Help w/ final ABV Calc

I have a challenging calculation I need help with.

I have the following numbers:

OG: 1.040

At week two I racked to secondary on top of 2 quarts of juice...

Wort Grav: 1.009
Juice Grav: 1.059

And then two weeks later at bottling:

FG: 1.015

Can anyone help with the ABV calculation? Given the juice addition, I know it's not as simple as it normally is.

Thanks!

Ah, I see. Good math question. I'm sure someone has it on the top of their head, but I'm going to try to figure it out. It's not going to be much but still a fun problem.

I can't do the math for you without knowing your batch size, but it's just a weighed average. You can compute a "theoretical OG" (your OG if you had added the juice at the beginning), and use this to estimate your ABV.

( wort volume * wort OG + addition volume * addition OG ) / ( wort volume + addition volume )

6 gallons was batch size.

So is this right (i've converted everything to quarts):

(24 * 1040 + 2 * 1059) / (24 + 2)
=
(24960 + 2118) / (24 + 2)
=
27078 / 26
=
1041.46

So Theoretical OG would be 1041 and I'd use the actual FG of 1015 to come up with an ABV of 3.42%

Is that right?

yup, except something went wrong with one of your SG readings. even if the juice didn't ferment at all, the FG would have only went up to 1.013

The math is right, but on second look there's something fishy about your readings.

If your FG before racking onto the juice was 1.009, there's no way you could end up with a FG of 1.015 after racking onto two quarts of 1.059 juice.

Two quarts of 1.059 juice has 29.5 points of sugar per gallon, and thus should have only increased things by a couple units of gravity (to 1.013 by my calculations). It's not possible to have a post-secondary gravity above that.

Even if we just dismiss that fact as measurement error, it means your juice didn't ferment at all. What was it?

Edit: oops...dcp beat me to it

hmm... i don't know. i guess one of the readings could have gotten flubbed. i'm usually pretty good about that sort of thing.

i had no apparent fermentation activity after adding the juice, and my hygrometer reads in increments of 2, and before temp correction the FG reading was 1014 (w/ temp correction bringing it to 1015... or so i thought). i suppose i could have been off a tick-mark and it was actually 1012???