Efficiency Math Questions

[joshbmace]

I'm not sure if I'm having a major brain fart, but I cannot wrap my head around how to determine efficiency (conversion or brewhouse) using PKL or SG. It seems to me that SG as a unit of measure is a concentration of sugar in a solution. For example, your wort will increase in SG between the beginning and end of the boil due to evaporation, despite the fact that the total amount of sugar in the wort is unchanged. My instinct for a logical method of calculating efficiency would be to compare the total amount of sugar extracted from your grain to the max amount of sugar possible to extract as dictated by the malt analysis sheet. This way, there's no need to correct for changes in volume throughout the process. It seems like this is the point of using PKL, but PKL is still a unit based on SG, not total sugar quantity.

Let's use the brew I just finished as an example. My malt bill consisted of 3 grains:
Pale ale malt - 1.5kg - 80%FGDB
Rolled oats - 0.4kg - 70%FGDB
Aromatic Munich malt - 0.1kg - 77%FGDB

Using the PKL of sucrose (384) and my mash volume (8L) gives us the PKL values for these grains:
Pale ale - 307
Rolled oats - 269
Aromatic - 296

And, I can determine the PKL of my actual brew: [OG (1.047) * volume in fermenter (8.5L)] / 2kg = 200 PKL

So, how am I supposed to compare these values to determine brewhouse efficiency? Do I multiply each grain's PKL value by its percentage of the total grain bill, then sum those values to get a total theoretical PKL to divide my actual PKL by? And why, when talking about efficiency, do we use SG and not a measure of total sugar?

 

[Gnomebrewer]

There are several questions in there. I'll try my best to answer them!
Firstly, your instinct for calculating efficiency is absolutely correct - total amount of sugar extracted divided by the maximum amount possible from the grains. Whether you calculate it as pre-boil or post-boil is irrelevant (both should be the same). Efficiency into the fermenter will be a bit lower, because you'll typically lose some wort between the kettle and the fermenter.

Second: Not many brewers on here use PKL. Most are 'merican, so tend to be metric impaired (but there are some, particularly those working in science, who use metric). PPG is far more common.

How you are calculating things will work (you need to multiply each grains PKL by its mass to work out the points contribution). However, you are doing more steps than needed. It's quicker and easier to just work in points.
Available points = Points from Pale Ale + Points from Rolled Oats + Points from Aromatic
= 307x1.5 + 269x0.4 + 296x0.1
= 460.5 + 107.6 + 29.6
= 597.7
Actual points = 47 x 8.5
= 399.5
Efficiency = Actual Points / Available Points x 100%
= 399.5/597.7 x 100%
= 67%

Hope this makes sense!

 

[doug293cz]

The reason we don't work directly with amounts of sugar, is that there is no simple way to measure sugar directly. Instead we measure SG which has been correlated to sugar concentration (first by Balling, then by Brix, and then Plato.) SG times volume then gives you amount of sugar. SG is almost linear with sugar concentration, but not exactly. You can fairly rigorously calculate the actual sugar amount using empirically fit equations that correlate SG to sugar concentration (taking into account the non-linearities), but it's much easier to use the points method that assumes linearity of SG vs. sugar concentration.

Brew on

 

[VikeMan]

So, how am I supposed to compare these values to determine brewhouse efficiency? Do I multiply each grain's PKL value by its percentage of the total grain bill, then sum those values to get a total theoretical PKL to divide my actual PKL by? And why, when talking about efficiency, do we use SG and not a measure of total sugar?

There's a presentation on Mash Efficiency and Brewhouse Efficiency at this link that might help reinforce how they are computed and why.

http://sonsofalchemy.org/library/

 

[joshbmace]

Thanks for the replies, everyone! Gnome and doug282cz both hit what I was looking for - SG*Vol is an approximation of "total sugar" that I can use to calculate efficiency, and I don't even need to use my mash volume to figure out theoretical yield because multiplying my grains' PKL values by their weight results in the same unit: SG*L that can be compared to my actual wort.

 

[Birrofilo]

Interesting discussion, but what does FGDB mean?

EDIT.
Found: Dry Basis Fine Grind (DBFG): Measures the theoretical maximum sugars and dextrins that can be extracted from a dried, finely ground malt, expressed as a percentage of the total (dried) malt weight. Example: a DBFG value of 80% means that a maximum of 80% of the weight of the (dried) malt can be extracted as sugars and dextrins.

This raises another question: when the potential of a fermentable is given as, let's say, 1,046 pound per gallon, or 46 points, are those points the theoretical maximum, or is the theoretical maximum given by 46 points * DBFG?

I suspect the 46 number is the "definitive" one for the brewer. We don't need the DBFG data to know the theoretical sugar yield, and determine our mashing efficiency, if we know the potential. Is that right?

PS Made my first AG brew yesterday. Lots of new things to learn...

 

[doug293cz]

Interesting discussion, but what does FGDB mean?

Fine Grind, Dry Basis. It is basically the maximum percentage of extract that can be created from a grain. To use it you have to correct the "as is" (measured) grain weight by the moisture content. If the moisture content is 4%, then the dry weight is equal to 0.96 times the "as is" weight.

Brew on

 

[doug293cz]

Thanks for the replies, everyone! Gnome and doug282cz both hit what I was looking for - SG*Vol is an approximation of "total sugar" that I can use to calculate efficiency, and I don't even need to use my mash volume to figure out theoretical yield because multiplying my grains' PKL values by their weight results in the same unit: SG*L that can be compared to my actual wort.

One thing you need to remember is that using points requires that you work with wort volume, not strike water volume. Wort volume is what you naturally measure in your BK and fermenter, so the point method works well for mash efficiency and brewhouse efficiency.

You can't easily use the point method to determine conversion efficiency or lauter efficiency (mash efficiency = conversion efficiency * lauter efficiency. In order to use points for those, you would have to know the volume of wort in the MLT, not the volume of strike water you started with. Calculating wort volume in the MLT requires calculations using water weight, grain weight, and grain potential.

Brew on

 

[doug293cz]

Interesting discussion, but what does FGDB mean?

EDIT.
Found: Dry Basis Fine Grind (DBFG): Measures the theoretical maximum sugars and dextrins that can be extracted from a dried, finely ground malt, expressed as a percentage of the total (dried) malt weight. Example: a DBFG value of 80% means that a maximum of 80% of the weight of the (dried) malt can be extracted as sugars and dextrins.

This raises another question: when the potential of a fermentable is given as, let's say, 1,046 pound per gallon, or 46 points, are those points the theoretical maximum, or is the theoretical maximum given by 46 points * DBFG?

I suspect the 46 number is the "definitive" one for the brewer. We don't need the DBFG data to know the theoretical sugar yield, and determine our mashing efficiency, if we know the potential. Is that right?

PS Made my first AG brew yesterday. Lots of new things to learn...

The only thing that has a potential of 1.046 is pure sugar. All grains have lower potential than that. Base grains are usually in the 1.036 to 1.038 range. Specialty grains come in below those potentials.

To determine potential in SG form given % DBFG, use the following formula:

SG potential = 1 + 0.04617 * DBFG​

​

Sugar (sucrose) has a DBFG of 100%, and if you mix 1 lb of sugar with enough water (0.926 gal) to make one gallon of solution, it will have an SG of 1.04617.

Brew on

 

[Birrofilo]

Sugar (sucrose) has a DBFG of 100%, and if you mix 1 lb of sugar with enough water (0.926 gal) to make one gallon of solution, it will have an SG of 1.04617.

Very interesting, and from what I get from the underlined part, when PPG is used the "gallon" is the total volume, not the volume of water.

So if a fermentable has a potential of 36 points per pound per gallon, that's not one pound of fermentable in a gallon of water, but one pound of fermentable added to water for a total volume of one gallon.

I was always puzzled about whether the volume of the fermentable was included or excluded in the PPG potential.

EDIT I see you also state it in #9 when you talk about "wort volume" and "strike volume".

 

[doug293cz]

Very interesting, and from what I get from the underlined part, when PPG is used the "gallon" is the total volume, not the volume of water.

So if a fermentable has a potential of 36 points per pound per gallon, that's not one pound of fermentable in a gallon of water, but one pound of fermentable added to water for a total volume of one gallon.

I was always puzzled about whether the volume of the fermentable was included or excluded in the PPG potential.

EDIT I see you also state it in #9 when you talk about "wort volume" and "strike volume".

Correct. The definition is often misunderstood. Volumes are wort volumes, not strike (or other water volumes.)

Brew on