## Tuesday, February 5, 2013

### Refractometer Corrections for Alcohol

Recently I purchased a refractometer for measuring the gravity of test worts.  Without a refractometer the test worts needed to be fairly large.  With a one gallon fermentation vessel a large enough sample can be pulled without picking up the trub at the bottom of the fermentor.  A smaller size fermentation could be trouble.  Now with a refractometer only a few drops are needed so test worts can be just a few milliliters.

A hydrometer is great at measuring density, and a refractometer is great at measuring refraction index, but neither the refractometer or the hydrometer are great at measuring alcohol in a finished beer.  To use either of them assumptions must be made about the amount of alcohol produced by the sugar.  The most famous of these relations is the Balling observation.  In a post later I'll go over the details.

Even when correcting for alcohol (like in the equation below) there is still more error with a refractometer than a hydrometer, but I don't see this as a large problem.  The extra error is introduced because the scale is effectively smaller due to the alcohol compensation.  With a hydrometer fermentation may go from 20°P (1.083) down to 4°P (1.016).  However with a refractometer the same fermentation will start at 20°P but end at 10.5°P.  The 16°P change is effectively condensed to a 9.5°P change.
The main goal would be to determine if the beer has reached terminal gravity, which is indicated by equal coincident readings, not absolute gravity.  Being able to take a reading by pulling out the air lock and taking a small sample with a pipette is attractive.  It means no more messing with the lid to take a gravity reading.

There are a couple of ways that the ABV and percent sugar equations can be derived for use with a refractometer.  The first, and a common method of the online calculators is to measure with a hydrometer, and then measure with a refractometer and design an equation to fit the data.  A second method is to use analytical chemistry to formulate the equation.

It looks like this equation will produce the same results as some of the popular calculators:

OG = original gravity in Brix
CG = current gravity reading in Brix
SG = current gravity in specific gravity

SG =0.00628*CG-0.0025*OG+1.0013

converting to percent sugar by weight, or degrees Plato:

P = 1.57*CG-0.625*OG+0.325

(1) http://www.primetab.com/formulas.html