joshbuhl
Active Member
I‘ve published an article in the Journal of the American Society of Brewing Chemists on the equations that relate Extract to Specific Gravity.
Both a review of the equations historically used for this relation as well as the derivation of new, more accurate equations are given in the article. Several heretofore unknown correlations amongst the historical equations and their connection to the so-called partial specific volumes of sucrose and water in solution are shown.
Below are links to the official published version, a pre-print version that can be accessed for free, and also a TL;DR summary of the main useful result for brewers.
The official, reviewed and published version can be found here: https://doi.org/10.1080/03610470.2023.2267947
You can access a free pre-print of the AOM (Author‘s Original Manuscript) here: OSF
(TL;DR)
========
If you want to calculate Extract from specific gravity measured at 20°C, then you should use the following equation:
E(°P) = 260.4 -260.4/SG
which will give you the extract value in degrees Plato(°P) as found in the ASBC tables on Wort, Beer and Brewing Sugars corresponding to a Specific Gravity value measured at 20°C with a mean absolute error of less than 0.0198°P and a maximal error of only 0.05°P.
The Rule-of-thumb conversion which we all know as „gravity points divided by four“, which mathematically is
E(°P)= 1000*(SG-1)/4 = 250*SG -250,
is simply a linear approximation to the correct conversion equation, and although not really simpler than the equation I recommend above (and derive from physical principles in the article) is much less accurate, especially above SG = 1.040.
Both a review of the equations historically used for this relation as well as the derivation of new, more accurate equations are given in the article. Several heretofore unknown correlations amongst the historical equations and their connection to the so-called partial specific volumes of sucrose and water in solution are shown.
Below are links to the official published version, a pre-print version that can be accessed for free, and also a TL;DR summary of the main useful result for brewers.
The official, reviewed and published version can be found here: https://doi.org/10.1080/03610470.2023.2267947
You can access a free pre-print of the AOM (Author‘s Original Manuscript) here: OSF
(TL;DR)
========
If you want to calculate Extract from specific gravity measured at 20°C, then you should use the following equation:
E(°P) = 260.4 -260.4/SG
which will give you the extract value in degrees Plato(°P) as found in the ASBC tables on Wort, Beer and Brewing Sugars corresponding to a Specific Gravity value measured at 20°C with a mean absolute error of less than 0.0198°P and a maximal error of only 0.05°P.
The Rule-of-thumb conversion which we all know as „gravity points divided by four“, which mathematically is
E(°P)= 1000*(SG-1)/4 = 250*SG -250,
is simply a linear approximation to the correct conversion equation, and although not really simpler than the equation I recommend above (and derive from physical principles in the article) is much less accurate, especially above SG = 1.040.
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