> I almost want to go back and look at the math of how fast they must have been going

While there's a rough polynomial (v =~ c * w^3, I think) for post-TOS Star Trek warp factors, the only consistent rule: a starship travels at a velocity that helps tell a good story.

It's fun to try mapping Star Trek stories, anyway; it helps you ponder how much time they must have spent in transit. They have to find things to occupy their time.

Yes I think you are spot on, they move at the speed of how fast the plot needs them to move. After posting my comment and looking online at some suggested speeds for the various warps speeds it is very inconsistent and far from realistic given the size of the universe. One would need to be able to travel at something like 100,000 times the speed of light to realistically travel just around our galaxy. Probably would need to travel at about 1,000,000 times the speed of light wanting to make it to the next galaxy in a realistic time. Even at 1,000,000 times the speed of light it is going to take years to just reach the next galaxy so it is no where near fast enough to get around like they did in star trek.

But I absolutely loved the show growing up so not here to knock them. I am sure in hindsight they may have come up with a better definition of how warp speed works and how they can travel great distances. I won't think about it too much.