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 *
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.