Sorry, this was a wall-of-text thread drift.
I moved it to
here, where it's on-topic.
With thanks to AnotherDilbert for the math, Air/Raft performance:
Quick summary:
[Edit: it takes 1 hour to get to 30km (drag-limited maximum airspeed of 30kph since it's a flat plate as it goes straight up... After that the air's thin enough that it accelerates normally.)]
An Air/Raft takes 12 minutes to ascend above the mesosphere (100km) and into soft vacuum.
Up there, travel time to anywhere on the planet is essentially T=2*(sqrt(D/0.1G)), plus the 30 minutes spent on the ascent and descent. EXCEPT average travel speed is 12,500kph (maximum speed 25,000kph at midpoint) to keep from exceeding escape velocity. Aerobraking, if the craft has re-entry heat shielding, can cut about a third off that but the passengers experience 3G for a few minutes.
Wind has at most 12 minutes to affect the ascent path.
Geographic displacement from vertical ascent at 100km due to planetary rotation is under 10m/sec at the equator. It's far more significant at orbital altitudes.
Orbit:
Time to establish Low Earth Orbit (2000km altitude, 7.8km/sec):
5.66 hours [Edit: 4.66 hours is incorrect.]
Time to 2000km altitude:
3.5 hours [Edit: 2.5 hours ws incorrect.]
Time spent accelerating laterally at 0.1G: 2.16 hours, starting 1.25 hours after takeoff.
This is for a nonspecific orbit. Achieving a specific orbit (a particular orbital inclination, or rendezvous with an object in a specific orbit) may take substantially longer -- which may explain the nominal 8-hour trip time.
Descent takes similar time, especially if aiming for a specific destination from an arbitrary point in the orbit. Aerobraking can help; see above.
This excludes the contribution of the surface rotational velocity at the point of departure (460m/sec at the equator, 390m/sec at 45N or 45S)