No one really likes waiting in an airport. When I'm there stuck in a sort of travel purgatory, I try to do something fun. For me, fun is video analysis. It's easy. Just find something and make a video. It's easy now that I almost always have a video camera with me (my phone). So, that's what I did. The above video is from the Baltimore-Washington International Airport.
Let me give you a couple of tips in case you want do this yourself.
- Use a stationary camera. You probably don't have a tripod with you, but you can improvise. I put my phone on the ledge of a window. If you can sit your phone on anything, it will help. Another option is to brace your phone against a wall. The point is to have a video where the only thing moving is the object of interest and not the background.
- Get a perpendicular view. If you have a nice stable video but the plane is taking off towards you, that's not going to be as easy to analyze. You want the motion of the object perpendicular to your point of view for the simplest analysis.
- Don't worry about finding the coolest thing to video. Sometimes you can record a video and discover something awesome while you are doing the analysis. You just never know what you are going to find.
There is one other thing to consider, the scale of the video. In this case, I could use the length of the plane to determine the size of things. I think the aircraft in motion is a Boeing 737-700 (or maybe a 737-300). They are both about the same length at either 33.4 meters or 33.6 meters. I'll just estimate 33.5 meters for the length.
But wait! There's another way to get the size and scale and that is to use the angular size and distance from the camera. If you know the angular field of view for your camera (and I experimentally determined this for the iPhone 5) then you can use the angular size of the object. Here is my favorite diagram showing this relationship between distance and angle. Yes, it only works for objects that are fairly far away.
But what about the distance? Ah, ha! Here is the cool part using Google Maps. I pretty much know where I was standing as well as the location of the aircraft.
That puts the distance at 316.6 meters. The angular field of view for the video camera is 0.888 radians. Using Tracker Video Analysis, I measure an angular length of the plane at 0.104 radians. This gives a total length of 32.9 meters. That's way closer to the expected value than I anticipated.
Video Analysis
Now for the analysis. This is fairly straight forward. I already know the scale so I just need to mark the location of the plane in each frame. Here is what I get for the position of the aircraft.
I already fit a parabolic function to the data (as you can see in the plot). This is just like the very common kinematic equation that says:
The fitting term in front of the t2 is then half of the acceleration. This means the aircraft has a horizontal acceleration of 8.52 m/s2. That's a bit higher than I expected. If you were in this plane, you would feel an acceleration of about 0.87 g's.
What about the speed of this air craft? If I use the same plot, I can fit a linear function to the last part of th data. Here's what that looks like.
This gives a final speed around 75.3 m/s or 168 mph. Just a quick Google search it seems like the take off speed should be around 150 mph. So, that looks good.
Homework
You know there's going to be homework with this, so why complain?
- In my analysis, I set the scale based on the length of the aircraft. As the object moves across the screen, it is farther away at some points. How much does this change the scale? Can you fix the video so that this distortion is accounted for?
- Suppose the pilot wants to lift off the ground at a speed of 80 m/s. If he has a constant acceleration during the whole take off, how long of a runway would he need? How long is that particular runway at BWI (use Google maps - oh, but you will have to switch to "classic" mode to get the measurement tools)?
- If the plane was to abort the take off, what acceleration would it need during the stop so that it still had 10% of the runway left over?
- How fast is that truck moving?
- Estimate the thrust from each engine.
That's it. Remember, airports don't have to be boring, but you still can't bring bottled water through the security check point.
