How To Use the Pearson Square

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djrockinsteve

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How To...Use The Pearson Square.

The Pearson Square is a simple equasion to allow you to determine a specific gravity, or ph level for your wine.

The best way to explain this is with an example. In this case you have a wine that is too sweet and you want to blend with another dryer wine but don't know how much of each to use. This has nothing to do with volume.

picture.php

A). Represents the gravity of one of your dry wine.
B). Represents the gravity of your sweet wine.
C). In the middle represents the final gravity you want.

The difference of "C" from "A" is "E".
The difference of "C" from "B" is "D".

Now this tells you how much of each wine is needed to achieve the gravity you want. "E" is the number of parts of "A" that you need and "D" is the number of parts of "B" that you need.

In the diagram above "A" is 1.000 a dry wine.
"B" is the sweet wine 1.010
You would like to have your wine at 1.008
After doing the math, "D" is 2 and "E" is 8

You need two parts of the sweet wine blended with eight parts of the dry wine, or one to four.
 
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How To...Use The Pearson Square.

The Pearson Square is a simple equasion to allow you to determine a specific gravity, or ph level for your wine.

The best way to explain this is with an example. In this case you have a wine that is too sweet and you want to blend with another dryer wine but don't know how much of each to use. This has nothing to do with volume.

picture.php

A). Represents the gravity of one of your dry wine.
B). Represents the gravity of your sweet wine.
C). In the middle represents the final gravity you want.

The difference of "C" from "A" is "E".
The difference of "C" from "B" is "D".

Now this tells you how much of each wine is needed to achieve the gravity you want. "E" is the number of parts of "A" that you need and "D" is the number of parts of "B" that you need.

In the diagram above "A" is 1.000 a dry wine.
"B" is the sweet wine 1.010
You would like to have your wine at 1.008
After doing the math, "D" is 2 and "E" is 8

You need two parts of the sweet wine blended with eight parts of the dry wine, or one to four.

So doing the math this way would it mean:
A=.992
B=1.008
C=.998

D=.01
E=.006

therefore it's a 6-1 ratio?
 
Following his method if my math is correct. ( Check my math) E=.006,D=.01.. Then you take the number parts of sweet you need per part dry ie .01/.006= .6 parts sweet needed for every part dry.. ie if you had 10 gallons of dry you wold need to add 6 gallons of sweet to it.

However, I have honestly never been a big fan of Pearson squares and I tend to like to think about these matters in a logical manner instead of following a formula.

http://www.brsquared.org/wine/CalcInfo/HydSugAl.htm


So our desired gravity can be described as a sugar density. Lets call that Df for density final. .998 corresponds roughly to 3 grams per liter according to the above chart.

Our initial gravity of .992 roughly corresponds to 1 gram per liter of sugar. lets call that Di for density initial

The amount of sugar we have is by definition the sugar density multiplied by the volume we have. Thus our initial sugar in grams would be 1g/L times*Volume-liters.
Lets assume we start with 25 liters. Thus our wine initially has 25 grams of sugar in it.or Si

The final sugar density that we want is in units of grams per liter. So, .998 roughly gives us 3 grams per liter. Lets call this Df. So logically Df must be equal to the total amount of sugar in the wine after sweetening divided by the final volume after it has been sweetened. The final volume can be expressed as Vf=Vi+Va or the final volume is the initial volume + the added Volume.

Lets call Si the initial amount of sugar in the wine, and Sf the final amount of sugar in the wine and finally lets call Sa the added amount of sugar to the wine. Logically the final amount of sugar in the wine can be expressed as Sf=Si+Sa Ie the sugar in the wine after sweetening is the the initial amount of sugar plus the added amount of sugar.

This gives us the equation Df=(Si+Sa)/(Vi+Va) or the final sugar density is the amount of sugar in the wine divided by the volume of the wine.

Si=Di*Vi Initial sugar is initial sugar density (g/l)* initial volume (liters)
Sa=Da*Va Added sugar is Added sugar density (g/l)* Added volume (liters)
Vi=Volume initial (liters)
Va=Volume to be added (Liters)
Df=Wanted final sugar density (g/l)
Di=Initial Sugar density (g/l)
Da=Sugar density of added substance (g/l)


Lets substitute this in.
xBzuK9a1T1PvjAAAAAElFTkSuQmCC

( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)( Attached as a PDF!)

Lets say we want to solve for the volume of 1.008 wine you need to blend in with this guy to hit .998 assuming an inital volume of 25 liters and inital gravity of .992

Df=3g/l
Di=1g.l
Da=23.5 g/l ( I took the average between 1.005 and 1.010 so this point is actually for 1.0075 instead of 1.008 (17+30)/2 =23.5)
Vi=25 liters

Do a little bit of algebra...


xBzuK9a1T1PvjAAAAAElFTkSuQmCC


U3so2Tkv0FkAAAAASUVORK5CYII=


= 2.439024390 Liters at 1.008 needed to sweeten 25 liters at .992 up to .998.

Anyways, just giving a different method. If you see any errors please give me a shout out. I am pretty sure it is correct because it verified that if I start out with 10 liters at 0 G/L sugar and and sweeten it up with 80 g/L sugar density with a target of 40 g/l sugar density, it said I would need to add 10 liters at 80 g/l to hit 40 g/l/

View attachment Wine.pdf
 
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Lol Seth now my head hurts ! I've gotta be honest and say that is way over this old gals head. Algebra was never my thing.How about when I need the math done I just pm the numbers to you :)
 
Either way eh lol? BTW, the PDF has it all worked out and algebrated already, All ya gotta do is plug the numbers in. But I understand that if it is not how you want to do it. My background leads me to do things this way whenever possible.
 

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