### Author Topic: % ABV mathematics ???  (Read 1264 times)

#### duxx

• Cellarman
• Posts: 37
• Good Karma Brewing, Warrensburg, MO
##### % ABV mathematics ???
« on: June 08, 2015, 03:35:47 AM »
I've been making fruit beers, for my wife, using various commercial purees and/or fruit concentrates added near the end of primary fermentation.  (Finally found a beer she will drink!)  Anyway, now she wants to know the ABV of the beer?  So how do you figure that out?

Example:
Base beer (Saison) 3 Gallons  OG 1.055  SG 1.003 (before adding fruit)  ABV = 6.8%
Then add 1 pint of wine juice concentrate at 68 Brix = 1.3421 SG
Do you need to know the FG?  I just added it today, so IDK yet.  Can we assume the grape juice will ferment to 0.999?

Help!  Its not good to look dumb in front of your wife.
"Tan and lean like a longneck bottle."  Zac Brown Band.

#### erockrph

• Official Poobah of No Life.
• Posts: 6229
• Chepachet, RI
##### Re: % ABV mathematics ???
« Reply #1 on: June 08, 2015, 03:40:38 AM »
The easiest way is to just calculate a "virtual" original gravity by adding the gravity of any additions you make to the original gravity, then using the measured final gravity to determine the ABV.

In other words, if your beer starts at 1.060 OG and gets down to 1.010, then you add enough fermentables to bring it back up to 1.015, you would simply use 1.065 as your OG for calculating ABV.
Eric B.

Finally got around to starting a homebrewing blog: The Hop Whisperer

#### dmtaylor

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• Two Rivers, WI
##### Re: % ABV mathematics ???
« Reply #2 on: June 08, 2015, 11:54:37 AM »
I know the calculations can get complicated when adding fruit or lactose or whatever after fermentation is almost complete.  It’s not too terrible, you just need to understand that it makes no difference when you add the sugar, you always need to treat it like it’s been there the whole time and add it to the OG.  The other basic concept is of gravity units (GU), and for calculation purposes they need to be multiplied with the volume that they apply to, in order to keep everything on a parts sugar mass basis, then divide by the final volume at the end to get the final gravity of the final volume.  You can always ignore the 1.0 in front of your gravity measurements and just deal with the digits after.  So, 1.055 at 3 gallons becomes 55 * 3 = 165 parts sugar; 1.342 at 1 pint becomes 342 * 1/8 = 43 parts sugar, etc.

In your case, the extra pint of grape juice concentrate adds barely any volume at all (0.125 gallon out of 3.125 gallons total), however since it is concentrated, the sugar it adds (43 total parts sugar) is quite significant.  As stated above, you get 165 parts sugar from the beer itself, then 43 parts sugar from the beer, for a total of 208 sugar points.  Then this is divided evenly among the total volume of 3.125 gallons, so that’s 208 / 3.125 = 67 GU, or 1.067 effective original gravity.

So, your grape concentrate kicked up your effective OG from 1.055 to 1.067.  Yes, you do need to find out your final gravity, because then, like normal, you’ll need to subtract OG from FG then multiply by 131 to get your alcohol by volume.  If gravity heads down to about 0.999, then that’s (1.067 - 0.999) * 131 = 8.9% ABV

Hope this helps.  It is a little complicated, but it makes more sense conceptually if you pretend the fruit concentrate was in the fermenter for the entire time.  This mathematical method ignores time and pretends everything was always in there.
Dave

The world will become a much more pleasant place to live when each and every one of us realizes that we are all idiots.

#### Alewyfe

• Brewer
• Posts: 493
• Fighting for Truth, Justice & Home Brew
##### Re: % ABV mathematics ???
« Reply #3 on: June 08, 2015, 03:46:15 PM »
Good explanation Dave.
Diane
Roseburg, Oregon
Member: Umpqua Valley Brewers Guild
AHA

"Have no fear of perfection...you'll never reach it" ~Salvador Dali

"Growing old is mandatory. Growing up? Definitely optional!"

#### ynotbrusum

• I spend way too much time on the AHA forum
• Posts: 2994
##### Re: % ABV mathematics ???
« Reply #4 on: June 08, 2015, 05:34:28 PM »
Dave - that really was helpful, but how do you handle raw fruit additions after the primary?  Is there a schedule somewhere that can be used to approximate this based on weight added?
Hodge Garage Brewing: "Brew with a glad heart!"

#### erockrph

• Official Poobah of No Life.
• Posts: 6229
• Chepachet, RI
##### Re: % ABV mathematics ???
« Reply #5 on: June 08, 2015, 08:06:49 PM »
Dave - that really was helpful, but how do you handle raw fruit additions after the primary?  Is there a schedule somewhere that can be used to approximate this based on weight added?
I think there is a chart in Denny & Drew's book that estimates pppg for many common (and less common) fruit additions.
Eric B.

Finally got around to starting a homebrewing blog: The Hop Whisperer

#### homoeccentricus

• Brewmaster General
• Posts: 2008
• A twerp from Antwerp
##### Re: % ABV mathematics ???
« Reply #6 on: June 08, 2015, 09:35:55 PM »
There's a formula in American Sour Beers as well.
Frank P.

Staggering on the shoulders of giant dwarfs.

#### duxx

• Cellarman
• Posts: 37
• Good Karma Brewing, Warrensburg, MO
##### Re: % ABV mathematics ???
« Reply #7 on: June 08, 2015, 09:51:30 PM »
Thanks for the explanation, that makes perfect sense.  IDK why I didn't think of it like that.

After my post I thought of the whole fruit question as well.  I'll look those numbers up.

So what about commercial fruit puree?  I guess treat it just like a sugar addition since the Brix concentration is typically on the label?
"Tan and lean like a longneck bottle."  Zac Brown Band.

#### ynotbrusum

• I spend way too much time on the AHA forum
• Posts: 2994
##### Re: % ABV mathematics ???
« Reply #8 on: June 08, 2015, 10:20:25 PM »
Dave - that really was helpful, but how do you handle raw fruit additions after the primary?  Is there a schedule somewhere that can be used to approximate this based on weight added?
I think there is a chart in Denny & Drew's book that estimates pppg for many common (and less common) fruit additions.

There's a formula in American Sour Beers as well.

I have them both, so I will use that information in my upcoming early autumn Bretted Blackberry Saison....the harvest should be plentiful according to my source.
Hodge Garage Brewing: "Brew with a glad heart!"

#### HoosierBrew

• Global Moderator
• I must live here
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• Indianapolis,IN
##### Re: % ABV mathematics ???
« Reply #9 on: June 08, 2015, 10:32:45 PM »
so I will use that information in my upcoming early autumn Bretted Blackberry Saison....the harvest should be plentiful according to my source.

That sounds like a really nice beer. I look forward to seeing how it comes out for ya.
Jon H.

#### ynotbrusum

• I spend way too much time on the AHA forum
• Posts: 2994
##### Re: % ABV mathematics ???
« Reply #10 on: June 09, 2015, 11:35:22 AM »
so I will use that information in my upcoming early autumn Bretted Blackberry Saison....the harvest should be plentiful according to my source.

That sounds like a really nice beer. I look forward to seeing how it comes out for ya.

Yea - my source is my brother-in-law, who has a patch behind his house....he was a BMC guy who has fully converted to Homebrew lover.  He got into sours last year when I used his Blackberries as a secondary addition to a saison...it seems if you can get folks involved in even a small way with your beers, they look at homebrewing from an altogether different viewpoint and they open up to new varieties that they otherwise would not even try.
Hodge Garage Brewing: "Brew with a glad heart!"