Mechanics of F9 first stage return-to-launch-site (from CRS-10)

[Electroman]

(mod note: conversation moved from SpaceX Falcon 9 FT launch - CRS-10 - LC-39A)

Can someone please help me understand the exact trajectory of the first stage from MECO to landing. I have replayed this over a dozen times and I am still lost.

- When MECO happens how far downrange is the rocket? The telemetry shown on the video only has speed and altitude but nothing about how far down range?

- The boostback burn apparently starts at T+3:00 and burns for exactly 30 seconds, but if you look at the video there are no flames coming out of the nozzle in the bottom.. atleast not visible from the camera angle.

- When the boostback burn happens does the rocket tilt sideways parallel to ground? And at that point, is the vertical velocity zero?

- Obviously after MECO the first stage continues to climb due to inertia. So at some point it has to lose all the vertical speed and also the horizontal speed, so that it can come back. When do these events happen?

Looking at the video it is kind of hard to get a sense how this all works out, unless there is a camera that captures from a plane high up and on a clear day.

ideally it will be great to get a telemetry data from MECO for every second, on a) horizontal speed b) vertical speed c) position in 3d coordinates and d) attitude of the rocket itself.

 

[Fiver]

The onboard camera was slightly delayed from the ground camera. In the feed you noticed this as the ground camera showed it landing a few seconds before the onboard camera showed it as touchdown (they were split screened). The boost back burn happened, just not as they announced it on camera. Slight delay.

 

[YellyYeti]

This is my enthusiast's understanding of how things work. It is best viewed with the Technical Webcast that Mike1080i linked a few posts above. At MECO it looks like it is traveling up and east, in a suborbital trajectory. Stage 2 needs to burn to get to LEO, stage 1 would follow the suborbital trajectory and re-enter the atmosphere and burn up if it was anything but a Falcon 9. With Drone Ship landings the ship would be positioned at the end of this trajectory.

Stage 1 starts to flip to point back west (17:12 on the webcast) as soon as the second stage separates.You can see the boost back burn starting at 17:22, you can see the tiniest hint of a flame, especially as compared to the previous frames. You can also notice that the first stage starts moving to the right.

So now the first stage is pointing west and parallel to Earth and burning for 30 seconds. I do not know why no flames are visible, I am guessing no atmosphere interaction, but you can occasionally see the whisps of gas against the blackness of space

At 18:20 they announce stage 1 boost back shutdown, and at this point the first stage in a ballistic trajectory that should closely (?) follow the same line it took up, so it is heading west and down. 30 seconds with 1 to 3 engines must have been plenty to reverse the course given the much lower massing first stage. From the video it looks like the boost back burn is mostly parallel to Earth, so the vertical component of the stage's velocity is probably mostly due to gravity, it was a suborbital trajectory after all.

Stage 1 then flips butt-first for the re-entry burn, which happens at around 21:18. I would guess that at the re-entry burn most of the horizontal speed is shedded, and that stage 1 is almost directly above the LZ at this point. The grid fins help keep it on the correct trajectory, and then the landing burn slows the booster down for a soft landing.

Again, this is my own understanding of how things work. While I am an engineer, I do not work with orbital mechanics.

 

[Grendal]

Can someone please help me understand the exact trajectory of the first stage from MECO to landing. I have replayed this over a dozen times and I am still lost.

- When MECO happens how far downrange is the rocket? The telemetry shown on the video only has speed and altitude but nothing about how far down range?

- The boostback burn apparently starts at T+3:00 and burns for exactly 30 seconds, but if you look at the video there are no flames coming out of the nozzle in the bottom.. atleast not visible from the camera angle.

- When the boostback burn happens does the rocket tilt sideways parallel to ground? And at that point, is the vertical velocity zero?

- Obviously after MECO the first stage continues to climb due to inertia. So at some point it has to lose all the vertical speed and also the horizontal speed, so that it can come back. When do these events happen?

Looking at the video it is kind of hard to get a sense how this all works out, unless there is a camera that captures from a plane high up and on a clear day.

ideally it will be great to get a telemetry data from MECO for every second, on a) horizontal speed b) vertical speed c) position in 3d coordinates and d) attitude of the rocket itself.

I'll give it a shot but my answers will not be anywhere near official.

- When MECO happens how far downrange is the rocket? The telemetry shown on the video only has speed and altitude but nothing about how far down range?
I think it is similar to how far out the ASDS are parked for their landings so 20 or 30 miles.

- The boostback burn apparently starts at T+3:00 and burns for exactly 30 seconds, but if you look at the video there are no flames coming out of the nozzle in the bottom.. at least not visible from the camera angle.
You are right that it is the angle and the fact that it is only one or three engines firing. The initial boost uses all nine. The initial boost is vertical to a horizontal tilt for only 2 minutes and 30 seconds. So a much shorter boostback burn for however long it is creates a lot of change in speed. The boostback kills all the horizontal motion and generates enough to completely reverse the original movement. It's easy to forget that the booster is now nearly empty and doesn't have any of the weight from the second stage or the payload. It is basically an almost empty tube. A huge difference from what it originally had to lift.

- When the boostback burn happens does the rocket tilt sideways parallel to ground? And at that point, is the vertical velocity zero?
It still has some upward velocity but that would be quickly overcome by gravity. It wouldn't do to waste any fuel on slowing any upward velocity since gravity will do all that work for you. So all the boostback is lateral and parallel to the ground. I think the entry burn is done to slow the entry into the atmosphere so the booster isn't damaged by friction with the atmosphere when it hits it.

- Obviously after MECO the first stage continues to climb due to inertia. So at some point it has to lose all the vertical speed and also the horizontal speed, so that it can come back. When do these events happen?
Immediately. The boostback burn happened about 5 to 10 seconds after MECO. You would want that to happen as soon as possible since the booster will not be slowed whatsoever by atmospheric effects. Any delay would allow it to be moving further away from the landing zone because of inertia.

I think some enterprising person actually made a simulation showing the movement of the rocket and booster for fun. It might be on youtube.

Ha. Found it.

 

[ggr]

When the rocket is firing in a serious vacuum, there are no visible flames. Look at the pictures of the second stage, with a red-hot nozzle but almost nothing visible coming out. The boostback burn happens at a few hundred kilometers, so no flame visible. A bit more with three rockets firing for the re-entry burn, but it actually looks like less than one rocket firing for the landing burn.

 

[Electroman]

This is great guys. Really great. Couple of things I learnt from that animation - thanks Grendal and yeti.

A few things I learnt, or inferring

- MECO happens at around 60 km altitude with a speed of 6000 km/hr. Now only a portion of that velocity is horizontal. with a 70 degree angle of trajectory (based on the animation) the horizontal component would be 6000 * cos(70) ~= 2000 km/hr East. Vertical component is 6000*sin(70) = 5600 km/hr

- Boost back burn happens within a few seconds of MECO with the rocket tilting exactly horizontal. Primary objective of the boostback burn is to lose horizontal momentum and then reverse the direction to West. Here is where the animation comes short. Because it is quite difficult to judge when the rocket reverses direction.

- in any case the boostback burn cuts off after 30 seconds with the rocket still climbing at 117 km. The speed is now 2500 km/hr. Now how much if this is vertical component and how much of this is horizontal East, is very difficult to calculate. The animation appears to be at 45 degree trajectory towards West. So I am guessing 1800 km/hr West and the same speed still climbing vertical.


- so in essence the rocket changed from 2000 km/hr East to 1800 km/hr West in about 30 seconds of boostback burn. A speed change of 3800 km/hr in 30 seconds. That is quite a bit of change in a short amount of time.


- Now while all this happening, the rocket continues to climb upwards and reaches a height of 130 km, which is where it loses all its vertical momentum and starts to fall back. This is interesting that the engine cut off happened at 60 km altitude and the rocket stops climbing only after reaching 130 km a 'free' climb of 2 full minutes - reaching an altitude of twice the height after engine cut off.

- At this point the rocket is at the highest point and the horizontal speed is exactly the same as when the boostback burn stopped - which is 1800 km/hr due West. It did not lose any horizontal speed at all after boostback burn, which is to be expected with no atmosphere to slow it down.

- from this point it is free fall and you are still several miles downrange East. i am guessing around 10 miles. The rocket turns vertical, and starts to fall free. The vanes help it do course correction once it hits the atmosphere, and close the last 10 miles gap by directing the rocket Westward - purely by atmospheric maneuvers.

This has been a great education. I can sleep peacefully now Thanks to yeti and Grendal.

[Edit: swapped East and West]

 

[Grendal]

I just came to the realization with your questions that the entire sequence is done by computer as it is happening. The evidence is the fact that the timing for the boostback and entry burns are always different from what the announcers are saying. They are estimating the timing based on basic calculations but the computers are adjusting on the flight.

 

[Mike1080i]

I just came to the realization with your questions that the entire sequence is done by computer as it is happening. The evidence is the fact that the timing for the boostback and entry burns are always different from what the announcers are saying. They are estimating the timing based on basic calculations but the computers are adjusting on the flight.

Yep, all while the boosters mass is changing as it burns propellant and the Earth (and the landing target with it) is rotating under it.

@mkjayakumar that's pretty much it, just swap your East and West.

 

[Electroman]

@mkjayakumar that's pretty much it, just swap your East and West.

Ah..screwed up East and West !. Thanks for pointing it out. I fixed it now.

The last piece of the puzzle is to get a plot of horizontal velocity and down range position. None of the current telemetry gives you that data. It is all inference.

 

[Mike1080i]

The last piece of the puzzle is to get a plot of horizontal velocity and down range position. None of the current telemetry gives you that data. It is all inference.

Agreed, it would be nice if they would display telemetry from both stages after separation. Plenty of space to do that above their double box shots.

 

[Electroman]

Landing burn: 2700 km/hr to 0 km/hr; from 18 km altitude to zero in 55 seconds

During launch: 0 km/hr to 2700/km/hr; from 0 to 22 km altitude in 1:40 seconds

 

[ecarfan]

I just came to the realization with your questions that the entire sequence is done by computer as it is happening. The evidence is the fact that the timing for the boostback and entry burns are always different from what the announcers are saying. They are estimating the timing based on basic calculations but the computers are adjusting on the flight.

That does seem to be the case. And as @Mike1080i pointed out the calculations are done in real time during the flight (I assume by the onboard computers and inertial navigation system) while the mass of the rocket is changing.

How awesome is that! This is the real world "science fiction" stuff that I dreamed about happening when I was a kid. And now I'm seeing it, and I expect to live to see a human colony established on Mars.

It doesn't get better than that.

 

[swaltner]

I just came to the realization with your questions that the entire sequence is done by computer as it is happening. The evidence is the fact that the timing for the boostback and entry burns are always different from what the announcers are saying. They are estimating the timing based on basic calculations but the computers are adjusting on the flight.

Note that the live video feed looking down the side of the 1st stage booster on the Falcon 9 was delayed by about 10 seconds. You can see this by the ground and rocket views of the landing being out of sync. The two images below are taken right as the rocket shuts down after landing. The ground view at 22:43 in the technical webcast shows the rocket on the ground and the view looking down from the rocket doesn't even have the landing legs extended. I think this delay in processing the vide stream coming from the rocket is most of the difference you noticed on the lag between the commentary and video of what was happening.

I'm not saying that the rocket landing is anything other than fully computerized and automated, but the logic on the video being out of sync with the commentary being proof of that is faulty.

Have to add I'm loving this whole venture. Sent out a bunch of texts to friends over the weekend. One conversation was how this is almost becoming passé now and they are making this look so easy landing right on the mark time after time. This morning, asked another friend how many rockets they thought SpaceX had successfully landed. "One, right?" "Um, no" I may need to rethink my choice in friends...

 

[Doug_G]

Stage 1 then flips butt-first for the re-entry burn, which happens at around 21:18. I would guess that at the re-entry burn most of the horizontal speed is shedded, and that stage 1 is almost directly above the LZ at this point. The grid fins help keep it on the correct trajectory, and then the landing burn slows the booster down for a soft landing.

The re-entry burn does more than just slow the booster down. It acts somewhat as a heat shield - the high velocity gases jetting into the dense air ahead of the booster cause compression and heating a distance away from the booster. That distance isolates the rocket from excessive heating.

 

[AudubonB]

Huh. So create heat to shield from heat. That's.....interesting.

I'm not being contentious! I find it a delicious irony!

 

[Doug_G]

Fight fire with fire...

 

[rabar10]

Here's the "Flight Club" video model of altitude/speed from the recent CRS-10 launch: