Author Topic: KISS: Simple All-Grain Brewing Math  (Read 699 times)

Offline Saccharomyces

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KISS: Simple All-Grain Brewing Math
« on: November 26, 2021, 01:07:48 pm »
I know that I am starting to sound like a broken record when it comes to efficiency being a poor brewing metric, but it really is a poor metric after one looks beneath the covers.  Efficiency just not that useful in the brew house because it causes a brewer to often work backwards or rely on brewing software to do it for him/her.  However, at the heart of this problem are simple arithmetic equations.

When we look at a batch of wort in terms of original gravity (OG) at a specified volume, the problem with which we are dealing is actually one of total gravity points divided by volume, so we need to start by multiplying the whole number to the right of the number 1 for the desired OG by the desired volume to determine how many gravity points we need to extract from our grist.  Most all-grain batches are formulated with a specified amount of loss.  That is why most of the recipes we see posted are for 5.5 or 6 gallons of wort.  That is not the desired final yield volume.  It is the wort volume necessary to allow for losses to trub when casting-out and trub/yeast when packaging fermented beer.  Let's say, we desire to make a 5.5-gallon batch of wort with an OG of 1.052.

Let's convert an OG to gravity points:

OG_in_gravity_points = (OG - 1) * 1000

For our batch, the value is:

desired_OG_in_gravity_points = (1.052 - 1) * 1000 = 52

In practice, this calculation does not even need to be performed, because all it does is take the number to the right of the decimal point and make it a whole number. We can just use this shorthand rule to convert any specific gravity (SG) to its equivalent gravity points.

With our OG converted to gravity points, we can now calculate the total number gravity points needed to achieve this OG at our specified gravity.

desired_total_gravity_points = desired_OG_in_gravity_points * desired_volume

We want 52 gravity points for a volume of 5.5 gallons

desired_total_gravity_points = 52 * 5.5 = 286 gravity points

What is good about knowing the amount of gravity points necessary to achieve a desired OG at a desired volume is that we can sample our wort after the hot break has formed and see if our extraction rate was high enough to achieve our desired OG at our cast-out volume.  While there will still be cold break in solution, this value will close enough to work.

Most all-grain brewers who brew 5.5-gallon batches of wort usually start with 7 gallons of runoff from their lauter tuns; therefore, all we need to do is accommodate this dilution because there will be the same total number of gravity points in 7 gallons of runoff as there will be in 5.5 gallons of wort at cast-out.

dilution_factor_at_hotbreak = desired_volume / runoff_volume

dilution_factor_at_hotbreak = 5.5 / 7 = .786

desired_SG_in_gravity_points_at_hotbreak = desired_OG_in_gravity_points  *
dilution_factor_at_hotbreak

Simply put, we need to see an SG in gravity points of 52 * .786  ~= 41 (1.041) in the sample that is taken after the hot break has formed.  If the reading is higher, we will have to dilute the wort near the end of the boil to ensure we meet our desired gravity and that the water addition has been  Pasteurized.   If the reading is lower, we will need to concentrate the wort to a smaller volume or make a dry/liquid extract or brewing sugar addition.  Here is where working in gravity points is a beautiful thing because the points per pound per gallon (PPG) values for most extracts and sugars are known.

For example, if our SG in gravity points reading at hotbreak is 38 instead of 41, that means we need to  perform a gravity correction by adding fermentables. 

wort_gravity_correction_in_points_per_gallon  =  desired_wort_SG_in_gravity_points_at_hotbreak  - measured_wort_SG_in_gravity_points_at_hotbreak

wort_gravity_correction_factor_in_points_per_gallon  =  41  -  38 = 3

total_gravity_points_needed_to_correct_wort = wort_gravity_correction_factor_in_points_per_gallon * runoff_volume

total_gravity_points_need_to_correct_wort =  3  *  7  =  21
amount_extract_or_brewing_sugar_needed_in_pounds  =  total_gravity_points_need_to_correct_wort / extract_or_brewing_sugar_PPG

We know that spray malt (a.k.a. dry malt extract) has a PPG value of 46; therefore, we need to add 21 / 46 = 0.47 pounds of spray malt (in practice, we will more than likely just round up to half of a pound).  It is that simple.

Finally, if one starts to brew in gravity points, one will never have to rely on software to formulate or scale a grist because all an efficiency is is the extraction rate in PPG for a grist in one’s brew house divided by the value computed by taking each grist components’ theoretical maximum yield in PPG, weighting it by the amount used, summing the weighted values, and then dividing by the total weight of the grist.  In essence, efficiency is an overly complex and error prone way to look at extraction rate because it based on theoretical maximum values, not measured maximum values.  That is why we hear brewers state that their efficiency went up when they switched a different base malt when what really happened is that the amount of available substrate went up and the theoretical maximum for the malt in the brewing software or calculator being used is incorrect.

In my brew house, I average around 30 PPG for 90/10 (90% base malt/10% specialty malt) grists and around 29 PPG for 70/30 (70% base malt/30% specialty malt) grists.  How did I come about these values?  Well, I divided my recipes out into classes of base malt/specialty malt.  I pretty much brew mostly 90/10 and 70/30 batches.  I then took OGs and volumes measured at cast-out, calculated total gravity points values, divided each total gravity point value by its corresponding grist weight, summed these values, and divided by the number of values in the sum to yield an average batch PPG value.  In practice, all one needs to keep an eye on batch-to-batch extraction rate in PPG.  After a while, these values will stabilize. 

batch_extraction rate_in_ppg = OG_in_gravity_points * batch_volume_at_cast_out / grist_weight

If we used 10lbs of grist to produce 5.5 gallons of 1.052 wort at cast-out (i.e., the total volume in one’s kettle after the wort has been chilled), then our extraction rate in PPG is:

batch_extraction_rate_in_ppg = 52 * 5.5 / 10 = 28.6 (we can round this value up to 29 for all practical purposes)

If our running PPGs values are all very close to this value, then we can just use 29 PPG when computing grist weight.   If similar grist compositions do not produce a tight cluster of PPG values, then we need to work on our crush and/or lautering technique. 

After a brewer knows his/her average extraction rate for a given base malt/specialty malt composition, determining how much grist is needed to achieve a desired OG at a designed volume is trivial.  One just needs to calculate the desired total gravity points and then divide the result by the one’s extraction rate in PPG.

grist_weight_in_pounds = desired_total_gravity_points / extract_rate_in_PPG

For example, we want to make a 5.5-gallon batch of 1.064 ale wort that contains 90% pale malt, 5% 55L caramel malt, and 5% torrified wheat.  We know that our 90/10 extraction rate is 30 PPG.

desired_total_gravity_points =   64 * 5.5 = 352

grist_weight_in_pounds =  352 / 30 ~=  11.75lbs

Note: In practice, the above method is akin to taking the derivative of a polynomial using limits.   An easier method is to take one’s desired gravity and divide it by one’s extraction rate in PPG.  The result will be the amount of grist needed to make one gallon of wort at the desired gravity, a very handy figure.  From there, it is just a matter of multiplying the result by the total number of gallons of cast-out wort desired.

From here, formulating the grist is just mater or multiplying 11.75 by 0.9 to determine the weight of base malt needed and by 0.05 to determine the weight of the crystal malt and torrified wheat additions.

Base malt = 11.75 * 0.9 = 10.575 lbs

Crystal malt =  11.75 * 0.05 = 0.5875lbs

Torrified wheat =  11.75 * 0.05 = 0.5875lbs


Trust me, I have been using this method for close to 30 years, and it has proven to be as accurate as any brewing software package on the market.  I am not a luddite. I hold undergraduate and graduate degrees on the computer engineering side of computer science and have worked professionally with computer and communication systems for four decades.  For me, it is just that brewing software attempts to achieve a level of precision that is not possible nor is even necessary in a home brewery.  We do not have full-service quality labs to analyze all of our ingredients, perform accurate cell counts, and monitor the reduction of compounds such as vicinal diketones during fermentation.  These things are very important to industrial and large craft brewers who are looking for absolute batch-to-batch consistency.  They do not use alpha acid/essential oil ratings supplied by hop brokers and ASBC theoretical averages for maximum convertible malt substrate.   They perform all of these lab tests in-house on the actual ingredients.  Most industrial brewers are blenders.  They buy alpha acids and oils and blend for bitterness and flavor based on actual alpha acid content and measured essential oil breakdown.


« Last Edit: November 26, 2021, 06:28:07 pm by Saccharomyces »

Offline Bob357

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Re: KISS: Simple All-Grain Brewing Math
« Reply #1 on: November 26, 2021, 02:24:42 pm »
Did everything by hand for quite some time before discovering BeerSmith. Between the various calculations, brewing notes, keeping track of recipes and everything else, one could get writer's cramp. I will admit though, knowing what to expect is a skill that catches a lot of entry errors, so definitely comes in handy.
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Offline chinaski

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Re: KISS: Simple All-Grain Brewing Math
« Reply #2 on: November 26, 2021, 03:37:11 pm »
I use a set of spreadsheets.  Some folks use software.  It all depends on how how comfortable you are with math, the tool available to you, and how much you like to spend money on certain aspects of your hobby.  For me, my mantras are "consistent efficiency is more important that high efficiency" and "spend money on quality (maybe local) ingredients rather than equipment."  I look at fancy equipment but am pretty good at not purchasing it. 

Offline Richard

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Re: KISS: Simple All-Grain Brewing Math
« Reply #3 on: November 26, 2021, 04:20:56 pm »
I agree that chasing high efficiency is not a good way to improve your beer. On the other hand, efficiency is a good metric to let you know if your brewing is on track, as chinaski said. My first all-grain mash had an efficiency of 40%. That was low enough to tell me something was very wrong, so I went to my LHBS and discussed it with them. The next time I added some acidulated malt and got 70%, so I knew I was on the right track to fixing things. Now I use brewing software to calculate an acid addition and I measure pH with a meter, and I get efficiencies in the 80s.
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Offline Saccharomyces

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Re: KISS: Simple All-Grain Brewing Math
« Reply #4 on: November 26, 2021, 06:56:48 pm »
The problem with efficiency is that it is calculated differently by different software and calculators. Not only is the calculation error prone, it is software and software user dependent. That is why efficiency is a poor metric. Brad Smith takes the case for taking a straight forward calculation and twisting it beyond all recognition with his “brew house” efficiency, which is the least useful metric on the planet when exchanging recipes. It is almost like listening to the clueless being led by the blind when brewers who use BeerSmith converse about efficiency. An extraction rate is not relative. It is absolute measurement. If a brewer states a recipe in terms of a grist composition, O.G, cast-out kettle volume, and extraction rate, I can duplicate that recipe even if my extraction rate is different. I do not have to worry about how much wort was left out of the equation in the case of a BeerSmith’s made up brew house efficiency  calculation or what maximum achievable extraction rates were used in the calculation.  Brad Smith posted that there are fermentable extract loses between runoff and the end of the boil on his blog.  Here is a guy with a Ph.D. who was basically claimed that the law of conservation does not apply to brewing by asserting that there are fermentable extract losses between runoff and cast-out  Luckily, he got called on it. 

Offline Don

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Re: KISS: Simple All-Grain Brewing Math
« Reply #5 on: November 29, 2021, 05:37:05 pm »
Thanks for this post Saccharomyces... I have been struggling with Beersmith and getting the numbers to work out on my new system. I may need to abandon BS for something else to keep track of and build recipes.

Offline RC

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Re: KISS: Simple All-Grain Brewing Math
« Reply #6 on: November 29, 2021, 06:07:53 pm »
I have been struggling with Beersmith and getting the numbers to work out on my new system.

You could also simply calibrate Beersmith's numbers with what your palate is telling you. Should only take a couple of batches to get close.

V1G1=V2G2. Same relationship as in the first half of this post, in an approachable format and with slightly different terminology: V & G = volume & gravity points, respectively, and the subscripts 1 & 2 are pre-boil & post-boil (vs. hot-break & cast-out).

If you wish, you can adjust for the refraction of glucose vs. maltose with your refractometer, and even for the volume shrinkage that occurs between boiling temp and knockout temp. But I have found that that level of detail is not needed to make good, consistent beer.

Offline fredthecat

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Re: KISS: Simple All-Grain Brewing Math
« Reply #7 on: November 29, 2021, 07:28:30 pm »
______ takes the case for taking a straight forward calculation and twisting it beyond all recognition with his “brew house” efficiency, which is the least useful metric on the planet when exchanging recipes.

i always saw this efficiency vs brew house efficiency stuff on various homebrew forums, and at first just conflated them, assuming it was some technical description of efficiency. then i realized people were saying these are two different values. it never made sense to me, but i have always used brewtarget.

i use it because it is and was free, and i have since adapted to it so much, i cant imagine another way of brewing. i think the very first brews i did were without software, but cant remember how i did them.

Offline BrewBama

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Re: KISS: Simple All-Grain Brewing Math
« Reply #8 on: November 29, 2021, 07:59:32 pm »
The first few brews I brewed I had instructions in a kit of extract, hops, and yeast. Just add water. No software required.



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Offline Kevin

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Re: KISS: Simple All-Grain Brewing Math
« Reply #9 on: November 30, 2021, 03:52:04 pm »
I have been struggling with Beersmith and getting the numbers to work out on my new system.

The problem with and the beauty of Beersmith is that it is entirely user defined. If your results are not matching the estimates then your profiles have not been customized fully.
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Offline Don

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Re: KISS: Simple All-Grain Brewing Math
« Reply #10 on: November 30, 2021, 03:56:34 pm »
I have been struggling with Beersmith and getting the numbers to work out on my new system.

The problem with and the beauty of Beersmith is that it is entirely user defined. If your results are not matching the estimates then your profiles have not been customized fully.

Exactly my issue... it's finding the correct numbers to input...

Offline fredthecat

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Re: KISS: Simple All-Grain Brewing Math
« Reply #11 on: December 01, 2021, 08:06:21 am »
does anyone here not use brewsmith? tbh ive never used it

Offline ynotbrusum

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Re: KISS: Simple All-Grain Brewing Math
« Reply #12 on: December 01, 2021, 08:31:44 am »
I used to use Brewsmith, but transitioned to Brewer's Friend years ago and still use it.  I will often run water aspects through Brunwater for confirmation on my water and grist adjustments (I use acidulated malt, typically, as well as small amounts of salts and from time to time, liquid acid in the mash or boil kettle).
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Offline narvin

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Re: KISS: Simple All-Grain Brewing Math
« Reply #13 on: December 01, 2021, 08:40:35 am »
I still use ProMash.  If it ain't broke...

I no sparge in an anvil foundry so that keeps it really simple.  Brewhouse efficiency = mash efficiency * lauter efficiency, more or less, and there are no losses or sparges to worry about.  I find this chart to be a very useful starting point for a theoretical "average" base malt mash.



If I can find a spec sheet for the lot of grain I bought, I'll look to see if it's far out of line from 80% FGE, but generally it's not worth it for me.  Country malt does provide that info online for their brands (https://countrymaltgroup.com/malt-lot-analysis/)
« Last Edit: December 01, 2021, 08:43:00 am by narvin »

Offline MagicRat

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Re: KISS: Simple All-Grain Brewing Math
« Reply #14 on: December 17, 2021, 08:25:49 am »
Sorry, but I don’t see anything particularly simple about all that!😆
But that’s fine, when it comes to brewing, I’ve always been a big believer in finding what works for you and sticking to it.
I use the Brewer’s Friend Recipe Calculator to formulate recipes.  I used OG/FG results on a few early brews and worked backwards to figure out what kind of “Brewhouse Efficiency” percentage I was getting.  I was regularly 70-75%.  So when I use BF to come up with a recipe, if I use 75% BHE, I’m going to come within a point or two of what I’m shooting for with the recipe. And even when I occasionally miss the mark by a little bit more, the beer that results is still pretty much what I want it to be.
That’s as in-depth as I feel the need to get when it comes to efficiency.  Works for me!