# Question about Formula Quoted in Greg Noonan's "New Brewing Lager Beer" Book

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#### Barfield

##### Honey, put on that party dress
On page 12 of Greg's book, there's a familiar and frequently requoted formula for as-is, coarse grind yield. The formula is also reposted by Stan Hieronymus at ProBrewer here.

DBCG/(1 + moisture content) - .002 = AICG (as-is coarse grind)
My question is: what is the magic number "0.002"? It's not discussed in the text. Assuming a typical malt from Crisp, for example, with a dry basis, coarse grind extract potential of 80.8% and a 4% moisture content, as-is coarse grind potential (including the 0.002 magic number) is 0.808/(1+0.04) - 0.002, or 0.7749 etc. If the magic number were left out, the AICG yield is 0.808/(1+1.04) = 0.7769 etc. The percentage difference between these two values is (0.7749 - 0.7769)/0.7769 = -0.0026, or -0.25 percent. That's a terribly small difference, particularly given the uncertanties elsewhere in the equation (i.e., moisture content and DBCG measurement).

What am I missing?

The difference is the 0.002 or 0.2% factor. I can't find any direct source for the number, but it looks like a correction factor for laboratory condition efficiency versus what the average brewing environment can produce. Most likely it has been derived from measuring the yields under both strict laboratory conditions with strict analytical processes and the yields obtain by bulk brewing methods.

As to what the cause of the difference may be, it could be atmospheric moisture uptake during the bulk grinding process where laboratory conditions are explicitly designed to eliminate both malt moisture content and atmospheric moisture; or maybe something eliminated in the laboratory when the ground samples are sieved for uniformity that isn't done in the bulk processes.

It is a small correction, but it must be significantly reproducible for it to be in there in the first place.

I'll keep digging in the documentation, it has to be somewhere in a research paper or thesis. Probably dating back fifty or sixty years.

As far as I can tell, it's sloppy math. The correct formula is:

AICG (or AIFG) = DBCG (or DBFG) * (1 - moisture content)​

Where "moisture content" is the fractional moisture content: i.e. 4% = 0.04. So, at 4% moisture, and 80% DBFG, the AIFG becomes:
AIFG = 0.80 * (1 - 0.04) = 0.768​
I like working with fine grain potential rather than coarse grain, so I will use that in the explanation below. The math is the same whether you use fine of coarse grain.

To see why this is correct, assume you have 10 lb of grain at 4% moisture and 80% DBFG. In this case you have 0.4 lb of water in the grain, and 9.6 lb of dry grain. So, your extract potential is:

Max extract = 9.6 lb * 0.80 = 7.68 lb which is the same as: 10 lb * 0.80 * (1 - 0.04) = 7.68 lb​
If you use "Greg's" formula, without the fudge factor you get:

Max extract = 10 lb * 0.80 / (1 + 0.04) = 10 lb * 0.7692 = 7.692 lb​
Throw in the fudge factor, and you have:

Max extract = 10 lb * (0.80 / (1 + 0.04) - 0.002) = 10 lb * 0.7672 = 7.672 lb​
This is a little closer to the correct answer, but still not right. The fudge factor is an attempt to correct for the difference between (1 - moisture) and (1 / (1 + moisture)). But, isn't it just easier to use the correct math? I think the correction factor of 0.002 gets a little better as the moisture content increases.

Brew on

Ah, that makes sense. Looks like two separate derivations of the same formula with one that failed to understand how to calculate the effect of the moisture content. So when the measured numbers came up differently, they fudged the incorrect formula to match reality. Then the incorrect formula made its way into the world.

The fudge hits unity with the correct formula at 5.25% moisture and then starts exceeding the result. Makes you wonder if a specific maltster presented the incorrect formula, corrected for their malt moisture content, in an analysis document and Greg or someone else picked it up and ran with it.

Thanks Doug and Bruce for the rapid response!

Bruce, I did read somewhere (I can't recall the source) that one of the attributes about the laboratory mash where theoretical maxima are attained is that they purposefully over sparge, whereas no brewer (home or otherwise) would do that. That could be a source of the quarter percent.

Doug, your explanation makes perfect sense, too. I think could be sloppy math, too.

Just reducing the factor to its simplest: it's a matter of (1-0.04) = 0.96 as a factor versus 1/(1+0.04) = 0.9615... as a factor, assuming 4% moisture.

I agree that "AICG (or AIFG) = DBCG (or DBFG) * (1 - moisture content)" is the correct formula.

Bruce,

I did a few hours of Googling and its funny how often that formula with the fudge factor is repeated, without any explanation!

I will give you an alternate answer which assumes no knowledge of the particular relationship. They may have collected data and fit a model to it and the -0.002 is what came out as the intercept term. Biological relationships aren't always perfectly measured and not always perfect relationships.

I don't know anything about this relationship though. Should DBCG = AICG if moisture content were 0?

I will give you an alternate answer which assumes no knowledge of the particular relationship. They may have collected data and fit a model to it and the -0.002 is what came out as the intercept term. Biological relationships aren't always perfectly measured and not always perfect relationships.

I don't know anything about this relationship though. Should DBCG = AICG if moisture content were 0?
Efficiency is a well defined mathematical construct:

Efficiency = What's actually achieved / The maximum possible or theoretical.​
In brewing, dry basis fine grind testing is supposed to tell you the maximum possible. There is no need to do any empirical fitting.

Yes, if moisture = 0, then DBCG = AICG, and DBFG = AIFG. I prefer FG, as it gets you the maximum possible. CG is just a way for brewers to make their efficiencies look better for the bean counters, as it gets the "maximum" closer to what they actually achieve using a coarse grind that eases their processing but drops their conversion (and thus mash and brewhouse) efficiency . But, in a commercial setting, maximum efficiency of any specific process shouldn't be the goal. The commercial goal should be lowest end cost per unit of product. In brewing that means accepting a lower conversion efficiency to get higher throughput, may lower your total costs (when you include labor, capital, and other fixed costs.)

Brew on

That's how lore gets started...

Stan Hieronymous reposts it at ProBrewer: Understanding Malt Analysis Sheets

It shows up in the BeerSmith blog: Grain - TYPICAL ANALYSIS: Institute of Brewing / EBC Methods of Analysis

Shows up in the coloradobeer.org blog: How to Read a Malt Certificate of Analysis - Colorado Brewers Guild

Again, in the North Texas homebrewer's assoc: https://www.nthba.org/nthba_documents/docs/techcorner_malt_extract_yield.pdf

etc...
Yeah, the internet makes it far too easy to cut 'n paste erroneous information, and cause it to overwhelm correct information.

Brew on

Bruce, I did read somewhere (I can't recall the source) that one of the attributes about the laboratory mash where theoretical maxima are attained is that they purposefully over sparge, whereas no brewer (home or otherwise) would do that. That could be a source of the quarter percent.
Yes, this is the way the "Congress Mash" is specified. This is an attempt to get all of the extract (mostly sugar) that is created in the mash, separated from the spent grain (after all they don't have to worry about tannins, do they?). The more you sparge, the less extract is left in the grain.

I believe it was specified this way because at the time they designed the Congress Mash, they hadn't figured out that you can determine the potential without having to separate the wort from the grain (lauter) at all! All you have to do is measure the SG of the wort at the end of the mash, do some simple math, and you have the grain potential. (ref) I can derive the math here if anyone is interested.

In my opinion (which I am sure no one at the standards bodies cares about) is that the Congress Mash method should be modified to just measure the wort SG at the end of the mash, and skip the lautering (which if sparging is insufficient, will give you erroneously low grain potential.)

Brew on

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Indeed. Efficiency is sort of a universal concept. Any physical process will incur some loss, and a the ratio of actual / theoretical quantifies that.

With respect to expected gravity at the end of the mash, I've always felt that we should teach beginning brewers how to calculate that, because they're always fretting about whether or not conversion is complete. It's one thing to measure gravity into the kettle (or after the boil), but knowing what to expect at the end of the mash is incredibly useful.

With respect to expected gravity at the end of the mash, I've always felt that we should teach beginning brewers how to calculate that, because they're always fretting about whether or not conversion is complete. It's one thing to measure gravity into the kettle (or after the boil), but knowing what to expect at the end of the mash is incredibly useful.
Yes, I preach that regularly. I have linked to the post by Braukaiser uncountable times.

Brew on

When I was taught how to interpret a COA the instructor said that the difference between the course grind and the fine grind ,if over 2 could be undermodified malt. Of course there are other factors you need to include , but that one is important. I got some Full Pint malt once where it was 4 points and did not get a COA until after the first batch left me (was a while ago) 8 points low. Now that I think about it instead of increasing my quantity I should have decocted to see it that would have helped.