A Practial Method for Grist Formulation and Scaling

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Introduction

The hobby has come a long way since the I started brewing all-grain beer in the early nineties. While not unheard of, it was very rare for an amateur brewer to jump straight into all-grain brewing at that point in time. Almost every new amateur brewer started out as a can-based kit brewer. From there, he/she usually transitioned to extract plus steeped specialty grain brewing using recipes out of books. Many amateur brewers never transitioned beyond this point before abandoning the hobby.

At some point after brewing his/her kit beer, an adventurous brewer attempted partial-mash brewing, usually using standard kitchenware and a Zapap lauter tun. This approach to brewing was driven primarily by the layout of what was considered to be the amateur brewer's bible; namely The Complete Joy of Homebrewing. However, the fact that amateur-scale all-grain brewing equipment had to be fabricated played a large roll in the step-wise progression from kit to all-grain brewing. The Internet had not yet been commercialized, which meant that a brewer had to source stainless steel fittings and commercial-grade stockpots through trade-oriented supply channels that often did not sell to retail customers.

With that said, brewers who took the "old school" route to all-grain brewing often built up a sizable portfolio of extract and/or partial-mash recipes that needed to be converted to all-grain recipes. A fundamental concept that is learned while formulating recipes that include dry or liquid malt extract is points per pound per gallon; therefore, it was natural for brewers who took this path to continue to use points per pound per gallon after making the transition to all-grain. Those who jump into all-grain recipe formulation with the aid of brewing software often do not learn this concept or only see it as intermediate unit of measure that is used while calculating table-based extraction efficiencies. However, points per pound per gallon is powerful concept that can simplify the formulation and scaling of all-grain recipes. This article focuses on a practical application of points per pound per gallon in an all-grain brew house. The method that is outlined in this article will completely eliminate the need to use brewing software to calculate and/or scale recipe grists.


Incorporating Points Per Pound Per Gallon

In order to use points per pound per gallon effectively, a brewer needs to establish the average extraction rate for his/her brew house. This process starts by calculating the points per pound per gallon values for batches of wort that one has made in the past using the following equation.

points_per_pound_per_gallon = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_gallons / batch_grist_mass_in_pounds

In practice, the (batch_original_gravity - 1.0) x 1,000 subexpression can be simplified by taking the original gravity reading, lopping off the "1," and converting the number to the right of the decimal point to a whole number (e.g., 1.056 becomes 56).

Using a 5.5-gallon batch of 1.056 wort that was made with 11 pounds of grist to put the equation into practice yields:

batch_original_gravity = 1.056
batch_volume_in_gallons = 5.5
batch_grist_mass_in_pounds = 11

points_per_pound_per_gallon = (1.056 - 1.0) x 1,000 x 5.5 / 11 = 28

Now, if we perform this calculation for several batches, sum the points per pound per gallon values, and divide by the number of batches that were summed, we will arrive at our average brew house extraction rate in points per pound per gallon.

Batch #1 = 26.5 points per pound per gallon
Batch #2 = 27 points per pound per gallon
Batch #3 = 30.5 points per pound per gallon
Batch #4 = 28 points per pound per gallon
Batch #5 = 29 points per pound per gallon

average_points_per_pound_per_gallon = (26.5 + 27 + 30.5 + 28 + 29) / 5 = 28.2

In practice, the only time that a brewer should experience the large variance in values shown above is when he/she is working with a new brew house or purchasing grain one batch at a time. A brewer who is looking for predictable batch-to-batch results should purchase his/her base malt in bulk.

With that said, it is important to use a sliding sample point window that is weighted towards the most recent batches, so that variations in extract potential are tracked accurately. The maximum extract that can be obtained from any given malted grain can change from season to season, malting to malting, and even bag to bag.


Putting Points Per Gallon Gallon Into Practice

Let's put the average brew house extraction rate calculated above into practice using a hypothetical 11-gallon recipe that we would like to adjust for our 5.5-gallon primary volume brew house.

A Simple Pale Ale

batch_original_gravity = 1.064
batch_volume_in_gallons = 11
batch_grist_mass_in_pounds = 23

Grist Composition

British Pale Malt: 20.75 pounds
60L Crystal Malt: 2.25 pounds

Calculating the recipe points per pound per gallon extraction rate yields :

recipe_points_per_pound_per_gallon = (1.064 - 1.0) x 1,000 x 11 / 23 = 30.6

If we compare the recipe's extraction rate to ours, we will clearly see that we cannot just cut the recipe in half; therefore, we need to scale the grist to fit our brew house extraction rate. We can handle scaling two different ways. The easiest and most logical way is to calculate the amount of grist that we will need to hit the recipe's original gravity (O.G.) in our brew house, and then divide this mass into grist percentages that are proportional to those found in the original recipe.

Calculating how many pounds of grist that we need to hit 1.064 yields:

batch_grist_mass_in_pounds = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_gallons / average_points_per_pound_per_gallon

batch_grist_mass_in_pounds = (1.064 - 1.0) x 1,000 x 5.5 / 28.2 ~= 12.5lbs

With that calculation complete, we need to calculate grist percentages from the original recipe.

recipe_total_grist_mass = 23lbs

recipe_british_pale_ale_percentage = 20.75 / 23 x 100 ~= 90%
recipe_60L_crystal_percentage = 2.25 / 23 x 100 ~= 10%

With these numbers, we can now formulate our grist.

Our Simple Pale Ale

batch_original_gravity = 1.064
batch_volume_in_gallons = 5.5
batch_grist_mass_in_pounds = 12.5

British Pale Malt: 12.5 x 0.9 = 11.25lbs (11.25 is 90% of 12.5)
60L Crystal Malt: 12.5 x 0.1 = 1.25lbs (1.25 is 10% of 12.5)

The second way to adjust a recipe based on one's brew house extraction rate is to calculate a grist scaling factor that takes into account the differences in brew house extraction rates and a batch volume divisor that takes into account the differences in batch volumes.

grist_scaling_factor = recipe_extraction_rate / our_average_extraction_rate

grist_scaling_factor = 30.6 / 28.2 ~= 1.085

batch_volume_divisor = recipe_batch_volume / our_batch_volume

batch_volume_divisor = 11 / 5.5 = 2

brew_house_extraction_rate_adjusted_malt_mass = malt_mass x grist_scaling_factor / batch_volume_divisor


Our Simple Pale Ale

batch_original_gravity = 1.064
batch_volume_in_gallons = 5.5
batch_grist_mass_in_pounds = 23 x 1.085 / 2 ~= 12.5


British Pale Malt: 20.75 x 1.085 / 2 ~= 11.25
60L Crystal Malt: 2.25 x 1.085 / 2 ~= 1.25

(note: the symbol "~=" denotes approximately equal to)

Over a period of time, a brewer will more than likely begin to cluster brew house extraction rates into groups based on the percentage of base malt used in the grist, which will lead to even more accurate average points per pound per gallon extraction rates. For example, I have a cluster known as the 90/10 group. This group contains recipes in which 90% of the extract is derived from base malt with the remaining 10% of the extract being derived from specialty malts and/or adjuncts. If one examines the grain ratios found in the most common pale ale recipes, one will discover that most fall into the 90/10 group +/- a few percentage points. Another popular cluster is the 80/20 group. While there are outliers such as wheat beer recipes, these two groups encompass a large percentage of recipes in use today.


The Metric System

The system that I outlined above works with the metric system. When using the metric system, a brewer works in points per kilogram per liter using the equations shown below.

points_per_kilogram_per_liter = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_liters / batch_grist_mass_in_kilograms

batch_grist_mass_in_kilograms = (batch_original_gravity - 1.0) x 1,000 x batch_volume_in_liters / average_points_per_kilogram_per_liter

points_per_pound_per_gallon_to_points_per_kilogram_per_liter = points_per_point_per_gallons x 8.35

points_per_kilogram_per_liter_to_points_per_pound_per_gallon_ = points_per_kilogram_per_liter / 8.35

While I am comfortable working with English and metric units of measure, I prefer to formulate recipes using English units of measure. In my humble opinion, points per pound per gallon is more intuitive because it is a non-concentrated unit of measure. If I want to formulate a beer with an original gravity of 1.056, and my brew house extraction rate is 28 points per pound, then I know that I need to use two pounds of grain for every gallon of wort that I want to produce. Points per kilogram per liter is not nearly as tidy.


Concluding Remarks

Points per pound per gallon is a powerful unit of measure that is rarely used directly by modern all-grain amateur brewers. Modern amateur brewers tend to prefer to use software for grist formulation and scaling. However, I guarantee that brewers who put the method outlined in this article into practice will find that they rely on software far less than they did before adopting it.

A Practial Method for Grist Formulation and Scaling - EAZ - mashtuninternal-518.jpg
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19 COMMENTS
Posted: 
January 20, 2014  •  02:31 PM
great technical article, and very accessible. I am just starting to delve into BIAB and am in the process of obtaining those 'brewhouse' efficiency data. I will certainly be referencing this technique in the future.

thank you
Posted: 
January 20, 2014  •  03:56 PM
Thanks for taking the time to read my article. If you read old Brewing Techniques articles and postings on rec.crafts.brewing, you will discover that points per pound per gallon as a measure of brew house efficiency used to be more common than it is today.
Posted: 
January 20, 2014  •  11:50 PM
I was a prime example of your first two paragraphs. lol.
Posted: 
January 21, 2014  •  01:46 AM
We all learned that way.
Posted: 
January 21, 2014  •  01:07 PM
This likely a helpful article for many. I'm not denying that. But, since when is using PPG as a measure of efficiency not common today? Do you mean many people don't know the math behind the efficiency calculations in their brewing software? That might be true--I don't know.
Posted: 
January 21, 2014  •  05:12 PM
What I have discovered since rejoining the ranks is that many amateur brewers are amazed to discover that they can accurately formulate and scale grists based on their actual brew house results without the aid of brewing software and/or a spreadsheet. Modern all-grain brewers have been conditioned to think in terms of efficiency percentage calculations that weigh each cereal grain used in a recipe in terms of theoretical potential extract. Even many of those who know the inner workings of their software package of choice in gory detail are surprised to discover that accurate grist formulation and scaling can be performed using a much easier to compute metric.
Posted: 
January 22, 2014  •  10:18 PM
WHERE CAN I GET THAT FALSE BOTTOM????
Posted: 
January 23, 2014  •  06:15 PM
Maybe I'm just nitpicky, but I've always had an issue with the phrasing of points per pound per gallon. If I mash a pound of malt and extract the sugars and dilute it with one gallon of water then I will have x number of points of sugar. Now, if I mash two pounds of malt, but still dilute with one gallon of water then I have 2x number of points of sugar. However, if I mash one pound of malt and dilute with two gallons of water I have x/2 points of sugar. Therefore we can conclude that the correct unit is points*gallon/pound. We want to multiply by the weight of malt and divide by the gallons of water to figure out SG.

One way to say this is points-gallon per pound (ala foot-pound per second as a measure of power). Another way could be points per pound per gallon, so long as we understand this to mean points/(pound/gallon) = points*gallon/pound. However, I find this unnecessarily ambiguous because points per pound per gallon could just as easily mean points/pound/gallon = points/(pound*gallon) which is incorrect.

All the math and content of the article is correct, I'm just bothered by the name of the unit is all.
Posted: 
January 24, 2014  •  05:42 AM
@McCoy When I first started brewing and using pounds per gallon I came to the same conclusion. From a math perspective it is very confusing, however from a practical standpoint I understand the terminology. It just seems more natural to think in terms of how many pounds of grains you want to add to a gallon of water to reach a certain gravity then how much water to add to a pound of grain to reach a certain recipe.

Basically a lot of brewers, myself included, tend to design a recipe by first choosing the volume you want to brew and then scale the grist to reach the desired gravity. I guess this type of thinking translates better in saying pounds per gallon though the units of ppg are actually gallons per pound.

I still agree with you though and feel like a lot of people can get confused because of this.
Posted: 
January 24, 2014  •  08:01 PM
The false bottom shown in the photograph was purchased from Adventures in Homebrewing. It's actually an assembly that consists of the following parts:

One 9" stainless steel domed false bottom, 16% open area (item 99-2649)

One stainless steel 1/2" NPT x 3/8" barb 90-degree (item 73-4109)

Two stainless steel 1/2" NPT lock nuts (item 73-1744)

If you are building a 10-gallon beverage cooler-based mash tun, you will need to substitute item number 99-2570 for item number 99-2649.
Posted: 
January 24, 2014  •  08:38 PM
@McCoy

Points per pound per gallon (ppg) is basically just a measure of a solute when dissolved in a one-gallon solution, which is not the same thing as adding extract to one gallon of water. Adding extract to one gallon of water increases the volume of the solution.

We can dilute or concentrate the extract from one pound of grain, but the base ratio remains the same. All we are doing is creating a coefficient other than one. Producing a two gallon solution with one pound of grain is just 1/2ppg. Producing a one gallon solution with two pounds of grain is 2ppg.

By the way, the expression points / pound / gallon does in fact equal points / (pound * gallon) because the second and third terms in the ratio are 1.

28 / (1 * 1) = 28
28 / 1 / 1 = 28

The expressions (points * pound) / gallon and points * pound * gallon also produce the same result.
Posted: 
January 24, 2014  •  09:26 PM
@Qcbrew

"Basically a lot of brewers, myself
included, tend to design a recipe by first choosing the volume you want to brew and then scale the grist to reach the desired gravity. I guess this type of thinking translates better in saying pounds per gallon though the units of ppg are actually gallons per pound"


That's exactly what the "batch_grist_mass_in_pounds" equation outlined in the article accomplishes. The portion of the equation to the left of the divisor calculates the total number of gravity points as a function of original gravity and batch volume in gallons. Total gravity points is just the number to the right of the decimal point in the O.G. converted to a whole number multiplied by the batch volume size.

total_batch_gravity_points = (0.G. - 1.0) x 1,000 x batch_volume_in_gallons


batch_grist_mass_in_pounds = total_batch_gravity_points / average_points_per_pound_per_gallon

I often shorten points per pound per gallon to gravity points because total batch gravity points and points per pound per gallon are both referenced to the gallon as a unit of measure. A problem encountered with this practice is that an Imperial gallon is larger than a US gallon (not to mention that a liter is smaller than a US gallon and a kilogram is larger than a pound). Twenty-eight points per pound per US gallon is equal to 23.3 points per pound per Imperial gallon.
Posted: 
January 26, 2014  •  06:41 PM
I recant my comment. I read something that changed my mind about the correct unit the correct unit for potential extract is points per pound and then the unit for gravity (being a density, essentially) is points per gallon. Of course the natural consequence is you must multiply the potential of your grain (given in points per pound) by pounds of grain, and then divide by the volume of your batch (yield points per gallon) to get a gravity. This makes is so "points" refers to an amount or mass of sugar rather than a density of sugar in solution. I think this is more clear, since the amount of sugar yielded by a pound of grain has nothing to do with how much water dissolves that sugar.
Posted: 
January 26, 2014  •  09:07 PM
Exactly! If one examines the extraction efficiency as a percentage calculation, one discovers that it is merely a percentage of a percentage of a mass when dissolved in a one gallon solution. The maximum theoretical extract for any given malted grain is little more than a theoretical (or actual) dry basis, fine grind (DBFG) percentage applied to the density of a one gallon solution that contains one pound of dry malt extract.

Example

base_malt_DBFG = 80%
DME_ppg = 46

base_malt_max_ppg = DME_ppg x base_male_DBFG

base_malt_max_ppg = 46 x 0.8 ~= 37

(assuming that our grist only contained base malt)

base_malt_extraction_efficiency = brew_house_base_malt_ppg / base_malt_max_pgg

base_malt_extraction_efficiency = 28 / 37 ~= 76%

In reality, what we are saying with the above equation is that we are able to extract approximately 6/10ths (0.76 x 0.80 or 28 / 46) of a pound of malt sugar from each pound of base malt. The beauty of ppg as a measure of brew house extraction efficiency is that it allows us to determine the amount (mass) of grain that we need hit a specific gravity given a volume fairly easily. DBFG values never enter the equation because they are not needed in practice. PPG also allows extract brewers to easily convert recipes to all-grain because all they need to do is apply the following equations to their old recipes:

pounds_of_base_malt = 46 / average_brew_house_ppg x pounds_of_DME

or

pounds_of_base_malt = 36 / average_brew_house_ppg x pounds_of_LME
Posted: 
February 2, 2014  •  06:47 PM
love this article, thank you. When calculating my average ppg, what does using a sliding sample point window that is weighted towards the most recent batches mean? Is it just that I only use my most recent batches, say 5, instead of an average of all of the batches I have brewed on my system?
Posted: 
February 2, 2014  •  06:57 PM
Also, do you notice a difference in extract efficiency when mashing at a different temperature? I am not sure if mashing at 148 will yield the same ppg as 156, because of the different levels of enzyme activity. I am wondering if average ppg is affected by mash temp, and if that could be another category to group recipes into in addition to the 90/10 80/20 groups. For example, low mash temp group (148-152) vs high mash temp group (153-158)
Posted: 
February 2, 2014  •  07:10 PM
Yes, it means that ppg values from the most batches tend to be more accurate than older values, especially when purchasing base malt in bulk.
Posted: 
February 2, 2014  •  07:25 PM
While one will usually achieve a higher extraction rate if one raises the mash bed temperature before lautering, the temperature at which one performs saccharification rests generally only affects the balance of sugars in the extract. What's critical when mashing low is to verify that conversion is complete.

With that said, while modern malt is high converted, one can achieve a small increase in extraction rate by performing a decoction mash. I tend to achieve a point higher extraction rate when I perform a single decoction mash with domestic 2-row.
Posted: 
April 16, 2014  •  05:28 AM
so like bakers percentages with your own efficiency in mind simple enough concept.
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