Speed in Star Trek

Question

How fast is Impulse, Warp and Warp X speed?

As I have understood it, Warp (1) speed = 1x Speed of Light (SoL), i.e. ~300.000 km/s. However, in ST:VOY, they are hurled 70.000 LY from Earth, which will take 70 years to travel at Warp 9, i.e. Warp 9 = 1000x SoL. That makes no sense to me.

If Warp doubles for each full number (binary numbers), then Warp 10 would be 1024x SoL ~ 68 years journey. That works fine, in approximation, given they need to make various stops on the way and/or take small detours to fly through star systems on the way. But no... Not only is Warp 10 impossible (why is that, anyway?), but anything over Warp 9,0 is reserved for burst only. Thus sustained travel is limited to Warp 9, which would (by my calculations) be 512x SoL ~ 135-140 years journey. But this doesn't match any known numbers..

Bonus question: How fast is Impulse drive? You can travel in a shuttle from Earth to Jupiter in a few hours. We only ever hear about quarter, half and full Impulse speed. But at the same scale, you can travel to Jupiter in a few hours, but you can also navigate a safe landing on a planet/moon, through the atmosphere.. Again, I see no consistancy in this..

Answer 1

TOS and TAS, and the TOS Movies

In TOS, we do not have an explicit conversion, but all stated velocities used WF^3.

The following are rounded to 1 decimal place.

So...

 OWF = Old Scale Warp Factor
 NWF = New Scale Warp Factor
   C = Speed in multiples of the speed of light
D/LY = Days per Light year 

 OWF:  1   2    3    4    5    6    7    8    9    10    11    12    13    14    15
   C:  1   8   27   64  125  216  343  512  729 1,000 1,331 1,728 2,197 2,744 3,375
D/LY: 365 45.6 13.5 5.7  2.9  1.7 1.1  0.7  0.5   0.4   0.3   0.2   0.2   0.1   0.1

Post Movies

TNG, DS9 and Voyager use about WF^(10/3) through warp 9.0...

 NWF:    1   2     3      4      5      6      7       8       9
   C:    1  10.1  38.9  101.6  213.7  392.5  656.1  1024.0  1516.4
 OWF:    1   2.2   3.4    4.7    6.0    7.3    8.7    10.1    11.5
D/LY:  365  36.2   9.4    3.6    1.7    0.9    0.6     0.4     0.2

Above 9.0, between 9.0 and 10, the exponent increases dramatically, and warp 10 is theoretically infinite speed.

It is worth noting, however, that in All Good Things (the closing Episode of TNG), the scale appears to continue to Factor 14 at this same WF^(10/3) progression. The on-screen stated speed for factor 13 is a match.

Further, the TNG Tech Manual mentions that this is an average speed, and that factors in local subspace topology can affect the speed in either direction.

Impulse is given several explicit speeds in various episodes. The term Full Impulse seems to be relative, and as per naval tradition, Full Impulse appears to be maximum the engines can provide, which varies from about 0.05C to an explicit 0.8C (in Voyager).

References

http://www.ex-astris-scientia.org/treknology/warp6.htm

Answer 2

Memory Alpha has a nice table of speeds in relation to "c" (the speed of light). In brief, it's very inconsistent (though more inconsistent between eras, i.e. from TOS to TNG), but it follows an approximate logarithmic (or exponential, perhaps?) increase: Warp 1 is equal to c, but warp 2 is equal to 8x c.

EDIT: Incidentally, in this scale, warp 10 is impossible because it's classified as "infinite speed", with the ship's speed approaching the asymptote of infinite speed as it adds more decimal places to its speed. Starfleet likely chose Warp 10 to be an arbitrary speed very high on the curve that they thought they would never reach, only to draw closer and closer to it as they built better and more efficient engines. A failure of imagination perhaps? Blame the Vulcans.

As for impulse, Memory Alpha references a few episodes where impulse was stated to have a speed far, far smaller than c (full impulse described as 2.5% of c), leading to an Earth-Jupiter run of over 34 hours. But it also means you're traveling at 7,500 km/s, so rather difficult to land at that speed.

Answer 3

Impulse speed (for a starship) is between 0.25c and 0.8c (maximum speeds of course) and usually restricted to sublight.

Warp drive is a bit more trickier, but it was established that the technical manuals are not canon. Still, even if Warp 9 = 3000 times LS (for example), in Voyager, it was established on screen that Warp 9.9 = 21 473 times LS.

Now, if in TNG Warp 9.9 = 3000 times LS, that could simply mean that the Warp scale might have been re-calibrated (again) and 9.9 now ended up at 4 billion miles per second.

At any rate, Warp factors and speeds fluctuate wildly in canon. I usually stick with the on-screen dialogue however and use higher values as the technology and science in Trek certainly should allow for them. So, Warp 9.9 = 21 473 times LS.

But I think that doubling of speed with every incremental increase is valid for Warp speeds above 9.9 (meaning that 9.91 = 42946 times LS, etc.) Of course, past Warp 9, speeds start increasing quite fast anyway. So, if Warp 9 (or 9.2) = 1500 times LS and 9.9 = 21 473 times LS, then we have several decimals of large increases to work with.

Warp 10 was stated to be in Voyager 'infinite velocity'. Anywhere in between you can have a large range of speeds that can be achieved through say more efficient/powerful Warp drive (recalibrated Warp scale in TNG final episode where they said Warp 13, etc), Slisptream, Transwarp and Coaxial warp drive (to name a few).

Slisptream v1 seemed to have equaled 300 ly's per hour at maximum from on-screen dialogue. For protracted periods of time though, it was suggested the crew of Voyager would need to be in Slipstream for 3 months (which in itself suggests the ship would have needed to go much slower for extended periods of time to allow crew survival - or it was possible the engines on the Dauntless couldn't sustain maximum velocity for long periods of time).

Slisptream V2 as developed by Voyager crew (who used a number of technologies) in 'Timeless' seemed to have allowed speeds of 10 000 ly's per minute (and if you check the dialogue, it says that the slisptream variance doesn't appear until about 17 seconds into the flight... which doesn't leave much time for Voyager to experience issues and crash into its doom or for future Kim to send the needed data back in time to help disperse the Slipstream).

This version of Slipstream even seemed to surpass Borg Transwarp capabilities (at least until the Dauntless and Arturis were assimilated by the Borg, which could have lead to the Collective to improve their TW drives by the end of Voyager series).

Anyway... There are also Soliton Waves which traveled at below Warp 9 (though showed evidence they can increase in speeds), but the thing is that ships using soliton wave technology wouldn't need actual Warp engines (further research into this technology might have yielded SF with better mobile control that didn't require another station at the end to disperse the wave, but could otherwise be done on the go via a ship using the waves to traverse space).

Borg Transwarp through use of TW coils for independent TW conduit generation seemed quite fast... it allowed the Delta Flyer to traverse 200 Ly's in a few seconds (10, maybe 20 seconds?).

We know that when Voyager equipped its engines with 1 Borg TW coil, they traversed 20 000 ly's... although, they didn't say how long it took them to do that... it could be about 33 or 34 minutes (if the above assessment of 200 ly's per 20 seconds is accurate).