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.
And as you pointed out, the scales were changed between TOS and TNG. (Part of the "technology unchained" philosophy of TNG.)
According to the TNG Technical Manual, if a (next gen) ship were able to achieve a speed of warp 10, it would simultaneously occupy all points in the universe.
Then, they changed it up again in All Good Things when the Super Enterprise and Dr. (Capt.) Crusher's medical ship could apparently achieve warp 14-15.