The Homebrewer’s Companion – Mash Calculations
What follows might be among the most boring and scope limited book reviews of all time.
If you should happen to take up home brewing. There is a pretty good chance that you will learn from Charlie Papazian’s very excellent book, The Complete Joy of Homebrewing. I would recommend it to anyone. If you get through that and want to learn more, you could end up with a copy of The Homebrewer’s Companion by the same author. It is also a very good book that I would recommend. However, if you are like me, there is a chance that you will end up with your head in a knot while trying to apply the equations for mashing that are provided in the latter book.
You see there are a couple of math errors. And if that wasn’t enough, the accompanying text that explains those equations has a few subtle pitfalls in its layout. Perhaps some of this is corrected in later printings. I have one with a 1994 copyright.
The problem lies in the scanned pages below. They explain how to estimate the amount of barley sugars that can be extracted through the mashing process. It is actually a very simple calculation when all is said and done. It is basically just the extracted sugar, multiplied/divided by constants, then divided by the total volume of wort. See equation number 4. This is basically rewritten in equation numbers 6 and 8. But wait a minute, the “x4” should not be in the denominator in numbers 6 and 8. A very simple and obvious math mistake. If you take the correction at face value and move along, you will be much happier.
If you’re like me, you’re going to cycle back through the previous equations and step through the derivation real quick, just to make sure you didn’t miss anything. One of the first things you will notice is that in with equation number 1 there is a note that says “multiply by 100…”. Wait? There’s no 100x multiplier in either equations #s 6 or 8. Where’d it go? Oh, there’s a note between equation numbers 2 and 3 that percentages are expressed as whole numbers, as in 75 instead of .75. That is a factor of 100 so that’s probably it.
Now you might really be at risk of falling down a rabbit hole. It goes something like this. Knowing that using a percentage as a whole number introduces a 100x multiplier, you’ll think you can connect the dot’s. So, you’ll go back up and start the step-by-step math evaluation over with that in mind. Wait again. There’s no percentage noted in equation number 1. Instead, there is a value of .75 lbs. The extract percent mentioned in the paragraph above is 75% so the number makes sense. But by expressing it as a lb. measure in one equation (number 1) and a unitless percentage in others (numbers 6 & 8), doesn’t that create a unit problem? It has to. Unit errors are easy to make though and easy to check. By breaking down the equations a little more, it should be obvious which equation has the problem. Unit consistency gets drilled into anyone who has studied engineering and those with that background will have some compulsion to resolve this. Backup another step and reread the paragraph above equation 1. In there, it notes that 1 degree Balling (a measure of sugar) is one pound of extract in 100 lbs. of water. It turns out the 100x number in the note below equation #1 is referencing Balling equivalency not percentage at all. It throws a little curveball in the unit consistency check, but it in the end it can be verified that the units square up in both equations. At this point, except for the “x4” error that served as the first domino, everything looks correct. The fact that the 100x conversion factor to put the units in degrees Balling cancels out the 1/100 normally used in percentage multiplication is a strange coincidence. They are two completely separate items. It’s weird enough that it is hard to resist going back to square one and confirming that it is actually so. It is true though.
There is a bit of self-gratification in knowing that you have logically worked through a mathematical problem. But the mental exercise just puts my little brain in a place that is vulnerable to overthinking, and sure enough something else catches my attention in equation 9. A variable “EP” is introduced. That’s “EP” for extract potential. I can see what is supposed to be happening here. Extract potential for each grain type is being added together and divided by volume. Something’s not quite right though. It’s the units again. The text assures the reader that “EP” is in units of Balling or as a specific gravity (unitless). “EP” is more like extract potential per lb, per gallon. I see where Papazian is going here and I do not even think it is technically wrong, but I think there are better ways to present. I think we would be better off to just say that “EP” is defined as the product is the grain specific extract percentage and a conversion factor. Oh, and by the way, the extract percentage value is a way of quantifying the amount of extract a grain is capable of producing. So, it is by definition an extract potential. That means, in those last couple of equations, there are three separate things that could be described as extract potential; percent extract of the grain, this EP variable and the overall extract potential of the wort (the product of equation numbers 5 through 10). As I’m in a state ripe for overthinking, every time I read the words “extract potential” I need to assure myself which one of these Papazian is talking about. In the end the only thing I can do is another thorough breakdown of some very simple equations.
After all this review all that can be said is that the methodology for mash efficiency is as simple as advertised, and except the placement of the “x4” in equation numbers 6 and 8 all the equations are correct. Of course, I never write any of this down. Consequently, every time I started to plan a recipe, I would see the misplaced 4x and know that it was wrong and know that I found some other funny things going on in the math, but I can never quite remember what they were. And then I go through the whole process again. Unfortunately, I probably had a couple of beers on brew day and would decide to double check my calculations and do it again with a buzz.
I recently created a brew program that does all the math for me. All I really need to do is input the grain bill and hop additions. Everything else is done automatically. I will go into the details of that program in separate posts. The creation of it did force me to go through the derivation and analysis one more time very carefully. I think it was therapeutic in a way. I as forced to write a program that captured every step of the process. Just doing that I believe cemented the proper methodology in my head. I have confidence in what the program produces. Although the program was designed to capture all the calculations needed for brew planning, it was made to help reduce the reliance on them. As much as it is a planning calculator, it is also a data collection format. The idea is that the calculations are a good tool, but experience is equally important. The program is a step to start collecting data with each batch. The data will then be used to evaluate the accuracy of the calculations and make improvements where needed.
