I know I'm late to the game. Rhett Allain, John Burk, Frank Noschese, among many others have been sharing how they use Tracker (or a similar tool) to analyze the physics of videos. Since I'm working on picking up my teaching certification in Physics this year, I figure this would be a nice addition to the teaching toolbox1.
So, what is Tracker? It's a free and open-source video analysis and modeling tool designed to be used in physics education. It works on Macs, PCs, and Linux boxes. Logger Pro is a similar tool, but it's not free or open-source2.
To begin, I watched Rhett Allain's video tutorial, but it includes a few more complicated pieces that I wasn't quite ready for. Luckily sitting in the Related Videos sidebar on YouTube was this tutorial, which went over the super-basics for n00bs like myself. Alright. Tracker downloaded & installed. Basic tutorial viewed. Now I need me a video to analyze.
I wanted something pretty easy to break myself in: a fixed camera angle, no panning, with an object moving directly perpendicular to the camera. I figured YouTube must be full of videos of people jumping bikes, and I went out to find my first video analysis victim. Amazingly, one of the first videos I found was both interesting, funny, and had the perfect still camera and perpendicularly-moving object:
Perfect! OK, now I needed to calibrate Tracker so it can accurately determine scale. Hmm...well Napoleon is standing fairly close to the sidewalk. I wonder if Jon Heder's height is online? Well, of course it is. In fact, Google gives me an estimated height right on top of the search results by just typing in height Jon Heder. However, I think I'll use IMDb's data, which lists his height at 185cm (sans 'fro).
There might be a small error there since he is standing a few feet back from the ramp, but it should be OK.
Did Pedro get, like, 3 feet of air that time?
It took me awhile to realize that I needed to shift-click to track an object...once I figured that out things went smoothly. I tracked the back tire of Pedro's bike. Here's a graph of the back tire's height vs. time:
There are a couple hitches in the graph. A few times the video would advance a frame without the screen image changing at all. Must be some artifact of the video. I added a best-fit parabola to the points after the back tire left the ramp. Hmm...the acceleration due to gravity is -8.477 m/s^2. That's a bit off the expected -9.8 m/s^2. That could be a result of the hitches in the data, my poor clicking skills, or my use of Napoleon Dynamite's height as my calibration. We'll go with it, since it's not crazy bad.
Coming up to the ramp the back tire sits at 0.038m and reaches a maximum height of 0.472 m. How much air does Pedro get? ~0.43m, or 1.4ft. Napoleon's estimate is a little high.
Maybe Napoleon meant Pedro's bike traveled forward three feet in the air? Let's check the table.
I highlighted the points of interest. We can look at the change in x-values from when the tire left the ramp (at 0 meters) until the tire lands back on the sidewalk (at y = 0). The bike traveled 1.3 meters while airborne; about 4.25 feet. So maybe that's what Napoleon meant.
Who was faster?
Let's check the position-time graphs for Pedro and Napoleon.
I added best fit lines to both sets of data. We can easily compare their velocities by checking the slope of their best fit lines.
- Pedro's velocity: 5.47 m/s (12.24 mph)
- Napoleon's: 5.44 m/s (12.16 mph)
If I account for potential errors in measurement, their velocities are basically the same. Though if forced to pick a winner, I'd Vote for Pedro.
How tall is Pedro?
It should be fairly straightforward to find Pedro's height using the data in the video. The first thing I need to do is verify that the camera angle is exactly the same when Pedro is standing behind the sidewalk as it was earlier. After switching back and forth between the two parts, it's pretty clear that the camera angle is a little different. Nuts.
So, I need to find and measure an object that is visible in both parts of the video. I chose the left window on the (Pedro's?) house. Going to the first part of the video where I'm pretty sure the calibration is accurate, I used the measuring tape to measure the height of the window. I got 1.25 meters.
Jumping to the second part, I calibrated the video by setting the height of the window to 1.25 meters. Then I used the measuring tape to determine Pedro's height. I got 1.67 meters, or about 5' 6". Seems like a reasonable result. Let's compare it to what the Internet says about Pedro's height. IMDb gives Efren Ramirez's (a.k.a. Pedro) height as 1.70 meters (5' 7").
Not too shabby for my first time using Tracker.
- You might notice this post is pretty similar in style to Rhett Allain's video analyses on Dot Physics. Well, it is. When just learning how to do something, it's always best to start by imitating the masters, right? Oh, if you haven't yet, you should definitely check out his many, many amazing examples using video analysis to learn all sorts of crazy things. The guy's a Tracker ninja. [↩]
- To be fair, it's only $189 for a site license of Logger Pro, which ain't too shabby. According to Frank Noschese, Logger Pro is a little more user-friendly. Tracker has a bit of a learning curve. [↩]