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From Star Trek: The Next Generation onward, warp speed has a basically cubic scale from warps 1 - 9. But then, close to warp 10, it suddenly develops its own puzzling scale, as can be seen in this table.

In this scale, warp 10 is considered infinite, occupying all points in the universe simultaneously and therefore effectively teleporting instantaneously.

My question is why have this confusing scale? Why not have a uniform cubic scale? Was there ever any "official" explanation for this?

Clarification: I'm looking for why the writers decided on this, not the "in-universe" explanation.

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    The relationship between warp factor and multiples of light speed is not logarithmic, it's cubic. But because they chose a logarithmic scale for the multiples of light speed, the graph is that of 3 ln(w) . – Raskolnikov Feb 10 '11 at 13:14
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    Besides, if the relationship between warp factor and multiples of light speed had been logarithmic, warp would have been worfless! – Raskolnikov Feb 10 '11 at 13:21
  • @Raskolnikov - thank you, question corrected. – Wikis Feb 10 '11 at 13:42
  • Because the writers needed it (for story reason)? If you ask what a canon/in-universe reason there is or could be, that is a whole different question. – Jürgen A. Erhard Feb 11 '11 at 19:27
  • I think I saw an episode or a movie where they pass over warp 10, maybe it was =Q= related – Elzo Valugi Apr 7 '11 at 20:30
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If you're looking for the "canon-ish" answer for the change, according to the "Star Trek: The Next Generation Technical Manual" the scale was recalibrated in the 24th century. The old scale was calculated based on "observed" speed (much like our MPH/KPH), but the amounts of energy needed to maintain that speed could be vastly different from one moment to the next based on interstellar conditions and quantum drag forces. For instance you spend a few seconds traveling through a smallish eddy and it greatly reduces your velocity. Since such great distances were being covered in such a short time, a great deal of turbulence exists. Since the engines aren't actually fluctuating power to maintain a constant speed, the observed (averaged) speed was little more than a guess. I imagine this like driving a car at 6000 RPM over a surface that is at one second oil and the next sandpaper, with large rocks mixed in here or there. You could certainly figure out what your speed was for the last mile, but it may not be indicative of your speed for the next mile.

In TNG, the scale was changed to the amount of power required to transition from one warp plateau to another. The idea here is that it's easy (power-wise) to maintain a particular speed, but a power spike is needed to make that jump from Warp 1 to Warp 2. A larger spike is needed to get from Warp 1 to Warp 9. At that time, they decided Warp 10 was infinite power required. So all the "undiscovered" plateaus between 9 and 10 had to be squeezed in. I liken this to the metric system, where they decide a gram was a rather small amount of mass, but rather than recalibrate, people just decided to measure things in kgs.

Outside of canon, I recall an interview with Roddenberry. He put in a speed limit to keep writers from inventing more speed as the way out of trouble. You can see this a few times in the first season where the Enterprise tries to outrun things, but cannot (Qs grid springs to mind).

Edit: Just found online link to the TNG Technical Manual with a note alluding to Gene's decision.

Figuring out how "fast" various warp speeds are was pretty complicated, but not just from a "scientific" viewpoint. First, we had to satisfy the general fan expectation that the new ship was significantly faster than the original. Second, we had to work with Gene's recalibration, which put Warp 10 the absolute top of the scale. These first two constraints are fairly simple, but we quickly discovered that it was easy to make warp speeds TOO fast. Beyond a certain speed, we found that the ship would be able to cross the entire galaxy within a matter of just a few months. (Having the ship too fast would make the galaxy too small a place for the Star Trek format.) Finally, we had to provide some loophole for various powerful aliens like Q, who have a knack for tossing the ship millions of light years in the time of a commercial break. Our solution was to redraw the warp curve so that the exponent of the warp factor increases gradually, then sharply as you approach Warp 10. At Warp 10, the exponent (and the speed) would be infinite, so you could never reach this value. (Mike used an Excel spreadsheet to calculate the speeds and times.) This lets Q and his friends have fun in the 9.9999+ range, but also lets our ship travel slowly enough to keep the galaxy a big place, and meets the other criteria. (By the way, we estimate that in "Where No One Has Gone Before" the Traveler was probably propelling the Enterprise at about Warp 9.9999999996. Good thing they were in the carpool lane.)

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    @Wikis - The answer is Gene Roddenberry said Warp 10 is the universe's speed limit. The writers then had to accommodate that decree. – Steve Jackson Feb 15 '11 at 15:49
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    good enough for me! :) – Wikis Feb 15 '11 at 16:46
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    Did the ST:TNG in the final episode (All Good Things) have Captain Picard saying to engage Warp 13? – Wayne In Yak Mar 28 '13 at 19:11
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    @Wikis: Logarithmic scales are commonly used in science to cover large ranges. Scales are a cognitive and computational tool. So it's important to pick a scale that correlates with your analytical objectives. If you're more concerned with the order of magnitude, then a logarithmic scale makes the most sense. A linear scale isn't as useful if value changes aren't equally significant across the full range of the scale. A logarithmic scale makes much more sense when a single unit change is far more significant on the low end of the scale than on the high end. – Lèse majesté Aug 31 '13 at 21:12
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    In other words, when you get close to Warp 10, a 1c change in velocity is not nearly as significance as when you're close to Warp 1, so why should it be represented as equally significant on the scale? Doesn't it make more sense to compress the scale at the high end? This also has the convenient effect of dramatizing the effort required to accelerate at high warp. Ships jump from Warp 2 to Warp 5 with ease, but once you reach Warp 9, just .1 increases take enormous coaxing of the warp drive. – Lèse majesté Aug 31 '13 at 21:18
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The Original Series didn't have that scale (I don't know if they ever made an 'official' scale for TOS). You can see this in Star Trek IV: The Voyage Home where they go to Warp 14 to enter Time Warp.

They rejiggered the scale before TNG to make the new ship seem faster while not constantly pulling out bigger numbers. Otherwise, the Borg would go Warp 25 and Voyager could hit Warp 40 ... and so on. The numbers would get absurdly big quickly and ruin suspension of belief.

I don't know what the in-universe explanation is.

  • I just watched Changeling (TOS season 2 ep ... erm 6?), last night, where the Nomad probe 'fixes' inefficiencies in their drive and catapults the Enterprise up to Warp 15. Remembering the god-awful Voyager episode, Threshold, when Paris and Janeway become lizards for reaching warp 10, I had to wonder why the TOS cast didn't suffer a similar fate. – johnc Feb 10 '11 at 21:14
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    @johnc - that was using the old TOS scale. See Wikipedia link above for explanation. It changed in TNG. – Wikis Feb 10 '11 at 21:39
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    @johnc - Paris and Janeway as hyper-evolved salamander parents... best plot ever! – Mark Rogers Feb 10 '11 at 22:21
  • @CajunLuke - I am looking for the writer explanation, not the in-universe one. Is that the only reason - otherwise the numbers would get too big? It just seems crazy complicated... – Wikis Feb 15 '11 at 10:25
  • Yeah, read the quote in Steve Jackson's answer. That's what I'd read, just it was awhile ago. – CajunLuke Feb 15 '11 at 15:22
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Warp 10 corresponds with infinite velocity, and a ship traveling at warp 10 would be in every point of space at once. After warp 10, you go into Transwarp. Traveling at warp 10 is possible, and was done by Tom Paris in a shuttle with a rare form of dilithium. The "problem" is that travel at warp 10 leads hyper-evolution, and backwards time travel. In TNG, "The Traveler" modified the engine, and also went faster than warp 10. In an alternate universe, warp 13 was possible for Federation ships. The "Starfleet Technical Manual" also says that the surrounding interstellar phenomena can change warp factors (phenomena like electric and magnetic fields and quantum drag forces. The formulas for calculating warp factor are:

(under 9) wf=(10/3)sqrt v/c and over 9, v=wf^(10/3) c Warp 1=c

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    "In an alternate universe, warp 13 was possible for Federation ships." -- if 10 is infinity, what is 13??? – Martin Mar 18 '12 at 20:11
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    Don't question Admiral Riker. If he says go warp 13, you go warp 13. – corsiKa Jul 10 '15 at 16:40
  • So warp 10 corresponds to infinite improbability drive. Heart of Gold did this without turning the captain and pilot into giant salamanders. Then again (iirc) it did turn Marvin into a pot of petunias. – Jim2B Mar 26 '16 at 16:58
  • It turned one of the missiles targeting the Heart of Gold into a pot of petunias (the other missile was turned into a whale). Marvin was not transformed at that time. – Alex White Jun 29 '16 at 11:01
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Gene Roddenberry (GR) made a decision during the prep for Next Gen to rescale warp factors to keep the normal ranges low, but also to increase the values for the lower ranges. He then set WF 10 as a hard limit.

The rescaling was in part a response to authors (both TOS and books) inflating speeds for their various stories, according to one interview with GR that was aired on TV in the late 1980's.

GR left it up to the production staff to implement it. He set several benchmarks, tho'. In order to meet those benchmarks, it was required to produce an asymptotic and multi-regional curve. That curve is published in the ST:TNG Tech Manual, by Michael Okuda. Region 1 is to warp 9; it's a simple bump of the old method, using 10/3 power (=3.333... power) instead of 9/3 power (=3 power). Region 2 is WF in the range 9-10, and the forumlae for the second range, which was a hand drawn curve, are hard to describe... one fan has a really good (but complex) fit; it's a graphic at this thread at Flare Sci Fi forums.

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