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I'm new here, and I am delighted this forum exists! I'm working on a spaceflight simulator (FSX SpacePort) and currently, developing automated guidance module (I guess, a space autopilot). The analogue (baseline) launcher is NASA's SLS. My understanding of the general sequence of events is: (for circular, 400 km orbit)

  • Launch
  • As soon as tower cleared, roll to desired orbit inclination
  • As soon as roll complete, pitch for gravity turn
  • Penetrate atmosphere at zero angle of attack
  • When out of atmosphere (~120km), attain apogee of 400 km using main engines gimbal in pitch
  • At 400 km altitude and apogee locked (pitch at 0), burn till eccentricity 0 (stage if neccessary)
  • engines off at eccentricity 0, 400 km altitude

Am I on the right track? Is there something missing?

Thanks!

Mitch

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  • $\begingroup$ You may want to include the dogleg maneuver for orbits with inclination lower than latitude of the launch site. Launch more towards equator than desired inclination, and a turn upon reaching the relevant latitude. $\endgroup$
    – SF.
    Commented Mar 8, 2019 at 13:26

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Your general picture of ascent guidance is on track, but everything is complicated.

As soon as roll complete, pitch for gravity turn

The exact timing and initial pitch for the start of the gravity turn controls the overall trajectory. Turning too soon or too far means you are not going to space today; turning too late or too shallowly will make you overshoot your apogee.

Penetrate atmosphere at zero angle of attack

Near-zero angle-of-attack is necessary in the lower dense atmosphere, but some launchers pitch up to a slight positive AoA later to take some atmospheric lift. (It was surprising to me to learn this -- I would have thought the drag penalty would be prohibitive.)

When out of atmosphere (~120km), attain apogee of 400 km using main engines gimbal in pitch

At 400 km altitude and apogee locked (pitch at 0), burn till eccentricity 0 (stage if neccessary)

Unfortunately the apogee and eccentricity can't be independently achieved. If you're on a suborbital trajectory with 400km apogee and you burn horizontally, your apogee increases. You can hold the 400km apogee by pitching down during the circularization burn, but that's less efficient than reaching the desired apogee at the same time as reaching circular orbit velocity.

Typically an iterative guidance system is used to reach the desired orbital parameters all at once. The starting point for learning about this in more detail is "powered explicit guidance" (Orbiter Wiki).

engines off at eccentricity 0, 400 km altitude

Note also that some launchers do it differently, cutting off the engines while in an eccentric orbit with a perigee inside the atmosphere (or lithosphere!), then doing a separate circularization burn after a "coast phase". For example, the space shuttle would shut off the main engines and discard the external tank from say a 215km x 50km orbit (ensuring that the external tank would reenter the atmosphere promptly), and then circularize at apogee using the OMS.

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  • $\begingroup$ Nice summary, +1. $\endgroup$
    – Organic Marble
    Commented Mar 8, 2019 at 4:11
  • $\begingroup$ The angle of attack isn't too surprising if you think about it: The resulting lift trades vertical movement which is needed in the beginning to escape the thick air for horizontal movement. For low parking orbits the optimal angle will be higher than for higher orbits. $\endgroup$
    – Christoph
    Commented Mar 8, 2019 at 8:16
  • $\begingroup$ Excellent - thank you very much! I am not sure what you mean by "cannot be independently achieved" statement...I find that (in my simulator), as soon as I exit the atmosphere, I can pitch the launch stack down to zero pitch (horizontal), and the Apogee value readout will stop increasing. This means that I am now "coasting" vertically till my apogee - correct? Then, when I reach apogee, I can maintain it at a desired value by controlling the rocket pitch, maintaining the burn while I circularize. So - in what way are apogee and eccentricity independently unachievable? $\endgroup$
    – Mitch99
    Commented Mar 8, 2019 at 19:12
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    $\begingroup$ Shouldn’t be; moving the apogee purely horizontally relative to the local horizon means its altitude increases because it is moved further down range along the curved surface of the earth. (Does your sim assume flat earth?) The difference is very small at the start when horizontal velocity is low, but becomes more significant as you approach circular orbital velocity. $\endgroup$
    – Russell Borogove
    Commented Mar 8, 2019 at 20:31
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    $\begingroup$ The sim has a real-sized, spherical Earth, and all the parameters are the real values. I see what you are saying now. Indeed, as I approach apogee, it does start to change value, and I wasn't sure why. I have to manually adjust pitch to keep it locked to the desired value. That I why I need guidance algorithms - so that it can make these corrections for me. Thanks! $\endgroup$
    – Mitch99
    Commented Mar 8, 2019 at 23:17
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Flight path have been calculated using the optimal control theory for a long long time (see e.g. this 1960 paper).

There's an analytic solution for vaccum flight which is a really good approximation (assuming a linear gravity field). But there are also several numerical solutions for atmospheric ascent (e.g. this which has a lot of simplifications and also includes the analytic solution IIRC).

Until rather recently the commands for the atmospheric flight were simply precomputed, copied to the rocket and statically executed. As far as I can tell from the papers on this topic this 2010 paper layed the foundation for practical closed-loop control (the commands are actually calculated in real time which improves precision and reduces losses). It's not the first closed-loop control algorithm for the atmospheric part but it is the first to allow contrains on the flight path (e.g. AoA * dynamic pressure < X to limit the bending moment on the rocket).

The solutions optained by these algorithm still match the idea you described quite closely but as Russell Borogove already noticed they always fly at a certain angle of attack. The vacuum phase always nearly matches the linear tangent steering law.

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