# Boiling (Spirit Indication) Calculator

### Introduction

The Boiling (Spirit Indication) Calculator estimates the alcohol content of a wine from two specific gravity (SG) measurements: one obtained on a sample of the finished wine, and one obtained on a sample of the wine in which the alcohol has been boiled off and distilled water has been added to restore it to its pre-boiled volume.  Four different calculation methods are used to estimate alcohol content:

The calculator will adjust the hydrometer readings for temperature if the measurement temperatures and the hydrometer calibration temperatures are provided.   If the entered SG values are already corrected for temperature, or if temperature corrections are not desired, simply enter 20°C (68°F) in all of the temperature fields and no corrections will be made.

### Input Field Definitions

Hydrometer SG Reading – The initial and final hydrometer SG readings.  The initial reading should be taken prior to boiling, and the final SG reading should be taken after boiling off the alcohol and restoring the sample to its original volume with distilled water.  Range: 0.77193 to 1.55454

SG Reading Temperature – The temperatures of the samples at the time of the initial and final SG readings.  Range: 0°C (32°F) to 40°C (104°F)

Calibration Temperature – The hydrometer calibration temperature(s) of the hydrometer(s) used to take the initial and final SG readings.   Range: 0°C (32°F) to 40°C (104°F)

### Output Field Definitions

Corrected SG (20°C/20°C) – The temperature-corrected initial and final SG values.

Alcohol Content – The alcohol content of the wine calculated from the difference between the initial and final corrected SG values using the four calculation methods listed above.

True Brix (Solids Content) – The total solids content of the wine calculated from the initial and final corrected SG values.

### Calculation Details

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 SG 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 SG of the distillate, which represents the SG of a pure water/ethanol mixture, from which the alcohol content can be estimated. The experimental procedure is summarized below.

1. Measure the SG (sgw) of the wine to be tested.
2. 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.
3. Allow the boiled residue to cool to room temperature.
4. Add distilled water to the residue until the total volume is restored to the original sample volume.
5. Measure the SG of this volume-corrected residue sgr, which will be greater than sgw because the alcohol has been replaced by water.

It is recommended that a narrow-range hydrometer be used for the SG 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 SG of the volume-corrected residue.  First we just need to convert the residue SG 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:

 Bt = Btr·sgr/sgw (5-35)

where:

Bt = true Brix (solids content) of wine, % by weight

Btr = true Brix (solids content) of the volume-corrected residue, % by weight

sgw = SG of wine

sgr = SG of the volume-corrected residue;

The four methods that FermCalc uses to calculate the alcohol content from the SG measurements are described below.

#### Tabarié (Division) Method

Tabarié originally proposed estimating the SG of the distillate from the ratio of the wine and residue specific gravities, or:

 sgd = sgw/sgr (5-36)

where:

sgd = SG of distillate

sgw = SG of wine

sgr = SG of the volume-corrected residue

FermCalc determines the alcohol content in % by volume from sgd by using the OIML formula (OIML, 1973).

This method has a temperature basis of 20°C (68°F).

#### Blunt (Subtraction) Method

T. P. Blunt (1891) suggested that the Tabarié division formula always underestimates alcohol content, and suggested calculating sgd from the difference between sgr and sgw instead of the ratio, or.

 sgd = 1.0 – (sgr – sgw) (5-37)

FermCalc uses the OIML formula to estimate alcohol content in % by volume from the results of equation (5-37).

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 The Analyst, A. H. Allen presented data for sugar and alcohol solutions ranging from 24% to 53% alcohol by weight suggesting that the Tabarié formula was more accurate.  While Blunt is generally credited with showing that the subtraction formula is more accurate than the division formula, the subtraction formula was clearly in use well before Blunt wrote his paper (Mulder, 1857).

This method has a temperature basis of 20°C (68°F).

#### Honneyman Method

This method is described on pages 124-126 of The Art of Making Wine (Anderson & Hull, 1970), and is attributed to the researches of Dr. William Honneyman (1966).  This method is really identical to the Blunt subtraction method described above, so it might seem redundant to include it here.  The main difference is that this method uses Dr. Honneyman’s table below to estimate the alcohol content, and in the Blunt method we’re using the OIML equation instead of a table.

I obtained a copy of Dr. Honneyman’s book and was able to determine that his table is based on the alcoholometric tables of Thorpe (1915), which have a temperature basis of 60°F.  With this information I was able to extend his table to higher alcohol levels and increase the resolution.  Now with the appropriate temperature correction the Honneyman method gives results that are nearly identical to the other boiling methods.  There are very small differences because the temperature corrections are not exact and because the basis of the Thorpe tables is different from that of the OIML equation.

This method has a temperature basis of 15.56°C (60°F).

#### 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 SG of a mixture from its sucrose (extract) and alcohol concentrations.  Since the spirit-indication procedure gives us measurements of the wine SG 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.

 Z = -1.020733575·10-2E1A0.5 + 6.223951696·10-4E2A0.5 – 3.463023825·10-6E3A0.5 + 7.234029153·10-3E1A1 – 4.496851490·10-4E1A2 + 9.045618812·10-6E1A3 – 5.427265684·10-8E1A4 – 1.719663278·10-4E2A1 + 2.302760700·10-9E3A3 (5-38) Eb = E·100/(100 – A) + Z (5-39) Ab = A·100/(100 – E) + Z (5-40) SGWE = (100 – Eb) / [100/fe(Eb) – Eb/fe(100)] (5-41) SGWA = (100 – Ab) / [100/fa(Ab) – Ab/fa(100)] (5-42) SGW = SGWE · SGWA (5-43) SG = 100/[E/fe(100) + A/fa(100) + (100 – E – A)/SGW] (5-44)

where:

Z = correction for solute interactions

A = alcohol concentration, % by weight

E = sucrose concentration (true Brix), % by weight

SG = SG of the ternary solution (wine)

Ab = alcohol concentration in the binary solution, % by weight

Eb = sucrose concentration (true Brix) in the binary solution, % by weight

fa(A) = 11th order polynomial for calculating SG from alcohol concentration based on the OIML general formula (OIML, 1973)

fe(E) = 10th order polynomial for calculating SG from sucrose concentration based on AOAC Plato tables

SGWA = SG of water in the binary solution of alcohol

SGWE = SG of water in the binary solution of sucrose

SGW = SG of water in the ternary solution (wine)

FermCalc solves equations (5-38) through (5-44) 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 SG calculated by equation (5-44) and the wine SG sgw is less than 10-8.

This method has a temperature basis of 20°C (68°F).