IBU) may be used. An IBU is defined as 1 mg/l of iso-alpha-acid in a solution. By estimating IBUs rather than HBUs, the brewer can get a more accurate (though admittedly still rough) approximation of the bitterness imparted into the beer by the hops. It is independent of batch size so that a 5 gallon batch with 29 IBU's has the same bitterness as a 50 barrel batch with 29 IBU's. The equations are commonly quoted from Jackie Rager's article in the "Zymurgy" Hops and Beer Special Edition published in 1990. Revised numbers and formulae have recently been presented by Glenn Tinseth and Mark Garetz, in separate works. Rager has been taken to task for not supplying enough background references, and not fully explaining how he got his numbers. In general, his utilization estimates are believed to be optimistic. Garetz has been accused of extrapolating scant laboratory information, and overgeneralizing because of it. His numbers have been labelled unrealistic on the pessimistic side. Tinseth has just presented a revised method and set of tables, and though they are thought to be quite accurate, they have not stood the test of time. The calculated numbers tend to fall in between Rager's and Garetz's. Note also that these are all estimates. Actual IBUs can be measured in a laboratory, but the average homebrewer has no access to such equipment. The Rager, Garetz, and Tinseth estimation methods follow.
Rager 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.
The unfortunate part of Rager's article is that it is completely lacking in references, so assumptions come with it part and parcel. Note also that Rager's numbers are often used for pellet hops thrown loose in the boil. Al Korzonas suggests adding 10% more hops if used in a hop bag, and 10% more than that if loose hops or plugs are used.
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:
BG - 1.050
GF = ---------- + 1
.2
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.
Tinseth Method
Glenn Tinseth's method doesn't involve as many factors, but is still a bit more complex than the original Rager method.Tinseth notes that his table is optimized for fresh whole cones loose in the boil, although easily adjustable for other forms of hops. He builds the gravity adjustment into the utilization tables and offers the following:
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
To calculate IBUs, the formula is simple:
IBUs = decimal alpha acid utilization * mg/l of added alpha acids
For those who want to make adjustments based on their own brewery, he offers the following:
Metric Units
mg/l of added alpha acids = decimal AA rating * grams hops * 1000
-------------------------------------
liters of wort
Non-Metric Units
mg/l of added alpha acids = decimal AA rating * ozs hops * 7490
-------------------------------------
gallons of wort
The decimal alpha acid utilization is calculated using Tinseth's two empirical factors: 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.
Bigness factor = 1.65 * 0.000125^(wort gravity - 1)
The Boil Time Factor gives the varying utilization based on boil time:
Boil Time factor = 1 - e^(-0.04 * time in mins)
--------------------------
4.15
Some comments from Tinseth:
"The numbers 1.65 and 0.000125 are empirically derived to fit my data. The number 0.04 controls the shape of the util vs. time curve. The factor 4.15 controls the max util value--make it smaller if your util 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.
You might notice that the shape of the util curves is very similar to that of Randy Mosher's. He and I seem to have independently arrived at the same conclusion.
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. The root of the equations is the basic first order chemical reaction, i.e. the AA isomerization seems be first order (or pseudo-first order)."
Bitterness Summary
It should be obvious that the alpha acid utilization is a widely debated topic, and that it is not an exact science. Homebrewing systems vary so widely that it is impossible to be very accurate with the IBU estimates. The homebrewer who strives to be accurate within 10% of actual can probably achieve it, and verify it with known commercial examples. The human tongue is accurate enough for this delightful experiment. Precision with IBUs is certainly achievable, with careful record-keeping, including personal sensory descriptions, and the use of a consistent set of formulae and utilization tables. These steps will go a long way toward consistent quality beer.
One question that appears on occasion is whether you lose bitterness if you boil the hops for too long, e.g. longer than two hours. According to Glenn Tinseth, multiple studies have shown that alpha acid utilization always increases with boil time, even out to 3 hours of boiling. The reason the tables quit around 60 minutes of boiling, is that little utilization is gained beyond that. In fact, after about 45 minutes the curve becomes quite flat. In other words, beyond that the utilization increase is small compared to the added time involved. It is speculated that commercial brewers found that beyond 45-60 minutes or so, the benefit of the added utilization was more than offset by the cost of the energy to continue the boil as well as the cost of the added time in the process.
A final note about bitterness: IBUs are not the final word when it comes to the perceived bitterness of beer. Sulfates, dark grains, tannins, and other compounds found in beer contribute to the bitterness sensation. For this reason, comparison of bitterness between styles (and sometimes even different beers within a style) is difficult.
