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FermCalc - Unit Conversions Introduction The 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 six categories of unit conversions:
Making a Conversion To make a conversion, follow these steps:
The converted value will appear in the Output Value field. Calculation details are provided below. Only the Specific Gravity, Acidity, and Proof conversions are covered in detail since the others are fairly straightforward. Follow the links below for the details. Calculation Details - Specific Gravity Conversions The equations for the following specific gravity conversions are described below:
Specific Gravity <--> Brix Brix is equivalent to the percent sugar by weight in the juice or must, and is virtually identical to the Balling and Plato scales. This is the most important conversion of them all because it us used to calculate percent sugar by weight in all of the sugar calculations. Based on tables relating Brix to specific gravity published in the USDA Technical Inspection Procedures, I developed the following curve fit:
where B = degrees Brix (% sugar by weight) The fit is shown in the graph below for the range of 10 to 30 Brix. The average absolute error of the fit is 0.02% for the range from 10 to 30 Brix, and 0.16% over the entire range from 0 to 80 Brix.
The calculated Brix values are constrained to a maximum of 100 and a minimum of -100. Specific Gravity <--> Oechsle The Oechsle scale is widely used in winemaking and brewing texts, often being referred to simply as "gravity". The conversion equation is:
where Oe = degrees Oechsle So, a specific gravity of 1.090 is the same as a gravity of 90. A specific gravity of 0.995 is a gravity of -5. Specific Gravity <--> Grams/Liter, Kilograms/Liter, Pounds/Gallon, etc. These are simple multipliers.
where sg is specific gravity. 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:
Both are included in FermCalc for completeness, but as far as I know only the scale for liquids heavier than water is used in winemaking. Specific Gravity <--> Twaddell The Twaddell scale is similar to the Oechsle scale above, but it uses a factor of 200 instead of 1000, or:
where Tw is degrees Twaddell. 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 I use the method proposed by Duncan and Acton, 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, I just assume the final specific gravity sgf is 1.0. The equations are as follows in terms of sg:
where ap = potential alcohol (% by volume) Combining equations (12) through (14) 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 (15) above. The FermCalc results agree well with the lower trend. The higher trend of points (from Duncan & Acton and Leverett) presumably do not account for non-sugar solutes (dissolved solids which increase the specific gravity but are not converted to alcohol during fermentation).
Calculation Details - Acidity Conversions There are two types of conversions we need to make here: Acid Reference Conversions 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 hydrogen ions (H+) each molecule of the acid contributes to make the solution acidic. The table below lists these values for the most common acid references.
To convert from one acid reference to the other, the acidity multiplied by the ion/molecular weight ratio for one reference will equal the same quantity for the second reference. In equation form:
where a = acidity Rearranging 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% Tartaric Percent <--> Grams/Liter Conversions This is a simple conversion. Since percent is parts per hundred, and grams/liter is parts per thousand (ppt), we simply need to multiply percent by 10 to get grams/liter, or:
Calculation Details - Proof Conversions Below are details of the following four proof conversions:
All proof 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%. % Alcohol by Volume <--> % Alcohol by Weight Based on data in the CRC Handbook of Chemistry and Physics I developed the following equation to convert between % alcohol by volume (av) and % alcohol by weight (aw):
where av = % alcohol by volume The graph below compares the CRC data with the calculated values.
% Alcohol by Volume <--> Proof (US) The Proof scale in the United States is simply equal to twice the % alcohol by volume, or:
where Pu = Proof (US) % Alcohol by Volume <--> Proof (British) The British Proof scale is calculated as follows:
where Pb = Proof (British) % Alcohol by Volume <--> Degrees Sykes The Sykes scale is closely related to the British Proof scale and is calculated as follows:
where S = degrees Sykes
© 2007 Steve Gross |