How to Calculate Required Priming Wort at Bottling Time?

Question

I would like to understand how to calculate how much priming wort I need to add at the bottling stage to reach a desired carbonation.

Desired Carbonation: 6 g/l Extract: 17°P Amount of fermented beer: 17 l

1. I will fill at 22°C so I have 1.6 g/l.
2. I require 6 g/l so I need to add 4.4 g/l carbon dioxide.
3. Sugar(extract) is split 50% alcohol and 50% carbon dioxide so I need to add 8.8 g/l of extract.
4. My wart is 17°P which is 170 g/l so…

Working backwards with a guess I can see that I need to add approximately 0.9L but I would like to know how to perform the final calculation to get the precise amount.

Answer 1

Priming with wort (aka priming with gyle) is a bit tricky to accurately calculate. As Pepi mentions, you aren't working with fully fermentable sugars, so using a direct sugar calculation will be off.

When I primed with gyle, I used a calculation based on Papazian's guidelines in the Joy of Homebrewing. I made the assumption that his calculations were to get 2.8 volumes. Note that is entirely manufactured. From there, I used this calculation:

gyle in qts = (GALLONS_IN_BATCH / 5) * (60/(1000 * (SG - 1))) * DESIRED_VOLUMES/2.8

YMMV

In answer to Jards, my results were good for getting desired carbonation. I quit the practice for a couple of reasons, but not related to carbonation. When I would boil the gyle just before priming, it would add a tremendous amount of DMS. I also didn't like storing loads of gyle while everything was fermenting. I was a bit worried if I didn't boil it, the time it was stored (perhaps 6 weeks in some cases) might produce bugs, but in the end, it's probably better than boiling :) Otherwise, I guess you could boil it for longer, but that would make for a long "bottling" day.

Answer 2

This sort of question might be better suited for http://homebrew.stackexchange.com, they should be able to put a few more knowledgable eyes on your question if you haven't asked there already.

That said, I like the priming sugar calculator at Northern Brewer: http://www.northernbrewer.com/priming-sugar-calculator/ because it gives amounts of lots of sugars beyond just corn sugar, like treacle or maple syrup.

Answer 3

If your wort is 17°P, then it's 170 g per Liter. °P are approximately the same as % sugar, and I think you can finish the math.

BTW your added sugar 8.8g/L is in the right range for a highly carbonated beer.

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I came up with about 1 liter of wort (for a 20L batch) assuming the wort should be diluted about 19.3:1 for correct carbonation, but that isn't really right:

1. If the added wort did ferment all the way to zero, your beer would be effectively diluted about 5%.
2. The added wort won't ferment all the way to zero, so you'll be slightly under carbonated according to the above math.

None of that is a really big deal for a homebrewer, we all adjustments based on experience anyway. But if it bothers you, the easy way to avoid those issues is to use a 100% fermentable sugar, and dissolve it in a small volume of water.