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The generally accepted TNG warp scale is:

Warp Factor X = X^3 * X^1/3 for WFs up to 9, then rising asymptotically to infinity at WF 10

However, the Encyclopaedia and Technical Manuals are near canon sources, not true canon, such as an episode or movie.

Has any Canon source specifically stated that some specific warp factor equaled some specific multiple of lightspeed?

what's the difference between near canon and true canon? as per paramount only the live action shows, movies, and a Voyager book (or two i think) can be considered canon. Outside of the TMs though i don't think i remember hearing anything about the scales.

If Warp 10 is inifinity, how did the Voyager folks achieve it? And why did they become newts?

and why is there a warp 13 shown in various star trek episodes? they may be alternate realities but they shouldn't break star trek physics that much.

I think I've heard that the higher warp numbers, like in TOS, were actually part of a different warp scale. They were basically using a different system of measurement.

Superman wrote:I think I've heard that the higher warp numbers, like in TOS, were actually part of a different warp scale. They were basically using a different system of measurement.

there was a warp 13 in TNG, iirc. the Episode where Picard was bouncing back and forth through time and Dr Crusher was for some idiotic reason made Captain of a ship.

Darth_Zod wrote:and why is there a warp 13 shown in various star trek episodes? they may be alternate realities but they shouldn't break star trek physics that much.

The TOS scale was linear, went in a straight line, and just kept going, unlike the TNG scale.

The future warp 13 mentioned in AGT could have been of a new scale, which most accept.

The warp scale will varry according to the needs of the plot. Its as simple as that. Voyager for example supposedly would have taken 70 years at maximum warp to cross the Galaxy. Then they have crossed distances at maximum warp that would point to a FAR smaller time to cross the Galaxy.

I always assumed simply that the 70 years was a maximum sustainable cruise velocity for Voyager. They said they can only hold their warp 9.975 top speed for about 12 hours at a time before droping out of warp. But in other cases where they have been able to, for whatever reason, hold the speed for longer periods of time, they would get home in less then a year.

Darth_Zod wrote:

Superman wrote:I think I've heard that the higher warp numbers, like in TOS, were actually part of a different warp scale. They were basically using a different system of measurement.

there was a warp 13 in TNG, iirc. the Episode where Picard was bouncing back and forth through time and Dr Crusher was for some idiotic reason made Captain of a ship.

They probably recalibrated the scale so they didn't have to keep saying "Warp 9.99996", or whatever. The scale still tops out at some number that represents infinite velocity and would take infinite energy to attain, but it's been set higher than 10 for convenience.

As for "Threshold", I just ignore it.

The warp scales just don't gel with many of the actual episodes. There was a little more consistency in the first two seasons of TOS, but that started to go by the wayside around season three and the movies.

They achieved something like Warp 14 on a TOS episode also, although I will have to look up the specific episode.

IIRC, the TOS warp scale starts with WF 1=C, and each increasing value is the cubed value of the previous.

Superman wrote:They achieved something like Warp 14 on a TOS episode also, although I will have to look up the specific episode.

"That Which Survives", season three. The incident was the result of sabotage to the ship's matter/antimatter integrator control by a Kalandan computer simulacrum. However, simple mathematics demonstrates that the expected travel time for the Enterprise to cover a distance of 997 lightyears in 11.4 hours at Warp 8 doesn't correspond to the value of the TOS warp scale.

In last weaks episode of ENT "Damage", it was stated that to cover the 3 lightyear distance in 3 days, they could do it at warp 3, if they had a working warp coil, which they didn't. That, if I'm not mistaken, means Warp 3 is 365c or 1ly/day which is the same speed as TM Warp 6. We also find that it is the warp coil, a component not part of the nacelles, that creates the warp field.

Spanky The Dolphin wrote:IIRC, the TOS warp scale starts with WF 1=C, and each increasing value is the cubed value of the previous.

No, using that system, Warp 5 would be about 7.6 trillion times C! I think it was the cube of the Warp factor, i.e. WF2 = 8C, WF3 = 27C, WF4 = 64C, etc.

Taking cues from real technology, there's a distinct possibility that running the engine beyond safe limits can produce greater speeds, but only at the risk of damage to the engines.

For example, the 12-hour limit on warp 9.975 is probably a safety restriction. Ignore it and you may be able to go 16, 18 hours depending on how conservative the engineers were, but the longer you run them the more likelihood of damaging the engines. Similarly, it may be possible to go to warp 9.980, but only for even shorter periods of time and perhaps with the risk of damage to the spaceframe as well as the engine.

That's one way of explaining the inconsistency, anyway. After all, with a week between shows, it's hardly inconceivable that they spend a lot of time between episodes repairing episode damage.

Darth Wong wrote: Taking cues from real technology, there's a distinct possibility that running the engine beyond safe limits can produce greater speeds, but only at the risk of damage to the engines.

For example, the 12-hour limit on warp 9.975 is probably a safety restriction. Ignore it and you may be able to go 16, 18 hours depending on how conservative the engineers were, but the longer you run them the more likelihood of damaging the engines. Similarly, it may be possible to go to warp 9.980, but only for even shorter periods of time and perhaps with the risk of damage to the spaceframe as well as the engine.

That was suggested in "The Best of Both Worlds" and "Encounter at Farpoint," although it seemed they were actually more concerned about damage to the hull, so the stresses involved at high warp speeds must be large enough to threaten the ship itself with significant damage, as well as just the propulsion systems.

I also suggested that this may be the reason why the back of the War-GCS was armored. It's a crappy place to put battle armor, but it may help deal with large warp-related stresses, and allow the ship to go faster with greater safety.

DaveJB wrote:

Spanky The Dolphin wrote:IIRC, the TOS warp scale starts with WF 1=C, and each increasing value is the cubed value of the previous.

No, using that system, Warp 5 would be about 7.6 trillion times C! I think it was the cube of the Warp factor, i.e. WF2 = 8C, WF3 = 27C, WF4 = 64C, etc.

Yeah, now that I think about it, I think that's what it was, too.

The most common Warp factor formula for TOS era Trek I've heard quoted:

Warp factor = (v/c)^1/3

Where:
v is the speed of the ship
c is the speed of light

Okay, this should settle the TOS warp scale speed issue:

Checked on DITL (only site I knew off the top of my head that would cover it), according to The Making of Star Trek book, the TOS warp scale was indeed the warp factor cubed.

Why can't we just use multiples of c instead of these fancy asymptotic-at-the-number-10 scales which always produce a ridiculous number of 9s after the dot?

Einhander Sn0m4n wrote:Why can't we just use multiples of c instead of these fancy asymptotic-at-the-number-10 scales which always produce a ridiculous number of 9s after the dot?

Because it would make sense.

Einhander Sn0m4n wrote:Why can't we just use multiples of c instead of these fancy asymptotic-at-the-number-10 scales which always produce a ridiculous number of 9s after the dot?

I suppose the in-universe answer would be because starships can't manage speeds like Warp 9.9995 for any reasonable amount of time, there's no need to recalibrate the scale. Presumably when such speeds become practical, they'll recalibrate it.

(Note that I haven't ran it through my graphing calculator and viewed the graph, so I might be wrong)

A number of graphs that rise to infinity at a number (say 10) then decrease from infinity afterwards.

Warp 13 may be past warp 10- where warp 10 is infinite, but warp 11 is not.

Praxis wrote:(Note that I haven't ran it through my graphing calculator and viewed the graph, so I might be wrong)

A number of graphs that rise to infinity at a number (say 10) then decrease from infinity afterwards.

Warp 13 may be past warp 10- where warp 10 is infinite, but warp 11 is not.

That depends. What is true with some equasion is not true with others. The Warp Scale graph appears to be part of the Expodential family of equations. Those do not behave in that manner.

As such it appears that transwarp must run on different operating principles.