I know what TS is, I have been playing Travian for more than 10 ys. I do not intend to describe what I mean as it has already been described by OldScout, just read his message. I only say that his idea would be nice on 1x too.
Here we're talking about incremental speed. It means after a certain amount of squares they start to go faster and the like, it does not mean that 10hs distance is reduced to 5, but maybe it is reduced to 9/8.5 hs