Need help calculating abv

[eetu]

Wasn't sure where to post this but here it goes..

A while ago I brewed a "kitchen sink" RIS where I threw pretty much all leftover malts from previous batches. I tried to keep the recipe within reasonable norms but knew it was going to be very intense.

After a week or so it was still bubbling now and then so I racked into secondary and the plan was to keep it there for a good while. After a month I took my first sample and the gravity had dropped from 1.093 to 1.035 which makes 7.7% abv and only about 60% apparent attenuation. Not a huge surprise since this is my first really BIG beer.

The issue was the taste. Just way too harsh roasty aftertaste and together with firm bittering it was never going to be a pleasant sipper.

So I did this. Boiled some water and dry extract, chilled it, added to the fermentor and pitched some fresh yeast. It started fermenting just fine so no issues there.

But the question is this. How do I calculate my final abv? Just couldn't get my head around it. Here are the numbers.

Original batch size 7.5L minus trub loss.
OG 1.093
Volume after secondary 6.2L
FG 1.035
ABV 7.7%

Added after fermentation:
2.3L of vort with an OG of 1.082

So now I have 8.5 litres of beer fermenting in my Speidel with no clue how to calculate the final ABV.

 

[kh54s10]

I don't have a clue either. But, personally, I would focus on taste and not concern myself with what the ABV is.

 

[eetu]

I don't have a clue either. But, personally, I would focus on taste and not concern myself with what the ABV is.

Same here, I'm fine knowing I have 8 litres of (probably) crappy beer with an abv around 8. Just asking out of curiosity.

 

[JamesonFan]

How about high? The ABV is going to be high. Like "knock you on you a$$ after 2" high.

Honestly, just take another gravity reading and plug your OG and FG into a calculator and see roughly where you come in at.

 

[BitterSweetBrews]

Did you take a gravity after you added the extract?

I wonder if you could do some sort of blending formula average, based on the gravity of the initial amounts. I don't know if there is a plausible formula to use but bet there is probably one out there somewhere.

You may try something like this. Again, I have no idea if this is correct, but it might get you into the ballpark (I am just pulling this out of my ass).

It could be something like:
(7500ml * 1.093) = 8197.5,
(2300ml * 1.082) = 2488.6,
(8197.5+2488.6) = 10,686.1,
10686.1 / (7500+2300) = 1.0904 - the new SG to calculate final ABV and attenuation against.

Good luck.

 

[Hwk-I-St8]

I'm guessing you could do a weighted average type calculation. Take original volume * original gravity + addition volume * addition gravity. Take that, divide by total volume and I'd think that would yield an OG value.

Then take your final gravity and calculate ABV as normal.

This is just my guess on how to do it. I'm no guru.

 

[rmyurick]

What the last guy said, except: I would use 6.2L as the "original volume", so (6.2*93+2.3*82)/8.5 = 90

(1.090)

 

[daspooper]

BitterSweetBrews is correct! So is rmyurick! I did my analysis a little differently from BSB, but we came to the same answer.

We know that mass can't be created or destroyed, so the total mass of the sugars will be the same as the two added, or
(I) M_f = M_a + M_b,
where I've taken M_a to be the original mass of sugar, M_b to be the added, and M_f to be the final. The gravity of a solution can be written as
SG_a = M_a * g / V_a
where V_a is the volume of the solution and g is acceleration due to gravity. solving for M_a, we have M_a = SG_a * V_a / g. Plugging this back into (I) for each mass, we have
SG_f * V_f / g = SG_a * V_a / g + SG_b * V_b / g
solving for SG_f gives
SG_f = (SG_a * V_a + SG_b * V_b) / V_f.

Plugging in your numbers, where I put V_a = 6.2 L and V_b = 2.3 L, I find that SG_f, or your OG = 1.090. So by adding a bit of wort water you actually decreased your OG because the second mixture had a lower SG than your first wort. You'll get about 2.3 L more beer, though.

 

[eetu]

Nice, thanks! Actually I believe the final ABV will be slightly higher than rhe original 7.7%, since the extract is highly fermentable. Not like it really matters, though.

 

[BitterSweetBrews]

What the last guy said, except: I would use 6.2L as the "original volume", so (6.2*93+2.3*82)/8.5 = 90

(1.090)

Since that is the 6.2L volume is after he put it into secondary wouldn't that skew the result? If that is the case you would need to figure out trub loss from the DME he added too. Starting gravity is the a measure of sugars in the initial volume. Fermenter loss is not taken into account (or volume since you are not adding anything). Regardless, it still ended up at 1.090 when rounded. Anyway, this isn't rocket science, close enough is good enough.

I wonder how you would do the same if you were say adding a bunch of fruit into the secondary.

RDWHAHB.

 

[daspooper]

eetu - The final abv will not be higher than if you had not added the second bit of wort; yes you added more fermentables, but you added more water as well. That additional bit of water was large enough that you expanded your total volume more than you added fermentables. ABV is a measure of concentrations, and concentrations depend on the amount of solute (fermentables in this case) and solvent (water).

BitterSweetBrews - I also used the 6.2 L with the idea that what mattered is the amounts you are mixing together, not the initial volume that you had. As you say, though, with rounding it all comes to the same gravity.

For adding fruits, I suppose if you made a slurry in a blender or used those concentrate cans you could measure the gravity of the mixture, and then do this same math to get an idea of your effective original gravity.

 

[ed007]

This is a very good approximation that works for the majority of the brews:
(OG-FG)*131.25