Broken Bow: "Neptune and back in six minutes." The warp five engine will be a "hundred times faster" than those of 32 years prior, according to Zefram Cochrane. "Thousands" of inhabited worlds will then be "at our fingertips." QonoS is "four days there, four days back" - eighty hours' transit. Warp 4.4 is thirty million kilometers per second - 100c. The Enterprise makes a detour to Rigel. This proves complicated, as Rigel is 700-900 light years from Earth. Even more curiously, it is cited as 15 light years from the Enterprise's current position. Being on the way to QonoS and Klaang's last stop, we expect this to be less than eighty hours' travel away, for a speed of ~1600c. Putting in the actual distance to Rigel from the starting point of Earth (rather than a starting point of somewhere along the road on the way to Kronos) gives a speed north of 76,000c and quite possibly in the 100,000c range."Daedalus" places the Enterprise as being over a hundred light years from any star system. Aside from the difficulty of reaching such a region within our galaxy, this suggests speeds at least on the order of thousands of c.
By the beginning of the next episode, "Fight or Flight," the Enterprise has been launched for two weeks.
Episode four: Six weeks have passed. "Strange New World."
Four days after "Minefield," the Enterprise is roughly 130 light years from home - a decade at warp 2-2,1. Warp 2 is therefore roughly 13c. Sometime after this, Archer has a phone call from home in "The Seventh" - anticipated the night before in a call to T'Pol. A real-time conversation over 100 light years requires very fast subspace radio speeds.
"A Night in Sickbay" - the Enterprise needs five fuel injectors to run its warp drive right.
"Singularity" - the Enterprise flies within 2 million kilometers of a black hole, part of a trinary system of blue giants. The path out of the system - considered a half light year radius - is 17 minutes, representing a speed of ~15500c.
"The Catwalk" - it takes 20 minutes to charge the warp coils for a cold start.
"Cease Fire" - three days of pushing the warp engines to the red line gets the Enterprise a dozen light years, for a speed of 1451c.
In "Future Tense," the Enterprise is 100 light years from Earth. Two episodes later, in "The Crossing," they are 150 light years from Earth. This figure is repeated in "Horizon," in which the Enterprise makes a detour of "a few days" and 60 light years, including over a day of waiting around at the final destination and a ten hour detour to drop a crewman off. This suggests a speed in the neighborhood of 3000-10,000c. As of "Horizon," the Enterprise had visited 22 inhabited worlds.
"Congenitor" - the Enterprise is the first Earth ship to go within 10 light years of a "hypergiant." Curiously enough, the nearest hypergiant stars are thousands of light years away, barring redefinition of the term.
By "Bounty," there aren't any inhabited planets around for the next fifty light years while 6 light years from the Klingon border, suggesting again speeds in excess of 1000c. The Horizon, incidentally, is carrying 30,000 tons of cargo; the Tezra in "Bounty" can haul a million tons of cargo at warp 4.5, which the Enterprise cannot.
In "Regeneration," we learn that it would take 200 years for a subspace message to reach the Borg in the Delta Quadrant, placing subspace radio at a new low speed of ~350c; in "First Flight," we learn that the warp 2 barrier was first broken by an Earth vessel during Archer's career.
The Enterprise returns to Earth at the end of the second season in "The Expanse," then sets course for a three month journey to the Xindi homeworld throug
"Damage" - warp 3 allows one to travel 4 light years in three days, i.e., 487c.h the Delphic Expanse; after six weeks of travel through unusual space, the Xindi planet is 50 light years away in "The Xindi," making the overall speed of the Enterprise through the Expanse ~400c. "Anomaly" - the Enterprise can last a month on antimatter within the main reactor.
"Similitude" - a polaric field drops the Enterprise out of warp. In "Carpenter Street," the Enterprise was 90 light years from Earth after 10 episodes in the Expanse.
There are apparently 78 spheres in the Expanse, dispersed throughout its 2000 light year span. The Enterprise visits at least seven over the course of the third season. If the Expanse falls between a planar and spherical region with this overall diameter, we would expect spheres to be typically 200-400 light years apart, suggesting that the Enterprise travelled at least 1400-2800 light years of the Expanse in one year.
"Stratagem" - the Xindi use subspace vortices to travel, bringing them a half dozen light years in two minutes - i.e., ~1.58 million c.
"Doctor's Orders" - travelling through a spatial anomaly would only take 1 hour at warp 4; later, the ship is 0.25 light years from the far edge after 4 days at impulse. This suggests a speed of 2000-4000c, but without great certainty. Phlox did not exceed warp 2, placing the lower limit of warp 4 at 23c.
"Countdown" - the Xindi superweapon has a 10 hour trip to Earth. At a range of 100-200 light years, this would be a speed of 88,000-175,000c. From halfway through the Expanse, 1000 light years, it would be a speed of 880,000c.
In "The Augments," a Klingon vessel 0.3 light years away has an intercept time of 2 minutes, giving a speed of 79,000c for the Klingons.
"The Aenar" - realtime remote control can be exercised over multiple light years of distance, implying very high signal speeds for subspace.
"Damage" - warp 3 allows one to travel 4 light years in three days, i.e., 487c.