The Physics Behind a Fake Flying Samurai Battle
This video shows a battle between samurai with jet packs. Don’t get excited—it’s fake.
How do I know? There are a few obvious signs of fake-itude, starting with the shaking camera. This battle was likely recorded on a hand held phone—and if you went to all the trouble of creating a rocket pack, couldn’t you at least get a tripod to record this historic event? Yes, you could. Another piece of damning evidence: the vertical video. Sure, vertical is fine for Snapchat, but this is a rocket-powered samurai battle. If it was real, you’d at least take the time to record like a civilized human and turn the phone to landscape mode.
But wait! There is some physics working in our favor here, too. If these are fake flying samurai, they must be suspended on some sort of long cable, attached to a crane or something that can raise and lower them as though they’re flying. And in fact, I can even find the length of the cable they are using.
Just watch: You can find the length of the cable by looking at how the samurai swing after pushing on each other. Oh sure, you could try to find the radius of curvature for their trajectory as they move, but that wouldn’t be too simple. Instead, I am going to assume they are a simple pendulum and look at the period of oscillation.
I should point out the that the “simple pendulum” isn’t actually so simple to solve but I can give you the highlights of this physics problem. In order to qualify for the certified “simple pendulum” label, the string must be massless and all the mass of the object must be concentrated at the end. Also, the only forces acting on the mass (that’s the bob of the pendulum) should be the tension in the string and the gravitational force (no air drag). Of course both of these won’t be exactly true for the swinging samurai—but it’s close enough.
The tension in the string prevents the mass (or samurai) from getting farther away from the pivot point and forces the motion into a circular trajectory. The gravitational force has a component that always pulls the mass back towards the center (equilibrium). If the swinging angle is sufficiently small (we usually say less than 15°) then the swinging mass will exhibit simple harmonic motion just like a mass on a spring. However, the period of oscillation for a mass on a spring depends on the mass and spring stiffness. In the case of a simple pendulum, the period depends on the length of the string and gravitational field (g) based on the following equation.
Yes, the T represents the period of oscillation in seconds. L represents the length of the pendulum string in meters and g is the gravitational field with a value of 9.8 Newtons/kg—at least on the surface of the Earth (a different planet could have a different value of g). This means that I just need to find the period of oscillation in order to find the length of the cable.
Now for some quick video analysis (I like to use Tracker Video Analysis). Just looking at the motion of one of the samurai after a push, I get the following plot.
This is approximately half of a complete oscillation with a time of about 3.5 seconds. With a full period of 7 seconds, I can solve the above equation for the length. This gives a cable length of 12.2 meters (which is almost exactly 40 feet). Boom. That’s how you make a fake samurai jet pack—get a 40 feet long cable and lift him up.