FermCalc - Hydrometer Temperature Corrections and Alcohol Content Calculations - Introduction
- Making a Calculation
- Calculation Details
- Hydrometer Temperature Corrections
- Alcohol Content by the SG Drop Method
- Standard SG Drop Method
- Duncan & Acton Method
- Balling Method
- Cutaia, Reid & Spears Method
- Estimation of Solids Content (True Brix)
- Alcohol Content by the Hydrometer & Refractometer Method
- Rogerson & Symington Method
- Son et al. Method
- Roesener Method
- Barth & Race Method
- Alcohol Content by the Boiling (Spirit Indication) Method
- Tabarié (Division) Method
- Blunt (Subtraction) Method
- Honneyman Method
- Hackbarth Method
- OIML Calculator
Introduction The Alcohol Content panel has four functions: - Correcting your hydrometer readings for temperature.
- Calculating the approximate alcohol content using the specific gravity (SG) drop method.
- Calculating the approximate alcohol and residual sugar contents using the hydrometer & refractometer method.
- Calculating the approximate alcohol content using the spirit-indication (boiling) method.
To calculate the alcohol content using the SG drop method, you need to know the initial and final hydrometer SG readings. These calculations are only valid if you have not added any additional water or sugar between the initial and final readings. To calculate the alcohol content using the hydrometer & refractometer method, you need simultaneous hydrometer and refractometer readings. To calculate the alcohol content using the boiling off method, you need two hydrometer readings obtained by the procedure described below. FermCalc can make temperature corrections to the hydrometer readings for all three methods. Back to topMaking a Calculation To make a calculation, follow these steps: - Select Calculation > Alcohol Content from the menu, or select the Alcohol tab at the top of the main window.
- Select the type of calculation by selecting either the SG Drop Method tab, the Hydrometer & Refractometer Method tab, or the Boiling Off Method tab.
- Select the appropriate units for the input fields using the drop-down menus in the right-hand column.
- If the SG Drop Method was selected, enter the initial and final Hydrometer SG Readings of the wine.
- If the Hydrometer & Refractometer Method was selected, enter the Refractometer Reading of the wine and the Hydrometer SG Reading of the wine, both of which were measured on the same sample.
- If the Spirit Indication Method was selected, enter the initial and final Hydrometer SG Readings of the wine. See the procedure below for instructions on obtaining the initial and final SG readings.
- Where applicable, enter the Reading Temperature at which the hydrometer SG readings were taken, and the Calibration Temperature of the hydrometer(s) used to measure each of the specific gravities. (If you don't know what these are or if you don't want to do a temperature correction, just leave the reading temperatures and hydrometer calibration temperatures set at their default values.)
- If the OIML Calculator was selected, enter the Density and the Temperature to calculate alcohol content, or enter the Alcohol Content and the Temperature to calculate the density.
The temperature-corrected specific gravities and the approximate alcohol content of your wine will appear in the output fields as you type. All gravity/density values are converted to specific gravity when they are entered, and are subjected to a lower limit of 0.80 and an upper limit of 1.5545. Temperatures must range between 0ºC and 55ºC. If any of the entered values are outside of these ranges, output fields are highlighted in red and an error message is displayed. Calculation details are provided below. Back to topCalculation Details Hydrometer Temperature Corrections
FermCalc allows hydrometer readings to be corrected for temperature in all three
of the alcohol content calculation methods. FermCalc uses tables published in
the AOAC The specific gravity measured with a hydrometer is the ratio of the density of the liquid divided by the density of water at the hydrometer calibration temperature, or:
where
To correct the reading to a different calibration temperature, we simply need to multiply the hydrometer reading by the ratio of the water densities at the new and old calibration temperatures, or:
where
Water densities are calculated using the OIML formula (OIML, 1973) assuming 0% alcohol. After correcting for the hydrometer calibration temperature, we can correct for the sample temperature. According to the AOAC tables, temperature corrections to hydrometer measurements are functions of both the temperature and the Brix level of the must. Based on these tables, I developed the following equations to correct hydrometer readings.
where:
The plot below compares the AOAC data with the calculated Brix corrections from equation (3) above. Back to top Alcohol Content by the Specific Gravity (SG) Drop Method FermCalc includes four different methods for calculating alcohol content from the drop in specific gravity that occurs during fermentation. All four of these methods require hydrometer measurements of the initial and final specific gravities. (These methods do not work with refractometer measurements.) Agreement between the methods is generally excellent. Back to topStandard SG Drop Method
This is the most commonly used method, and is described on pages 79-80 of
where
A quick internet search will turn up a number of variations of equation (4) that use constants that are both higher and lower than the value of 0.00736 used above. However, I can only find experimental verification for the 0.00736 value. Ritchie Products Co. (2004) claims to have compared the results of equation (4) to the results of gas chromatography for a wide range of wines, and the results were within 0.3% vol/vol. Back to topDuncan & Acton Method
This method is described on pages 64-66 of
where
Combining equations (5) through (7) above yields the following equation: Back to top Balling Method
The Balling method is normally used for beer but gives results that agree very
well with the other methods. The equations used in FermCalc were taken from Michael
Hall's article "Brew by the Numbers" in the Summer 1995 issue of
where
The alcohol content (% by weight) is then calculated as:
where The result of equation (11) is then converted to % alcohol by volume as described here. Back to topCutaia, Reid & Spears Method Cutaia, Reid & Spears (2009) analyzed data from 532 beers to develop equation (12) below relating alcohol content to the initial and final specific gravities.
The alcohol content of the beers ranged from 3% to 7% by weight (approx. 3.8% to 8.7% by vol.). As with the Balling equation above, the specific gravities for the analyzed beers were expressed in degrees Plato, which is assumed by FermCalc to be the same as degrees Brix. The result of equation (12) is then converted to % alcohol by volume as described here. Back to topEstimation of Solids Content (True Brix)
After we know the alcohol content, we can estimate true Brix, which represents
solids content in % by weight, by using the model developed by James Hackbarth
(2011), which is described below. This is done by treating
the specific gravity Alcohol Content by the Hydrometer & Refractometer Method FermCalc includes four methods of estimating alcohol content and residual solids (true Brix) from simultaneous refractometer and hydrometer readings. All of the methods are designed to be used after fermentation, but they should be able to yield reasonable estimates of alcohol content during fermentation as long as there is enough alcohol to affect the measurements and the sample is degassed enough that the measurements are not affected by dissolved CO2. Back to topRogerson & Symington Method Rogerson & Symington (2006) developed a method to estimate alcohol content and residual solids (true Brix) from based on refractometer and hydrometer readings on 35 port wines. In the words of the authors, "It is not applicable for the analysis of dry wines, whether fortified or not, which contain insufficient soluble solids for Baumé determination by hydrometer, and is yet to be evaluated for sweet table wines, such as sauternes." However it is included in FermCalc because many home winemakers seem to find it useful for monitoring fermentation progress and calculating alcohol content.
FermCalc first converts the hydrometer reading
where Alcohol content is then calculated as:
where
True Brix, Back to top Son et al. Method H. S. Son et al. (2009) developed tthe following six empirical equations based on refractometer, hydrometer, and alcohol content measurements on 30 wines before and during fermentation.
where
Equations (20) and (21) allow calculation of alcohol content and true Brix directly
from hydrometer and refractometer readings. However, I found these equations to
be inaccurate, yielding estimates of alcohol content that appear too high in the
lower-alcohol range and too low in the upper range. Instead of using equations
(20) and (21), I developed alternative equations from equations (15) through (19)
that appear much more accurate. Combining equations (18) and (19) to eliminate
Combining equations (16) and (17) to eliminate
Equations (22) and (23) are used by FermCalc to calculate alcohol content and true Brix. Back to topRoesener Method This method was published online by Werner Roesener (2001) and is very popular among home winemakers, but there is no documentation regarding the derivation of the equations. My testing indicates that it yields results that are very similar to the other methods. Simplifying the original equations we get:
where Back to top Barth & Race Method This method was originally developed by Georg Barth (1905) in Germany for analyzing beers. The original equations are:
Where
FermCalc uses equations (29) and (30) to calculate alcohol content and true Brix because they were intended for higher alcohol concentrations and might be more applicable for winemaking calculations. The result of equation (29) is converted to % alcohol by volume as described here. Back to topAlcohol Content by the Boiling (Spirit-Indication) Method This method was first proposed by M. E. Tabarié in 1830 as a simplified alternative to the distillation procedure. It is based on the principle that alcohol causes the same depression in specific gravity in wine as it does in pure water. The method involves evaporating (boiling off) a portion of the wine sample until all of the alcohol is evaporated, and then replacing the evaporated volume with distilled water. The difference between the specific gravities of the wine and the volume-corrected residue are then used to estimate the specific gravity of the distillate, which represents the specific gravity of a pure water/ethanol mixture, from which the alcohol content can be estimated. The experimental procedure is summarized below. - Measure the specific gravity (
*sg*) of the wine to be tested._{w} - Take a sample of about 250-500 mL (1-2 cups) of the wine and boil the sample down to approximately half of its original volume to drive off all of the alcohol.
- Allow the boiled residue to cool to room temperature.
- Add distilled water to the residue until the total volume is restored to the original sample volume.
- Measure the specific gravity of this volume-corrected residue
*sg*, which will be greater than_{r}*sg*because the alcohol has been replaced by water._{w}
It is recommended that a narrow-range hydrometer be used for the specific gravity measurements since small errors in these measurements can result in large errors in the results. In addition to estimating the alcohol content, we can also calculate the solids content (true Brix) of the wine from the specific gravity of the volume-corrected residue. First we just need to convert the residue specific gravity measurement to a Brix value by using the Brix conversion equation. This conversion yields the solids content in % by weight of the residue. We then need to convert this value to the solids content in % by weight of the wine by multiplying by the ratio of specific gravities, or:
where
The four methods that FermCalc uses to calculate the alcohol content from the specific gravity measurements are described below. Back to topTabarié (Division) Method Tabarié originally proposed estimating the specific gravity of the distillate from the ratio of the wine and residue specific gravities, or:
where
FermCalc determines the alcohol content in % by volume from Blunt (Subtraction) Method
T. P. Blunt (1891) suggested that the Tabarié division formula always underestimates
alcohol content, and suggested calculating sg and
_{r}sg instead of the ratio, or.
_{w}
FermCalc uses the OIML formula to estimate alcohol content in % by volume from the results of equation (33).
S. Harvey (1892) presented experimental results suggesting that Blunt's formula
is more accurate than Tabarié's. However, a few pages later in the same issue
of Honneyman Method
This method is described on pages 124-126 of
If the difference ( sg)
is greater than the maximum value in the table, FermCalc extrapolates the table
using the OIML formula as a guide._{w}
Hackbarth Method James Hackbarth (2009) showed that the Tabarié approach works reasonably well for dry wines and low-extract beers, but is inaccurate for beverages with higher alcohol and sugar concentrations due to solute-solute interactions that take place at the higher concentrations, an idea that was first proposed by Leonard (1897). Based on extensive laboratory experimentation and detailed analysis of the results, Hackbarth (2011) developed a new model for estimating the specific gravity of a mixture from its sucrose (extract) and alcohol concentrations. Since the spirit-indication procedure gives us measurements of the wine specific gravity and the extract concentration (true Brix), we can treat these as known quantities and use the Hackbarth model to solve for the alcohol content. The Hackbarth model utilizes the following equations.
where
FermCalc solves equations (34) through (40) iteratively using the alcohol content
calculated from the Blunt model as the initial estimate. The iteration loop is
repeated until the difference between the value of ^{-8}.OIML Calculator
The OIML Calculator uses the general formula for calculating the densities of
mixtures of ethanol and water found in
where
Given an alcohol content and a temperature, equation (41) can be solved directly for the density of the mixture. Given a density and a temperature, FermCalc calculates the associated alcohol content using an iterative technique.
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