Gravity (alcoholic beverage) Information & Gravity (alcoholic beverage) Links at HealthHaven.com

A floating hydrometer in use to test the specific gravity of beer.

[edit] Gravity in Brewing and Winemaking

Gravity, in the context of fermenting alcoholic beverages, refers to the specific gravity of the wort or must at various stages in the fermentation. In the following we will emphasize the brewing industry. Practices in the wine making industry are similar.

Initially (before alcohol production by the yeast commences) the specific gravity of a wort is dependent mostly on the amount of sugar present and,therefore, specific gravity readings can be used to determine sugar content by the use of formulae or tables (see article Plato). This sugar content is expressed in units of grams of sugar per 100 grams of wort equivalent to % w/w and called, in the brewing industry, "degrees Plato" (abbreviated °P) and in the wine industry "degrees Brix". Even when specified in terms of °P it is not uncommon to refer to the pre-fermentation reading as the "Original Gravity", (abbreviated OG) though it is more correct to term it the "Original Extract" (abbreviated OE). It is, of course, correct to refer to the original specific gravity reading as the OG. By considering the original sugar content 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" and so on.

As fermentation progresses the yeast convert sugars to carbon dioxide, ethanol, more yeast and flavor producing compounds. The decline in the sugar content and the presence of ethanol (which is appreciably less dense than water) both contribute to a lowering in the specific gravity of the wort so that the formulae relating sugar content and specific gravity no longer apply. Nevertheless, 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. A gravity measurement taken at this time compared to the original gravity reading can be used to estimate the amount of sugar consumed and thus the amount of ethanol produced. Specific gravity is measured by a hydrometer, pycnometer or oscillating U-tube electronic meter.

Gravity (specific gravity) measurements are used to determine the "size" of the beer, its alcoholic strength and how much of the available sugar the yeast were able to consume (a given strain can be expected, under proper conditions, to ferment a wort of a particular composition to within a range of attenuation, that is, they should be able to consume a known percentage of the extract).

[edit] Terms related to gravity

Brewers calculate a range of parameters from specific gravity measurements. They are summarized here. We begin with the definition of specific gravity itself

[edit] 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 sample and water. The pressure is always considered (in brewing) to be 1 atmosphere (1013.25 hPa) 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 (20°C/20°C) meaning that the density is measured at 20°C and referenced to the density of water at 20°C (0.998203 g/cc). Mathematically

$SG_{true} = {\rho_{sample} \over \rho_{water}}$

This formula gives the true specific gravity i.e. based on densities. Brewers cannot (unless using a U-tube meter) 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 (see article Specific Gravity for details) and are called "apparent" readings. True readings are easily obtained from apparent readings by

$SG_{true} = SG_{apparent} - {\rho_{air} \over \rho_{water} }(SG_{apparent}-1)$

but as the ASBC table uses apparent specific gravities, electronic density meters have all the math built in and will automatically produce the correct °P numbers and the differences are in the fourth decimal place and beyond this is not something that needs to be worried about in most cases.

[edit] Original Gravity (OG); Original Extract OE)

The OG is the specific gravity measured before the commencement of fermentation. From it the analyst can compute the OE which is the number of grams of sugar in 100 grams of wort (°P) by use of the formulas or table discussed in the Plato article. For OE we will use the symbol $p$ in the formulas which follow.

[edit] Final Gravity (FG); Apparent Extract (AE)

The FG is the specific gravity measured at the completion of fermentation. AE 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. We symbolize AE by $m$

[edit] True Extract (TE)

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

$n = P_{recon}{SG_{recon} \over SG_{beer}}$

See the Plato article for details. We denote TE by the symbol $n$ . This is the number of grams of extract remaining in 100 grams of beer at the completion of fermentation.

[edit] 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, we should be able to determine how many grams of alcohol were formed during the fermentation. This is indeed the case and the formula, attributed to Balling^[1]

$A_w = {(p - n) \over (2.0665 - 1.0665p/100)} = f_{pn}(p - n)$

where $f_{pn} = {1 \over (2.0665 - 1.0665p/100) }$ ,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 $(p - n)$ but also on the multiplicative factor $f p n$ which depends on the OE. De Clerck^[2] tabulated Ballings values for $f p n$ but they can be calculated simply from p

$f_{pn} = {1 \over (2.0665 - 1.0665p/100)} = 0.48394 + 0.0024688p + 0.00001561p^2$

This formula is fine for those who wish to go to the trouble to compute TE (whose real value lies in determining attenuation) which is only a small fraction of brewers. Others want a simpler, quicker route to determining alcoholic strength. This lies in Tabarie's Principal^[3] 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 (on a w/w basis) has been added. Use of Tabarie's principal lets us calculate the true extract of a beer with apparent extract $m$ as

$n =P(P^{-1}(m) + 1 - \frac {\rho_{EtOH}(A_w)} { \rho_{water}})$

where $P$ is a function that converts SG to °P (see Plato) and $P - 1$ (see Plato) its inverse and $ρ E t O H (A w)$ is the density of an aqueous ethanol solution of strength $A w$ by weight at 20 °C. Inserting this into the alcohol formula we get, after rearrangement

${[p - P(P^{-1}(m) + 1 - \frac {\rho_{EtOH}(A_w)} { \rho_{water}})] \over (2.0665 - 1.0665p/100)} - A_w = 0$

Which can be solved, albeit iteratively, for $A w$ as a function of OE and AE. It is again possible to come up with a relationship of the form

A w = f p m (p - m)

De Clerk also tabulates values for $f p m = 0.39661 + 0.001709 p + 0.000010788 p 2$ .

Most brewers and consumers are used to having alcohol content reported by volume (ABV) rather than weight. Interconversion is simple but the specific gravity of the beer must be known:

$A_v = A_w{SG_{beer} \over 0.79661}$

This is the number of cc of ethanol in 100 cc of beer.

Because ABV depends on multiplicative factors (one of which depends on the original extract and one on the final) as well as the difference between OE and AE it is impossible to come up with a formula of the form

A v = k (p - m)

where $k$ is a simple constant. Because of the near linear relationship between extract and (SG-1) (see specific gravity) in particular because $p \approx 1000(SG-1)/4$ we can write the ABV formula as

$A_v = 250f_{pm}(OG -FG){SG_{beer} \over 0.79661}$

If we use the value for $f p m$ corresponding to an OE of 12°P which is 0.4187, and chose 1.010 as a typical FG then this simplifies to

A v = 132.715(O G - F G) = (O G - F G) / 0.00753

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 0 which is more likely to be the case in wine making than in brewing and it is to vintners that these are usually sold.

[edit] 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 (RDF) is based on TE

$RDF = 100 {(p-n)\over p}$

and the Apparent Degree of Fermentation (ADF) is based on AE

$ADF = 100 {(p-m) \over p} \approx 100 {(OG-FG) \over (OG-1)}$

Because of the near linear relationship between (SG-1) and °P specific gravities can be used in the ADF formula as shown.

[edit] Brewer's Points

Many brewers like to exploit the near linear relationship between (SG -1) and °P to simplify calculations considerably. They define

$p t = 1000(S G - 1)$ , call it "points" or "brewer's points" or "excess gravity" and use it as if it were extract. As an example, a wort of SG 1.050 would be said to have 50 points. 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 (SG-1).

[edit] See also

Beer portal

Wine portal

[edit] References

^ De Clerck,J. A textbook of Brewing,Translated by Kathleen Barton-Wright, Chapman & Hall,, London 1958 Vol. II p427
^ De Clerck, op. cit, Vol. II p428
^ De Clerck, op. cit, Vol. II p428

[0] De Clerck,J. A textbook of Brewing,Translated by Kathleen Barton-Wright, Chapman & Hall,, London 1958 Vol. II p427

[1] De Clerck, op. cit, Vol. II p428

[2] De Clerck, op. cit, Vol. II p428

[1]

[2]

[3]

Contents