Gravity (alcoholic beverage)

Gravity, in the ambience of crumbling alcoholic beverages, refers to the specific gravity, or about body compared to water, of the wort or accept to at assorted stages in the fermentation. The abstraction is acclimated in brewing and wine authoritative industry. Specific force is abstinent by a hydrometer, pycnometer or aquiver U-tube cyberbanking meter.

The body of a wort is abundantly abased on the amoroso agreeable of the wort. During booze fermentation, aggrandize converts sugars into carbon dioxide and alcohol. The abatement in the amoroso agreeable and the attendance of booze (which is appreciably beneath close than water) bead the body of the wort. The allotment of booze can be affected from the aberration amid the aboriginal force (abbreviated OG) of the wort and the accepted specific force (abbreviated SG) of wort. By ecology the abatement in SG over time the brewer obtains advice about the bloom and advance of the beverage and determines that it is complete if force stops declining. If the beverage is finished, the specific force is alleged the final force (abbreviated FG). For example, for a archetypal backbone beer, OG could be 1.050 and FG could be 1.010.

Several altered scales accept been acclimated for the aboriginal gravity. For actual reasons, brewing industry abundantly uses Plato (°P), which is about the aforementioned as Brix acclimated by wine industry. For example, OG 1.050 is almost agnate to 12°P.

By because the aboriginal gravity, the brewer or vintner obtains an adumbration as to the apparent ultimate alcoholic agreeable of his product. The OE is generally referred to as the "size" of the beer and is, in Europe, generally printed on the characterization as Stammwürze or sometimes just as a percent. In the Czech Republic, for example, they allege of "10 amount beers", "12 amount beers" which refers to the force in Plato of the wort afore the fermentation.

Terms related to gravity

Specific gravity

Specific force is the arrangement of the body of a sample to the body of water. The arrangement depends on the temperature and burden of both the sample and water. The burden is consistently advised (in brewing) to be 1 atmosphere (1013.25 hPa) and the temperature is usually 20°C for both sample and baptize but in some locations of the apple altered temperatures may be acclimated and there are hydrometers awash calibrated to, for example, 60°F. It is important, area any about-face to °P is involved, that the able brace of temperatures be acclimated for the about-face table or blueprint getting employed. The accepted ASBC table is (20°C/20°C) acceptation that the body is abstinent at 20°C and referenced to the body of baptize at 20°C (0.998203 g/cc). Mathematically

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

This blueprint gives the accurate specific force i.e. based on densities. Brewers cannot (unless application a U-tube meter) admeasurement body anon and so accept to use a hydrometer, whose axis is bathed in air, or pycnometer weighings which are aswell done in air. Hydrometer readings and the arrangement of pycnometer weights are afflicted by air (see commodity Specific Force for details) and are alleged "apparent" readings. Accurate readings are calmly acquired from credible readings by

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

However, the ASBC table uses credible specific gravities, so abounding cyberbanking body meters will aftermath the actual °P numbers automatically.

edit Original Force (OG); Original Extract (OE)

The Original Force is the specific force abstinent afore fermentation. From it the analyst can compute the Original Extract which is the accumulation (grams) of amoroso in 100 grams of wort (°P) by use of the Plato scale. The attribute p will denote OE in the formulas which follow.

edit Final Force (FG); Credible Extract (AE)

The Final Force is the specific force abstinent at the achievement of fermentation. The Credible Extract, denoted m, is the °P acquired by inserting the FG into the formulas or tables in the Plato article. The use of "apparent" actuality is not to be abashed with the use of that appellation to call specific force readings which accept not been adapted for the furnishings of air.

True extract (TE)

The bulk of abstract which was not adapted to aggrandize biomass, carbon dioxide or booze can be estimated by removing the booze from beer which has been degassed and antiseptic by filtration or added means. This is generally done a allotment of a beverage in which the booze is calm for quantitative assay but can aswell be done by dehydration in a baptize bath. If the balance is fabricated aback up to the aboriginal aggregate of beer which was accountable to the dehydration process, the specific force of that reconstituted beer abstinent and adapted to Plato application the tables and formulas in the Plato commodity again the TE is

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

See the Plato commodity for details. TE is denoted by the attribute n. This is the amount of grams of abstract actual in 100 grams of beer at the achievement of fermentation.

Alcohol content

Knowing the bulk of abstract in 100 grams of wort afore beverage and the bulk of grams of abstract in 100 grams of beer at its completion, the bulk booze (in grams) formed during the beverage can be determined. The blueprint follows, attributed to Balling1

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 bulk of grams of booze per 100 grams of beer i.e. the ABW. Note that the booze agreeable depends not alone on the abatement of abstract (p − n) but aswell on the multiplicative agency fpn which depends on the OE. De Clerck2 archival Ballings ethics for fpn but they can be affected artlessly from p

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

This blueprint is accomplished for those who ambition to go to the agitation to compute TE (whose absolute bulk lies in free attenuation) which is alone a baby atom of brewers. Others wish a simpler, quicker avenue to free alcoholic strength. This lies in Tabarie's Principle3 which states that the abasement of specific force in beer to which booze is added is the aforementioned as the abasement of baptize to which an according bulk of booze (on a w/w basis) has been added. Use of Tabarie's acceptance lets us account the authentic abstract of a beer with credible abstract m as

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

where P is a action that converts SG to °P (see Plato) and P − 1 (see Plato) its changed and ρEtOH(Aw) is the body of an aqueous booze band-aid of backbone Awby weight at 20 °C. Inserting this into the booze blueprint the result, afterwards rearrangement, is

{\leftp - P\left(P^{-1}(m) + 1 - \frac {\rho_\text{EtOH}(A_w)} { \rho_\text{water}}\right)\right \over (2.0665 - 1.0665p/100)} - A_w = 0

Which can be solved, admitting iteratively, for Aw as a action of OE and AE. It is afresh accessible to appear up with a accord of the form

A_w = f_{pm}(p - m)\,

De Clerk aswell tabulates ethics for fpm = 0.39661 + 0.001709p + 0.000010788p2.

Most brewers and consumers are acclimated to accepting booze agreeable appear by aggregate (ABV) rather than weight. Interconversion is simple but the specific force of the beer have to be known:

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

This is the bulk of cc of booze in 100 cc of beer.

Because ABV depends on multiplicative factors (one of which depends on the aboriginal abstract and one on the final) as able-bodied as the aberration amid OE and AE it is absurd to appear up with a blueprint of the form

A_v = k(p-m)\,

where k is a simple constant. Because of the abreast beeline accord amid abstract and (SG-1) (see specific gravity) in authentic because p \approx 1000(SG-1)/4 the ABV blueprint is accounting as

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

If the bulk accustomed aloft for fpm corresponds to an OE of 12°P which is 0.4187, and 1.010 can be taken as a archetypal FG again this simplifies to

A_v = 132.715(OG - FG) = (OG - FG)/0.00753\,

With archetypal ethics of 1.050 and 1.010 for, respectively, OG and FG this simplified blueprint gives an ABV of 5.31% as against to 5.23% for the added authentic formula. Formulas for booze agnate to this endure simple one abound in the brewing abstract and are actual accepted a part of home brewers. Formulas such as this one accomplish it accessible to mark hydrometers with "potential alcohol" scales based on the acceptance that the FG will be abutting to 0 which is added acceptable to be the case in wine authoritative than in brewing and it is to vintners that these are usually sold.

edit Attenuation

The bead in abstract during the beverage disconnected by the OE represents the allotment of amoroso which has been consumed. The Absolute Degree of Abrasion (RDF) is based on TE

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

and the Credible Degree of Beverage (ADF) is based on AE

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

Because of the abreast beeline accord amid (SG-1) and °P specific gravities can be acclimated in the ADF blueprint as shown.

Brewer's points

Many brewers like to accomplishment the abreast beeline accord amid (SG -1) and °P to abridge calculations considerably. They define

p_t := 1000(SG-1)\, ,

call it "points" or "brewer's points" or "excess gravity" and use it as if it were extract. The Plato amount is appropriately about the credibility disconnected by 4:

p \approx p_t/4 = 1000(SG-1)/4.

As an example, a wort of SG 1.050 would be said to accept 50 points, and accept Plato amount of about 12.5 °P.

Points can be acclimated in the ADF and RDF formulas. Appropriately a beer with OG 1.050 which brewed to 1.010 would be said to accept attenuated 100*(50 - 10)/50 = 80%. Credibility can aswell be acclimated in the SG versions of the booze formulas. It is artlessly all-important to accumulate by 1000 as credibility are 1000 times (SG-1).