From the HBD Archive
From: Louis Bonham <lkbonham@phoenix.net>
Subject: Alcohol determination by refractometry [long]
Date: 1999-01-07 20:26:03 GMT

Hi folks:

[Warning: hard-core beer geek information follows. <g>]

Many of us use a refractometer to assay the gravity of wort during the mash or
before fermentation starts. Once fermentation begins, however, the alcohol in
the wort/beer skews the reading because it has a different refractive index than
water; i.e., it causes light to bend more than water. As a result, a beer that
actually has a specific gravity of, say, 1.010 (as measured by a hydrometer,
pycnometer, digital density meter, etc.) might read as 5.5 degrees Brix (SG
1.022) on a refractometer. Because of this significant discrepancy, the
conventional wisdom has been that refractometers are useless once fermentation
starts. (I plead guilty to being one of the parties promulgating this.)

In fact, the difference between the actual specific gravity and the "apparent"
gravity as measured by a refractometer has long been used as a method of
determining the alcohol content of beer. Indeed, DeClerck notes that the SG +
refractometer method he describes was adopted as the official method of
assessing alcohol content in Germany on the 1930's. The problem, however, in
using the formulas such as the Berglund, Emlington, and Rassmussen regression
equasion cited by DeClerck is that they typically call for refractometer
measurements of the beer in Refractometer Scale Units (a/k/a Zeiss Units), which
was the scale used on the old immersion refractometers. (Most refractometers
used today measure in terms of Refractive Index readings ("RI"), or in degrees
Brix (% sugar; essentially equal to degrees Plato) . The relationship between
Zeiss Units and RI is polynomial -- IOW, there's not a simple conversion factor
between the two.)

In doing the labwork for the HBD Palexperiment, I researched these conversion
issues, and have derived a formula that appears usable by most homebrewers with
a refractometer, a good narrow scale hydrometer (or pycnometer + milligram
balance, or other exotic SG measurement device), and some basic tables. As you
will see, there is a bit more to be done to make it more user friendly, but I
submit it to the HBD collective for use, comment, and revision.

To determine alcohol content, take a sample of the beer (100 mls or whatever
amount you typically use for gravity determination). Degas the sample (shake it
in a flask, use a blender on low, etc.). Warm/chill the sample to 20C, and
determine its specific gravity at this temperature. Now put a drop of this
degassed, 20C sample in your refractometer and note the measurement. Record
your refractometer reading in terms of the refractive index ("RI") of the sample
- --if your refractometer reads in degrees Brix, you'll need to use a conversion
table such as found in the CRC Handbook (look for a table showing the "Index of
Refraction of Aqueous Solutions of Sucrose") to convert degrees Brix (percent
sugar) to RI. [At present, I have been unable to find a formula that provides
this conversion. If anyone knows of one, lemme know and I'll revise the
formula.]

Using this data (SG and RI of the sample at 20C), calculate the alcohol by
weight (A) of the sample as follows:

A = 1017.5596 - (277.4 x SG) + RI ((937.8135 x RI) + 1805.1228)

While you're at it, you can use this data to calculate your Real Extract (RE):

RE = 194.5935 + (129.8 x SG) + RI ((410.8815 x RI) - 790.8732)

(These formulas were derived from those contained in DeClerck and others from a
1980 ASBC Journal article by K.J. Siebert, and have been checked against
examples given in those articles as well as in the ASBC Methods of Analysis.)

Example: SG 1.0104, Refractometer reads 5.5 Brix.
According the the CRC Table, 5.5 Brix = 1.3411 RI

And thus:

A = 1017.5596 - 277.4(1.0104) + 1.3411(937.8135(1.3411) + 1805.1228)

A= 1017.5596 -280.2850 - 734.1465 = 3.1281 ==> 3.1%

RE = 194.5935 + 129.8 (1.0104) + 1.3411(410.8815(1.341) - 790.8732)

RE = 194.5935 + 131.1400 - 321.6806 = 4.0529 ==> 4.1%

If you want percentage alcohol by volume, you'll need to use the ASBC conversion
tables (again, if anyone knows the formula to convert alcohol by weight to
alcohol by volume, lemme know).

Caveats: While this basic procedure is approved by the ASBC, the official ASBC
method uses a different formula that includes a factor derived from
experimentally-derived calibration curves for each type of beer, because factors
like ash content, color, etc., can marginally affect the results. Of course, if
you need to really need to know your alcohol content to the nearest 0.01%, then
such methods are necessary (indeed, you're probably better off just using the
approved distillation or GC methods). Further, while these formulas give
results of within 0.1 of the values given in the textbook examples in the
references cited above, my derivation of them has been purely on paper -- I did
not derive them by any sort of independently researched empirical data.

Additionally, remember that garbage in = garbage out. This method works *only*
if you take accurate gravity and refractometer readings, and errors in either
will dramatically skew the results. (For instance, in the example above, if the
gravity reading was misread as a 1 point higher, the resultant alcohol content
would be about 0.3% lower (i.e., 2.8% alcohol rather than 3.1%). So use
calibrated instruments and know that the temperature issues are important.
Nevertheless, with good instruments and some care, I suspect that most of us can
use this method to get reasonably accurate results.

Try it out and lemme know if it works for you. Of course, if there are errors
in this, lemme know.

Louis K. Bonham

PS -- using a similar formula, it is also possible to track your gravity
throughout a fermentation using only a refractometer (i.e., if you have an
accurate OG reading to start with, you can calculate your actual SG from a
refractometer reading and the OG figure -- IOW, you'd need only a few drops of
beer to check the gravity, rather than a hydrometer sample). But that is
another story . . . . . .



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