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Old 01-08-2013, 03:31 PM   #1
SMc0724
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Default Fermentables,Attenuation, and Specific Gravity Mathematics

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/index.php/Understanding_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).
THOUGHTS?
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Old 01-08-2013, 05:12 PM   #2
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http://beertech.blogspot.com/2009/12/considerations-when-predicting-final.html
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Old 01-08-2013, 05:21 PM   #3
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The only other thing that I would add to my original post is that High ABV beers may need some gravity adjustment by a point or two since published attenuation values seem based on lower ABV values.

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Old 01-08-2013, 05:25 PM   #4
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Gavagai, as I noted in the OP, there is published information out there for what I call LAP (I saw your referenced Web page before posting the OP). However, that page does not demonstrate how to incorporate the mathematics of all the unfermentables.

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Old 01-08-2013, 05:36 PM   #5
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It would be difficult to make a prediction that would be true for everyone due to the mash. Everyone mashes differently in a variety of vessels. There is a heat gradient created, even though there is a target temperature. This gradient affects the efficiency of enzyme activity in different areas of the mash, and therefore affects the ratio of sugars left over after mashing (monosaccharides, disaccharides, dextrins, oligo, etc..) which in turn affects fermentability. Their water pH also affects enzyme activity. I think that your equation would have to include an experimental number of some kind which is related to mash efficiency of an individual's system, and everyone would have to do a little experiment to find it out for their own system.

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Old 01-08-2013, 05:39 PM   #6
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There's information at the bottom here about how to calculate attenuation effects of crystal malts: http://beertech.blogspot.com/2011/03/crystal-malt-experiment-attenuation.html

As for the fermentability of other specialty malts, I don't think we really have the information yet.

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Old 01-08-2013, 05:54 PM   #7
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Gavagai, that post on beertech is also available in homebrewtalk at http://www.homebrewtalk.com/f128/testing-fermentability-crystal-malt-208361/?referrerid=0.

Based on his work, it seems reasonable to make some simple assumptions about fermentability based on Lovibond value. Also, I have complied these ideas from http://forum.northernbrewer.com/viewtopic.php?f=1&t=82885:

"...my recollection is that Pale Malt was roughly 80% fermentable (which is about what I get when mashed around 148-150F.) I believe toasted malts, like Munich were about 12% less fermentable and Crystal Malt was about 50% unfermentable, in their experiment, IIRC. There was a lot of variability between specific malts and Lovibonds, though, so I rounded and averaged a few numbers to get something I could carry around in my head."

and
"I'm looking through some notes and it looks to me like the values maybe be more like 10% unfermentables in base malts, maybe 15% in kilned malts and 20-30% in crystal. This comes closer to what I'm seeing in the way of FG in some all-malt beers."

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Old 01-08-2013, 05:58 PM   #8
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dbsmith,
thanks, very good idea. Another option would be to decrease/increase the value of LAP based on the personal system. It is a bit of a guess anyway. :-)

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Old 01-08-2013, 08:12 PM   #9
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Quote:
Originally Posted by SMc0724 View Post

THOUGHTS?
If you are serious about this you should throw away the amateurs' PPG concept and work in the advanced amateurs'/professionals Extract. This is the percent by weight of everything dissolved in wort/beer which is dissolved in it. Thus a sucrose solution which has specific gravity of 1.040 contains 10% extract by weight.

One monitors efficiency in the brew house by comparing the weight of grain employed to the amount of extract obtained e.g. if you have 100 L of wort of specific gravity 1.040 (adjust by the density of water for precision) you have 104 kg of wort containing 10% extract by weight or 10.4 kg. If you mashed 15 kg of grain your efficiency is 100*10.4/15 %. The efficiencies published by the maltsters are all in terms of kg extract per kg grain and usually run aroun 80% for base malts, less for specialty, roast etc. The estimated extract in the mash tun is then a simple sum of terms each of which is the Congress mash extract (what the maltster reports) times the weight of the grain times the brew house efficiency.

You can then move on to use Ballings formula to estimate the amount of alcohol produced by calculating the amount of extract the yeast consume. Note that attenuation here refers to RDF = 'Real Degree of Fermentation' not the ADF (Apparent Degree of Fermentation) that home brewers usually talk about. RDF is the percentage of extract consumed - not the change in 'points'.

There is nothing mysterious about this - the details are in most brewing texts. Measuring TE (True Extract) is harder than AE (Apparent Extract) because the alcohol has to be removed from the beer before its SG is measured but that's not hard to do. There is also a little math but not something that isn't easily handled by a spreadsheet.
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Old 01-08-2013, 08:16 PM   #10
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OK, I will look into it.

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