Moved from a thread where it was off-topic
Agree completely, except that in atmosphere the thrust giving the 0.1 g is used to maintain the 100 km/h speed. So in atmo, we are limited to 100 km/h horizontal speed with no extra acceleration.
Exactly. The ascent profile I proposed was essentially vertical (aside from wind drift, which may be significant but could likely be accounted for in advance) until clear of atmospheric effects. Once out of the atmosphere, that limit doesn't apply.
[Sentence deleted]
Agreed, but any result we calculate has to be reasonably close, despite that number being presumably picked at random.
I may disagree with your definition of "reasonably close" but fair enough.
Agreed, unfortunately.
But it is difficult to ascend and descend vertically in a rotating system. Ovals and spirals are the natural shapes of movement in rotating system in a gravity field. As you ascend you have to increase speed to stay over the same spot on the ground as the angular speed is constant but the radius is increasing. But in atmo we have a top speed of ~100 km/h so we can't increase speed, hence the planet will rotate away from us.
So float "straight" up and take the drift, then go fast when you're above the atmosphere.
1 hour and 15 minutes due to aerodynamic drag below 30km gets you to the 100km Karman line (effectively out of the atmosphere).* That's not much time for wind to push the vehicle sideways, and you retain the surface rotational velocity of your point of departure. This will yield a westward displacement at altitude, but the effect at 100km is under 10m/sec at the equator.
As far as getting to orbit,the first half of the ascent to orbital altitude (not velocity) takes
2.25 hours
: 1 hour to get to 30km altitude, 1.25 hours to get to 1000km altitude. The second half of the ascent has the 0.1G that was used for ascent thrust redirected laterally to achieve orbital velocity.** After another 1.25 hours of this, the craft is at the 2000km orbital altitude but at only half orbital velocity (about 4km/sec). At this point the antigravity is dialed back to about 0.5G and progressively reduced to zero over the next hour of continued lateral acceleration. 55 minutes later it will have achieved 7.8km/s orbital velocity at 2000km altitude.
Time to establish Low Earth Orbit (2000km altitude, 7.8km/sec):
5.66 hours [Edit: 4.66 hours was incorrect.]
Time to 2000km altitude:
3.5 hours [Edit: 2.5 hours was incorrect.]
Time spent accelerating laterally at 0.1G: 2.16 hours, starting
2.25 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 significantly reduce this if the craft has the capability to do so.†
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)
* Due to the low vertical acceleration and the exponential decrease in atmospheric density with altitude, the Air/Raft never reaches its drag-limited airspeed even considering it's a 3m*6m flat plate when going straight up.
** Antigravity is turned down to 0.9G (effectively a 0.1G downward gravitational effect) in order to neutralize the vertical vector by the time orbital altitude is reached. I'm assuming that this "extra" 0.1G can't be used laterally, just the normal 0.1G that was used for vertical acceleration until this point.
† Air/Rafts carried on commercial starships might be equipped with a re-entry kit (single-use spray-on ablative foam, and a stabilizing drogue), while military or Scouts' Air/Rafts likely incorporate re-entry shielding as standard equipment. These enable 3G deceleration within the mesosphere (<100km altitude in standard atmosphere). General-purpose civilian Air/Rafts aren't capable of this degree of aerobraking and need to slow to a safe speed using their grav drives before re-entering the mesosphere.