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 seven categories of unit conversions:

1. Volume
2. Mass
3. Temperature
4. Specific Gravity
5. Acidity
6. Proof
7. Concentration

Making a Conversion

To make a conversion, follow these steps:

1. Select Calculation > Unit Conversions from the menu, or select the Conversions tab at the top of the main window.
2. Select the tab corresponding to the category of unit you wish to convert.
3. Select the Input Units.
4. Select the Output Units.
5. Enter into the Input Value field the value to be converted.

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.

Calculation details are provided below. Only the Specific Gravity, Acidity, Proof, and Concentration conversions are covered in detail since the others are fairly straightforward. Follow the links below for the details.

• Specific Gravity Conversions
• Acidity Conversions
• Proof Conversions
• Concentration Conversions

Calculation Details - Specific Gravity Conversions

The equations for the following specific gravity conversions are described below:

• Specific Gravity <--> Brix
• Specific Gravity <--> Oechsle
• Specific Gravity <--> Grams/Liter, Kilograms/Liter, Pounds/Gallon
• Specific Gravity <--> Baumé
• Specific Gravity <--> Twaddell
• Specific Gravity <--> Potential Alcohol

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 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.

FermCalc linearly interpolates values from tables relating Brix to specific gravity published in the USDA Technical Inspection Procedures, which cover a range from 0 to 80 Brix. I extrapolated the tables above 80 Brix so that the specific gravity at 100 Brix is that of pure sugar, or 1.5805. The USDA data and the extrapolation are shown in the plot below.

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:

Oe = 1000(sg - 1.0)

(1)

where

Oe = degrees Oechsle
sg = specific gravity

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.

Specific Gravity <--> Grams/Liter, Kilograms/Liter, Pounds/Gallon, etc.

These are simple multipliers.

grams/liter = 1000·sg	(2)
kilograms/liter = 1.0·sg	(3)
kilograms/cubic meter = 1000·sg	(4)
pounds/gallon (US) = 8.345406·sg	(5)
pounds/gallon (Imperial) = 10.022415·sg	(6)
pounds/cubic feet = 62.42796·sg	(7)

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:

Bé = 145 - 145/sg

(8)

where Bé is degrees Baumé.

The equation for liquids lighter than water is:

Bé = 140/sg - 130

(9)

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:

Tw = 200(sg - 1.0)

(10)

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 FermCalc uses 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 sg_i of a must, FermCalc assumes the final specific gravity sg_f is 1.0. The equations are as follows in terms of sg:

ap = 1000(sgi - sgf)/F	(11)
F = 7.75 - 3000(sgc - 1.0)/800	(12)
sgc = sgi - 0.007	(13)

where

a_p = potential alcohol, % by volume
sg_i = initial specific gravity
sg_f = final specific gravity
F = conversion factor
sg_c = initial specific gravity corrected for non-sugar solutes

Combining equations (11) through (13) above and assuming that sg_f equals 1.0 yields the following equation.

ap = 1000(sgi - 1.0)/[7.75 - 3.75(sgi - 1.007)]

(14)

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 (14) 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
• Percent <--> Grams/Liter

Acid Reference Conversions

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.

The number of moles of H⁺ ions an acid contributes can be calculated as:

M = i(m/mw)

(15)

where

M = moles of H⁺ ions
i = number of H⁺ ions per molecule
m = mass of acid, grams
mw = molecular weight of acid, grams/mole

The mass of the acid in solution is simply the acidity multiplied by the volume, or:

m = a·v

(16)

where

v = volume of solution, liters
a = acidity, grams/liter

Combining equations (15) and (16) we get:

M = i(a·v/mw)

(17)

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:

i1(a1/mw1) = i2(a2/mw2)

(18)

Rearranging equation (18) to convert from on acid reference to another we get:

a2 = a1(i1/i2)(mw2/mw1)

(19)

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:

grams/liter = 10·percent

(20)

Calculation Details - Proof Conversions

Below are details of the following four proof conversions:

• % Alcohol by Volume <--> % Alcohol by Weight
• % Alcohol by Volume <--> Proof (US)
• % Alcohol by Volume <--> Proof (British)
• % Alcohol by Volume <--> Degrees Sykes

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

The percentages of alcohol by weight and alcohol by volume for a water/alcohol mixture are defined respectively as:

aw = 100(ma/mm)

(21)

av = 100(va/vm)

(22)

where

a_w = alcohol content, % by weight
m_a = mass of alcohol, kg
m_m = mass of the water/alcohol mixture, kg
a_v = alcohol content, % by volume
v_a = volume of the alcohol, liters
v_m = volume of the water/alcohol mixture, liters

We can relate the volumes and the masses of the alcohol and the mixture as:

ma = vasga

(23)

mm = vmsgm

(24)

where

sg_a = specific gravity of alcohol, kg/liter
sg_m = specific gravity of the water/alcohol mixture, kg/liter

Substituting equations (23) and (24) into equation (21) we get:

aw = 100(va/vm)(sga/sgm)

(25)

Then we can substitute equation (22) into equation (25) to get:

aw = av(sga/sgm)

(26)

Re-arranging equation (26) we get:

av = aw(sgm/sga)

(27)

The CRC Handbook of Chemistry and Physics lists values of a_w and the corresponding values of sg_m for water/alcohol mixtures with a_w ranging from 0% to 100%. Using these data along with equation (27) we can construct a table relating a_w to a_v. This table is shown graphically below. FermCalc linearly interpolates values from this table to perform the conversion.

% Alcohol by Volume <--> Proof (US)

The Proof scale in the United States is simply equal to twice the % alcohol by volume, or:

Pu = 2.0av

(28)

where

P_u = Proof (US)
a_v = alcohol content, % by volume

% Alcohol by Volume <--> Proof (British)

The British Proof scale is calculated as follows:

Pb = 1.75av - 100

(29)

where

P_b = Proof (British)
a_v = alcohol content, % by volume

% Alcohol by Volume <--> Degrees Sykes

The Sykes scale is closely related to the British Proof scale and is calculated as follows:

S = 1.75av

(30)

where

S = degrees Sykes
a_v = alcohol content, % by volume

Calculation Details - Concentration Conversions

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:

(1 g) (1 lb / 453.59 g) / [(1 mL) ( 1 gal / 3785.4 mL)] = 8.3454 lb/gal

(31)

Concentrations expressed as mass per unit mass - 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.

© 2007-2010 Steve Gross
Last updated 16 May 2010.