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close this bookFood Chain No. 17 - March 1996 (ITDG, 1996, 16 p.)
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View the documentJak fruit - one of nature's gifts
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View the documentOpen-pan sulphitation sugar processing
View the documentWadian - A fermented Indian food
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View the documentThe Pearson square - common calculations simplified
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The Pearson square - common calculations simplified

Many small-scale food manufacturers find difficulty with the calculations involved in mixing two raw materials together to give a final product of known composition (fat content, alcohol content, sugar content etc). The use of the Pearson square makes this type of calculation very simple. The Pearson square was developed many years ago and found particular application in the dairy industry for standardizing milk and blending milks to give a final product with a standard fat content.

Before looking at some examples of the use of this tool it is very important to understand that it can only be used in a two component system for example blending two wines (to give a known alcohol level), or two milks (to give a standard fat content). If more than two components such as protein level and fat level are involved, then more complex 'mass balance' calculations are required.

USE OF THE PEARSON SQUARE

Producing a 10 par cent butter fat cream

In this example homogenized milk with a fat content of 3.5 per cent is to be mixed with a 20 per cent fat cream to give a light cream containing 10 per cent. In what proportions should they be mixed?

First draw a rectangle and label the two horizontal lines with the names of the two products used as shown here.


Figure

Now enter the composition of each ingredient as shown below putting the required final product fat content in the centre of the box.


Figure

Mix the two components by crossing diagonally through the centre figure; subtracting each from the larger figure. The square now appears as shown here.


Figure

Read the results; these show that we need 10 parts milk (shown by the top line) to be mixed with 6.5 pans of cream (bottom line).

PRODUCTION OF PURE SWEETENED FRUIT JUICE

In this example pure orange juice with a sugar content of 10 per cent is to be mixed with a 60 per cent sugar syrup to give a final sweetened juice containing 15 per cent sugar. Drawing the square as described above it should look like this.


Figure

Subtracting diagonally shows that 45 parts (litres) of orange juice needs to be mixed with 5 parts (litres) of sugar syrup to produce a final 15 per cent sugar sweetened juice.

FORMULATING A JAM

In this example fruit pulp containing 10 per cent natural sugar is to be mixed with pure cane sugar to give a jam containing 70 per cent sugar.

Draw the square as before, enter the numbers and subtract diagonally.

The square should look like this.


Figure

This indicates that 30 mixed with 60 parts (kg) a 70 per cent sugar jam. pasts (kg) of fruit of sugar will, give.