FermCalc - Blending Calculations

Introduction

The Blending Calculations panel calculates the resulting property and volume of a blend of two wines based on the properties and volumes of the wines being blended.  It can also calculate the volumes of the two wines required to achieve user-specified target values of the blend's property and volume.  This will work for just about any property, such as specific gravity, alcohol content, acidity, etc.

Making a Calculation

To make a calculation, follow these steps:

1. Select Calculation > Blending Calculations from the menu, or select the Blending tab at the top of the main window.
2. Select the appropriate volume units for the input fields using the drop-down menus in the right-hand column.
3. Select the desired option in the Solve For dropdown box.
4. Depending on which option is selected, the input fields for the Property and Volume of Wine 1, Wine 2, and the Blend will be either white or grayed-out.  Enter the known values in the white fields, and the calculated values will appear in the grayed-out fields.  Input is required in all of the white fields.

Calculation Details

The blending calculations simply solve a system of two equations for the two unknowns. The volume of the blend is equal to the sum of the volumes of both wines, or

vb = v1 + v2

(1)

where

v_b = volume of blend, liters
v₁ = volume of wine 1, liters
v₂ = volume of wine 2, liters

The property of the blend is equal to the volume-weighted average of the properties of both wines, or

pb = (p1v1 + p2v2) / (v1 + v2)

(2)

where

p_b = property of blend
p₁ = property of wine 1
p₂ = property of wine 2

Given the equations (1) and (2) above, we can do some simple algebra and solve for any two unknowns provided that all of the other quantities are known. FermCalc provides four options:

1. Solve for the Property and Volume of the Blend.
2. Solve for the Volumes of Wine 1 and the Blend.
3. Solve for the Volumes of Wine 2 and the Blend.
4. Solve for the Volumes of Both Wines.

For cases 2 through 4, the property value of the blend must be between the property values of the two wines.  If this is not the case, output fields are highlighted in red and an error message is displayed.

Case 1: Solve for the Property and Volume of the Blend

For this case we specify the properties and volumes of both wines, and we simply need to apply equations (1) and (2) above to calculate the property and volume of the blend.

Cases 2 and 3: Solve for the Volumes one Wine the Blend

For this case, we specify the properties of both wines, the desired property of the blend, and the volume of one of the wines. We need substitute equation (1) into equation (2) and re-arrange to solve for one of the wine volumes. When solving for the volume of wine 1 the equation becomes:

v1 = v2(pb - p2) / (p1 - pb)

(3)

When solving for the volume of wine 2 we need to switch the volumes and properties of the wines as follows:

v2 = v1(pb - p1) / (p2 - pb)

(4)

The blend volume in either case is then calculated from equation (1).

Case 4: Solve for the Volumes of Both Wines

For this case, we specify the properties of both wines and the desired property and volume of the blend. Substituting and re-arranging equations (1) and (2) again we get:

v1 = (vbpb - vbp2) / (p1 - p2)

(5)

The volume of wine 2 is then calculated by re-arranging equation (1) as

v2 = vb - v1

(6)

© 2007-2010 Steve Gross
Last updated 07 January 2010.