This group of topics discusses the calculations in general, including the source for the formulae. The implementation of these formulae in Java is available as a source code file by anonymous cvs access to the project archive at sourceforge.net/projects/strangebrew.
The following topics are covered in this chapter:
See Calculating Hop Bitterness
See Calculating Hydrometer Correction
StrangeBrew uses George Fix's formulae, as posted in HBD #1319 -
> alcohol by vol. = 1.25*F1*(OG - FG),
> Note that this and the rule 1.25*105*(OG-FG) give the same results for OG = 1.048 and FG = 1.010, namely 5%. However as OG -FG increases the factor 105 becomes less accurate.
An interesting colour table was posted to HBD:
Beer colour
Dan A. Morey wrote a letter to Brewing Techniques about Ray Daniels' colour formula (logarithmic divergence after LOV/MCU > 10) with this interesting formula, which StrangeBrew uses:
" What I did was: Assume MCU = SRM from 0 to 10.5, Daniel's equation holds in the range of 10.5 < MCU < 37, and Mosher's formula holds for MCU < 37. Then I plotted In (MCU) vs. In (SRM) and performed linear regression. This exercise resulted in a R^2 value of 0.97 (This is better than my linear fit with force zero intercept on the MCU vs. SRM graph - R^2 0.96). My resulting equation is:
SRM = 1.4922 [(MCU) ^ 0.6859] - for values of SRM < 50
Now there is a single equation that can be used to estimate the final color of beer. Also, in the age of calculators and computers, it is no more difficult to calculate than a linear equation."
I wrote my own formula for estimating beer colour based on SRM and showing RGB (computer screen swatch), which is still being tweaked. I will post it to HBD some day soon.
The topics in this section quote heavily from Norm Pyles Hop FAQ at http://realbeer.com/hops/FAQ.html. This is the best summary I've found of information about hops in general, and bitterness specifically.
StrangeBrew provides four methods of calculating hop bitterness:
From Norm Pyles Hop FAQ at http://realbeer.com/hops/FAQ.html:
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:
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.
From Norm Pyles Hop FAQ at http://realbeer.com/hops/FAQ.html:
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:
IBU = (GRAMS OF HOPS) * %UTILIZATION * %ALPHA * 1000
------------------------------------------------
IBU = (OUNCES OF HOPS) * %UTILIZATION * %ALPHA * 7462
-------------------------------------------------
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.
From Norm Pyles Hop FAQ at http://realbeer.com/hops/FAQ.html
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.
Boil time vs. hop utilization
According to Garetz, there are several adjustment factors, that he brings together in the formula with the term "combined adjustments" (CA):
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
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.
IBU = (%Utilization) * (%Alpha) * Hop weight(grams) * 0.1
---------------------------------------------------
IBU = (%Utilization) * (%Alpha) * Hop weight(ounces) * 0.749
------------------------------------------------------
Garetz goes to allow for a yeast factor (YF), pellet factor (PF), bag factor (BF), and filter factor (FF), and comes up
CA = GF * HF * TF * PF * BF * FF
This allows you to adjust the formula based on your own brewery and practices.
From Norm Pyles Hop FAQ at http://realbeer.com/hops/FAQ.html:
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
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:
mg/l of added alpha acids = decimal AA rating * grams hops * 1000
-------------------------------------
mg/l of added alpha acids = decimal AA rating * ozs hops * 7490
-------------------------------------
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)
"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)."
StrangeBrew's mash calculator provides for three types of mash step: infusion, decoction, and direct heat. The first step is always assumed to be an infusion mash, and both the amount of water added and its temperature is calculated for the first or strike step. In terms of calculation, the direct heat step is a no brainer. Just add heat! The other types of calculations are outlined here:
StrangeBrew's infusion calculations are based on an article written by Ken Schwartz and posted on his homepage at http://home.elp.rr.com/brewbeer/. His calculations were based on grain heat capacity and mash volume information from HBD issues 1879, 1792, and 1793.
Here are is the relevant section of the article:
"I have a 5-gallon cooler that I would like to mash in. How much grain will it hold?"
1 lb grain occupies about 0.08 gal or 0.32 quart when added to water (and allowed to soak). 1 kg grain occupies about 0.67 liters when added to water (and allowed to soak).
Total volume of mash = Wg (0.08 + MWR/4) gallons
MMWR = Metric Mash Water Ratio, liters/kg
"If I could find the amount of water which has the same heat capacity as a certain amount of grain, it would make my strike water and other calculations easier."
Although some may argue that it's an extra step or something along those lines, I believe it's easier to visualize water calculations when you're dealing with just water -- the resulting temperature is basically just the constituent temperatures "averaged" over the total volume. Besides, for multiple strikes, once you figure the "water-equivalent" of a certain amount of grain that number stays fixed, so you only need to figure it once.
The "water equivalent" (W.E.) of grain is the volume of water whose heat capacity is equivalent to that of a given mass/weight of grain (based on specific heat of grain being 0.4) and is calculated like this:
Example: 20 kg of grain has the same heat capacity as
The water-equivalent for a mash (grain plus water) is:
W.E. = Wg (0.0479 + MWR/4) gallons
Example: My 10 lb, 1.3 qt/lb mash has the same heat capacity as
"I'm doughing-in at a certain MWR (or MMWR) using grain at room temperature (Tg), trying to hit my dough-in temperature of Td. I can figure how much water I need from my Mash Ratio, but how hot (Ts) should the strike water be?"
Td = Desired Mash Temp after Strike (F or C)
WEF = "Water Equivalent Factor", depending on units:
0.0479 when dealing in gallons
Tg = Temperature of grain (F or C) (room temp)
FF = "Fudge Factor" to account for thermal mass
of vessel (3 deg F or 1.7 deg C is typical)
(M)MWR in gal/lb, qt/lb, or liters/kg
Example: Doughing-in 10 lb grain at 70F with MWR = 1.3 qt/lb for a final temperature of 142F, figuring 3 deg F for "fudge factor", I'll need
= 13 quarts (3.25 gal) of strike water at
T = [142 + 0.192 * (142-70) / 1.3] + 3
"If I add a certain amount (Vs) of water at temperature Tb to a mash of water-equivalent Vm at temperature Tm, what is the resulting new temperature Tn?"
Calculate the "water equivalent" volume of the existing, resting mash (grain plus water), to find Vm:
(for other units use other equations previously given)
...keeping in mind that your MWR includes all water added so far (in the
Example: If I add 2 quarts of boiling (212F) water to a 142 deg F mash (10 lb, MWR = 1.3 from previous example), the water equivalent of the original mash is
so the resulting temperature will be
T = (14.92 * 142 + 2 * 212) / (14.92 + 2)
Rearranging this equation answers the more practical question, "My mash is resting at temperature Tm; I wish to raise it to Tn by adding water at temperature Tb. How much water do I add?"
StrangeBrew uses a decoction formula developed by AJ Delang and John Palmer:
Vd (quarts) = [(T2 - T1)(.4G + 2W)] / [(Td - T1)(.4g + w)]
Td = decoction temperature (212F)
W = volume of water in mash (i.e. initial infusion volume)
g = pounds of grain per quart of decoction = 1/(Rd + .32)
w = quarts of water per quart of decoction = g*Rd*water density = 2gRd
Rd = ratio of grain to water in the decoction volume (range of .6 to 1 quart/lb)
thick decoctions will have a ratio of .6-.7, thinner decoctions will have a ratio of .8-.9. You need to choose an Rd based on how thick you think your pulled decoction is.
A measure of how much extract obtained from mashed grain, based on a theoretical yield of 100%. EG: typical two row malt has a theoretical yield of 1.036 (1 lb in 1 gallon of water). If you mash 1 lb of two row and get one gallon of wort at OG 1.018, your efficiency is 50% (18/36 * 100 = 50).
A measure of how much fermentable sugar has been consumed by yeast. More accurately, apparent attenuation. Based on the difference between Original Gravity (OG) and Final Gravity (FG). Attenuation is a function of wort fermentability (simple sugars vs complex sugars) and yeast.
* A lower saccrification rest will make for a more fermentable wort.
I found this formula on the web, which describes how PSI is calculated:
P = -16.6999 - 0.0101059 T + 0.00116512 T^2 + 0.173354 T V + 4.24267 V - 0.0684226 V^2
This is a perennial problem for carbonation - beer has carbonation dissolved in it, a different amount at different temperatures. This affects how much priming sugar should be added at bottling to create the correct amount of carbonation. The following formula calculates the amount of CO2 still in solution at bottling depending on temperature.
Alex Santic posted this to HBD #????:
Pierre Dumont (pierre_dumont@unb.ca) was kind enough to modify the formula to express volume of dissolved CO2 as a function of temperature and (atmospheric) pressure. In other words, he did the hard part and came up with the following equation:
VolCO2 = 1.266789 * tempF + 31.00342576 - 0.0000009243372 * (SQRT((1898155717178 * tempF^2) + 91762600000000 * tempF + 839352900000000 - 1710565000000 * 14.5))
The number 14.5 near the end represents 1 bar of pressure (14.5 psi) so that we can compare with the tabular data. One could try substituting actual atmospheric pressure according to elevation.
Alex points out that the formula isn't perfect, but it's within a few percent of measured results. Also, I do not account for altitude, but I may in a future release.
Finally, the brewery.org library has an excellent "Primer on Priming" by Mark Hibberd (Bayside Brewers Club, Melbourne, Australia) which had this information:
Determining the amount of priming sugar is based on the fact that adding 4 grams of sucrose (cane/beet/granulated sugar) per litre will ferment to give 1 volume of CO2:
4 g/l (1/2 oz/US gal) sucrose --> 1 vol. CO2
He does not say at what temperature the beer is to be served at, but I'm assuming that it's 40F. Hibberd goes on to suggest the following adjustments for the above formula for the following priming sugars:
Once again, A. J. DeLange posts the goods in HBD 3701 (the "someone" he mentions is me):
Someone asked about hydrometer corrections the other day. When things like this come up I always advocate using the ASBC's methods if they have one and in this case they do. One can calculate a correction from
The coefficients depend on the units used and the specific gravity reading. For corrections in units of a hundredth of a degree P and temperature in C the following coefficients are valid for temperatures between 4 and 26 C for hydrometers calibrated 20C/20C. They were obtained by polynomial fitting to data in Table I, p 2, Beer-3 in the ASBC Methods of Analysis:
0 - 4.99 56.084 -0.17885 -0.13063
5 - 9.99 69.685 -1.367 -0.10621
10 - 14.99 77.782 -1.7288 -0.10822
15 - 19.99 87.895 -2.3601 -0.10285
20 - 24.99 97.052 -2.7729 -0.10596
For hydrometers correct at 60C/15.5F, I use the above calculation at both temperatures, and divide by the difference.
The data used to calculate water profiles, salt additions, and acidification are all available on the internet, and I will add them to this help file when I have a chance. Have a look at www.hbd.org/library/ for a lot of good information.
The automatic water profile calculation algorithm is called "simulated annealing", and can be used to solve lots of different problems (the traveling salesman problem is the classic example).
The estimated mash pH calculation is from Ray Daniels' Designing Great Beers. The calculation is: pH = 5.8 + (0.028 X [(ppm CaCO3 X 0.056) - (ppm Ca X 0.04) - (ppm Mg X 0.033)]).