Warp Drive - In the Orginal Series...

[Dee007]

Which Episode was it in that they discuss Warp drive for the first time.

I know it was in the original Series.

 

[FalTorPan]

The original pilot, "The Cage," mentions "time warp," as in "time warp factor seven." The second pilot, "Where No Man Has Gone Before," mentions "space warp capability."

 

[Dee007]

I believe it was the Cage, Thanks FalTorPan

 

[Mytran]

What I like about Warp drive in TOS is that it's much more flexible than in later Trek incarnations. It is featured as the "main drive" in all respects and seems to be pefectly usable at sub-light speeds as well as FTL ones.
Impulse was often nothing more than a backup system for emergencies.

 

[jefferiestubes8]

It always seemed in TOS that the Warp speed was something like a steam locomotive on a train. The more you turned the dials, tweaked, and adjusted everything just so the more speed you could coax out of this Warp drive propulsion technology above Warp 6 speed.

as per Memory Alpha during the five-year mission (2265-2270)

the Constitution-class had standard cruising speeds of warp 6 and emergency speeds as high as warp 8 (although under the right conditions the engines could reach warp 9).

In the 23rd century

At some point in the century, a new warp factor scale came into use, which placed warp 10 as a theoretical maximum. (VOY: "Threshold")

In TOS it seemed that Warp 9 was difficult to get to for this emergency speed and it always made for some suspense while Scotty did his engineering thing to give Kirk the speed.
Probably like coating coal to burn hotter with something before putting it in a steam furnace. similar to Doc Browns scheme in Back to the Future Part III (1990).