Why are officers of flag rank (Rear Admiral Upper Half and up) commanding starships and not flying their flag from them?
As for ship speeds, for the C24 shows (TNG, DS9, and Who The Hell Let Janeway Navigate??), given a warp factor w (w being between 1.0 and 9.0), velocity was w ^ (10/3) * c - 1516x c for warp 9, meaning 4.2 light years in a day (365-day year), or Terra to Alpha Centauri inside 24 hours.
Above warp 9, well.. it's difficult fitting a formula to a hand-drawn curve. One approach I like (due to its simplicity) is outlined here
, which adds a correction term to the exponent for speeds > warp 9.
Said correction factor is -0.5 log10(10 - w) (where, as above, w is warp factor in question). Zum beispiel:
W9.5 - exponent is 3.48, speed is ~2548x c , or 7.0 ly/day.
W9.8 - exponent is 3.68, speed is ~4472x c, or 12.3 ly/day
W9.9 - exponent is 3.83, speed is ~6555x c, or 18.0 ly/day
W9.975 - exponent is 4.13, speed is ~13,485x c, or 37.0 ly/day (Intrepid-class sustainable cruise speed, per Memory Alpha)
W9.99 - exponent is 4.33, speed is ~21,451x c, or 58.8 ly/day
Kinda weird that for long distance travel, ships don't simply punch up out of the densest part of the disk, transit "above" the disk, then drop back down at the destination. Voyager would have gotten home in 5.2 years entirely under its own power (neglecting punch times) assuming it could have sustained that high cruise speed (yes, I know, I know, Rick Berman's pockets needed to be lined, thus a half-assed story).
Of course, astrographic features may make it inadvisable to open the throttles wide (rifts, gas clouds, tollgates, passing TARDIS, etc).