What is the fuel limited flight range of the Enterprise?

Question

In Star Trek there have been various star ships with the name Enterprise. All of the ones featured on TV and in movies have, at one time or another, been on missions of exploration and discovery. These missions would be limited by the amount of on-board provisions each ship could carry (food, fuel, spare parts, etc).

How much fuel are these ships able to carry? Assuming they were each traveling at their top FTL speed, how far would each featured* ship named Enterprise be able to travel before being effectively dead in the water.

*_{for this question please include: NX01, 1701, 1701-A, 1701-D and 1701-E}

Answer 1

This is hard, if not impossible, to answer for three major reasons:

1. There are only one or two canon instances of a ship running out of fuel or close to it (the one example I can think of is Voyager in "Demon"), and in those instances the ship doesn't run out of fuel from burning at top speed, but because of other factors like extended mission lifespans or sabotage.

2. Instead, the limiting factor for a ship running at top speed is stress on the ship itself: the forces involved can damage the warp propulsion system or even the ship itself, making traveling at top speeds not safely sustainable for any extended period of time.

3. The the top speed of a starship in Starfleet is not a set number: it's a function of the efficiency of the propulsion system (which can fluctuate based on the nature of the crew and the parts available) and of set times.

So in order to answer this question, it needs to be slightly reframed away from how far can a ship go at top speed with its fuel reserves, because throughout the Star Trek canon ships wind up damaging themselves at top speeds long before they exhaust their fuel reserves.

For example, one of only explicit mentions of fuel range comes from the Star Trek: The Next Generation Technical Manual where it describes a number of "top speeds" for a Galaxy-class starship:

• Warp 6 until fuel exhaustion
• Warp 9.2 as a "maximum cruising speed"
• Warp 9.6 for 12 hours

But these aren't proven numbers: they're design specifications. In fact, in the very first episode, "Encounter at Farpoint", Data suggests the Enterprise can hit Warp 9.8 at "extreme risk".

Thus it's very difficult to pin down exactly what the fuel-limited range of each of the Enterprise ships is: they're generally rated for a top safe speed for a specific time (12 hours is the only milestone mentioned), but—for the sake of a dramatic scene—regularly attempt to hit speeds that are well beyond their rating for a few seconds or even up to a mission destination.

So the technical answer to your question is at top speed, generally for a very short period time: up to a few hours.

Now, in terms of what the top speeds are and how they translate into ranges:

NX-class Enterprise (NX-01)

In "E²", it's mentioned that Enterprise in theory could get to Warp 6.9 with the right parts and modifications, but would only last until they reach a rendezvous.

However, in "Affliction" they reach a speed of Warp 5.2, which Carter didn't think they could hold "for long". This is continued past a cliffhanger into "Divergence", where it's revealed that:

there's less than an hour until a reactor breach.

But it's unclear if it's solely due to hitting Warp 5.2 or if it's because of all the other stress put onto the ship in the previous episode.

Constitution-class Enterprise (NCC-1701)

In "The Paradise Syndrome", Enterprise travels at Warp 9¹, which Spock calls maximum warp speed. He also acknowledges they're traveling at that speed for "a period that exceeds the recommended safety margins". Montgomery complains to Spock that he "can't give him Warp 9 much longer", but Spock insists it needs to last until they get to "the deflection point".

No distance or time is mentioned, but Scotty doesn't seem to move between the scenes when the Enterprise is at this speed, indicating the incident lasted for less than a shift, or a few hours.

And in "That Which Survives", Enterprise is able to reach Warp 11.9 for a few minutes and Warp 14.1 for about a second.²

Constitution-class Enterprise (NCC-1701-A)

None are mentioned (it's only featured in three feature-length movies), but presumably features similar engine and safety ratings as the original Constitution-class Enterprise.

Galaxy-class Enterprise (NCC-1701-D)

As mentioned above, Warp 9.8 was hypothesized as possible, but with extreme risk, but it was not attempted. The maximum rated speed of Warp 9.6 for 12 hours was never exceeded.³

Sovereign-class Enterprise (NCC-1701-E)

Like the Enterprise-A, this Enterprise was only used in feature-length movies and a maximum warp speed is not mentioned.

However, a close analogue would be the Intrepid-class Voyager, which had a "maximum sustainable cruising speed" of Warp 9.975, as mentioned in "Caretaker".⁴ It's not clear how long Voyager could hold that speed, but given it was only commissioned a few years after the Galaxy-class Enterprise (which was still in service), it's likely Warp 9.975 is its "12-hour" rated speed.

Notes

^{Note 1}: Old warp scale. If comparing to the other series, it's roughly Warp 7.5.
^{Note 2}: Old warp scale. Compared to other series, it's about Warp 9.2 and Warp 9.6, respectively.
^{Note 3}: As far as I'm aware.
^{Note 4}: The speeds mentioned in "Caretaker" are problematic in their own right though, and can't be necessarily trusted. The maximum speed mentioned is contradicted by the (albeit non-canon) unpublished technical manual for Voyager and even in the same episode, when they calculate the length of the trip back home.

Answer 2

Hm... not sure. But we might know something about how long the ship can operate in deep space... USS Voyager was mentioned on-screen by Janeway that their Warp core can go on for 3 years before refilling.

This might indicate that SF likely developed some kind of compression techniques for storage that are able to (at least from our point of view) store and release much more anti-matter than the physical space on board would allow. That, plus like any technology, these systems are extraordinarily efficient... meaning that the laws of ephemerialization dictate you can do more with less over time... and SF certainly operates under those guidelines given they have no monetary based economy to get in the way of technical efficiency.

The USS Enterprise-D for example was stated in the Technical Manuals (which are not canon btw... I'm only using it as a reference) its Warp core can operate for 5 years before refilling... given its size in comparison to the Intrepid class, this is not impossible. Again, Voyager was of newer design and was more advanced so despite the Galaxy having more internal volume, Voyager probably has more advanced storage technology which give a ship of its size really good amount of time before Warp core needs refilling ... but I'm reasonably certain that the Galaxy class would undergo similar enhancements so it would allow the ship greater range and operational time for exploration.

The fuel is usually described as Deuterium, though to be honest, this never really made too much sense to me as a necessity. You have the Warp core which produces massive amounts of energy (which is generally what is needed to power the Warp engines and every other system on board... along with Dilithium crystals which regulate matter/anti-matter reactions) and bussard collectors which can take matter from space and convert it into energy as the ship goes on (producing energy).

To me, Deuterium never made any sense as a 'fuel source'. For that matter, wouldn't a starship be more comparable to an EV car (which doesn't need fuel - it simply needs electricity/energy to run - it also generally needs power generation to power the battery allowing the car to run, which in the real world can be generated via solar, wind, geothermal, etc. - again, you don't need 'fuel' as such)?

A starship has both fusion and matter-antimatter generators to produce energy... so, why would it need separate 'fuel' such as deuterium (which presumably is used to 'power the Warp engines' that already get power from the Warp core)?