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Say you're playing space ops engineer and want to simulate an orbital insertion---but you're petrified by the calculations needed to get the coefficients of the linear tangent law behind Powered Explicit Guidance (PEG).

You have a good feedback controller to point your rocket where you tell it to point, but you don't know the best place to point it because you can't do the math for PEG.

How would you approximate your target pitch angle as a function of time so that you can arrive from your initial post-MECO pitch to a final zero pitch at the correct altitude and velocity?

I'm essentially saying I'm OK with dropping the optimization part of the PEG algorithm and just figuring out some pitch program---any pitch program---that will take me from where I am at some time t post-MECO to orbital insertion.

Has anyone done this?

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I have also been unable to implement PEG and struggled to find an adequate approach in my orbital launch sim.

I have tried simply steering proportional to fraction-of-orbital-altitude-reached in the orbital insertion phase. I have tried various forms of quadratic guidance (inspired by the the Apollo LM's landing guidance). None have gotten good results.

At present, I use a time-scheduled pitch program for the early phase of launch and a fixed-coefficient LTG for the insertion phase, and tune the LTG coefficients manually for each launcher, which is extremely tedious. I've considered setting the sim up to automatically search for the best LTG coefficients, but haven't done it.

I think the right answer is to buckle down and really understand and implement PEG, but I haven't been able to do so myself. Section 4.2.1 of the Ascent Guidance, Navigation, and Flight Control Workbook that Organic Marble dug up looks like it might be helpful in that effort.

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  • $\begingroup$ Thanks for pitching in, @RusselBorogove! It's a tough thing to do, huh? Dumb question, but what is LTG? Also, do you do the gravity turn using a precomputed program, or do you use a feedback controller to hold angle of attack at zero? I've read the Saturn V used a precomputed pitch program for the gravity turn (not just the pitchover), but why wouldn't they use a feedback controller to actively keep angle of attack at zero---do you know? $\endgroup$
    – user36480
    Jan 13, 2021 at 6:19
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    $\begingroup$ @Alex they were worried that active gimbaling of the F-1s was not safe. In particular, they were worried that if some strong disturbance (e.g. wind shear) would induce such a strong control reaction that the structural integrity of the vehicle would be compromised. So instead they recorded the deviation from intended path and corrected it only just before orbital insertion. $\endgroup$
    – Ludo
    Jan 13, 2021 at 7:12
  • $\begingroup$ LTG = linear tangent guidance. $\endgroup$
    – Russell Borogove
    Jan 13, 2021 at 7:13
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    $\begingroup$ There's a pretty lucid explanation of PEG in section 4.2.1 of this document: gandalfddi.z19.web.core.windows.net/Shuttle/… The document is old and there are some differences with how it worked in the latter part of the program - the whole TFAIL thing was removed when the TAL abort came about - but it's pretty informative. $\endgroup$
    – Organic Marble
    Jan 21, 2021 at 20:45
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    $\begingroup$ That does look interesting. $\endgroup$
    – Russell Borogove
    Jan 21, 2021 at 21:11

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