How did you arrive at "transwarp factors" as being TWF^5?
That was FASA's numbering from Transwarp in their last few supplements.
That is not my answer. The question was "how did you arrive at TWF^5?" The answer you gave has NOTHING to do with the answer to the question.
CuttingEdge...
Think basic mathematics. In order to do any velocity calculations, or any other "physics-type" calculations for that matter, you need to have both positive and negative numbers.
Now... take any number to a POSITIVE power (^2, ^4, ^6, etc) and you only get positive numbers. So it's impossible to do the math. And as a result, the use of these power to calculate higher-order warp speeds is impossible.
"Transwarp" is established on-screen only as being a generation ahead of "warp drive." It's got to be dramatically better.
Someone, very early on (it may have been someone in the ST-III Production team, but I can't be sure) decided that, with WF^3 being "warp drive," going to the fifth power was the obvious next step.
FASA, later on, PICKED UP on that, but they did NOT originate the concept. They adopted it. I knew of this long before FASA published any of their materials on the topic.
Mathematically, it sort of makes sense, as well. Imagine that you have a propulsion system that sort of "layers" your "warp drive" concepts... a "warp field" inside of a "warp field"... You'd expect that incremental jump, wouldn't you?
The way I envision it (and how I understood, at the time, it was supposed to work) is that you create a subspace field (maybe that's what the big "hump" on the Excelsior was for?) and then, within that "hump," you create a warp drive field, warping subspace instead of warping real space.
It was WIDELY accepted that "Transwarp" was simply "TWF^5." That gives you some pretty great speeds, without that pesky mathematical problems that Roddenberry's "WF10=infinity" thing (which came along later, of course) gives you.
Of course, then came a bad episode of TNG which simultaneously destroyed the Borg as a credible threat, AND altered the definition of "transwarp" entirely. And then, Voyager put even more nails in the coffin, effectively transforming "transwarp" into Babylon 5's "jumpgates."
But for a while, TWF^5 was the accepted "rule of thumb" and I still stick to that. FASA simply followed along with the crowd.
