Originally Posted by vuedoc
There was a change in the warp scale between TOS (including the movies) and TNG, in order to allow for greater speeds to be reached. In the newer scale, maximum warp by any vessel is defined as 9.99... with warp 10 being defined as "infinite speed." In any case, warp 10+ in the old scale was probably the equivalent of 7 or 8 on the newer one. There is a formula used to calculate this but I don't have it at the moment. There are a few threads on this elsewhere.
I can deal with that, but what kind of annoyed me in TOS was where in some episodes such as "By Any Other Name" and "The Changeling" as you mentioned, is that sometimes warp speeds greater than 10 were attained with engine modifications only, but at other times, anything greeater than warp 9 caused iminent hull damage. I would have appreciated a little consistency there.
Actually, there was a sort of consistency there. The Enterprise
first traveled beyond Warp 9 in "The Changeling" and reached Warp 11 thanks to modifications made by the Nomad probe. When the ship was modified again by the Kelvans in "By Any Other Name" it was once again at Warp 11. It's feasible that both times these modifications were subsequently removed to be studied by Starfleet and the ship was returned to its original specifications (damn alien tampering!). But anything faster than Warp 9 was generally considered unsafe in TOS, IIRC...