I Calculated the Mass of a Star Wars Blaster Bolt for You
Everyone knows the weapons in Star Wars aren’t lasers. If they were lasers, you wouldn’t see them from the side very well and, more importantly, they would travel at the speed of light. But just what comes out of these blasters? I call them blaster bolts, and as I’ve shown before, the speed of these blaster bolts is around 35 m/s (78 mph).
But what is the mass of these bolts? Check out this clip from a trailer for Star Wars: The Force Awakens. It appears that Han Solo shoots a stormtrooper who flies backward from the impact. Now, it’s entirely possible Han is shooting at something else, but let’s go with Han shooting the trooper.
Notice how the stormtrooper flips and flies backward? We can use this to learn something about the blaster bolt—in particular we can determine its mass. Consider the bolt as it hits the stormtrooper and the forces involved.
Since there is an interaction between the bolt and the stormtrooper, the force of the bolt pushing on the trooper is the opposite of the force of the trooper pushing on the bolt. We also have the momentum principle. This says the total force on an object changes the momentum of that object.
Here momentum (we use p) is the product of mass and velocity. This means the momentum of the bolt and the stormtrooper will change due to this interaction. Since the magnitudes of the forces are the same, the bolt and trooper will have opposite momentum changes. We could also say the total momentum before the collision is the same as the momentum after the collision. Since the interesting stuff happens in one dimension (and the stormtrooper starts at rest), conservation of momentum says:
Here I am assuming the bolt sticks to the stormtrooper and has the same final velocity. Hopefully it’s clear that I am using “b” subscripts for the bolt and “s” for the stormtrooper. Solving for the mass of the bolt, I get:
Now I just need to find the mass of the stormtrooper, the speed of the bolt before impact, and the recoil speed of the trooper.
In many cases, I would jump right into Tracker Video Analysis and get position-time data for the recoiling stormtrooper. However, in this case the stormtrooper moves diagonally away from the camera, making the position difficult to determine. There is one thing I can get from the video: time. Plotting the vertical position of the stormtrooper will at least give me a good estimate of how much time he spent airborne. Here is that vertical position plot.
From this plot, the stormtrooper was in the air for about 0.835 seconds. If I had the horizontal distance traveled during the trooper’s fall, I could use it to estimate the velocity. I’m going to have to guess. It looks like he moves back at least one body length. Let’s go with an estimate of 1.7 meters to 2.3 meters. Also note that I am ignoring the vertical velocity of this stormtrooper’s motion (we can talk about that later). Using these values, I get a recoil velocity of about 2.0 m/s to 2.8 m/s.
I need one last estimate—the mass of the stormtrooper. Assuming he is a typical human, I am going to use a value of 75 kg. Since I don’t have enough data from the above scene to measure the speed of the blaster bolt, I am just going to use my average value of 35 m/s. Using these values in the conservation of momentum equation, I get a bolt mass of 4.5 kilogram to 6.5 kilograms (10 to 14 pounds). It could even be more massive than that. If I take into account the vertical recoil velocity of the storm trooper, the bolt would have to be moving even faster.
OK, you don’t like that value, I get it. What if I double the speed of the blaster bolt? In that case, I have a bolt mass of at least 2.2 kg (more than 4 pounds). Compare this to the mass of a modern bullet like the huge 50 caliber at around 50 grams. Also, as the MythBusters showed, a 50 cal bullet does not have enough momentum to knock a person down.
Now a few more considerations (along with a couple of homework problems).
- Where does this bolt mass come from? The ammo in the weapon? If so, that weapon is going to be very heavy with the mass for 20 shots or so. In fact, 20 shots is around the mass of a person. Imagine carrying around a weapon with the mass of a person.
- What about the density of the blaster bolts? I guess you could estimate the diameter and length of a bolt—it’s kind of like a cylinder. Using this and the mass, you could calculate the density. Why would you do that? I don’t know—why did I estimate the mass? Because I could.
- What if this mass isn’t stored in the weapon as ammo. How could you still make the weapon work? What if the blaster somehow had enough energy to create electron-positron pairs (matter and antimatter)? Could that work? What if the bolt picks up mass from the air as moves from the blaster to its target? I don’t know—see if you can find a way to make this work.
- Perhaps this proves Han isn’t a normal dude. Maybe Han is a Jedi and uses The Force to repel the stormtrooper …
- Why do stormtroopers even wear armor? It doesn’t look like it’s much defense against blasters.
- Finally, one important point: if Han shot a blaster bolt with that mass and velocity, he would experience the same force the stormtrooper does. He would be thrown back after shooting his blaster.
Of course, I probably need more data to get a better estimate of the blaster bolt mass.
Here is another short clip that shows BB-8 in the Millennium Falcon. I’ve looked at this before, but my previous analysis only had part of BB-8’s motion. This new clip show the whole motion, including the fall to the floor. Of course, I had to finish what I started. Here is the same shot with a correction for the motion of the camera.
Using the size of BB-8 to scale this video, I get the following plot of the vertical motion (in the Falcon reference frame):
It’s tough to get a perfect fit for the “falling” BB-8 since it (or he or she) isn’t just a point mass. In the plot, I have included both the position of the head and the body. You can see that the acceleration of BB-8 is 11.66 m/s2 (you get this by comparing the fitting equation to the kinematic equation). This acceleration is fairly close to the acceleration of a free falling object on Earth—at 9.8 m/s2. In fact, if you took into account the actual center of mass of BB-8 (somewhere between the head and the body), I think you would get an even better fit.
But what does it mean? I am going to say that there is a good chance this scene is not CGI, but a real BB-8 in a spinning Falcon set. I don’t know enough about CGI and moviemaking to be sure, but it’s at least plausible. If true, this is pretty cool.
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