The basis of the FC/CYA relationship is very simple and covered in detail in many of the threads linked to in the previous posts. Basically, you need enough hypochlorous acid (HOCl) concentration in the water to satisfy the CT kill rates for various waterborne pathogens (although algae isn't really considered a "pathogen" but a nuisance). Your kill rates have to be faster than the ability of the colony forming unit (CFU) or individual microbe to reproduce itself. Most CT kill rates are reported as the number of Log reductions in CFUs or pathogen count per unit of time. So if a specific concentration of hypochlorous acid has a 6-log reduction in say 2 mins of exposure, then that means that 99.9999% of the pathogens were destroyed. Again, your rate of inactivation has to be greater than the pathogen's intrinsic rate of reproduction (typically measured as a time to double their numbers) in order to keep the water clean.
Ben Powell ("PoolDoc" at the The Pool Forum) used his long time experience with commercial pool management and service to figure out the rough amounts of FC needed for specific CYA levels to maintain a "clean" pool. Richard Falk ("chem geek" here and on many other forums) used that data as a starting point and scoured CDC, EPA and other sources of biological science papers on pathogen kill rates for chlorine as well as calculated the chemical equilibrium reactions between chlorine, water and cyanuric acid. This led to a determination of the threshold disinfection level of ~ 0.01ppm HOCl for bacteria and ~0.05ppm for algae. Once you know that level, you can then back-calculate the amount of CYA and FC needed to achieve it. A ratio of 7.5% FC/CYA gives you roughly the correct amount of HOCl needed to maintain clean water. However, given the daily loss of FC to sunlight and oxidation of organics, one should target 11.5% FC/CYA to be safe. The other ratios of FC/CYA are what are considered shock levels of chlorine.
