How are Warp Factors Calculated ? is it safe to say that the speeds of all the shows were simply the same ? How are they measured?
Onscreen, warp factors are not calculated or measured at all. A starship travels at the speed of plot: it takes as long to reach any destination as the story requires. There have been various alleged formulae for warp velocities; various behind-the-scenes books about TOS claimed that the velocity was the warp factor cubed times the speed of light, while TNG-era warp factors were supposedly based on a formula where the velocity went as the warp factor to the power of 10/3 (3.333333...), except above Warp 9 where it was based on a supposedly exponential increase to infinite velocity at Warp 10. But in practice, the shows never obeyed these formulae, and onscreen velocities were routinely far greater than the formulae would suggest, and in quite an inconsistent ratio. Fans have tried to rationalize this by assuming the existence of a fudge factor related to the conditions of the space a ship is travelling through; indeed, the TNG Technical Manual explicitly stated that its warp table (based on the Wf^10/3 formula) was only a rough guideline and the actual speeds would vary based on local conditions (because the authors of the manual knew perfectly well that the needs of storytelling would require considerable variations in actual speed).
A long time friend of mine Walter Albert Glaze told me that warp factors were based on calculating the cube of the speed of light so warp one equaled 3X 186,000 miles per second warp two was 9 X 186,000 miles per second,and so forth etc,etc. that how in theory warp speed factors are measured. The movie franchise warp factors were based on a recalcuation of the 1 to 1 ratio of M/AM reactions in the warp drive itself,and the fact that the weapons were charged or supplied with power directly from the drive's energy reactions also was a factor in the ship's abilty to move at warp speeds. Does that make this a lttle clearer. Signed Buck Rogers
Not very well. It's a symptom of the TNG creators making stuff up as they went and having to merge a couple of conflicting ideas. At the start of TNG, Roddenberry decided he wanted there to be an "absolute" limit on warp velocity, which he arbitrarily decided would be called Warp 10 (even though higher warp factors had been mentioned in TOS; Roddenberry was nowhere near as concerned with continuity as many Trek fans are). Presumably he intended this to be a finite limit, which is how we got Geordi's line "We're passing Warp 10" in "Where No One Has Gone Before." But later on, the technical staff decided to treat Warp 10 as just a nickname for infinite velocity, perhaps because they wanted to have the option of extreme FTL speeds available. The TNG Tech Manual rationalizes this by saying that the first nine warp factors are velocities where the nested warp fields are in a stable relationship, reducing the necessary power to generate them, which is why integral warp factors are favored (e.g. Warp 4 would require less energy than Warp 3.8). So the energy required goes up along a curve, then drops off, then rises, then drops off again, and so forth. The warp factors are the dropoff points. But it claims that W9 is the highest stable configuration, so after that the curve just keeps rising to infinity, with no more dropoff points. Hence the conceit of referring to infinite velocity as "Warp 10." Personally, I think this was a very bad idea; referring to infinite speed with a finite number has only led to confusion among the fans.
IIRC, wasn't that partly to eliminate the really high warp numbers in some TOS eps? I.E. Gene didn't want an ep where the ship was made to go warp 37 or something of the like (the speed was something like that in the ep where the Andromedans commandeered the ship)?
To me, if "Eugene's Limit" had been more strictly adhered to, most ships would never get anywhere near Warp 9, much less Warp 10. Anything above Warp 9 would pretty much be "haulin' ass" speed, and the Enterprise's presumed top velocity of Warp 9.6 would be more than sufficient to convey that it was really clocking some light-years there, possibly fast enough to cross an entire quadrant in a really short period of time, who knows? Somewhere along the way, though, Warp 9 was considered not fast enough and things started getting really kinda silly, IMO. The VOY episode that shall not be named ("T--------") was the ultimate culmination of this. I always thought that Warp 10 should have been an unattainable velocity except by higher beings like Q, the Traveler, etc. Warp engine efficiency would drop off rapidly beyond Warp 9, causing the dramatic rise in energy needed to keep accelerating. You would need infinite energy to hit Warp 10 and that would have been enough to make it impossible--except for the crew of a lost Federation ship in the Delta Quadrant with nothing else to do in their spare time... That was supposedly the story and also to keep the Galaxy seem like a really big place. I could see Roddenberry wanting to simplfy the warp scale, but in the end, it didn't turn out that way...
If they wanted the galaxy to seem large, they shouldn't have the Enterprise go from Erath to Quonos to Romulus and back in one freakin episode, even if it was a 2-parter!
I think by the time those kind of stories came about nobody was really listening to Roddenberry anymore or his failing health no longer enabled him to be actively involved as he was earlier and the Galaxy correspondingly became a very small place after all. It's for this reason that I really no longer think of warp factors as measurements of velocity but more like measurements of engine output because actual mileage certainly varies...
I prefer to think of the 10/3 TNG warp factor exponent as being a constant from the word go (ie. 2063 Phoenix onwards) instead of the originally supposed cube factor, and that it represents a fundamental characteristic of space-time as opposed to having "individualized" warpdrives which fold space/time at different rates (coaxial, slipstream and such drives aside - the approach velocity of many alien ships was often noted as a certain warp factor, inferring a constant scale of reference). A sort of 10 higher dimensions over 3 spatial ones idea kind'a rings true to yours truly, and it gives ENT and TOS speeds a little kick in the pants. I think the whole warp recalibration scale thing simply involved the warp 9+ to warp 10 as infinity regime and happened soon after (and probably as a result of lessons learned from) the failure of the 2280's transwarp program. This era would have been the first with any significant amount of warp 9+ dashes anyway. P.S. I also like to think that references to "warp 13" in TNG:All Good Things represented a verbal shorthand adopted in an era when warp 9.9999... speeds have become common - less of a mouthful that way.