Parrondo's paradox

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

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 (which is appreciably less dense than water) drop the density of the wort. The percentage of alcohol can be calculated from the difference between the original gravity (abbreviated OG) of the wort and the current specific gravity (abbreviated SG) 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 (abbreviated FG). 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 (°P), 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 (Original Extract) 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 (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, Template:Convert. 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/cm³). Mathematically

$SG_{\text{true}}={\rho _{\text{sample}} \over \rho _{\text{water}}}$

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

$SG_{\text{true}}=SG_{\text{apparent}}-{\rho _{\text{air}} \over \rho _{\text{water}}}(SG_{\text{apparent}}-1)$

However, the ASBC table uses apparent specific gravities, so many electronic density meters will produce the correct °P numbers automatically.

Original Gravity (OG); Original Extract (OE)

The Original Gravity is the specific gravity measured before fermentation. From it the analyst can compute the Original Extract which is the mass (grams) of sugar in 100 grams of wort (°P) by use of the Plato scale. The symbol $p$ will denote OE in the formulas which follow.

Final Gravity (FG); Apparent Extract (AE)

The Final Gravity is the specific gravity measured at the completion of fermentation. The Apparent Extract, denoted $m$, 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 (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. TE is denoted by the symbol $n$. 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 (in grams) formed during the fermentation can be determined. The formula follows, attributed to BallingPrimarily based on the most recent URA personal property value index (PPPI) flash estimates, we know that the PPPI, which represents the overall real property price development, has dipped in 2013Q4. That is the first dip the market has seen within the final 2 years.

To give you some perspective, the entire number of personal properties in Singapore (together with govt condominiums) is 297,689 in 2013Q3. Primarily based on the projection that there will be 19,302 units accomplished in 2014, the rise in residential models works out to be more than 6%. With a lot New Ec Launch Singapore provide, buyers might be spoilt for alternative and this in flip will lead to their reluctance to pay a premium for potential models. The complete textual content of the Copyright Act (Cap sixty three) and different statutes regarding IPR might be found on the Singapore Statutes Online Website online The Group's income jumped forty.1 p.c to $324.5 million from $231.6 million in FY 2013, lifted by increased development income and sales of growth properties in Singapore and China. Actual Estate Shopping for

One factor we've on this nation is a big group of "economists," and "market analysts." What's interesting about this group of real property market-watchers is that there are two very other ways wherein they predict Boomers will affect housing markets over the subsequent decade. Let's check out those two opposites and see how every can change the best way real property investors strategy their markets. The good news is that actual property buyers are prepared for either state of affairs, and there's profit in being ready. I'm excited and searching ahead to the alternatives both or each of these conditions will supply; thank you Boomers! Mapletree to further broaden past Asia Why fortune will favour the brave in Asia's closing real property frontier

The story of the 23.2 home begins with a stack of Douglas fir beams salvaged from varied demolished warehouses owned by the consumer's household for a number of generations. Design and structure innovator Omer Arbel, configured them to type a triangulated roof, which makes up one of the placing features of the home. The transient from the entrepreneur-proprietor was not solely to design a house that integrates antique wood beams, however one which erases the excellence between inside and exterior. Built on a gentle slope on a large rural acreage surrounded by two masses of previous-development forests, the indoors movement seamlessly to the outdoors and, from the within looking, one enjoys unobstructed views of the existing natural panorama which is preserved

First, there are typically extra rental transactions than gross sales transactions, to permit AV to be decided for each property primarily based on comparable properties. Second, movements in sale costs are more unstable than leases. Hence, utilizing rental transactions to derive the AV helps to maintain property tax more steady for property homeowners. If you're buying or trying to lease a property. It's tiring to call up individual property agent, organize appointments, coordinate timing and to go for particular person property viewing. What most individuals do is to have a property agent representing them who will arrange and coordinate the viewings for all the properties out there based mostly on your necessities & most well-liked timing. Rent Property District 12 Rent Property District thirteen

The Annual Worth of a property is mostly derived based mostly on the estimated annual hire that it may well fetch if it have been rented out. In determining the Annual Worth of a property, IRAS will think about the leases of similar properties within the vicinity, dimension and condition of the property, and different relevant components. The Annual Worth of a property is determined in the identical method regardless of whether the property is let-out, proprietor-occupied or vacant. The Annual Worth of land is determined at 5% of the market price of the land. When a constructing is demolished, the Annual Worth of the land is assessed by this method. Property Tax on Residential Properties Buyer Stamp Responsibility on Buy of Properties – Business and residential properties Rent House District 01

Within the event the Bank's valuation is decrease than the acquisition price, the purchaser has to pay the distinction between the purchase value and the Bank's valuation utilizing money. As such, the money required up-front might be increased so it's at all times essential to know the valuation of the property before making any offer. Appoint Lawyer The Bank will prepare for a proper valuation of the property by way of physical inspection The completion statement will present you the balance of the acquisition price that you must pay after deducting any deposit, pro-rated property tax and utility costs, upkeep prices, and different relevant expenses in addition to any fees payable to the agent and the lawyer. Stamp Responsibility Primarily based on the Purchase Price or Market Value, whichever is larger

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

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 $f_{pn}$ which depends on the OE. De ClerckPrimarily based on the most recent URA personal property value index (PPPI) flash estimates, we know that the PPPI, which represents the overall real property price development, has dipped in 2013Q4. That is the first dip the market has seen within the final 2 years.

To give you some perspective, the entire number of personal properties in Singapore (together with govt condominiums) is 297,689 in 2013Q3. Primarily based on the projection that there will be 19,302 units accomplished in 2014, the rise in residential models works out to be more than 6%. With a lot New Ec Launch Singapore provide, buyers might be spoilt for alternative and this in flip will lead to their reluctance to pay a premium for potential models. The complete textual content of the Copyright Act (Cap sixty three) and different statutes regarding IPR might be found on the Singapore Statutes Online Website online The Group's income jumped forty.1 p.c to $324.5 million from $231.6 million in FY 2013, lifted by increased development income and sales of growth properties in Singapore and China. Actual Estate Shopping for

One factor we've on this nation is a big group of "economists," and "market analysts." What's interesting about this group of real property market-watchers is that there are two very other ways wherein they predict Boomers will affect housing markets over the subsequent decade. Let's check out those two opposites and see how every can change the best way real property investors strategy their markets. The good news is that actual property buyers are prepared for either state of affairs, and there's profit in being ready. I'm excited and searching ahead to the alternatives both or each of these conditions will supply; thank you Boomers! Mapletree to further broaden past Asia Why fortune will favour the brave in Asia's closing real property frontier

The story of the 23.2 home begins with a stack of Douglas fir beams salvaged from varied demolished warehouses owned by the consumer's household for a number of generations. Design and structure innovator Omer Arbel, configured them to type a triangulated roof, which makes up one of the placing features of the home. The transient from the entrepreneur-proprietor was not solely to design a house that integrates antique wood beams, however one which erases the excellence between inside and exterior. Built on a gentle slope on a large rural acreage surrounded by two masses of previous-development forests, the indoors movement seamlessly to the outdoors and, from the within looking, one enjoys unobstructed views of the existing natural panorama which is preserved

First, there are typically extra rental transactions than gross sales transactions, to permit AV to be decided for each property primarily based on comparable properties. Second, movements in sale costs are more unstable than leases. Hence, utilizing rental transactions to derive the AV helps to maintain property tax more steady for property homeowners. If you're buying or trying to lease a property. It's tiring to call up individual property agent, organize appointments, coordinate timing and to go for particular person property viewing. What most individuals do is to have a property agent representing them who will arrange and coordinate the viewings for all the properties out there based mostly on your necessities & most well-liked timing. Rent Property District 12 Rent Property District thirteen

The Annual Worth of a property is mostly derived based mostly on the estimated annual hire that it may well fetch if it have been rented out. In determining the Annual Worth of a property, IRAS will think about the leases of similar properties within the vicinity, dimension and condition of the property, and different relevant components. The Annual Worth of a property is determined in the identical method regardless of whether the property is let-out, proprietor-occupied or vacant. The Annual Worth of land is determined at 5% of the market price of the land. When a constructing is demolished, the Annual Worth of the land is assessed by this method. Property Tax on Residential Properties Buyer Stamp Responsibility on Buy of Properties – Business and residential properties Rent House District 01

Within the event the Bank's valuation is decrease than the acquisition price, the purchaser has to pay the distinction between the purchase value and the Bank's valuation utilizing money. As such, the money required up-front might be increased so it's at all times essential to know the valuation of the property before making any offer. Appoint Lawyer The Bank will prepare for a proper valuation of the property by way of physical inspection The completion statement will present you the balance of the acquisition price that you must pay after deducting any deposit, pro-rated property tax and utility costs, upkeep prices, and different relevant expenses in addition to any fees payable to the agent and the lawyer. Stamp Responsibility Primarily based on the Purchase Price or Market Value, whichever is larger tabulated Ballings values for $f_{pn}$ 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 PrinciplePrimarily based on the most recent URA personal property value index (PPPI) flash estimates, we know that the PPPI, which represents the overall real property price development, has dipped in 2013Q4. That is the first dip the market has seen within the final 2 years.

To give you some perspective, the entire number of personal properties in Singapore (together with govt condominiums) is 297,689 in 2013Q3. Primarily based on the projection that there will be 19,302 units accomplished in 2014, the rise in residential models works out to be more than 6%. With a lot New Ec Launch Singapore provide, buyers might be spoilt for alternative and this in flip will lead to their reluctance to pay a premium for potential models. The complete textual content of the Copyright Act (Cap sixty three) and different statutes regarding IPR might be found on the Singapore Statutes Online Website online The Group's income jumped forty.1 p.c to $324.5 million from $231.6 million in FY 2013, lifted by increased development income and sales of growth properties in Singapore and China. Actual Estate Shopping for

One factor we've on this nation is a big group of "economists," and "market analysts." What's interesting about this group of real property market-watchers is that there are two very other ways wherein they predict Boomers will affect housing markets over the subsequent decade. Let's check out those two opposites and see how every can change the best way real property investors strategy their markets. The good news is that actual property buyers are prepared for either state of affairs, and there's profit in being ready. I'm excited and searching ahead to the alternatives both or each of these conditions will supply; thank you Boomers! Mapletree to further broaden past Asia Why fortune will favour the brave in Asia's closing real property frontier

The story of the 23.2 home begins with a stack of Douglas fir beams salvaged from varied demolished warehouses owned by the consumer's household for a number of generations. Design and structure innovator Omer Arbel, configured them to type a triangulated roof, which makes up one of the placing features of the home. The transient from the entrepreneur-proprietor was not solely to design a house that integrates antique wood beams, however one which erases the excellence between inside and exterior. Built on a gentle slope on a large rural acreage surrounded by two masses of previous-development forests, the indoors movement seamlessly to the outdoors and, from the within looking, one enjoys unobstructed views of the existing natural panorama which is preserved

First, there are typically extra rental transactions than gross sales transactions, to permit AV to be decided for each property primarily based on comparable properties. Second, movements in sale costs are more unstable than leases. Hence, utilizing rental transactions to derive the AV helps to maintain property tax more steady for property homeowners. If you're buying or trying to lease a property. It's tiring to call up individual property agent, organize appointments, coordinate timing and to go for particular person property viewing. What most individuals do is to have a property agent representing them who will arrange and coordinate the viewings for all the properties out there based mostly on your necessities & most well-liked timing. Rent Property District 12 Rent Property District thirteen

The Annual Worth of a property is mostly derived based mostly on the estimated annual hire that it may well fetch if it have been rented out. In determining the Annual Worth of a property, IRAS will think about the leases of similar properties within the vicinity, dimension and condition of the property, and different relevant components. The Annual Worth of a property is determined in the identical method regardless of whether the property is let-out, proprietor-occupied or vacant. The Annual Worth of land is determined at 5% of the market price of the land. When a constructing is demolished, the Annual Worth of the land is assessed by this method. Property Tax on Residential Properties Buyer Stamp Responsibility on Buy of Properties – Business and residential properties Rent House District 01

Within the event the Bank's valuation is decrease than the acquisition price, the purchaser has to pay the distinction between the purchase value and the Bank's valuation utilizing money. As such, the money required up-front might be increased so it's at all times essential to know the valuation of the property before making any offer. Appoint Lawyer The Bank will prepare for a proper valuation of the property by way of physical inspection The completion statement will present you the balance of the acquisition price that you must pay after deducting any deposit, pro-rated property tax and utility costs, upkeep prices, and different relevant expenses in addition to any fees payable to the agent and the lawyer. Stamp Responsibility Primarily based on the Purchase Price or Market Value, whichever is larger 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 principle lets us calculate the true extract of a beer with apparent extract $m$ as

$n=P(P^{-1}(m)+1-{\frac {\rho _{\text{EtOH}}(A_{w})}{\rho _{\text{water}}}})$

where $P$ is a function that converts SG to °P (see Plato) and $P^{-1}$ (see Plato) its inverse and $\rho _{\text{EtOH}}(A_{w})$ is the density of an aqueous ethanol solution of strength $A_{w}$by weight at 20 °C. Inserting this into the alcohol formula the result, after rearrangement, is

${\left[p-P\left(P^{-1}(m)+1-{\frac {\rho _{\text{EtOH}}(A_{w})}{\rho _{\text{water}}}}\right)\right] \over (2.0665-1.0665p/100)}-A_{w}=0$

Which can be solved, 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

$A_{w}=f_{pm}(p-m)\,$

De Clerk also tabulates values for $f_{pm}=0.39661+0.001709p+0.000010788p^{2}$.

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:

$A_{v}=A_{w}{SG_{\text{beer}} \over 0.79661}$

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 $p\approx 1000(SG-1)/4$ the ABV formula is written as

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

If the value given above for $f_{pm}$ 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

$A_{v}=132.715(OG-FG)=(OG-FG)/0.00753\,$

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 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 (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.

Brewer's points

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

$p_{t}:=1000(SG-1)\,$,

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:

$p\approx p_{t}/4=1000(SG-1)/4.$

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 (SG-1).

See also

• Plato scale
• Gravity (chemistry)

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.