Brewing mystery! And math!
I brewed a Belgian Quadrupel today and it ended up a lot stronger than expected. I haven't worked out why.
A big part of brewing is achieving a certain "gravity": amount of dissolved sugar in wort as measured by density. 1.000 is water, and my target was 1.087. Doesn't seem like much, but that's pretty big.
I use BeerSmith, software which helps me with the math. Its prediction for the wort, pre-boil (and pre candi sugar addition) was 1.064 at 7.6 gallons. I stopped the sparge at around 7.2(ish) gallons at a lower 1.057.
There is no arguing with the fact that there's less sugar in the pot than expected. I expected 486 "points" of sugar (7.6 x 64, for 1.064) and instead got 410.
No matter what I do there will never be more sugar in that pot. Unless I add it. Which I did: a 1.8kg brick of candi sugar I'd made using 1kg of table sugar.
The 7ish gallons was boiled down, and eventually I got 5 gallons of wort in the fermenter. My predicted gravity of that wort (the Original Gravity, or OG, for this beer) was 1.087. Instead I got... 1.107.
Which is a jaw dropping difference.
So where did the extra gravity come from anyway? Well, sugar can't appear out of thin air, but there's some things to cover.
Most interestingly, I realized I'd made a recipe error. Remember that 1kg of sugar? Well, I called it 1kg of candi sugar *syrup* in the recipe. Instead, it was a 1.8kg brick of something denser (800g of which, can you believe it, is water... despite its solidity.)
But I knew it had 1kg of actual sugar in it so I made that switch. And my predicted OG went from 1.087 to... 1.092.
OK, so. Next is volume of wort. If you boil off water, the sugar stays behind. So my 5 gallons was actually a little less than my target of 5.25. Let's also say that my kettle loss (amount of wort left behind in the boil pot full of sludge-like "trub"-- the leftover hop residue and protein break- estimated 3/8 gal) was a little less than expected. No more than 1/8 gallon though. So in total, 0.375gal less water.
Running the numbers on that, I get an expected gravity of 1.098-99. Now we're getting closer. But I'm still missing 9 points of gravity after having accounted for the recipe error, boil-off and lossage differences.
But I haven't touched on the low measured pre-boil gravity. If I factor that in, that expected 1.098 becomes 1.084. Versus a measured 1.107. That's a huge discrepancy.
Let's come at it another way. Using my imperial units, 1kg of sugar is 2.2lb. A pound of sugar contributes 46 sugar points (if dissolved in 1gal water you'd have a 1.046 gravity.)
So 2.2lb sugar is good for 101 points. 410+101=511.
511 points of sugar in 5.25 gal of water (our total fermenter volume plus lossage) is... 1.097. Which doesn't match either reality or adjusted prediction.
So. There's a probable arithmetic error on my part somewhere but not enough to account for the discrepancy between 1.097 and 1.107.
What can account for that? Well, possibly a measurement error. Maybe my pre-boil measurement was off. If I hadn't mixed the wort properly, it's possible. Too late to find out.
Anyway, I did adjust gravity from 1.107 down to 1.092 by adding 0.75gal of boiled, cooled water. It'll still be a potent Quad, without being crazy. And it will have a permanent air of mystery...