2.5 gallon batch, started with 14.5 quarts water aiming for 12 quart boil size.
I pull 3.6 quarts, my boil rate is 0.05 qt / minute, which means in the 15 minutes I boiled, I lose 0.75 quarts.
First, what is this voodoo you've divined that gets you 2.5 gal of packaged beer starting with only 3gal pre-boil? Have you discovered a way to practically eliminate boil-off, trub and losses? (kidding of course, but I *am* curious)
Second, that is a crazy amount of boil-off for that short of time. (especially considering your main system has practically no boil loss) Boil-off rate is determined by a nutty amount of variables, a few of which are ambient temp, wind-speed, and humidity. (not even considering the heat of the flame under the pot) If you are indoors, that practically eliminates those three variables unless you have a stove hood on full gale sucking the decoction out through the roof. Perhaps you are boiling your decoctions 'too hard'?
Another thing I noticed, you're working with math to way too many decimal places for the instruments you are using. For example, how did you measure 2.73 qts for the first decoction?
.23 of a quart (since 2.5qts is easy enough to measure) is 7.36 ounces. Are you really measuring to that resolution? .36 ounces could be easily less than 1/16 or 1/32 of an inch in a measuring cup. That could be the difference in the thickness of the *line* on the cup.
My point here is that first, I'd figure out what my measurement 'resolution' is, then realize that my real-world ± when I measure is going to thus cause a bigger ± in my equations. (thus, you are estimating/rounding throughout, not just at the end)
And that could very well be why your volumes seem whacky. You're assuming a precision that isn't there.
Find a metal 'yard stick' or other ruler tall enough for your vessels. It needs to be incremented to 1/32. (1/64 is just too hard to read) Then figure out your vessel dimensions. For a kettle, you'll need your diameter. Your gallons/inch will be:
[π (d ÷ 2)^2] ÷ 231
Then multiply your height (vessel or actual level, whichever you want to measure) by that result. That is about as accurate as you are going to get. Measuring with cups or pitchers just won't cut it. (if you need precision) You can figure a similar factor for your decoction pot. If you have an odd shaped vessel (like a rectangular cooler with rounded corners) you're going to have to do more fancy math, or estimate, (!!) or install and carefully calibrate a sight-glass with very precise gradations.
I've traversed that rabbit hole. Then I poured a beer and relaxed and stop worrying about it. After all, we're just cooking, not engineering an interplanetary lander.
'Close enough' counts not only for Horseshoes and Hand Grenades, but also beer.
