So here we go. In this post, I am going to look at that weird rolling droid as seen in the Star Wars VII: The Force Awakens trailer. As a reminder, I am going to useTracker Video Analysis—it’s FREE.
Rolling Speed From Angular VelocityThis droid probably has a name, but I’ll just call him R2 Rolling (because his top looks like R2 D2). There are two ways to estimate his moving speed – but both require some type of size. Since I already said he (or she) looks like R2-D2, let me assume the head is the same size. Wookepedia lists R2 has having a height of 0.96 meters. This means that his head diameter would be about 0.43 meters and the rolling droid has a ball diameter of 0.76 meters.
Now for the video. This first method assumes that R2 Rolling is indeed rolling on that ball thingy (and not flying or skipping or something else). If I measure the rotational speed of the bottom ball, I can use that to find his rolling speed.
Here is the plot of angular position vs. time for the droid. Note that I had to export the data from Tracker to Plotly because Tracker always displays an angle less than 2π.
From this, you can see that the slope of the linear fit is 16.1 radians/sec. That’s the angular speed of the rolling part of droid. If the ball rolls without slipping, then there is the following relationship between the velocity of the center of the ball and the angular speed (ω):
Using a ball radius of 0.38 meters, this gives a droid land speed of 6.118 m/s (13.7 mph). So, about the speed of a human powered bike (but not a professional cyclist).
Rolling Speed From Relative Ground MotionWhat about another method? In this second measurement, I am going to track the motion of an object on the ground relative to the droid. Using the same clip (and scale), this will give me the position of the droid.
Based on this, the droid has a linear velocity of only 4.17 m/s. That was the plot from the best piece of “ground” that I could see. For two other plots, I have a ground speed (and thus droid speed) of 3.65 m/s, 4.68 m/s, and 5.93 m/s. None of these speeds are quite as high as the speed I calculated from looking at the angular velocity.
So, why are the two droid velocities different? Honestly, they aren’t THAT much different. If you notice the speeds of things on the ground change. That’s because when an object on the ground is farther away from the droid, it has less apparent motion (same reason the moon seems to follow you when you drive). I suspect even the fastest moving part of the ground is behind the droid making it’s motion seem slower.
That’s too bad. I thought I would be able to show that this little droid isn’t rolling at all and instead spinning out or flying. In the end, I think he is indeed rolling. That means that this Star Wars trailer is probably real and not a fake.
Just for fun, here is the motion of the droid with the camera stabilized (this is something that Tracker Video Analysis can do for you).
That’s it for the rolling droid. How fast is this compared to the flying R2-D2 in Star Wars II? The rolling droid is faster. From my estimation (and video analysis), R2-D2 flies at about 2.2 m/s. I should also point out that R2-D2 flies incorrectly in Episode II. While moving at a constant speed, he should have his thrusters pointed down instead of back.
Yes, there will be more video analysis posts from the Star Wars VII trailer.