Take the guessing out of efficiency

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When creating all-grain recipes, whatever program you use will ask to input an efficiency to calculate the OG of the beer. But what value do you enter? In BYO, they use a nominal extract efficiency of 65%.
In general people are told that with experience and good brewing practices you should start hitting consistent efficiency values. But what if you brew extremes? It is obvious that brewing a 3.8% ABV special bitter will yield higher extraction efficiency than an 11.8% ABV barley wine.
(Note: This is the first article of a series of 3 articles which are geared mostly towards those who write their own brewing spreadsheet, but the info can be very useful for anyone writing who brew all grain)
Say you mostly brew beers with an OG range of 1.050 to 1.060. Using your calculated extract efficiency from these beers to brew the special bitter you will most likely overshoot your target gravity for the special bitter, while you risk to undershoot in the case of the barley wine. So what do you do? Do you just try to guess a correction factor when brewing these more extremes beers? The simple way is to always undershoot the extract efficiency and add water before pitching the yeast to always reach the target gravity. But this can lead to slightly lower hop utilization. Also the water you added at the end could have been used during the sparge to extract more sugars.
Ultimately, I will show you how to estimate the efficiency for any beer you make. An important assumption I will be making is the use of batch sparging (no-sparge is basically a single batch
sparge). Batch sparging is easy to model mathematically with just a few variables since equilibrium is reached every time. On the other hand, fly sparging is a transient system, which means a whole lot of variables will be required and the math can get quite gruesome. Note I will be showing sample calculations in both SI and US units. Small discrepancies will exist due to rounding off error.
But first step what is efficiency? Malting companies provide specific analysis for all their malts which contains the extract content of the malt using a coarse grind on a dry basis (abbreviated Extract CGDB) and the moisture content of the malt. If you are so inclined, you can look up the exact value for each malt you use with the given lot number, but that can be hard to find sometimes.
At any rate, a very common value is 80% CGDB and 4.0% moisture content, which I will be using all along this article. Programs like BeerSmith and online spreadsheet have pre-entered values for every particular malt. Now say you are making 21L (5.5 gal) of beer using 5 kg (11lb) of grain. The lab tells you that 80% of the dry weight of the grain is extractable sugars and 4% of the total weight is water. So:
Dry weight of grain: SI 5*(1-0.04)=4.8 kg US 11*(1-0.04)=10.56 lb
Sugar content: SI 4.8*0.8=3.84 kg US 10.56*0.8= 8.45 lb
We know that sugar increases the volume by 0.63 L/kg (0.0755 lb/gal). So if we want 21L
(5.5 gal) of final beer and have 3.84 kg (8.45 lb) of sugar we have 21-0.63*3.84=18.58L (4.91 gal) of pure water. This water weighs 18.58 kg (40.96lb).
Weight percent of sugar 3.84/(3.84+18.58)*100=17.1%
Now this is basically the Plato value of the original density. You can use the simple formula:
There are much more precise formulas that can be found on the net, but for the sake of keeping the math simple, I'll use this one. So we have 1+17.1*4/1000=1.068 wort right? Wrong. Except if you carried out an ideal mash, over sparged like crazy and didn't lose a single drop of wort, you will end up with a lower gravity beer. Efficiency is how much of the sugar you actually got out of the grain.
Efficiency=Sugar extracted/Maximum extractable sugar
So using the 65% efficiency from BYO Sugar content: SI 5*(1-0.04)*0.8*0.65=2.50
US 11*(1-0.04)*0.8*0.65= 5.49 lb
Pure water content SI 21-0.63*2.5=19.43L
US 5.5-0.0755*5.49=5.09 gal
Plato (weight percent) SI 2.50/(19.43+2.50)*100=11.4%
US 5.49/(42.47+5.49)*100=11.4%
Which yields an OG of 1.046.
I will be looking at four different possible efficiencies as shown in the picture below (taken from brewersfriend.com)

Conversion efficiency is the efficiency of the enzymatic conversion of insoluble starch sugars into simpler soluble sugars such as maltose. This should always be higher than 90% (though 95% is easy to get using the right mashing conditions such as time, pH, calcium content and all that good stuff). If it is below than 90%, check using iodine test. Lautering efficiency is how much of the sugars you manage to get out while sparging.
Grain absorbs 1.56L/kg (.748 qt/lb) of liquid. This absorbed liquid contains sugar which was extracted from the grain, but that does not end up in your wort. Lautering efficiency therefore varies greatly between a special bitter and a barley wine. Multiplying these two efficiencies together yields the kettle efficiency. In the diagram, they define a pre-boil and ending kettle efficiency which is the exact same thing. You evaporate water not sugar so you should end with the same efficiency before and after a boil.
Finally when you transfer the wort to the fermenter, you should leave behind some of the trub and hop debris, though some people don't do this and just through everything in. If you do filter, but don't happen to have a super efficient filter to completely dry out the trub and hop debris you will also leave behind some wort which will lower your efficiency.
You should now be aware of what efficiency is and how to calculate extract content given an efficiency value.
Next article I will explain how to calculate the batch sparging efficiency and account for losses in volume during transfer.
I hope you enjoyed this article and will read the next one.
Well written. I'll be on the lookout for your next write up. Probably every third brew for me is either sessionable or a monster. I have basically just been going by 'big beer= big boil' but hitting target gravity on a session beer is a bit trickier as I suddenly find myself achieving ridiculous efficiency.
Hey guys! Thanks for the nice comments! Here is the link to the second part of this article
Great article. Thanks. I am trying to absorb it and I saw this:
We know that sugar increases the volume by 0.63 L/kg (0.0755 lb/gal).
Did you mean to say (for the US equation) "0.0755 gal/lb."?