How to calculate ABV when adding fermentable sugar or fruit to secondary fermentation?

Question

Fermentable Sugar, e.g. Maple Syrup
I brewed a Maple Stout before Christmas in which I racked the beer to a secondary fermentation vessel where I added 550g of Maple Syrup. I let it sit at 12ºC for 4 days before racking to keg. The schedule was as so:

Day 0,  O.G. = 1.067
Day 10, S.G. = 1.015, transfer to secondary, S.G. = ?
Day 14, F.G. = 1.017, transfer to keg

I didn't think to take a gravity reading after mixing the beer with the Maple Stout (doh), but even if I did, is that how the ABV would be calculated? Adding the 6.83% of 1.067-1.015 and X% of 1.0xx-1.017. E.g. 1.020-1.017 is 0.39% so 6.83% + 0.39% = 7.22%?

As Christmas was around the corner I just labelled it up as 7.2% and let it be, but for future brews I want to be able to know the exact ABV.

Fruit
Any sort of sugar or syrup would be the same as whatever method is described for above, but fruit I imagine would be more difficult.

How would one make the calculations if adding fruit? For example, using the same gravity readings above for Day 0 and Day 10 of 1.067 to 1.015, how would you work out the ABV if adding 500g of Mango and 500g Apricot into the secondary fermentation? Or any other fruit for that matter. How do the breweries do it?

Answer 1

The simple answer is: for whole fruit it's difficult to estimate - how much sugar was extracted from the fruit?!

The potential gravity contribution of fruit juice can be determined simply by putting some juice into a refractometer. Obviously it's possible to squeeze the juice out of the type of fruit in use. Generally fruit sugars are comprised of fructose, sucrose and glucose, all of which are 100% fermentable. So if the addition is fruit juice, that's some fermentables, and some dilution (from water in juice). However, if the juice-water contribution is just considered part of the brewing liquor, this part of the problem disappears, leaving just a sugar addition.

So say you add 1 litre of juice, at 12% sugar instead of 1 litre of brewing liquor, theoretically that's an addition of around 120 grams of sugars.

If we consider the maple syrup to be a juice, it's around 66% sugar. Thus in 500g there's 330 grams of sugars and 170 grams of water (approximately).

In the OP's question, the OG was 1.067, in say 20 litres.

Grams per litre of dissolved solids can be calculated from dissolved solids = SG * (SG_in_Brix * 10). So with an SG of 1.067 that's 175 grams per litre, and for 20 litres 3500 grams (175 * 20). So with the fruit-juice sugar addition, that's now 3800 grams in 20.17 litres.

Back-calculating this gives an OG of of 1.072 (roughly). This gives an AbV of 7.3%

The SG → Brix formula is: brix = ( 143.254 * sg_cubed ) - ( 648.670 * sg_squared ) + ( 1125.805 * sg) - 620.389

Further Reading: https://www.morebeer.com/articles/fruit_in_beer