Originally Posted by Yooper
In simplest terms, adding 2 gallons of (say) 1.026 wort and then boiling down won't really increase the gravity. Say you had 5 gallons of 1.050 wort, and it was too low. Adding two gallons of 1.026 wort and then boiling more won't appreciably increase the gravity due to the dilution factor. I'm not very good at explaining this- but if you have all day to boil more, and didn't oversparge then it's ok of course. Unnecessary, and probabably lowered the OG even more, but not harmful to the beer unless excess maillard reactions were formed in an ultra-long boil.
I try to not argue too much, especially w\ people with a good rep / track record. This doesn't make sense to me though. These are rough numbers, as I don't remember the exact amounts.
I am shooting for 6 gallons at 1.058.
After first runnings and batch sparge, I ended with 8.2 gallons (desired preboil volume) at 1.036. If I had boiled this down to 6 gallons I would have gotten an OG of 1.049.
OG = 1.036 * (8.2/6)
Instead, I sparged again with 2 gallons which gave me 2 gallons at 1.025. This was added to the 8.2 gallons at 1.036 to get 10.2 gallons at 1.0338. Then, this 10.2 gallons was boiled down to 6. Took a long time. 10.8 gallons at 1.0338 boiled down to 6 gallons ends up at 1.0575.
New pre-boil gravity = (1.036 * 8.2 + 1.025 * 2) / 10.2 = 1.0338
OG = 1.0338 * (10.2/6) = 1.0575
My measured OG matches the theoretical OG pretty closely.
So, by sparging for another 2 gallons and just boiling the excess off, I got 6 gallons of 1.058 instead of 6 gallons at 1.049. It wasn't the efficiency I was worried about, I just wanted to get as close to my intended recipe's OG as possible.
For the fuel cost, I agree completely. I use electricity though, so it isn't nearly as much.