In TNG, increasing speed from Warp 8.5 to Warp 9 resulted in lowering the distance of Ent-D to its destination from 14 hrs to 5 hrs (that's about 65% reduction in time, or 65% increase in speed going from just 8.5 to 9) - but it wasn't established how many times of C this was.
Warp 9.9 = 21 473 times C per Paris statement is not a problem.
That would mean that 10 000 times C could be in the realm of Warp 9.6.
Warp 9 could be 1500 times C... Warp 9.2 = 3000 times C, Warp 9.6 = 9000 times C (which would be consistent with Data's statement that at maximum Warp it would take Ent-D over 300 years to get back to the Federation), and 9.9 could land at 21 473 times C.
Most Federation (or other AQ) ships weren't able to sustain anything past Warp 9 during TNG per on-screen evidence anyway... and only seldom have we seen ships like Ent-D travelling at Warp 9.6 for brief periods.
Ent-D can sustain 9.2 for a while.
In DS9, the USS Prometheus (a Nebula class ship) was modified by O'brien to sustain Warp 9.6 in a pinch, even though the theoretical maximum for those engines was 9.5.
Voyager was supposed to have a sustainable cruise velocity of 9.975 (meaning that the ship should have been able to sustain this speed without problem for as long as it had fuel to run it), but being thrown into the DQ violently could have destroyed their ability to do that (the ship was heavily damaged by the time they were transported to the Caretaker's Array from the Badlands).
For all we know, Voyager might have been the first in its class to experiment with that kind of Warp propulsion (which also might have been sensitive enough for that kind of violent transport), but it ended up cruising at Warp 6.
Even in 'Threshold' episode (which was booted out of canon), Voyager's hull was starting to fall apart at Warp 9.9 and had to slow down to Warp 9.5.
If the Warp scale results in exponential increase per every increment past Warp 9.9... then Warp 9.975 = 3 435 680 times C.
It would allow Voyager to return home in 7.9 days (or let's round it up to 8 days).
Incidentally, that would put Warp 9.975 at 392.1666 ly's per hour (above maximum attainable speed by Slipstream version 1 which topped out at 300 ly's per hour).
Though Slipstream version 2 topped out at about 10 000 Ly's per minute (which would be just under Warp 9.999) - and that was a combination of Borg technology, benemite crystals, and had a proper quantum matrix (it was an overall different beast than Slipstream V1 or even Borgh TW).
One of the problems I have with Trek is that the Federation should have advanced to these speeds in the 23rd century given the kind of society it is and the fact that exponential returns would have easily granted them these velocities.
I could see TOS Enterprise topping at say 1000 Ly's a day for a limited time... and their Transwarp breakthrough (which was seen in the movies) would have increased that to say 10 000 Ly's a day (if you use that as a measure, then the TW experiment never failed and the Enterprise-A was equipped with it, which also allowed it to get to Sha'Ka'Re in the center of the Galaxy in a few days).
Earth is about 25 000 Ly's from the galactic core... so the Ent-A would get there in 2 and a half days (which would be consistent of a few days travel in ST: V).
Now, those TOS episodes with very high speeds either took place in alternate realities, or SF simply put the Transwarp engines on hold after they heard of the Borg from El-Aurian refugees when Enterprise-B was commissioned (and didn't want to risk early assimilation by spreading into the galaxy too fast before they are ready)... either explanation 'might' work.
I can also see how very high Warp speeds would drain deuterium that much faster, but you'd think SF would overcome this problem by the 24th century and use a method of power generation directly from subspace using the Bussard Collectors (which is what they are supposed to do anyway)... so that the faster you go, you end up feeding the engines at such high rates via subspace essentially... and generating deuterium and other needed substances on the go.
Warp 9.9 = 21 473 times C per Paris statement is not a problem.
That would mean that 10 000 times C could be in the realm of Warp 9.6.
Warp 9 could be 1500 times C... Warp 9.2 = 3000 times C, Warp 9.6 = 9000 times C (which would be consistent with Data's statement that at maximum Warp it would take Ent-D over 300 years to get back to the Federation), and 9.9 could land at 21 473 times C.
Most Federation (or other AQ) ships weren't able to sustain anything past Warp 9 during TNG per on-screen evidence anyway... and only seldom have we seen ships like Ent-D travelling at Warp 9.6 for brief periods.
Ent-D can sustain 9.2 for a while.
In DS9, the USS Prometheus (a Nebula class ship) was modified by O'brien to sustain Warp 9.6 in a pinch, even though the theoretical maximum for those engines was 9.5.
Voyager was supposed to have a sustainable cruise velocity of 9.975 (meaning that the ship should have been able to sustain this speed without problem for as long as it had fuel to run it), but being thrown into the DQ violently could have destroyed their ability to do that (the ship was heavily damaged by the time they were transported to the Caretaker's Array from the Badlands).
For all we know, Voyager might have been the first in its class to experiment with that kind of Warp propulsion (which also might have been sensitive enough for that kind of violent transport), but it ended up cruising at Warp 6.
Even in 'Threshold' episode (which was booted out of canon), Voyager's hull was starting to fall apart at Warp 9.9 and had to slow down to Warp 9.5.
If the Warp scale results in exponential increase per every increment past Warp 9.9... then Warp 9.975 = 3 435 680 times C.
It would allow Voyager to return home in 7.9 days (or let's round it up to 8 days).
Incidentally, that would put Warp 9.975 at 392.1666 ly's per hour (above maximum attainable speed by Slipstream version 1 which topped out at 300 ly's per hour).
Though Slipstream version 2 topped out at about 10 000 Ly's per minute (which would be just under Warp 9.999) - and that was a combination of Borg technology, benemite crystals, and had a proper quantum matrix (it was an overall different beast than Slipstream V1 or even Borgh TW).
One of the problems I have with Trek is that the Federation should have advanced to these speeds in the 23rd century given the kind of society it is and the fact that exponential returns would have easily granted them these velocities.
I could see TOS Enterprise topping at say 1000 Ly's a day for a limited time... and their Transwarp breakthrough (which was seen in the movies) would have increased that to say 10 000 Ly's a day (if you use that as a measure, then the TW experiment never failed and the Enterprise-A was equipped with it, which also allowed it to get to Sha'Ka'Re in the center of the Galaxy in a few days).
Earth is about 25 000 Ly's from the galactic core... so the Ent-A would get there in 2 and a half days (which would be consistent of a few days travel in ST: V).
Now, those TOS episodes with very high speeds either took place in alternate realities, or SF simply put the Transwarp engines on hold after they heard of the Borg from El-Aurian refugees when Enterprise-B was commissioned (and didn't want to risk early assimilation by spreading into the galaxy too fast before they are ready)... either explanation 'might' work.
I can also see how very high Warp speeds would drain deuterium that much faster, but you'd think SF would overcome this problem by the 24th century and use a method of power generation directly from subspace using the Bussard Collectors (which is what they are supposed to do anyway)... so that the faster you go, you end up feeding the engines at such high rates via subspace essentially... and generating deuterium and other needed substances on the go.
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