Found this short hand equation recently and really comes in handy. Thought I’d share. You’ve got a kettle of 1.048 pre-boil wort. It’s 15 gallons volume now. You only want to increase gravity a few points, shooting for 1.052 OG. Tv = Target Volume Cv = Current Volume Tg = Target Gravity Cg = Current Gravity Tv = (Cv x Cg) / Tg Tv = (15 x 48) / 52 Tv = 13.85 (gallons) To hit your OG, boil down to 13.85 gallons. Hope this may come in handy to you all. Cheers.
To scientists like myself, this is simple conservation of mass. Sugar doesn't evaporate (well not in any meaningful way for homebrewers anyway). Therefore volume times gravity points has to stay the same throughout the boil. You'll end up with the same V * G anywhere in the boil. So, starting with 15 gallons of 1.048, you've got 15 * 48 = 720 points to be divided later to any volume & gravity combo. You want 1.052? Simply divide 720 / 52 = 13.85. Same answer as you, just a different way of conceptualizing it. Might be helpful to some people.
So much of the important stuff in brewing is about concentrations/dilutions. If more people took the time to think about it, we'd see less claims of 95% mash efficiency with no-sparge BIAB, or one-pack-fits-all yeast pitches. It's funny, but when I read @hoptualBrew's formula, I thought about @dmtaylor's not yet posted conceptualization. Maybe I'm a scientist too.
