Impulse drive, how fast is it?
Throughout star trek we see various ships travelling at fractions of 'Impulse drive'. An impulse is a unit of force and thus converting to speed is difficult.
Here are some approximations I found on the memory alpha article on Impulse Drive:
In The Motion Picture, The Enterprise traveled at warp 0.5 ... or roughly 1/3 light speed
No mention of what fraction of impulse this would be though.
According to Jo'Bril in the episode "Suspicions", the shuttles aboard the Enterprise-D had a maximum impulse velocity of approximately 2.5% of light speed – he specified that at ¾ impulse the shuttle would travel a distance of one million kilometers in approximately three minutes (approximately 12,400,000 miles per hour)
12,400,000 miles per hour is 0.01849c making 1 Impulse drive 2.46% c. But is this inconsistent with the above value? 1 Impulse = ~2.5%c = 0.5*(1/3*2.5%) = warp 0.004. Is that the same for all of the ships?
A reference made in "Fair Haven" indicated that USS Voyager's impulse power would not be enough to outrun an approaching neutronic storm that was traveling at a velocity of 200,000 kilometers per second (447,387,258 miles per hour), or roughly 2/3 the speed of light. However, it is also commented in "Timeless" that at full impulse, Voyager could travel at roughly 80% light speed.
Now we have an inconsistent source (1 impulse <2/3 speed of light AND 1 impulse ~8/10) that disagrees with the above (1 impulse is 1/40 speed of light).
Is this inconsistancy explained by the differing inertias required to change the momentum of the space ships (I know, it's in space, but how else would an 'impulse' drive work?)?
Is impulse drive an absolute measure, and If not what is it relative to?
Answer
In the official Star Trek Universe, outside of TOS, it is implied strongly that Impulse Drive only works at sub-light speeds. The top impulse speeds seem to vary by ship, and "Full Impulse" seems to be whatever the peak designed safe impulse speed is.
Several TOS references, however, imply that an impulse drive can be used for FTL travel. It is most clear in Balance of Terror that the ship has to have something more than slower-than-light travel.
The extended universe, including the tabletop role-playing games, gives full impulse a specific speed, usually varying by timeframe. In the Decipher Star Trek RPG, maximum sustained impulse speeds are around 0.75C (75% of the speed of light).
In the Star Fleet Universe line of Games (Star Fleet Battles, Federation and Empire, Prime Directive), which are based upon TOS and TAS but developed differently from the core Trek Universe, such FTL impulse speeds as are implied by Balance of Terror are given a name: Non-Tactical Warp. They rely only upon impulse drives, and are capable of speeds up to about warp 5.5. (GURPS Prime Directive, page 160.)
It is not clear whether the reference in Where No Man Has Gone Before refers to colonies out to the edge of the galaxy, at which point the barrier might be only a few light years out, or to bases further in. It is clear that the ship is travelling on impulse drives at speeds approaching C, in that Gary isn't shown jumping in power massively as they cross 5 light-days distance on impulse drives.
It also is implied in that same episode that SS Valiant used impulse drives for deep space travel. It seems to be sloppy dialogue as much as anything else.
Combined with Balance of Terror, it's pretty clear that "Impulse Drive" is at worse high sublight. The logical requirements of a "pure impulse" vessel race making war upon a warp-capable race across a multi-light-year neutral zone pretty much requires some form of FTL integrated into the Impulse Drives.
Interpretations of Canon
Steven Cole of Amarillo Design Bureau interpreted the canon to include "FTL." FASA didn't in writing their first Star Trek RPG. Both predate TNG, where it's clear that FTL travel is Warp Drive. Both also provided for FTL combats, unlike the later series, based upon TOS and TAS evidence. In this case, it's best not too look too deeply at canon, as what you find is "Speed of Plot."
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