It's my tradition to look at Star Wars and physics on Star Wars Day (May the Fourth Be With You - May 4). Let's look at something from the latest trailer for Star Wars VII: The Force Awakens.
In one scene we see a Tie Fighter apparently shooting up some stormtroopers. I have no idea what is really going on, but I can still do an analysis. If you watch carefully, you might notice that there is an explosion that sends a stormtrooper flying into the air. How about a video analysis of his (or her) motion?
I will of course use my favorite video analysis program, Tracker Video Analysis (free). The very first thing I need to do with this video is to correct for the motion of the camera. The camera doesn't move much, but it moves enough that I will need to manually move the coordinate axis for each frame. After that, I have to make a decision.
Whenever you look at a video of an object moving due to a gravitational force (you could call this projectile motion), you have to pick 2 things that you know and one thing you can find.
In this case, I am going to assume both the frame rate and the scale are "known". The video plays at 24 frames per second. If this is "real time" then each frame would represent a time interval of 1/24 seconds. For the scale, I am going to assume a stormtrooper has an average height of about 1.75 meters (just a guess). I can then use the exploding stormtrooper to set the scale.
Now that I have these two estimates, I can make a plot of the vertical position of the stormtrooper.
Fitting a quadratic equation to the data, I can find the acceleration by comparing it to the following kinematic equation:
This means that the coefficient in front of the t2 term in the quadratic fit must be 1/2 the acceleration (since the terms must match up). I can use this to find the vertical acceleration of the exploded stormtrooper with a value of -10.16 m/s2. That's not a bad value. It's fairly close to the acceleration of a falling object on Earth (-9.8 m/s2). In fact, this scene could be on Earth or perhaps an identical planet. My estimate for the height of a stormtrooper could have been off by just a tiny bit to give a value that was a slight bit high.
But of course I know this is just a movie and not real (yes, I actually know it's a movie). However, this suggests that this scene was created by actually flinging a human stunt person up in the air to a height of about 2.5 meters without using wires or anything. Oh, it could be CGI -- but why would it be?
Since it's Star Wars Day, I thought I would also share some of my favorite Star War blog posts. Here are some of the things I have looked at in the past. I will include the answers here, but click on the links if you want more details.
- What is wrong with the way R2-D2 flies? The answer is of course that he shouldn't fly. But if you want him to fly, he should fly with his thrusters down when moving at a constant speed. In Episode II, he aims his thrusters back to fly at a constant speed. Oh, the answer to this question is also in my new book Geek Physics: Surprising Answers to the Planet's Most Interesting Questions.
- Should bigger star ships have bigger thrusters? Yes, of course. However, a ship twice the size should have 4 times the size of thrusters. Why? Because big things aren't the same as small things.
- How Much Does Darth Vader Weigh? In Star Wars Episode IV, Darth Vader picks up a rebel and holds him in front of him. In order to not tip over, the mass of Darth Vader would have to be possibly around 236 kg (520 pounds).
- How fast are the blaster bolts in Star Wars? After an extensive look at many of the blaster shots in Episodes IV through VI, the average speed was 34.9 m/s (78 mph). Just for comparison, a Nerf dart is about 10 m/s.
- Did Han shoot first? Could have have shot second? Please tell me you already know about the "Han shot first" thing. Looking at the video where Han shoots after Greedo misses, he might actually have time to shoot as a reaction to Greedo's shot. I think think Han should have shot first.
- How big of a battery does C3-PO need to function? If he ran on AA batteries, he would need 3,000.
- How fast does the "ring" move when a planet sized object explodes? When Alderaan exploded, the debris ring moved at about 1/10th the speed of light. Other weird things happened too.
- What would happen if students were able to rate their Jedi Masters? This is just a spoof of Rate My Professor.
Ok, that should be enough Star Wars posts for you. If you need more, here are most of my old Star Wars posts. Have fun and May the Force Be With You.
