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Refractometer FG Results

Last time I wrote about refractometry in brewing, I had developed a correlation for determining FGs from refractometer readings that, in my own brewing, seemed to be an improvement on the correlation used in (to the best of my knowledge) all contemporary brewing software, spreadsheets, etc. A total of eight brewer-instrument pairs contributed additional data for analysis: six volunteers in addition to myself, using both my own instruments and those at the brewery. The data submitted included four beers with very low attenuations, which I’m somewhat arbitrarily defining as anything below 50% RDF (61% ADF). Neither the old nor new correlations gave results even close to the measured FG values. I attempted to incorporate these beers into the correlation, but was unable to maintain accuracy for more typical worts while doing so. Removing those beers from the data results in 68 independent triplets, which were used to compare the standard refractometer correlation to two curves fit using the same twelve data points as before. First, a simplified cubic:

FG = 1.0000 – 0.0044993*RIi + 0.011774*RIf + 0.00027581*RIi² – 0.0012717*RIf² – 0.0000072800*RIi³ + 0.000063293*RIf³

And a linear polynomial:

FG = 1.0000 – 0.00085683*RIi + 0.0034941*RIf

A statistical analysis of the results makes it clear just how inadequate the original correlation was: it consistently under-estimates the FG, albeit not as much as in my own brewing. I assume that’s due to the average attenuation in the complete data set (62% RDF) being closer to the typical values assumed by the old correlation, as I noted in my first post on the subject. It is also noticeably less precise than even the relatively poor “triple scale” hydrometers used by most home brewers, let alone one designed for FG readings. Interestingly, the linear correlation is more accurate than the cubic, albeit slightly less precise. Both compare favorably to a consumer-grade hydrometer – which with perfect use could potentially be read to ±0.0005 SG.

I find it a little easier to understand when the data are presented graphically:

So it seems that – with the exception of very low-attenuating worts – either of the new correlations can provide accuracy and precision on par with the consumer-grade hydrometers typically used by home brewers. In a situation where a new correlation was being substituted for the old one, the cubic fit may be preferable since it only requires the coefficients to be altered. Otherwise, in my opinion, the linear fit provides wholly acceptable results. As always, though, your mileage may vary. In situations where the FG needs to be known precisely, testing with a properly calibrated precision hydrometer remains the best option.

I’ve updated my FG prediction spreadsheet to version 3.0, which, in addition to the two new correlations, incorporates a more accurate Brix-to-OG conversion, and reverts the default “wort correction factor” to 1.04, which would seem to be more typical for the overall data set. Download links are below.

Finally, I’d like to thank Dave, Enid, Gustav, James, Kai, and Scott for recording and sharing their data.
Update: 06 Jan 2012

I’ve (finally) written a PHP version of the basic FG calculation, so that people can use it without downloading the spreadsheet.
Spreadsheet download:
fg_calculator_v3.0.ods | fg_calculator_v3.0.xls

65 comments to Refractometer FG Results

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