> ... accelerate upward then turn 90 degrees and accelerate horizontally
I am not for such a scenario at all. The point of the upward (upward only and not considering the atmosphere) acceleration to the desired location is to give the lower bound of the energy requirements. This is the baseline (baseline-1) and the rocket equation is as simple as possible.
In reality with an atmosphere and to put the object in orbit, the aerodynamics change and the energy requirement increases beyond the above baseline-1.
If you "accelerate upward then turn 90 degrees and accelerate horizontally", you can calculate an energy requirement for that and it is easy. Only two vectors involved. That should give some limit (call it baseline-2). We should expect to do better than baseline-2, how better? A calculation using the diagonal of the vectors involved in baseline-2 should give us baseline-3.
We shouldn't do better than baseline-3. Our launch designs and ingenuity should have an energy requirement between baseline-2 (this is bad, we are not thinking) and baseline-3 (this is maybe closer to ideal).
The rockets and shuttles do "pitch-over manoeuvres" to turn the straight upward acceleration into an elliptical acceleration.
* Note, I have not addressed the complications of the variations in atmospheric drag, but if it varies close to linearly along the vertical cross-sectional then how I think about it above does not change unless there is some other oversight.
I don't get what idea you're communicating here. You seem to be saying that the best option for rockets is to accelerate upwards, out of the atmosphere, gradually transitioning to accelerating horizontally (if this is what you mean by baseline-3). Well okay, that's what we do, when using rockets.
Doing that with a track would be expensive because the track would have to be built hundreds of miles high over all of its length. It would be cheaper to build most of it lower, and maybe accept that we'll have to handle the air resistance somehow. If we build a track that doesn't go out of the atmosphere, we could still use it to build up a lot of speed and then turn the rocket upwards before the thing is self-powered. If we do build a track that goes out of the atmosphere, we'd still want to get as much ground-level acceleration as we can.
Maybe it's more practical to build the track on the Moon, where there's no atmosphere.
The scenario for baseline-3 is just a conceptual tool(pythogras theorem) to establish a bound. It still doesn't get you into orbit.
What I was grappling with, is. I presumed @ars (parent) knew he was talking and in expressing my contention it would get addressed with a little bit more information in what I was missing. I now see some emphasis in his explanation and additional links.
The key is was that tangential acceleration opens up none fuel based acceleration mechanisms i.e change to the type of energy and the quantity (you accelerate less fuel to burn up the fuel).
Okay. In this scenario where you accelerate upward then turn 90 degrees and accelerate horizontally, are you talking about this being powered by a rocket or by a track?
