I have a tradition of doing a little analysis on one of my favorite movie franchises to celebrate Star Wars Day (May the Fourth Be With You). Given that Rogue One: A Star Wars Story recently appeared on DVD and various streaming services, I think its OK to look at that film without worrying about spoilers. In this case, I will calculate Darth Vader's power output as he uses the Force.
If you've seen the movie, you know about the awesome scene at the end where the Sith Lord opens a can of whoop ass on some Rebel troopers. Vader uses the Force to pin a rebel against the ceiling and hold him there for just a while before slicing him with his light saber. That seems excessive, but I guess Vader wanted to make the rebel wait awhile before killing him because the Dark Side makes you cranky.
To calculate the power needed to lift this poor fellow, I can estimate how high Vader lifts him and at what speed. If I guess that the rebel is 1.75 meters tall (the average height of a man here on Earth, so I'll assume the same holds true on whatever planet the rebel calls home) then I can get an approximate scale for the scene. With that, I can use video analysis to plot the vertical position of the rebel as a function of time:
Just to be clear, I am using Tracker Video Analysis to get data from this video. But you can see from this plot that the rebel rises at nearly constant speed. Using the slope of this line, I get an upward velocity of about 3.3 m/s. The video provides another important measurement—how high the rebel rises. Based on the graph (which plots his approximate center of mass), Vader lifts him about 1.5 meters. Oh, wait! I need just one more thing—the time it takes Vader to lift the guy. This whole motion takes about 0.46 seconds.
Now for some physics. Let me start with power, defined as the rate at which work is done. Mathematically, it looks like this:
I can determine the work done by Darth Vader by looking at a system consisting of the rebel and the ship (I assume the ship uses some method of generating Earth-like gravity). The work-energy principle dictates that the work done on a system is equal to its change in energy. The rebel-ship system exhibits two types of change in energies—kinetic energy and gravitational potential energy:
Knowing the velocity and the change in vertical position, all I need is the mass of the rebel. Again, assuming he is a fairly ordinary person (and he must be; if he were extraordinary, he surely would have found a way to avoid getting killed), he has a mass of around 70 kg. I also can assume the inside spaceship has a gravitational field of about 9.8 N/kg (just like on Earth, where Gareth Edwards filmed this). Putting in these values, Darth Vader does 1,410 Joules of work. Because he does this in just 0.46 seconds, he has an output of 3,065 watts. That is the power of the Force.
