TOS warp scale

[MAGolding]

As most of us know, the warp speed scale used in TOS was officially described in various semi canon sources as the speed of light times the warp factor number cubed.

Thus warp factor one is one cubed times the speed of light, or the speed of light.
Warp factor two should be two cubed or eight times the speed of light.
Warp factor three should be three cubed or twenty seven times the speed of light.
Warp factor four should be four cubed or sixty four times the speed of light.
Warp factor five should be five cubed or one hundred twenty five times the speed of light.
Warp factor six - the maximums safe cruising speed - should be six cubed or two hundred and sixteen times the speed of light.
Warp factor seven should be seven cubed or three hundred forty three times the speed of light.
Warp factor eight - the maximum emergency speed - should be eight cubed or five hundred twelve times the speed of light.
Warp factor nine should be nine cubed or seven hundred twenty nine times the speed of light.
Warp factor ten should be ten cubed or one thousand times the speed of light.
Warp factor eleven should be eleven cubed or one thousand three hundred and thirty one times the speed of light.
Warp factor twelve should be twelve cubed or one thousand seven hundred and twenty eight times the speed of light.
Warp factor thirteen should be thirteen cubed or two thousand one hundred and ninety seven times the speed of light.
Warp factor fourteen should be fourteen cubed or two thousand seven hundred and forty four times the speed of light.

And everyone who has calculated the trip times in various episodes has noticed that sometimes the Enterprise reaches its destinations in much less time than it would take to travel that distance at the specified warp factor.

Thus there is much specification about various factors that might enable a star ship to travel faster than its warp factor.

In "That Which Survives":

RAHDA: No debris of any kind, sir. I've made two full scans. If the planet had broken up, there'd be some sign. But what bothers me is the stars, Mister Spock.
SPOCK: The stars.
RAHDA: Yes, sir. They're wrong.
SPOCK: Wrong?
RAHDA: Yes, Mister Spock. Look. Now here's a replay of the star pattern just before the explosion.
SPOCK: A positional change.
RAHDA: It doesn't make any sense. But somehow I'd say that in a flash we've been knocked one thousand light years away from where we were.
SPOCK: Nine hundred and ninety point seven light years to be exact, Lieutenant.

Later:

SPOCK: Please keep me fully advised. Spock out. He was in the transporter room. Someone may have entered after Captain Kirk and his party left. Mister Scott, since the Enterprise is obviously functional, I suggest we return to our starting place at top warp speed.
SCOTT: Aye, sir. But even at that it'll take a while to get there.
SPOCK: In that case, Mister Scott, I suggest we start at once. Can you give me warp eight?

Later:

[Bridge]

RAHDA: We're holding warp eight point four, sir. If we can maintain it, our estimated time of arrival is eleven and one half solar hours.
SPOCK: Eleven point three three seven hours, Lieutenant. I wish you would be more precise.

http://www.chakoteya.net/StarTrek/69.htm

Since there are about 365.25 days in a year and thus about 8,766 hours in a year, a distance of 990.7 light years is about 8,684,476.2 light hours. Traveling that distance in 11.337 hours requires a speed 766,029.47 times the speed of light - warp factor 91.5 would be 766.060.87 times the speed o flight. But warp factor eight point four is 592.704 times the speed of light. Thus some unknown "warped factor" was calculated to get the Enterprise to its destination 1,292.4317 faster than nominal warp factor eight point four.

Maybe the real TOS warp scale is the warp factor number cubed multiplied by 1,292.4317.

But in "This side of Paradise":

PAINTER: Approaching Omicron Ceti Three, sir.
KIRK: Standard orbit, Mister Painter.

Later:

(The group beam down into a farm, complete with wooden fence and a tarmacadamed paths. There are clap-board buildings and even a stable block.)
KIRK: Another dream that failed. There's nothing sadder. It took these people a year to make the trip from Earth. They came all that way and died.
ELIAS: Hardly that, sir. Welcome to Omicron Ceti Three. I'm Elias Sandoval.

Captain's log, stardate 3417.3. We thought our mission to Omicron Ceti Three would be an unhappy one. We had expected to find no survivors of the agricultural colony there. Apparently, our information was incorrect.

http://www.chakoteya.net/StarTrek/25.htm

So the colonists traveled from Earth to Omicron Ceti, or Mira, in "a year" - perhaps 0.5 to 1.5 years. The distance to Mira used to be estimated to be about 220 light years but data from the Hipparcos astrometic satellite indicate it is about 299 light years, plus or minus 11 percent, distant. Thus Mira is probably about 266.11 to 331.89 light years from Earth. So travelling that distance in 0.5 to 1.5 years would be travelling 177.406 to 663.78 times the speed of light.

At warp factor five a ship could travel that distance in 2.12888 to 2.65512 years.
At warp factor five point five (166.375 the speed of light) a ship could travel that distance in 1.599 to 1.994 years.
At warp factor five point seven five (190.109 times the speed of light) a ship could travel that distance in 1.399 to 1.745 years.
At warp factor six a ship could travel that distance in 1.231 to 1.536 years.

So maybe the colonist's ship had the same maximum cruising warp factor as the Enterprise.

Or maybe the colonist's ship traveled at a lower warp factor but those unknown factors multiplied it's speed.

If the colony ship traveled at warp factor four it's speed would be multiplied by 2.771 to 10.37 times.
If the colony ship traveled at warp factor three it's speed would be multiplied by 6.570 to 24.584 times.
If the colony ship traveled at warp factor two it's speed would be multiplied by 22.175 to 82.9725 times.
If the colony ship traveled at warp factor one it's speed would be multiplied by 177.406 to 663.78 times.

Thus the factor that multiplies a ship's speed (or divides it's travel time) can vary from between zero and 663.78 in one episode, "This side of Paradise", to 1,292.4317 in another episode, "That Which Survives".

In "By Any other Name":

ROJAN: Your ship, Captain Kirk. It will serve us well in the long voyage that is to come.
KIRK: Voyage? Where?
ROJAN: To your neighbouring galaxy, which you call Andromeda.

Later:

KIRK: What's the point of capturing my ship? Even at maximum warp, the Enterprise couldn't get to Andromeda galaxy for thousands of years.
ROJAN: Captain, we will modify its engines, in order to produce velocities far beyond the reach of your science. The journey between galaxies will take less than three hundred of your years.
Spock Fascinating. Intergalactic travel requiring only three hundred years. That is a leap far beyond anything man has yet accomplished.

I think that Kirk may have meant it would take the Enterprise 10,000 years or longer to reach the Andromeda galaxy, and not mere thousands of years. Since the distance to the Andromeda Galaxy is approximately 2,540,000 plus or minus 110,000 light years, or 2,430,000 to 2,650,000 light years, a travel time of 10,000 years would equal speeds of 243 to 265 times the speed of light, or about warp factor 6.25 (244.140 times the speed of light) to 6.42 (264.609 times the speed of light).

Since warp factor six is the highest sustainable warp factor for TOS, Kirk may imagine that any speed multiplier in intergalactic space might be only about 1.125 to 1.226 times. Or maybe Kirk did not believe there was any speed multiplier in intergalactic space. Perhaps Kirk had thought about visiting the Andromeda Galaxy and calculated it would take about 11,760 years at warp factor six and about 4,960 years at warp factor eight.

Later:

[Bridge]

ROJAN: Drea has computed and laid a course for Kelva, Captain.
CHEKOV: We've jumped to warp eight.
ROJAN: And we'll go faster yet. Increase speed to warp eleven.
KIRK: Increase speed to warp eleven, Mister Chekov.
DREA: On course and proceeding as planned. We will approach the barrier within an hour.

http://www.chakoteya.net/StarTrek/50.htm

This may mean the Kelvans plan to get to Andromeda galaxy in 300 years at warp eleven. To travel 2,430,000 to 2,650,000 light years in 200 to 400 years would require a speed of 6,075 to 13,250 times the speed of light, or 4.564 to 9.954 times warp factor eleven. So maybe the Kelvans calculate there is a speed multiplier of 4.564 to 9.954 in intergalactic space. Or maybe there is no speed multiplier in intergalactic space and the Kelvins were planning to increase the speed of the Enterprise to about warp factor 18.25 (6,078.39 times light speed) to warp factor 23.7 (13,312.05 times light speed) once they passed the barrier.

So there are three episodes of TOS with three highly different examples of how the speeds in the episodes relate to the TOS warp formula. Whatever unknown factors sometimes make starships reach their destinations much sooner than the warp formula indicates do not work everywhere or every time, and have highly variable effects when they do affect the travel time.

 

[wayoung]

Warp factors are the speed of light cubed by the plot.

 

[Nerys Myk]

Fast. Faster. Fastest. And not fast enough.

 

[wayoung]

Fast. Faster. Fastest. And not fast enough.

"Given 'er all she's got" and "any faster and the energizers will explode" are another two settings. They're like 11 on an amp.

 

[F. King Daniel]

Trek always has and always will move at the speed of plot. Pay too much attention and realise DS9 and Voyager can't possibly work in the same universe as TOS and the classic movies

 

[MAGolding]

Trek always has and always will move at the speed of plot. Pay too much attention and realise DS9 and Voyager can't possibly work in the same universe as TOS and the classic movies

you are wrong. The inconsistencies are within series, not between series. In TOS "This Side of Paradise" the ship that took the colonists to Omicron Ceti seems to have traveled at 177.406 to 663.78 times the speed of light.
in the first episode of Voyager it was said it would take Voyager 75 years to travel over 70,000 light years, or at about 933.33 to 1,000 times the speed of light.

Thus estimated travel times for long trips through unexplored space are consistent with TNG era ships being somewhat faster than TOS era ships. Janeway said twice as fast in "Flashback". But in many episodes both TOS era ships and TNG era ships reach their destinations many times sooner than they should - tens, hundreds, even thousands of times sooner.

It is not a problem between series as much as a problem within each and every series.

 

[MAGolding]

IMHO future English might have more astronomical words than contemporary English. There might be single words for super clusters of galaxies and other scales intermediate between galaxies and the entire universe. There might be a single word in future English for a region of a galaxy. Such regions might be the size of the Gould Belt, for example. https://en.wikipedia.org/wiki/Gould_Belt

So sometimes that word for a galactic region in future English might be mistranslated into contemporary English as "galaxy".

In "The Magicks of Megas-Tu" Kirk's log says:

Captain's log, stardate 1254.4. For years scientists have theorised that if our galaxy was created from a great explosion, then the centre of the galaxy might still be creating new matter. The Enterprise is now on a science mission to investigate.

http://www.chakoteya.net/StarTrek/TAS009.htm

Maybe by "center of the galaxy" Kirk means some place on the central plane of the disc shaped galaxy where long range scans indicate strange things are happening. Or maybe "center of the galaxy" should be"the center of the local galactic region", a region that might be only a few thousand light years in diameter.

Similarly in Star Trek V: the Final Frontier Sybok is looking for God behind the Great Barrier at the center of the Galaxy. But maybe "the center of the galaxy" should be "an area on the central plane of the disc shaped galaxy that has a force field, the Great Barrier, around one or more solar systems". Or maybe "the center of the galaxy" should be "the center of a galactic region" only a few thousand light years in diameter.

Thus the Enterprise might have traveled only a small fraction of 25,000 light years in "The Magicks of Megas-Tu" and Star Trek V: the Final Frontier.

in "The Alternative Factor" Kirk communicates with Commodore Barstow at Starfleet Headquarters:

BARSTOW [on viewscreen]: You're aware of the effect an hour ago?
KIRK: Yes, sir.
BARSTOW [on viewscreen]: You may not be aware of its scope. It occurred in every quadrant of the galaxy and far beyond. Complete disruption of normal magnetic and gravimetric fields, timewarp distortion, possible radiation variations. And all of them centring on the general area which you are now patrolling. The question is, are these natural phenomena or are they mechanically created, and if they are, by whom? For what purpose? Your guess, Captain.

http://www.chakoteya.net/StarTrek/20.htm

Possibly Bastow was mistranslated. Maybe he actually said "It occurred in every quadrant of this galactic region and far beyond." instead of "every quadrant of the galaxy".

In "Errand of mercy" Kor said:

KOR: Sentimentality, mercy. The emotions of peace. Your weakness, Captain Kirk. The Klingon Empire shall win. Think of it, as we sit here, in space above us the destiny of the galaxy will be decided for the next ten thousand years. Can I offer you a drink? We can toast the victory of the Klingon fleet

And Kirk said:

KIRK: We have legitimate grievances against the Klingons. They've invaded our territory, killed our citizens. They're openly aggressive. They've boasted that they'll take over half the galaxy.

And possibly Kor and Kirk were mistranslated, actually using a word meaning galactic region instead of galaxy.

http://www.chakoteya.net/StarTrek/27.htm

In other episodes like "Catspaw" and "By any Other Name", for example, "galaxy" seems to be a correct translation of the future English word used.

Many fans object to hypothetical "warp highways" and other proposed solutions to problems with warp speed But those problems need solutions. In every Star Trek series some trips are made with travel times consistent with the official warp formulas, in other episodes the travel time seems to be reduced by factors of tens or hundreds. And no fictional Starfleet characters ever mention factors that may influence travel time.

In all the hundreds of productions the lack of mention of factors influencing travel time is starting to seem very, very, very, very, very, improbable. But we can assume that the characters do discuss and mention those factors and the creators of Star Trek omit those discussions from their dramatizations of future history.

 

[wayoung]

...Dude, these shows arnt "dramatizations of future history" - it's fiction.

It's fun to talk and argue about utterly pointless and meaningless stuff in Trek. I'm doing so in two other threads today. But it's fiction. These aren't questions that "need to be examined" . They are not "future history" . They're imaginations from writers who didn't care enough to work it all out before hand. If you want to have fun trying to unify it all, great - but it's not a big deal.

 

[trekshark]

I've always liked the theory that different areas of space impact warp differently, resulting in faster speed in some places. Maybe nearness of gravity slow it down and deep space allows faster travel

 

[ian128K]

I've always liked the theory that different areas of space impact warp differently, resulting in faster speed in some places. Maybe nearness of gravity slow it down and deep space allows faster travel

Same. Christian Rühl did a good writeup of it on his old STDimension site: http://www.stdimension.org/int/index.htm

 

[Spock's Barber]

Just for kicks, I once put a plastic toy switch in my car that was labeled 'Warp Drive On'. Believe it or not, I once gave a ride to a hitchhiker who asked me in all seriousness, "Does that really work?"

 

[Ronald Held]

I assume the Vovhrane factor is spatially variable.

 

[ian128K]

Yeah. In my head, it relates to things like how "thin" the barrier between normal space and subspace is in a given place, and probably has to do with how much mass is in the area, too, since that mass would affect gravity, and gravity is something that naturally distorts spacetime. Whether or not higher local gravitational distortion would make going to warp easier or harder I don't know, but I suspect the latter.

FWIW, The TNG Technical Manual had this bit on page 55:

A subspace field of one thousand millicochranes or greater becomes the familiar warp field. Field intensity for each warp factor increases geometrically and is a function of the total of the individual field layer values. Note that the cochrane value for a given warp factor corresponds to the apparent velocity of a spacecraft travelling at that warp factor. [...]

The actual values are dependent upon interstellar conditions, e.g. gas density, electric and magnetic fields within the different regions of the Milky Way galaxy, and fluctuations in the subspace domain. Starships routinely travel at multiples of c, but they suffer from energy penalties resulting from quantum drag forces and motive power oscillation inefficiencies.

 

[publiusr]

Spacelanes with cosmic string are said to allow a variable speed of light. I'd say the slavers had spacelanes that allow warp factors to be enhanced. And I've heard it that warp factor one is actually a bit higher than lightspeed.

 

[Noname Given]

The whole "Warp Factor cubed" thing didn't appear until 1975 (in the Franz Joseph "Star Trek Technical Manual".)
I can tell you that fandom had widely varying ideas like:

Warp Factor = LY traveled per hour
^^^
Which would make the fact that Kirk was often calling out speeds like "Warp Factor 1" or "Warp Factor 2" still seem 'fast' - and would make situations like the distance travelled in "That Which Survives" more plausible.

 

[Warped9]

The whole "Warp Factor cubed" thing didn't appear until 1975 (in the Franz Joseph "Star Trek Technical Manual".)
I can tell you that fandom had widely varying ideas like:

Warp Factor = LY traveled per hour
^^^
Which would make the fact that Kirk was often calling out speeds like "Warp Factor 1" or "Warp Factor 2" still seem 'fast' - and would make situations like the distance travelled in "That Which Survives" more plausible.

Actually I'm pretty sure the Warp Factor Cubed formula was mentioned in The Making of Star Trek which was published in 1968.

 

[Shawnster]

Warp factor = light year traveled per hour would be incredibly fast

 

[Warped9]

Warp factor = light year traveled per hour would be incredibly fast

Years ago I worked out a formula that allowed for the references in TOS to make more (not perfect) sense. Warp Factor cubed times the factor of .02 = light years per hour. This would mean WF 1 is not actually the speed of light but .02 light years per hour. The speed of light is actually .000114 light years per hour. So WF 1 would be about 175 times the speed of light. So Alpha Centauri (4.3 light years) would be about 9 days away at WF 1.

 

[Tenacity]

Warp factor = light year traveled per hour would be incredibly fast

Would have gotten Voyage home in a comfortable ten months.

 

[Ronald Held]

I go with V=WF^3*CF, where WF is the warp factor and CF is the Cochrane coefficient, spatial and maybe time varying.