s ci e n c e
alcohol
determination is underpinned by a theory pertaining to fermentation and alcohol production, chemical mass
ABWt =
balance relationships of fermentation and, Carl Balling’s original theoretical work in brewing science. This topic has been covered elsewhere (Spedding, 2013, 2016 and
(OE − RE ) (2.0665) − (1.0665 × OE / 100)
references contained therein). To keep this present article as brief as possible only the details of the calculations
Where: ABWt is the percentage alcohol by weight (as
needed by the brewer to obtain key data are presented.
w/w, grams of alcohol per 100 grams of beer), OE, original
For brewers to be able to determine both the alcohol
extract and RE the real or present extract in degrees Plato. It
by weight and by volume for beer the following values
is assumed that the brewer is familiar with or will familiarize
must be known or obtained; the present or apparent
themselves with all these brewing terms.
gravity of the beer, the real extract of the beer and the original extract of the wort. To help solve for these various
The original extract of wort is the amount of material
terms an arithmetical relationship exists between them as
extracted from the mash and is measured in grams of
attributed to Carl Balling. The relationship which is known
extract per 100 grams of wort. The brewer will determine
as Ballings’s formula is:
the original extract by measuring the specific gravity of
OE % P =
( A% mass x 2.0665 + RE ) x 100 ( A% mass x 1.0665 + 100) (1)
the wort and will relate this to the established sucrose (= extract) tables (in grams per 100 grams) to report the original extract content in degrees Plato. Or more simply they will determine the OE using a Plato hydrometer. For the brewer limited to the use of a hydrometer, real extract (RE) can be approximated using the OE (of the
Where: OE is original extract (Plato; g/100g or mass/mass),
original wort) and AE (apparent extract of the final and
A% mass is alcohol by weight, RE is the real extract and
degassed beer) and by using another empirical equation
the numbers in the numerator and denominator are as
recently revised but based on Balling’s work:
described below. The above formula (equation 1) is based on an understanding of the mass balance relationship in
RE = (0.1948 × OE ) + (0.8052 × AE )
brewing – simply the chemical relationship dealing with
Where: AE = apparent extract – that extract value
the conversion of fermentable sugars to alcohol, carbon
determined when alcohol is present. This is the value for
dioxide and yeast biomass. Theoretically, 1 gram of
gravity obtained by the brewer on the final attenuated beer.
fermentable sugar will yield 0.51 gram of ethanol and 0.49 gram of carbon dioxide. In fact, some sugar is needed for
The real extract (RE) assessment here will always be
cell growth and so, more realistically, the ethanol yield
an estimate for reasons discussed elsewhere (Spedding,
is more likely 0.46 gram, and carbon dioxide 0.44 gram
2016). Using equation 3, the brewer will find satisfactory
from 1 g sugar. Or more simply put: 2.0665 g sugar yields
answers to RE values compared to those obtained from
1 g ethanol, 0.9565 g CO2 and 0.11 g yeast and - for the
official instrumentation over the typical ranges of OE, real
equations below: 0.9565g and 0.11g sum to 1.0665g which
degree of fermentation (RDF), and alcohol for most beers
is the extract not converted to alcohol.
(see Spedding, 2013 and 2016 for a fuller discussion on
An application of Balling’s formula and a minimum
limitations to the above approaches). Errors in evaluations
number of analytical measurements allows the brewer,
between official and less accurate methods are typically
without the full range of sophisticated instruments
quite small but are not considered further here. Operators
to obtain some quite accurate values for alcohol and
should be aware of accuracy and precision for all
extract using a series of approximate beer calculations. In
methods and instruments used.
simplifying the discussion, it is known, from above that a
Getting back to the use of Plato values - by
quite accurate estimate of alcohol content can be derived
substitution in the above formula (Eq. 3), it is possible to
by subtracting, from the original extract (OE), the final or
solve for the alcohol by weight without directly inputting a
present extract gravity (PG) as “real extract” (RE – not the
calculated or determined RE value:
apparent extract, AE), assuming no process dilution, and by applying conversion factors which infer the alcohol content from the drop in the wort gravity occurring during fermentation. Using an equation, deriving from Balling’s
ABWt =
0.8052 × (OE − AE ) (2.0665) − (1.0665 × OE /100)
formula noted above, alcohol weight can be calculated:
76
September~October 2017
The Brewers Journal