APOD: Falcon 9 First Stage Landing (2015 Dec 28)

[DavidLeodis]

Thanks Chris and neufer for your help.

Having read more of the many links I've now found this "Moving back at supersonic speeds that sent a sonic boom across Florida’s Space Coast, the first stage engines ignited to slow the booster down as it neared Landing Complex-1".

[JohnD]

Chris will correct me, neufer, but I don't think that the landing Falcon would have taken off again if the rocket had kept on firing.
It's thrust , and the acceleration it caused counteracted the acceleration due to gravity, but not quite.
The result was a system that behaved like a much lighter vehicle, that came down slowly.
Once it contacted Earth, the reaction of a solid surface provided a further acceleration that precisely counteracted gravity.
Continued rocket thrust (of the same amount) would have made gravity and the Earth's reaction less, but not enough to counteract gravity completely and launch the vehicle again.
John

[neufer]

I don't think that the landing Falcon would have taken off again if the rocket had kept on firing.
It's thrust , and the acceleration it caused counteracted the acceleration due to gravity, but not quite.
The result was a system that behaved like a much lighter vehicle, that came down slowly.

Assuming a constant thrust (with little change in total mass) the rocket is either:

• 1) accelerating up (i.e., decelerating down)
  2) hovering or
  3) accelerating down (i.e., decelerating up).

If the thrust more than counteracts the acceleration due to gravity (as I suggest)
then the rocket is 1) accelerating up (i.e., decelerating down) and the rocket lands softly.

If the thrust can't quite counteract the acceleration due to gravity (as you suggest)
then the rocket is 3) accelerating down (i.e., decelerating up) and the rocket lands with a thud.

[BMAONE23]

Would that be Elmer Thud?
Be Vewwy qwiet, we're hunting wetwo wockets

Click to play embedded YouTube video.

[Chris Peterson]

Chris will correct me, neufer, but I don't think that the landing Falcon would have taken off again if the rocket had kept on firing.
It's thrust , and the acceleration it caused counteracted the acceleration due to gravity, but not quite.
The result was a system that behaved like a much lighter vehicle, that came down slowly.
Once it contacted Earth, the reaction of a solid surface provided a further acceleration that precisely counteracted gravity.
Continued rocket thrust (of the same amount) would have made gravity and the Earth's reaction less, but not enough to counteract gravity completely and launch the vehicle again.
John

You're right. I'm right. Art's right. We're all just telling part of the story.

My original comment is correct, that landing involves controlling the thrust such that gravity is almost, but not quite compensated for. But that's just the global view of the entire landing sequence. What Art's getting at is the fact that any time you have a force, you have an acceleration. If you have a constant velocity, there is no net force.

Landing involves managing a specific velocity profile. Over the entire landing, the integrated force applied by the rocket is less than the integrated force of gravity, which is why you go down. Instantaneously, the thrust force may be greater or less than the force of gravity- if you're increasing your downward velocity, it will be less; if you're decreasing your downward velocity, it will be more (you'll be accelerating upward, even though your velocity is still downward). If you're maintaining a constant downward velocity, you might think that your two forces would be equal, but actually, you would have slightly less thust because if you have a non-zero velocity, you also have an upward directed drag force. And when you get very close to the ground, things probably get very complicated because now you don't have a purely Newtonian action/reaction system, but who-knows-what nonlinear ground effects.

[suicidejunkie]

If the engine were able to throttle down to get anywhere near "just counteract gravity", then the landing would be MUCH easier, since the rocket could hover until it got things right (or ran out of fuel).

Instead what happens is the rocket comes screaming down at a high speed, and the engines light up with a lot of thrust, but timed perfectly so that it slows to a dead halt just a tiny distance above the ground. The engines are then shut down so it doesn't start moving upwards again. (AKA suicide burn)
If you start thrusting a fraction of a second too late, you come to a stop embedded 10m into the ground. If you start thrusting a fraction of a second too early, you come to a stop 10m up, and then crash from there.

IIRC, the engine on that booster can be throttled between about 70%-100% thrust, which is close to 2g acceleration on the bottom end, but reduces the timing requirements from absolutely perfect to "very small margin for error, but doable". Also, you can't just shut the engine off and then start it up quickly to fake lower throttle; that's a good way to destroy your engine.
Apparently the longer term goal for future designs is to get a minimum throttle of 40% which would allow hovering, but throttle control is definitely on the hard end of rocket science .

[neufer]

If the engine were able to throttle down to get anywhere near "just counteract gravity", then the landing would be MUCH easier, since the rocket could hover until it got things right (or ran out of fuel).

Neal Armstrong had to do some hovering over the moon until he found a nice place to land (or run out of fuel).

The Falcon 9 knows exactly where it is & where it wants to land at all times so that hovering shouldn't be necessary.

Hover, v. i. [OE. hoveren, and hoven, prob. orig., to abide, linger, and

• fr. AS. hof house; cf. OFries. hovia to receive into one's house. See Hovel.]
  
  
  • Macbeth Act 1, Scene 1
  
  Witches: Fair is foul, and foul is fair:
  • Hover through the fog and filthy air.

[Chris Peterson]

If the engine were able to throttle down to get anywhere near "just counteract gravity", then the landing would be MUCH easier, since the rocket could hover until it got things right (or ran out of fuel).

We were, of course, discussing the nature of landing rockets in general. That said, I doubt hovering would ever be a desirable option, nor that it would actually make things any easier. To make this cost effective, the system needs to land on the least possible amount of fuel. I imagine that the landing profile is designed with that in mind. And all profiles should be equally easy (but not necessarily equally robust) given that it's just an elementary Newtonian dynamics problem and basic control theory. As long as the rocket actually does what it's commanded to do by the computer (which is an engineering problem), the actual landing profile is pretty arbitrary.

[suicidejunkie]

I think it is quite fair to say the *option* to hover is quite desirable, since it allows you to correct for quite a lot of undesirable situations. (Low velocity at any altitude becomes survivable) Needing to use it, however would not be good, but that's how safety margin works and at least it doesn't cost you mass when not used. Things diverge a bit from a simple Newtonian dynamics problem when you have air and wind and many other variables you can't control, after all.

Expanding the range of current speeds and altitudes from which you can safely land to me says "easier". "Robust landing profiles" is a good term to replace "easy" with, for when you're not anthropomorphizing the rocket systems.

... landing involves controlling the thrust such that gravity is almost, but not quite compensated for."

^ That's the bit I really worried about. Almost compensating for gravity means not accelerating much, but that is not all that relevant; you're not fighting gravity so much as you're fighting your own momentum over these small time scales. It is the velocity which is very important; you need to fall (0 thrust to be efficient) and then stop precisely (max thrust = quickest to be efficient, but also dangerous!)
Which leads back to the suicide burn stops as seen in the video.

[geckzilla]

I don't think hovering is an option at all given the mass problem. I get what you mean by it being desirable, though. Then again, if the rocket fails it'll probably fail with or without a few seconds of hovering. Computers don't need moments in time to correct things like humans do.

[Chris Peterson]

I think it is quite fair to say the *option* to hover is quite desirable, since it allows you to correct for quite a lot of undesirable situations. (Low velocity at any altitude becomes survivable) Needing to use it, however would not be good, but that's how safety margin works and at least it doesn't cost you mass when not used. Things diverge a bit from a simple Newtonian dynamics problem when you have air and wind and many other variables you can't control, after all.

The dynamics may not all be strictly Newtonian, but they are simple.

I don't see landing system like this being used for humans anytime soon, so it's just a question of recovering a booster. That will probably be configured with a near-zero safety margin, given the cost of carrying all that landing fuel up in the first place (assuming this system proves economical at all compared with what we do right now, which I think is still quite uncertain).

[alter-ego]

...To make this cost effective, the system needs to land on the least possible amount of fuel. I imagine that the landing profile is designed with that in mind.

In this SpaceX update article, it's stated that a landing at 2g's is 5.5x more fuel efficient than landing at 1.1g's. Knowing the 1st stage length = 70 meters, I fairly accurately determined the decent profile by analyzing the video in 1-sec increments. The plot shows a simple (de)acceleration profile at 0.9g, or a nominal thrust of ~1.9g which is consistent with the article's higher-g, more efficient algorithm and the previously mentioned engine specs. In the video, the rocket is descending at ~65m/s when the rocket base first becomes visible (at 2 sec), and the simple acceleration model closely predicts zero velocity at 7.5 seconds elapsed time and -2.7m altitude. Given the simplistic analysis, I think the fit surprisingly good (for this discussion anyway) supporting the Newtonian model and successful higher-g controlled descent.
 

[Nitpicker]

Nice work (once again), alter-ego.

[alter-ego]

Why thank you, Nit! I do occasionally get into these things
I was thinking of responding to the Earthset from the LRO APOD but then I said, nah, Nit will get it.

[neufer]

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Click to play embedded YouTube video.