or this thread could also be titled "Fun with algebra!"

I have heard some no-spargers say that they get better beer since they began no-sparging. I don't know how wide spread this opinion is and I've never tried it, but I got to thinking that it might have something to do with the gravity of the final runnings. So then I wondered if there was a way to increase the gravity of the final runnings of a single batch sparge without the full efficiency impact of no-sparge and if there is a way to specify what you would like that final running gravity to be. One method I came up with was to hold back some of the wort in the mash (simulating a large dead space), then add the sparge water, mix, and drain all the second runnings. Long story short, I got interested in the math and worked out all the equations for this and also for using very unbalanced runnings to get the same effect. Even though I don't really expect there will be a lot of interest in this, having done all the math, I figured I might as well write it up and maybe someone will find some use for it. One other thing I included in the writeup was the single batch sparge equations, ala Palmer and Ken Schwartz, but with a dead space added, since I wasn't able to find these anywhere. I did all this mainly for the math challenge, but the writeup also gave me a chance to use the equation editor in the Open Office Writer - a pretty cool tool, and easy to use. The write up is here:

http://www.mediafire.com/?s2fasgc65cv2v5l

and I also made a spread sheet just to check if my equations output numbers that made sense. I made no attempt to make this pretty or user friendly, but maybe you will have fun playing with it.

The spreadsheet is here:

http://www.mediafire.com/?g9ykpz5o9i8kwip