FermCalc - Unit Conversions
FermCalc provides eight categories of unit conversions:
Making a Conversion
To make a conversion, follow these steps:
The converted value will appear in the Output Value field. If the input value is outside of the range of physically realistic values for the selected conversion, it will be shown in red.Back to top
Calculation 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 Conversions
Brix 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 specific gravity in all of the sugar calculations. Calculating percent sugar from specific gravity 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 specific gravity. The equation is:
FermCalc uses an iterative technique to solve equation (1) for B given a value of sg. For values of sg less than 1.0, the slope of the B vs. sg curve at sg = 1.0 is extrapolated to lower values to obtain the associated negative Brix values.
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 <--> Oechsle
Oechsle is a scale of must weight based on specific gravity, and is used mainly in Germany for the Prädikat classification of wines. The Oechsle scale is also widely used in home winemaking and brewing texts, often being referred to simply as "gravity". The conversion equation is:
Oe = degrees Oechsle
So, a specific gravity of 1.090 is the same as a gravity of 90°Oe. A specific gravity of 0.995 is a gravity of -5°Oe.Back to top
Specific Gravity <--> Baumé
The 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 Bé is degrees Baumé.
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 <--> Twaddell
The Twaddell scale is a specific gravity scale for liquids heavier than water that is used mainly in the United Kingdom. The conversion to specific gravity is similar to that for the Oechsle scale above, but it uses a factor of 200 instead of 1000, or:
where Tw is degrees Twaddell.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 Oechsle scale as follows:
where KMW is degrees KMW. FermCalc converts between KMW and sg by direct solution of equations (2) and (6).Back to top
Specific Gravity <--> Density
The specific gravity of a substance is the ratio of its density at 20ºC to the density of water at 20ºC. To convert specific gravity to density we simply need to multiply the specific gravity by the density of water and by the appropriate conversion factor. The conversion factors used in FermCalc are:
sg = specific gravityBack to top
Specific Gravity <--> Potential Alcohol
While potential alcohol is not really a specific gravity 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 sgi of a must, FermCalc assumes the final specific gravity sgf is 1.0. The equations are as follows in terms of sg:
ap = potential alcohol, % by volume
Combining equations (13) through (15) above and assuming that sgf equals 1.0 yields the following equation.
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 (16) 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 specific gravity but are not converted to alcohol during fermentation).
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When we titrate a must or wine for acidity, all we really determine is the number of available hydrogen (H+) ions in the wine and not the types of acid present. For this reason we must choose an acid as a reference in order to express the acidity as a concentration.
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+ ions each molecule of the acid contributes to make the solution acidic. The table below lists these values for the most common acid references, compiled from Margalit (2004) and Weast (1977).
The number of moles of H+ ions an acid contributes can be calculated as:
M = moles of H+ ions
The mass of the acid in solution is simply the acidity multiplied by the volume, or:
v = volume of solution, liters
Combining equations (17) and (18) we get:
To convert from one acid reference to the other, we know that the number of moles of H+ ions and the volume are the same no matter what reference we use, so we can write:
Rearranging equation (20) 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 Conversions
This 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 Conversions
An 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 (18) into equation (23) we get:
Back to top
Alcohol Content Conversions
Below 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 Weight
The percentages of alcohol by weight and alcohol by volume for a water/alcohol mixture are defined respectively as:
aw = alcohol content, % by weight
We can relate the volumes and the masses of the alcohol and the mixture as:
ρa = density of alcohol, kg/liter
Substituting equations (27) and (28) into equation (25) we get:
Then we can substitute equation (26) into equation (29) to get:
Re-arranging equation (30) we get:
FermCalc uses the general formula for calculating the densities of mixtures of ethanol and water found in International Recommendation 22: International Alcoholometric Tables by the International Organisation of Legal Metrology (OIML, 1973) to calculate the densities of alcohol ρa and water/alcohol mixtures ρm at 20ºC that are required to perform the conversion. When performing the conversion for a wine with a specified specific gravity, the actual wine density is used in place of ρm in equation (31).Back to top
% Alcohol by Volume <--> Proof (US)
The Proof scale in the United States is simply equal to twice the % alcohol by volume, or:
Pu = Proof (US)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/m3, twelve-thirteenths of which is 922.74 kg/m3, which equates to an alcohol content of 57.15% by volume. The conversion then becomes:
Pb = Proof (British)Back to top
All 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 specific gravity 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
Refractive Index Conversions
In 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:
B = degrees Brix
In order to convert from Brix to refractive index, FermCalc uses an iterative technique to solve equation (34) for ri.
The 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):
ri = index of refractionBack to top
© 2007-2013 Steve Gross