Seth's combined sg and dilution abv formula

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seth8530

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Hey guys, I have not really posted all that much on here, but I know their are many of you who value knowing what your ABV is to as accurate of a degree as is possible.

First off, I am primarily a wine and mead maker. However I do have a growing internist in brewing. One of the things that always pains me is when someone says that when they make some wine and say the sg starts off at 1.100 and goes down to 1.000 then they add juice to reach 1.030. . then they drop back down to 1.00 When they calculate their ABV they claim that the ABV would be the same as if they started fermentation from just 1.130. Which is not true because they did not account for the dilution that juice had on the alcohol.

So, Instead of sitting idly by I went off and created a formula that calculates what the actual ABV should be taking into account the dilution the juice would of added.

Unfortunately, no one seems to care about this on any of the other boards I have posted this on. So I figured I would give you guys a go.


125{[OG1-FG1]*vol1+[OG2-FG2]*Vol2+[OG3-FG3]*vol3......}/Total Volume=ABV

Where Vol1 vol2 vol3.... is your total volume at that step.. So if step 1 is 5 gallons of beer and then at step 2 you add 1 gallon of wort vol2 would be 6 gallons.

The derivation of this will be in the next post.

So lets take my above example..

1.130 to 1.00 according to the charts should be around 17.7% alcohol

However, if you account to the dilution of the juice you get

125((1.1-1)*5+(1.03-1)*6)/6
=14.16 ABV
(17.7-14.16)/14.6 [Percent error]

Gives us a 21.23% percent error if we do not account for the dilution.

This can also be applied to any kind of volumetric dilution whether it be honey or sugar.. However, I suspect with sugar it would not cause that great of an impact.
 
% alcohol = alcohol volume/total volume

alcohol = step 1 + step2 + step3

( OG-FG)*125= %alcohol gain per step
Step1

( OG-FG)*125= alcohol gain per step

[(Alcohol gain per step)/]100*current volume = alcohol gained per step.

This may be re written as (OG-FG)*125*current volume /100

This is simplified into (OG-FG)*1.25*current volume = alcohol per step

So, to formulate this all out nice and pretty for your case

[(OG1-FG1)*1.25*volume1]+[(OG2-FG2)*1.25*volume2]+[(OG3-FG3)*1.25*volume3]

this can be simplified once again into

1.25{[OG1-FG1]*vol1+[OG2-FG2]*Vol2+[OG3-FG3]*vol3}= TOTAL ALCOHOL


[Total Alc/Total volume]*100= abv

Thus

125{[OG1-FG1]*vol1+[OG2-FG2]*Vol2+[OG3-FG3]*vol3......}/Total Volume=ABV
 
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