FermCalc - Unit Conversion Calculator - Introduction
- Calculation Details
- Specific Gravity / Density Conversions
- Specific Gravity <--> Brix
- Specific Gravity <--> Oechsle
- Specific Gravity <--> Baumé
- Specific Gravity <--> Klosterneuburger Mostwaage (KMW)
- Specific Gravity <--> Twaddell
- Specific Gravity <--> Density
- Specific Gravity <--> g/L Sugar
- Specific Gravity <--> Potential Alcohol
- Acidity Conversions
- Acid Reference
- Grams/Liter <--> Percent
- Grams/Liter <--> mEq/L
- Alcohol Content Conversions
- % Alcohol by Volume <--> % Alcohol by Weight
- % Alcohol by Volume <--> Proof (US)
- % Alcohol by Volume <--> Proof (British)
- Concentration Conversions
- Refractivity Conversions
- Refractive Index <--> Brix
- Refractive Index <--> Oechsle
- Refractive Index <--> Baumé
- Refractive Index <--> KMW
- Refractive Index <--> Zeiss Units
## IntroductionThe layout of the Conversions panel is somewhat similar to Josh Madison's excellent Convert program. Convert is freeware if you need a more comprehensive program for performing conversions. FermCalc provides eight categories of unit conversions: - Volume
- Mass
- Temperature
- Specific Gravity / Density
- Acidity
- Alcohol Content
- Concentration
- Refractivity
## Calculation DetailsCalculation details are provided below. Only the Specific Gravity, Acidity, Alcohol Content, Concentration, and Refractivity conversions are covered in detail here since the others are fairly straightforward. Unless otherwise stated below, the conversion factors are taken from F. Cardarelli (2003). Back to top## Specific Gravity / Density ConversionsThe specific gravity (SG) conversions are intended to convert between different hydrometer reading scales. The conversions to Brix, Oechsle, KMW, g/L sugar, and potential alcohol are only valid prior to fermentation. After fermentation begins these readings will be obscured by alcohol, and therefore reflect the apparent hydrometer readings for these quantities. All of these conversions assume a reference temperature of 20°C for SG. ## Specific Gravity <--> BrixBrix is equivalent to the sugar concentration in percent by weight in the juice or must. The Brix scale is virtually identical to the Balling and Plato scales. This is the most important conversion in FermCalc because it is used to calculate percent sugar by weight from SG in all of the sugar calculations. Calculating percent sugar from SG in this manner inherently assumes that there are no dissolved solids present in the must other than sugar. While this is never actually the case, since sugar calculations usually involve taking differences between initial and final specific gravities and sugar concentrations, this approximation usually yields acceptable results. FermCalc uses the equation developed by J. Hackbarth (2011), which is based on the AOAC Brix tables (Horwitz and Latimer, 2005), to convert from Brix to SG. The equation is:
where
FermCalc uses an iterative technique to solve equation (1) for Previous versions of FermCalc used the sucrose conversion table in the USDA Technical Procedures Manual for this conversion. Use of equation (1) results in a difference of less than 0.1% in the Brix conversions and sugar calculations compared to the previous versions. Back to top## Specific Gravity <--> OechsleOechsle is a scale of must weight and is used mainly in Germany for the Prädikat classification of wines. There are two definitions of Oechsle currently in use. The first is based on specific gravity, and is referred to as "old" Oechsle in Germany. It is still used in Luxemburg and Switzerland. This Oechsle scale is calculated as:
where
The new Oechsle scale is based on refractive index, and is the current official Oechsle scale in Germany. This scale is based on the following relationship with refractive index, and has a range of validity from 40° to 120° Oechsle (Schmitt, 1983 and Jakob, 1995):
where
FermCalc uses equations (1) and (37) to convert between
SG and refractive index in order to calculate Oechsle from equation (3).
Outside of the range of validity of equation (3), values of ## Specific Gravity <--> BauméThe Baumé hydrometer scale was devised by French chemist Antoine Baumé and is still used in the food and chemical industries. There are two Baumé scales: one for liquids heavier than water, and one for liquids lighter than water. For liquids that are heavier than water, 0°Bé corresponds to the reading for pure water, and 15°Bé corresponds to the reading of a solution of 15% NaCl by mass. For liquids that are lighter than water, 10°Bé marks the level for pure water and 0°Bé corresponds to a solution that is 10% NaCl by mass. Note that the heavy and light scales go in opposite directions. The equation for liquids heavier than water is:
where The equation for liquids lighter than water is:
Only the scale for liquids heavier than water is included in FermCalc because this is the only one used in winemaking. Back to top## Specific Gravity <--> Klosterneuburger Mostwaage (KMW)The Klosterneuburger Mostwaage (KMW) scale is used in Austria as a measure of the sugar content of a must. It is used to categorize wines into the various Austrian quality classifications. It is known as the Babo scale in Italy. It is legally related to the old Oechsle scale as follows:
where ## Specific Gravity <--> TwaddellThe Twaddell scale is an SG scale for liquids heavier than water that is used mainly in the United Kingdom. The conversion to SG is similar to that for the Oechsle scale above, but it uses a factor of 200 instead of 1000, or:
where ## Specific Gravity <--> DensityThe SG of a substance is the ratio of its density at 20ºC to the density of water at 20ºC. To convert SG to density we simply need to multiply the SG by the density of water and by the appropriate conversion factor. The conversion factors used in FermCalc are:
where: Back to top ## Specific Gravity <--> g/L Sugar
Sugar content in grams/liter (g/L) is not really an SG unit, but it's included
here because it's a useful quantity for a number of calculations. It's important to
note here that this conversion is only strictly valid for pure aqueous sucrose solutions,
so it cannot be used for any liquids that contain alcohol. Also, it should not be
confused with the density units of grams/liter. The equation to determine g/L sugar from
Calculating ## Specific Gravity <--> Potential Alcohol
While potential alcohol is not really an SG unit, this conversion is often
used by winemakers to relate the initial sugar content of a must to the potential alcoholic
content of the finished wine. For this calculation FermCalc uses the method proposed by
Duncan and Acton (1967), which requires measurement of both the initial and final specific
gravities. For the purpose of this calculation, which is generally used to establish the
initial sg is 1.0. The equations are as follows in terms
of _{f}sg:
where
Combining equations (15) through (17) above and assuming that
The calculated potential alcohol values are constrained to a maximum of 100% and a minimum of 0%. The graph below compares potential alcohol tables from various sources to equation (18) above. The FermCalc results agree well with the lower trend. The higher trend of points (from Duncan & Acton, 1967 and Leverett, 1995) presumably do not account for non-sugar solutes (dissolved solids which increase the SG but are not converted to alcohol during fermentation). Back to top ## Acidity Conversions## Acid Reference Conversions
When we titrate a must or wine for acidity, all we really determine is the number of available
hydrogen (H Different winemaking texts use different acid references when referring to titratable acidity levels. Most use tartaric acid as the reference, with units of either percent or grams/liter (parts per thousand, or ppt). However, other texts use different acids as the reference, with sulfuric acid being a popular alternative to tartaric acid.
To develop the conversion factors that convert from one acid reference to the other we need
to know their molecular weights and the number of H
The number of moles of H
where
The mass of the acid in solution is simply the acidity multiplied by the volume, or:
where
Combining equations (18) and (19) we get:
To convert from one acid reference to the other, we know that the number of moles of H
Rearranging equation (22) to convert from on acid reference to another we get:
For example, to convert from 0.420% sulfuric to % tartaric: (0.420% sulfuric)·(2/2)·(150.09/98.08) = 0.643% tartaricBack to top ## Grams/Liter <--> Percent ConversionsThis is a simple conversion. Since grams/liter is parts per thousand (ppt), and percent is parts per hundred, we simply need to divide grams/liter by 10 to get percent, or:
## Grams/Liter <--> mEq/L ConversionsAn milli-equivalent (mEq) is the amount of a substance that will react with or supply one-thousandth of a mole of hydrogen ions (H+) in an acid-base reaction. If we know the mass of an acid in solution, we can calculate the mEq/L as:
Substituting equation (20) into equation (25) we get: Back to top ## Alcohol Content ConversionsBelow are details of the alcohol content unit conversions. All alcohol content values are converted to % alcohol by volume when they are entered, and are subjected to an upper limit of 100% and a lower limit of 0%. Back to top## % Alcohol by Volume <--> % Alcohol by WeightThe percentages of alcohol by weight and alcohol by volume for a water/alcohol mixture are defined respectively as:
where
We can relate the volumes and the masses of the alcohol and the mixture as:
where
Substituting equations (29) and (30) into equation (27) we get:
Then we can substitute equation (28) into equation (31) to get:
Re-arranging equation (32) we get:
FermCalc uses the general formula for calculating
the densities of mixtures of ethanol and water found in
ρ at 20ºC that are required
to perform the conversion. When performing the conversion for a wine with a specified
SG, the actual wine density is used in place of _{m}ρ
in equation (33).
_{m}## % Alcohol by Volume <--> Proof (US)The Proof scale in the United States is simply equal to twice the % alcohol by volume, or:
where Back to top ## % Alcohol by Volume <--> Proof (British)
The term "proof" probably originated from test of alcoholic strength in which
the spirit was mixed with gunpowder and ignited (Schidrowitz, 1911). If the gunpowder didn't
burn, the spirit was deemed to be "under proof". According to the Alcoholic Liquor
Duties Act (1979), "Spirits shall be deemed to be at proof if the volume of the ethyl
alcohol contained therein made up to the volume of the spirits with distilled water has
a weight equal to that of twelve-thirteenths of a volume of distilled water equal to the
volume of the spirits, the volume of each liquid being computed as at 51ºF." Using
the OIML formula, we can calculate the density of water at 51ºF as 999.64 kg/m
where Back to top ## Concentration ConversionsAll concentrations in FermCalc are expressed in terms of mass of substance per unit volume of solution. Converting from one set of units to another is a simple matter of converting the mass units in the numerator and the volume units in the denominator. For example, to convert from g/mL to lb/gal we can write:
Concentrations expressed as mass per unit mass - such as percent, parts per thousand (ppt), and parts per million (ppm) - are often used interchangeably with their mass per unit volume counterparts. These mass/mass units are shown in parentheses next to the mass/volume units. Strictly speaking, these equivalencies are only accurate if the SG of the solution is equal to 1.0. Fortunately most of the solutions we deal with in winemaking have specific gravities close to 1.0. Back to top## Refractivity ConversionsRefractivity conversions are included mainly to allow the use of refractometers with a variety of different scales to be used for the calculation of alcohol content described here. These conversions are only valid for refractometers calibrated for aqueous sucrose solutions at 20°C. ## Refractive Index <--> Refractometer BrixIn order to convert between refractive index and refractometer Brix, FermCalc uses the equation published in the Sugar Journal (1970), which was derived from the work of Rosenhauer, Schneider and Emmerich (1966) for the International Commission for Uniform Methods of Sugar Analysis (ICUMSA), and serves as the basis for the AOAC refractive index tables (Williams, 1984). The equation is:
where
In order to convert from Brix to refractive index, FermCalc uses an iterative technique
to solve equation (37) for
The result of equation (37) is adjusted for small values of ## Refractive Index <--> OechsleFermCalc converts between Oechsle (old) and refractive index by combining the conversions in equations (1), (2), and (37). FermCalc converts between Oechsle (new) and refractive index using equation (3) inside its range of validity from 40 to 120 °Oe, and extrapolates to other values as described above. ## Refractive Index <--> BauméFermCalc converts between Baumé and refractive index by combining the conversions in equations (1), (4), and (37). ## Refractive Index <--> KMWFermCalc converts between KMW and refractive index by combining the conversions in equations (1), (2), (7), and (37).## Refractive Index <--> Zeiss UnitsThe Zeiss refractivity scale was originally used on older Zeiss immersion refractometers and is still used today on some handheld refractometers. This scale ranges from -5 to 105, corresponding to refractivity index values of 1.32539 to 1.36640 (Thurston, 1922). Thee upper end of the scale corresponds to a Brix value of 21.53, so it has limited applicability for winemaking. FermCalc converts between Zeiss units and refractive index using the equation adopted by the AOAC (Williams, 1984):
where Back to top
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