Calc ABV after secondary adds?

[Fern0022]

I brewed 5gal of cider in a single carboy. Then I added fresh pressed fruit juice to five separate 1gal carboys and topped each of them off with the fermented cider. They all experienced a healthy secondary fermentation, have cleared beautifully, and taste great. But I have no idea how to calculate the abv of these finished ciders due to the changes in water volume & gravity readings during secondary. I did however keep accurate notes.

So if there is anyone with superior knowledge who also happens to like a good puzzle, please help!


5gal Recipe:

5 gal Nature’s Nectar Apple Juice
1 packet Mangrove Jack Cider Yeast M02
5 tsp yeast nutrient
2.5 tsp pectic enzyme
OG: 1.047
FG: 1.00 (~6.17% ABV)

1gal Secondary Recipes:
Blackberry:
-30oz blackberry juice
-90oz fermented cider
-New OG: 1.08
-FG: 1.00

Raspberry:
-22oz raspberry juice
-106oz fermented cider
-New OG: 1.06
-FG: 1.00

Strawberry:
-20oz strawberry juice
-108oz fermented cider
-New OG: 1.04
-FG: 1.00

Cherry:
-22oz cherry juice
-106oz fermented cider
-New OG: 1.08
-FG: 1.00

Peach:
-16oz peach juice
-112oz fermented cider
-New OG: 1.02
-FG: 1.00

 

[magno]

So that I'm understanding correctly...

• I am assuming that the 'New OG' values are the SG of each mixture at the beginning of secondary fermentation... is this accurate? This leads to super high SG values for the juices - were they concentrates?
• Is it safe to assume that all of the mixture OG and FG values have a zero in the thousandths place? This seems like a very unlikely coincidence, and using this assumption if it is not known to be true will add considerable uncertainty to any estimate.
• It appears that you have around 118oz, just under a gallon, of unmixed cider... is this accurate?

Under the assumptions above, I get ABV's of around: 15.1%, 13.0%, 10.5%, 15.6%, and 8.0% in the order that you list the mixtures.

 

[Fern0022]

So that I'm understanding correctly...

• I am assuming that the 'New OG' values are the SG of each mixture at the beginning of secondary fermentation... is this accurate? YES This leads to super high SG values for the juices - were they concentrates? No, the juice is from frozen packs of fruit that I defrosted/re-froze several times, then crushed up, and strained.
• Is it safe to assume that all of the mixture OG and FG values have a zero in the thousandths place? This seems like a very unlikely coincidence, and using this assumption if it is not known to be true will add considerable uncertainty to any estimate. Yes, I used a physical hydrometer because i was under the impression that alcohol in the fermented cider would mess with refractometer readings.
• It appears that you have around 118oz, just under a gallon, of unmixed cider... is this accurate? For some yes, others were closer to 128oz. I try to keep volumes as around 128oz in each gal carboy to make things easier for bottling calculations.

Under the assumptions above, I get ABV's of around: 15.1%, 13.0%, 10.5%, 15.6%, and 8.0% in the order that you list the mixtures.

Thank you so much!!! I’d love to know how you achieved these ABV’s. For future purposes

 

[magno]

I wonder if the fruit that you mashed up left some solids in suspension that made your secondary OG values artificially high... the OG's seem high, and hence the ABV's seem high to me... but what do I know?

Understood about the hydrometer, but the readings without a thousandths place allow for an error of nearly 3% ABV in the estimates. Does your hydrometer have marks every 0.002 gravity points? You should be able to get reasonably accurate readings to the thousandths place with one like in the picture below. You are correct that the refractometer would give an incorrect reading with the fermented cider.

This is how I calculated the ABV's (using Blackberry as an example)... someone else may chime in with a different method:

V_fruit = volume of fruit juice [oz] = 30
V_cider = volume of cider [oz] = 90
V_mix = volume of fruit juice plus cider [oz] = 120

OG_cider = original gravity of cider [gravity points] = 47
OG_mix = original gravity of cider plus fruit juice = 80
OG_fruit = original gravity of fruit juice (solved for below)
OG_apparent = apparent original gravity of unfermented cider and fruit juice (solved for below)

FG = final gravity for all fermentations = 0

OG_mix = (OG_fruit*V_fruit + FG_cider*V_cider)/V_mix
=> 80 = (OG_fruit*30 + 0)/120
=> OG_fruit = 80*120/30 = 320
... the fruit juice is calculated to have an OG of 1.320 - this is around the OG of the cherry juice concentrate that I have used in chocolate cherry stouts... but that is a concentrate and you can almost stand a spoon up in it.

OG_apparent = (OG_fruit*V_fruit + OG_cider*V_cider)/V_mix
= (320*30 + 47*90)/120
= 115
... the mixture would have had an OG around 1.115 if the fruit juice had been added to unfermented cider.

This apparent OG can be used in your regular ABV calc

Of course, these calculations are only as good as the measurements, and the effect of the lack of precision on the SG readings is compounded when the calculated OG is used in another calculation.

BTW, these equations are from 'Designing Great Beers' by Ray Daniels... although he does not use them in quite this way.

 

[Chalkyt]

I was intrigued by your “good puzzle” but didn’t reply yesterday because here on Oz it was Melbourne Cup Day “the race that stops the nation”. It is a bit like Superbowl Sunday… lots of parties and beer leading up to the actual event which is televised nationally. However,

I usually approach such problems from “first principles” and in this case I looked at determining how much alcohol was contributed by fermenting the original cider and then the blackberry juice. I ended up with almost the same results as Mango although the approach is slightly different.

My calculations are rounded off but this doesn’t make much difference to the final result. You can get a false sense of precision using numbers to several decimal places if the initial numbers really aren’t accurate to that level in the first place. Let me put my old University Lecturer cap on and explain the “first principles” approach to your problem…

Firstly a bit of background explanatory stuff (in dark blue in case you want to skip it). but stick with it if you can, the explanation gets a little heavy, but your head shouldn’t hurt too much!

Without the availability of complex chemical analysis, as cidermakers we use SG as a proxy for measuring the amount of fermentable sugar in juice. But SG is a measure of the juice density and not just the sugar content, although most of the measured SG (about 80%) is due to the fermentable sugar with the rest due to non-fermentable compounds like tannins, acids, etc, etc.

In different juices having the same density or SG, this mix of fermentables and non-fermentables can vary by as much as 20% so the amount of sugar available to ferment will be different, possibly resulting in different ABVs. Claude Jolicoeur (The new Cider Makers Handbook) covers this in some detail in Chapter 8 of his book.

Working in metric for a moment (it makes the mental arithmetic easy), fermentation of the sugar in juice produces roughly 48% alcohol and 48% CO2, and in simple terms, a change of about 25g of sugar per litre will change the SG by 10 gravity points. So, a typical apple juice with a SG of 1.050 might have around 130g x 80% of fermentable sugar per litre (1000g or ml of juice) which when fermented produces 50g of alcohol. This results 62 ml of alcohol or a little more than 6% ABV .

Further, calculating ABV% using the common “rule of thumb” formulas will vary a bit according to which formula you use. For example, Andrew Lea (Craft Cider Making) suggests (OG-FG)/8 whereas Jolicoeur uses 127.8 x (OG-FG) which is sometimes rounded to 130 x (OG-FG). These formulas are based on empirical studies of juices and average out the assorted variables like composition of the juice, accuracy of the hydrometer reading etc. They get a close enough result of between 6.0% and 6.5% ABV from the above SG1.050 example, which Andrew Lea suggest is fine for craft cidermaking purposes.

Anyhow, back to solving your problem, using the Blackberry mix and working in fluid ounces…

You had 90oz of fully fermented apple cider (SG 1.000) with an ABV of 6.2% (i.e. 6.2% x 90oz = 5.6oz of alcohol) and 30oz of blackberry juice with an OG of “B” for a total blackberry cider of 120oz and a new OG of 1.080 which the residual yeast in the 90oz of fully fermented apple cider would start fermenting.

So, before the "secondary" fermentation, the now Blackberry Cider was made up of 120oz x SG 1.080 which was 90oz x FG1.000 + 30oz x SG “B”.

Simplifying this a bit, (90 + 30“B”) = (120 x 1.080 or 130) and solving for “B”, gives “B” (the blackberry juice OG) a value of 1.330

A SG of 1.330 will result in an ABV of somewhere between 41% ABV and 43% (say 42%) depending on which formula you use. So the original 30g of blackberry juice when fully fermented will have contributed something like 42% x 30oz =12.6oz of alcohol.

You therefore ended up with 5.6oz of alcohol from the original apple cider and 12.6 oz of alcohol from the now fully fermented blackberry juice for a total of 18.2oz of alcohol in 120oz of Blackberry Cider, so 18.2/120 =15.2% ABV.

Although some of the complicating variables aren't factored in (and in reality tend to cancel each other out), they simply don't make a significant difference. So, this approach can be used for the other ciders. After all, we want to keep things simple.

Hope this helps.

Cheers!

 

[magno]

Nice writeup chalkyt!

It's comforting to see that we got to similar results using different methods.

 

[Fern0022]

Wow guys… talk about a “teach a man to fish vs give him a fish” moment! Thank you for taking the time to educate an new brewer. I really learned a lot here. This is one of the many reasons I’m hooked on brewing. There’s always more to learn and figure out.

Cheers!

 

[Chalkyt]

Happy to help. Just bear in mind that the real answer might be "something like 15%". The calculations were done using your readings which might or might not be accurate to a decimal point or so. As well, we really don't know how much of the blackberry SG was from sugar and how much was from other non-fermentable stuff, so in reality the results are approximate, but good enough.

I guess the point of this comment is beware of "the sanctity of numbers" as I outlined above. Just enjoy the ride.

Good luck!

 

[Fern0022]

Just finished bottling. The colors came through pretty well for frozen fruit. Can’t wait to try them out after they age for few months.

Do you guys typically age your ciders?

If so, do you bulk or bottle age?

Thanks again for all the help!

Cheers,
-F

 

[Chalkyt]

I let mine bottle age. It goes make a difference. This isn't a deliberate plan it is just that my cider is usually bottled around the start of winter and the warmer "drinking" weather is then several months away, although a few "quality control" samples are tasted from time to time.

 

[Maylar]

I bulk age then keg.