I saw some arguments about warp speed and what it means, whats top sped etc. I did some research mostly at
http://ditl.org/ That's the website for the Daystrom Institute. They have a lot of information on nearly everything Star Trek as well as giving what source material it all comes from. The copy pastes come from there.
Where V = Velocity of the vessel, c = the velocity of light, and WF = the warp factor. This scale has the advantage of simplicity; the velocity in multiples of light speed at any given warp factor is that number cubed, hence :
Warp Factor Velocity (xc)
1......................11
2......................81
3......................271
4......................641
5.....................1251
6.....................2161
7.....................3431
8.....................5121
9.....................7291
10...................1,0001
11...................1,3311
12...................1,7281
13...................2,1971
14...................2,7441
The above chart is from TOS. How ever to account for TNG getting places faster and various other stuff they revamped the warp chart. Another part of this was that some places in space you just couldn't go as fast. Having the captain give the order for warp 7 was a statement of speed but you could burn out the engine in some places keeping that much stress on the engines. So they changed it to Chocranes where the warp factor instead of meaning actual speed now means a set amount of stress aplied to the subspace field.
This is the equation for the new chart.
For ideal conditions, such as are found in interstellar space, the speeds of TNG warp factors are calculated using either of two formulae :
Up to Warp 9 :
V/c = WF(10/3)
Which is very similar to the Cochrane Scale. Beyond Warp 9 the formula becomes somewhat more complex.2 It is best approximated by :
V/c = WF[<(10/3)+a*(-Ln(10-WF))^n>+f1*((WF-9)^5)+f2*((WF-9)^11)]
Where a is the subspace field density, n is the electromagnetic flux, and f1 and f2 are the Cochrane refraction and reflection indexes respectively. Under ideal conditions values of a = 0.00264320, n = 2.87926700, f1 = 0.06274120 and f2 = 0.32574600 can be expected within a "normal" area of deep interstellar space.
here is what that looks like in chart form.
http://ditl.org/Gengrafix/warpgraph.gif
Please note that the scale on both left and right go up by factors and is not linear.
Basically in these charts warp 9 is about twice as fast as warp 7 how ever in the game this is not the case. the warp speed in STO seems much more linear. But that's fine since we are not doing combat at warp speeds. That would be cool but seems to be outside the game engines abilities.
As for warp 10. Warp 10 isn't infinite speed but that it's takes more energy than any starship could hold to get that fast. At least that was how I interpreted the data I could be wrong on this point.
As for Transwarp. That is speeds in excess of warp 10, These are not infinite speeds but are far faster than standard warp drive. the following chart gives a good explanation but is rather rough but does show
how much faster transwarp is.
http://www.sfcommand.co.uk/images/images/transwarp.gif
Image from
http://www.sfcommand.co.uk/info/transwarp
As you can see as you approach transwarp 40 you are going about 100 billion times the speed of light. At that speed Voyager would have been home in about 3 minutes. That also makes the galaxy real small in travel time.
Hope this helps settle the argument.
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