Gordon Strong recently wrote an article in Brew Your Own magazine about "alternative" mashing techniques. Parti-gyle brewing was an old British method for brewing two or more beers of different strengths from a single mash. A strong first running (or gyle) was combined with a weaker second running to produce an intermediate strength beer. The article describes the basic concept for calculating the blended specific gravity, but does not go into much detail.
The parti-gyle blending calculator provides two useful calculations for parti-gyle brewers. The first option can estimate the gravity of a wort created by blending two worts of different strengths. This is similar to the calculations described in Strong's article. The second option will estimate the volume of the second running needed to achieve a target specific gravity in the blended wort. The calculations from both options are explained.
Strong, G. (2023, September). Alternative mashing techniques: Traditions of England, Germany, and the Czech Republic. BYO, p. 30 - 39.