The goal of this post is to propose a couple of ideas about the mathematics of fermentables and attenuation: One can find several posts here, and on other forums, where home brewers make some assumptions in there brewing calculations about attenuation, but I can find no proposed set of algorithms or equations available for public criticism and consumption. Am I wrong?
Before delving into this thread, please visit the page http://www.homebrewtalk.com/wiki/ind...ng_Attenuation
, because this post assumes a working understanding of specific gravity, original gravity, final gravity, PPG, etc., as well as knowledge of such definitions as apparent attenuation, actual attenuation, fermentable, among others.
Further, this post assumes the basics of attenuation are understood, that is the mathematical relationships of attenuation, OG, FG, as well as specific gravity both of water and ethanol.
One more thing, before delving into the ideas, the goal is to establish a quantitative methodology that can estimate FG and ABV, not to derive a equation that calculates FG and ABV with absolute certainty. This post intends to suggest a methodology that will get final gravity points to no more than plus or minus 4 FGPs. The premise of this post is a realization that predicting the FG of a beer is like predicting the weather, but it is a start.
Leading to the question of why predict FG and ABV? IMHO, I believe that most would say, primarily for the purpose of flavor, more than anything else. Most, especially seasoned brewers, use these numbers largely to compare against given style values to see if a decent beer is being created. Flavor in beer is a tradeoff among sweetness, ABV, IBU, malt character, yeast profile, among others. Getting a better prediction of FG and ABV, along with IBUs, etc., just provides a better idea of what lies beyond the brew.
Finally, these are my words and notions, though derived from others, please feel free to contribute. I'm just looking for a "better mouse trap."
Enough with the prelims....
It seems safe to say that attenuation is primarily influenced by these three operations: mashing, lautering, and fermenting; and these two substances: type of starches/sugar(s), type of yeast. (Some may want to introduce other factors here, so be it. For one, I can think of the presence of enzymes from base malts. IMHO, I suggest that only the most important factors be introduced, and only those that can be quantified. And by all means, please suggest a method for mathematically including these factors. Thanks.)
Starches/Sugar: Typically, the starting point to calculate the final gravity of wort is the PPG, a measure of specific gravity points contribution per gallon, called Max PPG. To predict FG, this post implements the idea (suggested by others) of splitting of PPG into three parts: simple (fermentable) sugars, complex (but potentially fermentable) starches/sugars, and unfermentable (not fermentable under normal brewing conditions) starches/sugars. Once split, this post intends to quantitatively track these three values through the brewing process. To do this, let's define Fermentable Percentage (FP) as the fraction of PPG that is both fermentable (simple) and potentially fermentable (complex). For example, extract from crystal malt grains have a high percentage of unfermentables (30-100%), and other sugars, like lactose, are 100% unfermentable. The Fermentable Percentage would be what remains if the unfermentables are removed.
Now perform a "PPG trace" through the brewing operations:
(1) Mash: In this operation, a "PPG trace" requires a measure for the enzymatic conversion of the complex starches/sugars to simple (fermentable) sugars, a conversion that varies with both temperature and grain mixture. This measure can be hard to find in published sources, but it is around. Palmer, for example, has a huge discussion on these topics in his book (pp. 144ff.) and even shows a figure in his book on "Apparent Attenuation Limit." For this post, let's define this variable as the Limits of Attenuation Percentage (LAP). Note that this value is defined in terms of apparent attenuation, that is OG and FG.
(3) Lauter: For this Operation, a "PPG trace" needs a measure for the efficiency of extracting sugar from grain. This measure is widely available, and is typically around 0.75 for all-grain and about 0.65 for partial mashes, but 100% for extracts. Let's call this variable the Extraction Percentage (EP), again defined in terms of apparent attenuation.
(4) Ferment: Here the yeast's ability to ferment is needed, commonly measured and known as attenuation, YA. It is important to remember that yeast attenuation assumes that the yeast does not stay mixed with the wort, but settles or rises.
Remember that all of these values are defined in terms of apparent attenuation.
Now the challenge is to use these values mathematically. Begin with the common equation for the original specific gravity:
Original Gravity Points, OGP = MaxPPG x W x EP / V;
where W is the weight of grain/extract, and
V is volume of wort.
Next, separate OGP into simple, complex, and unfermentable, using both the Limits of Attenuation Percentage (LAP) and the Fermentable Percentage (FP).
Unfermentable OGP, UOGP=OGP x [1-(FPxLAP)],
this calculation would be performed for each sugar used,
then added together.
And the fermentable gravity points are:
Fermentable OGP, FOGP = OGP – UOGP.
Fermentable original gravity points should be a much better value to use when estimating final gravity points, than what is currently suggested, total original gravity points.
Fermentable FGP = 1 + [(FOGP/1000)*(1 - YA)].
The above variables, FOGP and FFGP, should provide a better estimate of ABV:
ABV = use your favorite equation.
And Final Gravity is now calculated with:
= 1 + [(FOGP/1000) * (1 - YA)] + (UOGP/1000).