This is another of my "Covid-Projects," consequent to my "Star Trek History of the Twenty-First Century" project (which is drafted but still needs a lot of work). Basically, I wanted to work out an overall rationalization of the development of the Warp Drive that best fits what has been shown on screen and explains certain oddities that manifested themselves along the way. It varies considerably from a lot of fan-created Treknological assumptions through the years as well as semi-official resources published and statements made along the way, even by producers and technical advisers to the various series and films.
In the process of writing the "History of the Twenty-First Century," this kind of went on the back burner until I came upon an article on the blog Occasional Enthusiast entitled "Alternative Star Trek Warp Speed Scale and Related Equations" (2016) [LINK] which takes a very different approach but has some really cool ideas. My comment on that post led to a very helpful exchange with the author (at least, helpful to me) and inspired me to pull this back out, polish it a bit, and go ahead and post it.
Take it for what it is -- one fan's interpretation. And remember that, "Dammit, Jim, I'm an historian, not a mathematician!"