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So I'm struggling to model a Falcon 9 vertical landing.

And because Falcon 9 info is scarce, I'm looking for more public info sources---like the apollo missions.

The Apollos did basically vertical landings on the moon, and maybe there are bits in their control strategy that I can use to land a Falcon 9 stage 1.

As you can tell, I'm not looking to copy the Falcon 9 strategy. I just want to use some reasonable valid strategy, and if the Apollo strategy is it, so be it.

But this leaves me wondering: in what ways were the Apollo landings different from a Falcon 9 stage 1 landing? I'm interested in the controls perspective more than the physics of the problem (e.g., drag, etc), but feel free to comment on anything that seems relevant to the question.

Thanks!

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    $\begingroup$ The presence of atmosphere and use of grid fins has to be a huge difference. $\endgroup$ – Fred Larson Apr 12 at 16:47
  • $\begingroup$ "The Apollos did basically vertical landings on the moon" Not at all: 16 degress to the horizontal. See space.stackexchange.com/a/43204/26446 $\endgroup$ – DrSheldon Apr 12 at 16:51
  • $\begingroup$ That's close enough for me : D $\endgroup$ – user39728_i_said_user_39728_i_ Apr 12 at 17:20
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    $\begingroup$ @DrSheldon They certainly weren't 16 degrees from horizontal at touchdown. $\endgroup$ – Russell Borogove Apr 12 at 18:33
  • $\begingroup$ I concur, @RussellBorogove. The diagram on high gate to touchdown in your answer from a few years ago gives a much better picture of the final phases of landing on the Moon. $\endgroup$ – David Hammen Apr 12 at 20:48
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But this leaves me wondering: in what ways were the Apollo landings different from a Falcon 9 stage 1 landing? I'm interested in the controls perspective more than the physics of the problem (e.g., drag, etc),

There are certainly a lot of similarities.

The Falcon benefits massively from air resistance on the way down -- it gets slower and slower as it descends, as opposed to a lunar lander, which would accelerate all the way down if it wasn't firing the descent engine all the way.

Falcon stage recovery is extremely precise, usually hitting within a couple of meters of the center of the barge target. While the Apollo LM had some ability to control the intended touchdown point, it was more of a "best effort" control than precision guidance.

There was an automatic touchdown program on the Apollo LM, but it was never used. On every landing mission, the commander used the semi-manual "program 66" mode, in which the commander's controls provided the desired descent rate and spacecraft attitude to the computer, and the computer translated that to throttle and RCS commands. Typically the switchover to P66 happened at around 150 meters altitude, descending at about 5 m/s. By comparison to Falcon, even the automatic descent schedule would be pretty leisurely; the descent rate would decrease steadily all the way down, and the last 150 meters of descent would take around a minute, whereas Falcon does it in around six seconds. If the Apollo commander didn't like the look of the terrain, it was possible to stop the vertical descent and maneuver horizontally; there was over a minute of descent fuel budgeted for discretionary maneuvering. Under Earth's much higher gravity, Falcon 9 doesn't have the fuel budget to fool around like that.

Both Apollo and Falcon rely primarily on a large, gimbaled, throttleable engine (or three) for both descent-rate control and steering. Secondarily, Apollo had RCS for attitude control, but the main engine was faster and more efficient in that role; the RCS was needed to adjust yaw attitude (i.e. what a long cylindrical rocket would normally refer to as roll), but the landing strategy generally didn't require much yaw maneuvering. Falcon has both cold-gas thrusters and grid fins for secondary attitude control; the fins are critical to maintain the stage's attitude during the period when the main engines aren't firing, but I don't know what the relative contributions of fins, thrusters, and Merlins are to attitude control during the final powered descent phase.

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  • $\begingroup$ "in that role"?? $\endgroup$ – Organic Marble Apr 12 at 22:07
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    $\begingroup$ Thanks, I must have already been working on the following parenthetical in my head. ;) $\endgroup$ – Russell Borogove Apr 12 at 23:25
  • $\begingroup$ Additional note: the LM could throttle much more deeply than the Falcon can. In particular, a Falcon 9 booster is not capable of lowering its thrust enough to hover at 1g on an empty fuel tank; its descent is rapid not only for fuel efficiency, but also because a near-empty booster is not capable of any landing strategy other than a suicide burn (aka "hoverslam", but there's no hovering involved). $\endgroup$ – Charles Staats Apr 13 at 16:17
  • $\begingroup$ That's less a function of the throttle (LM engine could go down to 10%, but didn't go below about 25% during a nominal mission) and more that the LM carried down a complete, fully tanked, heavy ascent stage. $\endgroup$ – Russell Borogove Apr 13 at 16:23
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The Apollo landings and the Falcon 9 landings are superficially similar in that landed vehicles on a large spheroidal object. The differences are huge.

  • Apollo: No atmosphere. Falcon 9: A significant atmosphere.
    The Apollo vehicles didn't have to contend with a lunar atmosphere, but they also couldn't take advantage of it. The Falcon 9 first stages do have to contend with the Earth's atmosphere, but they can also (and do) take advantage of it.
  • Apollo: A single computer from the stone age of computing. Falcon 9: Multiple computers from the 21st century.
    The Apollo GNC computer had its design set in the mid 1960s. Apollo vehicles landed using a single computer with a whopping 4 kilobytes of RAM, a compute speed that was slower than that of your (or your father's) first brick cellphone, and was programmed in assembly. While SpaceX is reticent about revealing full technical details, they have released some. Their computers (many of them!) are from this millennium, have lots of memory, and are programmed in somewhat modern programming languages.
  • Apollo: A trio of auxiliary computers and associated sensors. Falcon 9: No human pilots.
    Even the most powerful 21st century computers cannot rival with the decision making and pattern recognition capabilities of trained humans. The Apollo program relied on that; all six Moon landings used P66 (manual control with software assistance) to perform the final landing phase. Falcon 9 landings on the other hand are fully automated.
  • Apollo: No GPS. Falcon 9: GPS.
    Dual frequency GPS is amazingly accurate. The Apollo vehicles had nothing like GPS. All the Apollo vehicles had was a radar altimeter and state updates from the Earth.
  • Apollo: Landing on a rocky, crater-filled surface. Falcon 9: Landing on a flat surface.
    The landing site that the Apollo 11 flight software wanted to use was at the edge of a crater and chock full of boulders. Neil Armstrong had the people in Mission Control holding their breath as he looked for a suitable landing site. This is a problem SpaceX does not have. Their Falcon 9s land on a nice flat barge or a nice flat landing pad.
  • Apollo: 1/6 of Earth's surface gravity. Falcon 9: Earth's surface gravity.
    This factor of six reduction in gravity made the Apollo landings much easier to perform compared to the Falcon 9 landings.
  • Apollo: Landing on an object with a lumpy gravity field. Falcon 9: Landing on an object with a smooth gravity field.
    NASA had already discovered how weird the Moon's gravity field was prior to the Apollo missions. It discovered after the fact that those lunar mascons were an even stronger influence than they thought. The Earth's gravity field doesn't have those bizarre mascons, and it is much better known than is the Moon's gravity field. As no local sensor can measure gravitational acceleration, any spacecraft that navigates itself must have a model of gravitation that enables it to estimate acceleration due to gravity. This is a much easier task for a vehicle landing on the Earth compared to a vehicle landing on the Moon (or on Mars).
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  • $\begingroup$ The Apollo landings used the semi-automatic P66 program, not the much-more manual P67. In particular, P66 allows the commander to specify rate-of-descent, while P67 allows the commander to specify throttle level. $\endgroup$ – Russell Borogove Apr 13 at 14:56
  • $\begingroup$ Fixed it, @RussellBorogove. Thanks. $\endgroup$ – David Hammen Apr 13 at 16:02

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