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I want to simulate a hover slam landing.

Is there an overview of the maneuver anywhere?

I'm especially interested in the control algorithm used to bring the rocket stage to a halt at just the right time. I don't care much for location control (where the landing happens)---I just want to land the rocket stage somewhere anywhere.

The algorithm must account for both altitude and velocity left to kill before touching ground and estimate how much time to go, when to fire the engine, how long to fire it for, and maybe the appropriate throttle level to stick the landing.

The estimates should reflect the effects of gravity, thrust, and drag (drag being an important complication not dealt with during PEG as that occurs in near vacuum).

Anyone know how the calculations might go?

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    $\begingroup$ Easy, just launch the rocket in your simulation, then play it backwards. $\endgroup$
    – uhoh
    Mar 25 '21 at 7:00
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    $\begingroup$ Ha ha ha. That’s one strategy :D $\endgroup$
    – user39728
    Mar 25 '21 at 7:06
  • $\begingroup$ Why look for a harder strategy if this works? Is there some part of the problem that this would not solve? $\endgroup$
    – uhoh
    Mar 25 '21 at 7:34
  • $\begingroup$ Look for the game KSP that will let you practice this $\endgroup$
    – lijat
    Mar 25 '21 at 9:35
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    $\begingroup$ That strategy doesn't work, @uhoh. A launch vehicle gets heavier when played backwards. On the other hand, a landing vehicle gets lighter as it approaches the landing site. $\endgroup$ Mar 26 '21 at 6:54
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There is nothing official from SpaceX so any algorithm will be based on assumptions. Unlike your question SpaceX will be very interested indeed in exactly where their rocket lands and they will also have to work in 3 dimensions.

A simplified and approximate algorithm should be possible to build “relatively” easily. I would assume each phase of the landing will have target parameters, so on final descent the rocket should already be at a specific location, velocity and acceleration plus or minus a margin.

The side thrusters and Merlin engine gimbaling will be used to position the rocket to the right location directly above the landing pad.

The key thing to remember is that the Merlin engine can’t throttle down sufficiently to make a nearly empty Falcon stage hover. In other words the engine thrust pushing the rocket up is always more than the force of gravity pulling it down. If it weren’t for the fact that the rocket already had considerable velocity towards the ground it would accelerate back up in the air.

So the calculation that must be made is to ensure the upwardly accelerating rocket eats through its downward velocity in such a way that the velocity equals zero at the same time as the rocket reaches zero altitude and the engine is cut off. This calculation requires the use of the laws of motion and must take into account the rate of propellant consumption and the decreasing mass of the rocket.

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