Gravity/Density/Sugar Conversions:
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| Temperature Conversions: |
| °C | |
| °F | |
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| Volume Conversions: |
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| Mass Conversions: |
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| Area Conversions: |
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| Alcohol by Ebulliometry: |
| Details: This calculation corrects the ebulliometer reading based on the calibration reading, and then calculates the alcohol content. |
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| Alcohol Prediction (pre-ferment): |
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| Hydrometer calibration temp (°C) | |
| Initial reading | |
| Initial temp (°C) | |
| Final reading | |
| Final temp (°C) | |
| Alcohol (%v/v) | |
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| Specific Gravity | |
| °Brix (refractometer) | |
| Alcohol (%v/v) | |
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| Initial °Brix (refractometer) | |
| Current °Brix (refractometer) | |
| Initial Gravity | |
| Current Gravity (SG) | |
| Current Gravity (°Brix hydrometer) | |
| True °Brix | |
| Residual Sugar (g/L) | |
| Current alcohol (%v/v) | |
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| Initial °Brix (hydrometer) | |
| Current °Brix (hydrometer) | |
| True °Brix | |
| Residual Sugar (g/L) | |
| Current alcohol (%v/v) | |
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| Dilution (%v/v of juice) | |
| °Brix reading (of dilution) | |
| Actual °Brix | |
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| Actual reading | |
| Reading in? | |
| Reading temp (°C) | |
| Calibration temp (°C) | |
| Corrected reading | |
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| SO2 Aspiration/Oxidation Calculation: |
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| Calculate Molecular SO2: |
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| Titratable Acidity: |
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| Dissolved Solids: |
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| Simple Deacidification: |
- Calcium carbonate - CaCO3
- Potassium carbonate - K2CO3
- Potassium bicarbonate - KHCO3
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| Double Salt Deacidification: |
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| Current | |
| Desired | |
| Units? | |
| Estimated finishing SG | |
| Correction for DSOS | |
| Potential alcohol (current) | |
| Potential alcohol (chaptalised) | |
| Volume of must (L) | |
| Mass of sugar to add (kg) | |
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| Initial must °Brix | |
| Desired alcohol (%v/v) | |
| Spirit alcohol (%v/v) | |
| Volume of wine | |
| Desired °Brix in finished wine | |
| Alcohol produced by fermentation (%v/v) | |
| Fortify when hydrometer reads (°Brix) | |
| Volume of spirit to add | |
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| Current alcohol (%v/v) | |
| Desired alcohol (%v/v) | |
| Spirit alcohol (%v/v) | |
| Volume of wine | |
| Volume of spirit to add | |
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| Concentration of fining used in trial (mg/L) | |
| Volume of wine used in trial (mL) | |
| Volume of fining solution used (mL) | |
| Concentration of fining for addition (mg/L) | |
| Volume of wine to fine (L) | |
| Concentration of fining in wine (mg/L) | |
| Volume of fining solution to add to wine (mL) | |
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| Desired concentration (mg/L) | |
| Volume of wine/juice (L) | |
| Mass of additive required (g) | |
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| Percentage active (%) | |
| Desired concentration (mg/L) | |
| Volume of wine/juice (L) | |
| Mass of additive required (g) | |
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| Details of Calculations:
Gravity / Density Conversions: Every value is calculated from specific gravity. If another value, such as Baume is provided, it is first converted to specific gravity, and then all other values are calculated from that. Calculating °Brix from SG is based on an expression from a polynomial fit to a large data set: brix = 143.254 * sg3 - 648.670 * sg2 + 1125.805 * sg - 620.389 Potential alcohol is calculated as discussed in the alcohol predicition section, with the assumption of a final gravity of 1.000, and a correction for DSOS of 0.007. Oechsle has a simple relationship with SG: oechsle = 1000 * (sg - 1.0) Baume is also a simple relationship: ba = 145 - (145 / sg) Babo/KMW is also a simple relationship: KMW = baume * 1.53 Grams per litre is obviously simply: gl = 1000 * sg Grams per litre of dissolved solids is calculated from the specific gravity, and the °Brix. Subtly, these measure different things, the specific gravity tells us the density of the liquid (grams per litre) and the °Brix tells us the dissolved solids (percentage mass of solute to solution - grams per 100 grams). This allows us to calculate the dissolved solids, thus: dissolved solids = gravity * (brix * 10) The gravity tells us how much 1 litre of the liquid weighs (in kg) - we then multiply this by the dissolved solids ratio to give dissolved solids per litre. 'brix * 10' simply corrects the °Brix value from being grams per 100 grams to being grams per kg. Thus, we time number of kg in one litre, by the number of grams dissolved per kg, and are left with the number of grams per litre. To get from any of those values back to specific gravity involves a rearrangement where possible. For °Brix to SG, another expression was generated by polynomial analysis: sg = 0.00000005785037196 * brix3 + 0.00001261831344 * brix2 + 0.003873042366 * brix + 0.9999994636 Potential alcohol to sg is a complex rearrangment, it works out to be: sg = (9221 * pa + 805600) / (3000 * pa + 800000) Temperature Conversions: Simple linear relationship: F = C * (9 / 5) + 32 C = (F - 32) * (5 / 9) Volume Conversions: Simple linear relationships: US gallons = litres * 0.2642 Gallons = litres * 0.22 Mass Conversions: Simple linear relationships: Tonnes = kilograms / 1000 Tons = kilograms * 0.0009842 Pounds = kilograms * 2.205 Area Conversions: Simple linear relationship: Acre = hectare * 2.4710538 Note that this is an international acre, a US survey acre is slightly different, with a conversion factor of 2.4710439. Alcohol Prediction (pre-ferment): This method of alcohol prediction is based on the method proposed by Duncan and Acton in Progressive Winemaking, the formula used is: pa = 1000 * ((sg - dsos) - estsg) / (7.75 - 3000 * ((sg - dsos) - 1.0) / 800) Where: dsos = Correction for Dissolved Solids Other than Sugar sg = measured specific gravity estsg = estimated finishing gravity Alcohol by Ebulliometry: Initially, the ebulliometer degree is calculated: ebulliometer degree = calibration - reading This essentially yields the number of degrees below the boiling point of water, at which the sample is boiling. Next, a polynomial expression generated from a large data set is used to give the alcohol (% by volume): alcohol = 0.0002590805845 * d4 - 0.0006404605357 * d3 + 0.001926392743 * d2 + 1.364664067 * d - 1.29216576 Where d = the ebulliometer degree. Alcohol by Spirit Indication: This calculator uses the same logic as in the 'Hydrometer Temperature Correction' calculator for correcting the readings for the temperatures at which they were taken. The difference between the initial and final gravities is then used to calculate the alcohol using the following formula: alc = 0.008032927443 * si2 + 0.6398537044 * si - 0.001184667159 Where: si = spirit indication (the difference between the gravities * 1000) Alcohol from Hydrometer & Refractometer: This calculation uses the following formula: alcohol by vol = 1.646 * b - 2.703 * (145 - 145 / s) - 1.794 Where: b = °Brix reading (from refractometer) s = specific gravity (from hydrometer) Monitor Ferment Progress with a Refractometer: A set of calculations are performed, first to calculate the initial gravity from the inital brix: ig = 1.000898 + 0.003859118 * ib + 0.00001370735 * ib2 + 0.00000003742517 * ib3 And then to calculate the current gravity from the initial and current brix: cg = 1.001843 - 0.002318474 *ib - 0.000007775 *ib2 - 0.000000034 * ib3 + 0.00574 *cb + 0.00003344 * cb2 + 0.000000086 *cb3 The alcohol by volume is calculated thus: abv = 0.93 * ( ( 1017.5596 - ( 277.4 * cg ) + ( 1.33302 + 0.001427193 * cb + 0.000005791157 * cb2 ) * ( ( 937.8135 * ( 1.33302 + 0.001427193 * cb + 0.000005791157 * cb2 ) ) - 1805.1228 ) ) * ( cg / 0.794 ) ) Where: abv = alcohol by volume cg = current specific gravity cb = current Brix reading (refractometer) NOTE The 0.93 conversion factor was added based on experimental results to make the alcohol prediction for this particular calculator more accurate. The residual sugar (in grams per litre) is calculated thus: residual sugar = specific gravity * true brix Spirit indication is calculated form the current alcohol thus, and used to adjust the current gravity, so that true Brix and residual sugar can be established: si = (2 * SQRT ( 626159497 ) * SQRT ( 35209254016727200 * abv + 448667639342033000 ) - 33520822512398 ) / 841662180975 This is then used to calculate the corrected SG: corrected_sg = current_sg - ( 1 - ( spirit_indication / 1000) ) + 1 Note that this alcohol calculation is different than the one used in the alcohol by refractometer and hydrometer as it gives more reliable results when coupled with the other calculations used to monitor fermentation using a refractometer. Monitor Ferment Progress with Hydrometer: This calculator uses an assumption of the efficiency of alcohol production to calculate the 'true' Brix from the fall in Brix observed with a hydrometer. The derrived formula is: True-Brix = ( 97 * i + 1200 * h ) / 1297 Where: i = initial Brix h = current Brix (from hydrometer) The above formula is derrived from the more easily understood: Hydrometer reading = ( Brix_initial - Brix_current_true ) / 1.8 High (off-scale) °Brix by Dilution: The calculations involved in this calculator are the same as those used in the gravity/density/sugar conversions. First the measured °Brix is used to calculate the gravity, which is then combined with the °Brix to calculate the dissolved solids. The dissolved solids is multiplied by (100/d), where d is the dilution percentage. So a dilution of 50% would mean multiplying the dissolved solids by 2. This number is then converted back to °Brix. Hydrometer Temperature Correction: The hydrometer temperatre correction for SG is performed with this expression: corrected-reading = r * ((1.00130346 - (0.000134722124 * t) + (0.00000204052596 * t2) - (0.00000000232820948 * t3)) / (1.00130346 - (0.000134722124 * c) + (0.00000204052596 * c2) - (0.00000000232820948 * c3))) Where: r = reading c = calibration temperature This expression is based on °F, so the temperatures are first converted. For °Brix, the expression used is: correction = 0.0000006907947565 * temp4 + 0.0000008650898228 * temp3 * apb + 0.0000002111610273 * temp2 * apb2 - 0.000000420289855 * temp * apb3 + 0.0000000000000000003388131789 * temp4 - 0.00002646880494 * temp3 - 0.00003812273795 * temp2 * apb + 0.00002132555958 * temp * apb2 + 0.0000003140096619 * apb3 + 0.001470413886 * temp2 + 0.0003854292164 * temp * apb - 0.00001254869767 * apb2 + 0.04799327348 * temp + 0.0002013056055 * apb - 0.002157758291 Where: correction = is the correction factor, added to the observed °Brix temp = is the temperature difference from calibration (that is, reading temperature - calibration temperature) apb = is the apparent °Brix, as read on the hydrometer SO2 Aspiration/Oxidation Method: The following formula is used: SO2 = ( t * m * 1.6 * 1000 * 20) / v Where: m = molarity of NaOH t = titre of NaOH required (mL) v = volume of sample used (mL) Calculate Molecular SO2: The following formula is used to calculate the molecular SO2 from the free SO2 and the wine pH: Molecular SO2 = FSO2 / ( 1 + 10( pH - 1.81 ) ) Where: FSO2 = Free SO2 pH = pH of the wine sample The formula is then rearranged to calculate the required level of free SO2 to achieve a desired level of molecular SO2: Free SO2 = MSO2 * ( 1 + 10( pH - 1.81 ) ) Where: MSO2 = Molecular SO2 pH = pH of the wine sample Titratable Acidity: The following formula is used: ta = ( t * m * 75 ) / v Where: m = molarity of NaOH t = titre of NaOH required (mL) v = volume of sample used (mL) Calculate Dissolved Solids: Initially the alcohol is calculated in the same way as for the 'Alcohol from Hydrometer & Refractometer', and then the following formula is used to calculate the dissolved solids: ds = ( ( s * 1000 ) - 1000 + a * 1.264 ) * 2.52 Where: s = specific gravity a = alcohol, percent by volume Simple Deacidification: Simple deacidification is straight forward to calculate. Firstly, the difference between the current TA and the target TA is obtained, giving us the number of grams per litre we need to remove, this is then multiplied by the number of litres, to give the total number of grams of tartaric acid to remove. As the deacidification agents used here react with tartaric acid in a 1:1 stoichiometric ratio, the factor to convert between grams of tartaric acid and grams of neutralising agent can be found by dividing the molecular mass of the agent by the molecular mass of tartaric acid. Thus, the overall formula is: mass of agent (g) = ( ( current TA - Target TA ) * vol ) * (Mr agent / Mr tartaric acid) Where: Mr = molecular mass 150.087 = Mr of tartaric acid 100.087 = Mr of calcium carbonate 138.2055 = Mr of potassium carbonate 100.11 = Mr of potassium bicarbonate Double Salt Deacidification: Double salt deacidification is somewhat more complex than simple deacidification. A portion of juice is removed and completely deacidified, that is, unlike with simple deacidification, tartaric and malic acid are removed. This portion is then blended back to the bulk of the wine to have the desired effect. The volume to treat is calculated with the following formula: volume (L) = ( ( current TA - target TA ) * total volume ) / current TA The recommended volume to treat is this minimum technical volume multiplied by 1.05. The following formula is then used to calculate the mass of calcium carbonate (or Acidex® etc): mass (kg) = ( ( current TA - target TA ) * total volume ) * ( ( 1 / 150.087 ) / 10 ) Where: 150.087 = the molecular mass of tartaric acid 10 = is simply a conversion to make the mass express in kg Chaptalisation: The alcohol calculation carried out here is identical to that carried out in the 'Alcohol Prediction (pre-ferment)' section. The chaptalisation calculation is based on calculation of dissolved solids (grams per litre) as discussed in the 'Gravity/Densit /Sugar Conversions' section. The difference between the desired and the current values is then simply multiplied by the number of litres to be chaptalised. Fortification Point: This calculator finds the fortification point for making fortified wines which contain residual grape-sugar, such as Port. The formulae are derrived from the following: Brix_in_fortified_wine = Brix_must / ( 1 + (1 / R) ) R = ( Alcohol_spirit - Alcohol_target ) / ( Alcohol_target - Alcohol_must) Alcohol_in_fortified_wine = ( Brix_initial - Brix_current ) / 1.8 True-Brix = ( 97 * Brix_initial + 1200 * Brix_Current ) / 1297 These are combined and used to derive: Fortification_Point = - ( 291 * Brix_initial * Alcohol_target + ( 3891 * Brix_final - 291 * Brix_initial ) * Alcohol_spirit - 2000 * Brix_final * Brix_initial ) / ( 3600 * Alcohol_target - 3600 * Alcohol_spirit + 2000 * Brix_final ) Fortification (spirit addition): This calculator is simple, the calculation is exactly the same as a traditional Pearson's square. The following is the formula used: spirit_to_add = vol_of_wine / ( ( spirit_alc_concentration - desired_alc_concentration ) / ( desired_alc_concentration - current_alc_concentration ) ) Fining Trial Based Additions: The first calculation is to find the concentration used in the trial: concentration = (fining-agent-conc * (vol-fining-used / 1000)) / ((vol-wine + vol-fining-used) / 1000) Where: fining-agent-conc = concentration of the fining agent vol-fining-used = the volume of fining agent used in the trial vol-wine = the volume of wine used in the trial Of course the divisions by 1000 are correcting for the units entered, the simplified equation is: concentration = (fining-agent-conc * vol-fining-used) / (vol-wine + vol-fining-used) This is an accurate calculation as the volume being divided by is the volume of wine AND the volume of the addition. This is often overlooked in calculations such as these, especially when performing them by hand. It is an important point to make, calculations from this equation will differ from quick calculations by hand. The next calculation is to find how much of a solution of a specified concentration must be added to bring the concentration of the juice/wine to a desired concentration, this is discussed in the 'Additions in Solution' section. Solid Additions: This is a very simple calculation: mass-to-add = desired-concentration * volume / 1000 The division by 1000 is simply to provide the correct units. Percentage Solid Additions: This is essentially the same as the solid addition calculation, except that the result is divided by the fraction of the solid that is active: mass-to-add = (desired-concentration * volume ) / (percentage-active / 100) Additions in Solution: This calculation finds the volume of liquid, of a known concentration, which must be added to a given volume of wine/juice to bring the total concentration up to a desired value: volume-to-add = (desired-concentration * wine-volume) /(additive-concentration - desired-concentration) Note that this calculation takes into account the volume of the solution being added, so rather than adding 1L of 100mg/L additive to 100L of wine to give the wine a concentration of 1mg/L, the calculation shows that we need to add 1.010L. Back to top |
