Warp Scale from 23rd to 24th Centuries

[PGoodman13]

I've looked at the warp speed scale in the NG, and noticed the fact that it's the TNG-era warp scale. Am I correct in assuming there's not a mathematical relationship between the warp factor and the multiple of c it represents in the TNG scale? I ask because I'm using the old "warp factor cubed" scale for my 23rd century series, and I want to set up my own table with both the 23rd century scale and the approximate equivalent in the 24th century, and I'm not seeing much relationship between the warp factor and the actual speed of the vessel. I'm trying to see how much I have to wing it when I make my table.

Thanks in advance.

[C5]

Trouble is, from what I once heard, that while the formula was written in TOS, it was only the curve of the TNG scale that was drawn. Hence, the difficulty of establishing an actual formula.
If you love maths (or have a good calculator at hand ), you can go there to find some very complicated warp formulaes... you've been warned

[Dan Stack]

In TOS, the most commonly accepted warp scale is...
Speed = (WF ^ 3) x c

In TNG, the most commonly accepted warp scale, up until about Warp 9 is...
Speed = (WF ^ (10/3)) x c


However, going by this and the size of the Federation as quoted by Picard in "First Contact" gives a Federation which would take decades to cross. It should be noted that whilst the size of the Federation has been actually given, the velocities for various warp factors have never been given on-screen, only in "official" material.

[PGoodman13]

Thanks, Dan! That seems to jibe with what I recall of that table (which is currently out in my truck; I could go look, I suppose).

[UNL LAW]

Hi. New guy here. I just did some computations off of that web site for warp drive. I figured that it takes 11 days to travel 20 ly at warp 7. Going warp 9.999 you could cover the distance in less than an hour. However, as we all know 20 lys is noting compared to the size given for the Federation. On top of that ENTERPRISE puts Chronos less that a week from Terra at warp 3 or 4 (have to see the pilot again). My points are these: 1) Terra (Earth) must be on the edge of Federation Space (not a good place for a capital system). 2) Starships must spend sometime traveling at warp 9 or higher, if they did not it would take a long time to simply perform a partrol of a given sector of space.

Now the questions. First, am I correct in my points? Second, in what direction is the Federation expanding? Third, would a starship use warp 9 or higher "sprints" to cover areas of space as a routine procedure and if so will the "enviromental" restrictions on warp speeds limit this practice?

Hope these questions are not too dumb