SpaceX once again successfully launched a Falcon 9 rocket with supplies for the International Space Station. The booster that launched the payload was then supposed to return, landing on a platform (at sea). Well, that didn’t go so well. The booster crashed on landing. Landing a rocket in this manner is clearly a difficult task. (Here is my previous explanation.) Maneuvering a tall rocket using the main thrusters would be like balancing a vertical broom on your hand and then moving this broom across the room and setting it down on the floor while still being upright. Try it. It’s not so easy—even for a computer.
Video Analysis
This isn’t such a bad video. In fact, the camera seems stationary and far enough away from the rocket that I can just mark the location of the bottom of the rocket to get the position. Of course, I will use Tracker Video Analysis. I only need to set the scale of the video. This site lists the length of the booster at around 43 meters long. Although it’s difficult to see the full length of the rocket booster, I can at least approximate the length to set the scale. After that, it’s just a matter of marking points. The bottom of the booster is fairly easy to see. Here is a plot of both the horizontal and vertical motion of the rocket. Note: this analysis uses the original lower quality vine video instead of the awesome HD video above. The analysis is still pretty much the same.
From this you can see that at first, the rocket had a fairly constant velocity in the vertical direction with a value around 35.8 m/s (86 mph). That seems quite fast—but what do I know? I’m not actually a rocket scientist. The horizontal velocity seems to be much smaller, but I will let you explore that for a homework question (see below). The other interesting thing is the tilt angle of the rocket. My original intention was to mark the top and bottom of the rocket in order to calculate the tilt angle. However, this didn’t work so well. The top of the rocket is much more difficult to see than the bottom (probably because of the flames and stuff coming out of the bottom). Fortunately, it doesn’t matter where I mark the top of the rocket as long as it is in a line along the length of the rocket. If I have these two points (top and bottom), I can calculate the angle. Here is a diagram showing how that would work.
With that, I can plot the angular position of the rocket as a function of time.
That plot turned out better than I expected. Clearly you want the rocket to end up with a zero degree deflection – but you can see that at the end it was significantly more than 0 degrees.
Homework
This is just too nice of a video to not include homework. So, here is your homework. Some of them are easy and some are not so easy.
Estimate the vertical acceleration of the rocket. At what time is the acceleration the greatest? How many g’s is that?
Estimate the mass of the rocket and determine the thrust needed to achieve this acceleration.
How much fuel would this rocket use to land? Yes, this is a tough question. Really, you need to know the speed of the propellent to determine the rate that fuel is used. I suspect you could look up the type of rocket engine and this would give you a starting point.
Make a graph of tilt angle as a function of height above the platform. You can do this with plotly. Just go to the data page and then click “fork and edit” and you can use the data.
What is the maximum horizontal velocity during the landing?
Make a plot of horizontal acceleration as a function of tilt angle. Is there some relationship between these two values? Should there be?
What was the vertical speed when the rocket touched the platform? SpaceX claims that it was a good landing, but it had lateral motion. Is this true?
How about a plot of vertical acceleration as a function of vertical position?
Finally, build your own spacecraft and see if you can land on a floating platform. Just kidding, that’s obviously pretty difficult.
Finally, I would like to thank SpaceX and Elon Musk. They don’t just make cool projects like a reusable rocket booster that lands itself, they keep trying to land it even though they have failed twice. More than that, they included a video that was way better than the last nighttime landing (crash).
Hopefully on their next attempt, SpaceX will include a high definition video for better analysis. Also, a note to Elon Musk: these projects are awesome. If you need someone to be an official SpaceX evangelist, I’m the right human for the job. Call me and we can work something out.
Update: Now SpaceX has released a much higher quality video of the landing and I have posted that at the top instead of the original vine (which is now down here). It doesn’t really change the analysis, but it is indeed nice. Notice the top horizontal thrusters trying to keep the rocket up at the very end.
