Star Trek
r/startrek: The Next Generation
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It is said in the pilot that their top speed and sustainable cruise velocity is warp 9.975.
At that speed 75,000 light years would take 14 years 7 months. Even stopping for fuel and maintenance every 5,000 light years would probably only add a year or two.
Even warp just 8 would be 73 years 3 months.
The Enterprise G could cover it just 2 years 4 months.
Whatever they said, Warp 9.975 is NOT the maximum sustainable speed of an Intrepid-class starship. It's the maximum possible speed... for a few hour at best, before the warp core needs to be powered down to prevent everything from melting.
It's not a stretch to assume that the initial 75-year estimate was based on average sustainable speed and taking into account time needed to stop, refuel, maintain, repair, etc. Over that long a time, it wouldn't be enough to just pour more deuterium into it. Most of the warp engine would have to be rebuilt or replaced.
Also, the computer was struggling to figure out exactly where they were, so it might have been off by a few years at first. When Seven built astrometrics, they immediately updated their ETA.
On-screen dialogue is cannon which states repeatedly that Voyagers maximum speed is warp 9.975. For how interesting these tech manuals are they aren’t considered cannon.
However I had no idea there was a Voyager technical manual. Do you have a link to the whole thing?
Google Lens turned up this: https://www.cygnus-x1.net/links/lcars/star-trek-voyager-technical-manual.php
So the writers had a manual their disposal and still managed to make a shocking number of mistakes.