I have a problem. When I see a great video, it seems the first thing that comes to my mind is "can I do a video analysis of this?" The above video isn't the best for analysis, but it is the best for a description of the whole landing process. Let the analysis begin. Here is the video that I am going to use.
Time
First, some data gathering. I have the video, but what do I want to get out of it? How about a plot of altitude as a function of time? That would be fun. So, for this video, what is the frame rate? I have seen claims that it is anywhere from 4 frames per second to 8 fps. Well, I am just going to trust the video above from JPLnews. Also, there is this other video that has time stamps.
There seem to be two events in the videos that I can match up. There is the heat shield separation - at 05:15:28.13. Also, there is rover separation at 05:17:43.80. This gives a event to event time of 135.67 seconds. The high-resolution video has this same time interval at 35.4 seconds at a frame rate of 15 fps. If I call the time unit in the video s', I can say 135.67 seconds (real seconds) = 35.4 s'. This means that 1 s' = 3.83 real seconds. The real frame rate would then be 3.9 frames per (real) second. This is very close to the claimed 4 fps - so I will go with that. Now, one more thing. Some of the videos claim that there are some skipped frames. This would through the real frame rate off. Of course this won't stop me from doing the analysis.
Altitude
What about the altitude? How can I get that from a video? Well, I have done this before. Here is a previous post with a video from a High School Space Balloon. The idea is the same, but backward. In the case of the Curiosity landing, the ground will be getting closer, not farther away. In short, I can use the angular size of some objects on the ground to determine how high the space craft is at that time. (Is it still a space craft if it is in the atmosphere?) Here, I will use the following formula:
Where h is the altitude, L is the distance of some object on the ground and θ is the angular view of the camera. Oh, s is the size of the ground object in terms of the percentage of the video size.
The biggest problem is the angular view of the camera. The best I could find is this page and image from NASA.
From the page, it says the image shows the heat shield at a distance of 16 meters from the spacecraft. If the heat shield has a diameter of 4.5 meters, this means it would have an angular size of 4.5 m/16 m = 0.28 radians. Since the diameter of the heat shield takes up 21 percent of the horizontal image size, this must mean the horizontal size of the image is 1.31 radians (75°). That seems reasonable enough for me to move on.
Mars
If I am going to look at the angular size of objects on Mars, I need to know the actual size of these things to determine the altitude. After playing and searching, I found the Curiosity landing site on Mars - via Google Earth. Here is the surface of Mars with the distance measurement between two noticeable features.
According to Google Earth (which is funny to call it Google Earth when you are using it to look at Mars), the distance between these structures is 13,195 meters. Of course, as the spacecraft gets closer to the surface of Mars I won't be able to see these same features. This means I will have to pick some other things. Craters will be the likely choice. When I get really close, this might be tough. Ok, looks like I am ready.
Video Analysis
Here is the plan.
- I will use Tracker Video Analysis to look at the landing movie.
- To scale the video, I will just say the horizontal width of the screen is 1. That way I if I want to change angular size of the camera, it will just be one change of a constant in the calculations.
- In each frame, I will mark the location of the noticeable feature.
- Now I can calculate the pixel distance between these two features.
If you want the data - here you go. Have fun with it, but not too much fun. Once I have this "frame" distance between the two points, I can calculate the height.
Here is my altitude data based on the camera viewing angle of 1.31 radians.
Go ahead and say it. What is wrong with that first part of the data? Why does it look so out of line with the other stuff? I suspect that this is because during the first part of the video, the lander is not moving straight down. So, the camera on the bottom of the lander is looking at an angle. This means that the feature I used was further away than the height of the space craft.
What about the other data? For the middle set of data, it looks fairly linear. I fit a linear function to this data and I get a descent speed of 76 m/s (170 mph). I guess this is the terminal speed of the lander before it uses the rockets. I couldn't get any data for the final rocket landing since there were no unique features to view in the frame.
What about the heat shield? Here is a pretty good shot of the heat shield colliding with the ground. If you know what to look for, you can find it in the full video too. From the video analysis, this shield looks like it collides at 77.5 seconds after the start of the video. I was going to use this time and the initial height to calculate the terminal velocity of the heat shield, but apparently my starting height is off anyway.
I didn't do it, but it would be cool to use those few frames that show the heat shield impact to calculate the speed. You would have to use the shadow along with the location of the heat shield. I did something like this before.
If you want, you could also look up (or estimate) the mass and drag coefficients for the Mars Science Laboratory and calculate the terminal speed. Remember that the atmosphere of Mars has a different density and the gravitational field is different too.
