Gravity, in the context of fermenting alcoholic beverages, refers to the specific gravity,
or relative density compared to water, of the wort or must at various stages in the
fermentation. The concept is used in brewing and wine making industry. Specific gravity
is measured by a hydrometer, refractometer, pycnometer or oscillating U-tube electronic
meter. The density of a wort is largely dependent
on the sugar content of the wort. During alcohol fermentation, yeast converts sugars into carbon
dioxide and alcohol. The decline in the sugar content and the presence of ethanol drop the
density of the wort. The percentage of alcohol can be calculated from the difference between
the original gravity of the wort and the current specific gravity of wort. By monitoring the
decline in SG over time the brewer obtains information about the health and progress
of the fermentation and determines that it is complete when gravity stops declining.
If the fermentation is finished, the specific gravity is called the final gravity. For example,
for a typical strength beer, OG could be 1.050 and FG could be 1.010.
Several different scales have been used for measuring the original gravity. For historical
reasons, the brewing industry largely uses the Plato scale, which is essentially the
same as the Brix scale used by the wine industry. For example, OG 1.050 is roughly equivalent
to 12°P. By considering the original gravity, the brewer
or vintner obtains an indication as to the probable ultimate alcoholic content of his
product. The OE is often referred to as the "size" of the beer and is, in Europe, often
printed on the label as Stammwürze or sometimes just as a percent. In the Czech Republic,
for example, they speak of "10 degree beers", "12 degree beers" which refers to the gravity
in Plato of the wort before the fermentation.
Terms related to gravity Specific gravity
Specific gravity is the ratio of the density of a sample to the density of water. The ratio
depends on the temperature and pressure of both the sample and water. The pressure is
always considered to be 1 atmosphere and the temperature is usually 20 °C for both sample
and water but in some parts of the world different temperatures may be used and there are hydrometers
sold calibrated to, for example, 60 °F. It is important, where any conversion to °P
is involved, that the proper pair of temperatures be used for the conversion table or formula
being employed. The current ASBC table is meaning that the density is measured at 20 °C
and referenced to the density of water at 20 °C. Mathematically
This formula gives the true specific gravity i.e. based on densities. Brewers cannot measure
density directly and so must use a hydrometer, whose stem is bathed in air, or pycnometer
weighings which are also done in air. Hydrometer readings and the ratio of pycnometer weights
are influenced by air and are called "apparent" readings. True readings are easily obtained
from apparent readings by
However, the ASBC table uses apparent specific gravities, so many electronic density meters
will produce the correct °P numbers automatically. Original Gravity; Original Extract
The Original Gravity is the specific gravity measured before fermentation. From it the
analyst can compute the Original Extract which is the mass of sugar in 100 grams of wort
by use of the Plato scale. The symbol will denote OE in the formulas which follow.
Final Gravity; Apparent Extract The Final Gravity is the specific gravity
measured at the completion of fermentation. The Apparent Extract, denoted , is the °P
obtained by inserting the FG into the formulas or tables in the Plato article. The use of
"apparent" here is not to be confused with the use of that term to describe specific
gravity readings which have not been corrected for the effects of air.
True extract The amount of extract which was not converted
to yeast biomass, carbon dioxide or ethanol can be estimated by removing the alcohol from
beer which has been degassed and clarified by filtration or other means. This is often
done a part of a distillation in which the alcohol is collected for quantitative analysis
but can also be done by evaporation in a water bath. If the residue is made back up to the
original volume of beer which was subject to the evaporation process, the specific gravity
of that reconstituted beer measured and converted to Plato using the tables and formulas in
the Plato article then the TE is
See the Plato article for details. TE is denoted by the symbol . This is the number of grams
of extract remaining in 100 grams of beer at the completion of fermentation.
Alcohol content Knowing the amount of extract in 100 grams
of wort before fermentation and the number of grams of extract in 100 grams of beer
at its completion, the amount alcohol formed during the fermentation can be determined.
The formula follows, attributed to Balling
where ,gives the number of grams of alcohol per 100 grams of beer i.e. the ABW. Note
that the alcohol content depends not only on the diminution of extract but also on the
multiplicative factor which depends on the OE. De Clerck tabulated Ballings values for
but they can be calculated simply from p
This formula is fine for those who wish to go to the trouble to compute TE which is only
a small fraction of brewers. Others want a simpler, quicker route to determining alcoholic
strength. This lies in Tabarie's Principle which states that the depression of specific
gravity in beer to which ethanol is added is the same as the depression of water to
which an equal amount of alcohol has been added. Use of Tabarie's principle lets us
calculate the true extract of a beer with apparent extract as
where is a function that converts SG to °P and its inverse and is the density of an aqueous
ethanol solution of strength by weight at 20 °C. Inserting this into the alcohol formula
the result, after rearrangement, is
Which can be solved, albeit iteratively, for as a function of OE and AE. It is again possible
to come up with a relationship of the form
De Clerk also tabulates values for . Most brewers and consumers are used to having
alcohol content reported by volume rather than weight. Interconversion is simple but
the specific gravity of the beer must be known:
This is the number of cc of ethanol in 100 cc of beer.
Because ABV depends on multiplicative factors as well as the difference between OE and AE
it is impossible to come up with a formula of the form
where is a simple constant. Because of the near linear relationship between extract and
in particular because the ABV formula is written as
If the value given above for corresponds to an OE of 12°P which is 0.4187, and 1.010
can be taken as a typical FG then this simplifies to
With typical values of 1.050 and 1.010 for, respectively, OG and FG this simplified formula
gives an ABV of 5.31% as opposed to 5.23% for the more accurate formula. Formulas for
alcohol similar to this last simple one abound in the brewing literature and are very popular
among home brewers. Formulas such as this one make it possible to mark hydrometers with
"potential alcohol" scales based on the assumption that the FG will be close to 1 which is more
likely to be the case in wine making than in brewing and it is to vintners that these
are usually sold. Attenuation
The drop in extract during the fermentation divided by the OE represents the percentage
of sugar which has been consumed. The Real Degree of Attenuation is based on TE
and the Apparent Degree of Fermentation is based on AE
Because of the near linear relationship between and °P specific gravities can be used in
the ADF formula as shown. Brewer's points
Many brewers like to exploit the near linear relationship between and °P to simplify calculations
considerably. They define ,
call it "points" or "brewer's points" or "excess gravity" and use it as if it were extract.
The Plato degree is thus approximately the points divided by 4:
As an example, a wort of SG 1.050 would be said to have 1000(1.050-1)=50 points, and
have Plato degree of approximately 50/4=12.5 °P.
Points can be used in the ADF and RDF formulas. Thus a beer with OG 1.050 which fermented
to 1.010 would be said to have attenuated 100*(50 - 10)/50 = 80%. Points can also be
used in the SG versions of the alcohol formulas. It is simply necessary to multiply by 1000
as points are 1000 times. Software tools are available to brewers to
convert between the various units of measurement and to adjust mash ingredients and schedules
to meed target values. The resulting data can be exchanged via BeerXML to other brewers
to facilitate accurate replication. See also
Plato scale Gravity
References