In case you missed it, NASA successfully launched the Orion spacecraft into orbit. The mission only lasts 4 hours, so it isn’t yet (at the time of this post) fully completed.
Here is my challenge. Create a video analysis showing the motion (and determine the acceleration) of the Orion spacecraft before the end of the actual NASA mission. In this assignment, I will use the free and awesome Tracker Video Analysis software. Yes, it’s so easy to use that I can finish this before the Orion splashdown.
Let’s get started.
The first step is to download the video. I find the easiest place to get the video is from youtube. Here is the link to the NASA launch video. I will assume you know how to download it from there – but there are many options (just google it).
Next, I need something to scale the video. The Orion spacecraft was launched using the Delta IV Heavy Rocket. With just a simple search, I can find several images with the dimensions of the Delta IV. From this site, I can get the size of one of the side boosters with a height of about 46.48 meters (from the bottom of the nozzle to the top of the cone). I can now use this scale in the first shot of the launch. Yes, it’s difficult to see exactly where the bottom of the nozzle is located so I am sort of guessing.
Now for the fun part. All I have to do is to use Tracker Video Analysis to mark the location of some point on the rocket. What about perspective errors from the camera? It seems as though the camera is far enough away that the distance from the rocket to the camera doesn’t change much. If you really wanted to explore this, you could measure the lenght of the rocket in each frame and see how it changes (or doesn’t change).
This is the plot I get from Tracker Video for this first shot.
That looks awesome. You can see that in this vertical position plot, the slope of the line is increasing with time. This means that the velocity is increasing and the rocket is accelerating. Even better, I can fit a quadratic function to the data. By matching this fitting function up with the kinematic equation, I find that the rocket has an acceleration of 2.296 m/s2.
But what can we do with this acceleration? Let’s estimate the rocket thrust. First, the mass of the Delta IV is about 733,000 kg (from Wikipedia) and the Orion is about 35,000 kg. This puts the total mass around 768,000 kg.
If I assume the air drag is negligible (I will also need to assume a constant mass – which it isn’t), then I can draw the following force diagram.
If I just look at the y-direction, I can write the following:
Using my mass, acceleration and a value of g = 9.8 N/kg (also 9.8 m/s2), I get a thrust force of 9.29 x 106 Newtons. Just checking with Wikipedia, it lists the total thrust of the Delta IV Heavy boosters at 6.28 x 106 Newtons and the first stage at 3.14 x 106 Newtons. This gives a liftoff thrust of 9.42 x 106 Newtons.
Ok, based on these numbers I am going to assume that this NASA Orion liftoff was a real event and not fake.
But here you can see, video analysis is fairly straight forward. I finished this assignment before the end of the Orion mission.
Oh, but you want some homework? Ok.
- Finish the video analysis. In the next few seconds, the video switches to a camera view from much farther away. In this scence, the camera seems to be panning and zooming out. You will need to adjust the size of the video in each frame. I suggest you use Tracker’s calibration point pairs.
- In that first set of data, how much fuel did the Delta IV Heavy use? How much did the mass of the rocket change? Would this have a significant impact on the acceleration?
- At would speed do you think the air resistance would be a significant factor on the calculation of the acceleration and thrust? Make some estimates about the size and shape of the rocket.
- If the rocket turned off it’s engines at the end of the data analysis above, how high would the rocket go before moving back down towards the Earth?
- If you were an astronaut on board the spacecraft, how many g’s would you feel?
No comments:
Post a Comment