The Physics of RWBY
RWBY pronounced Ruby is an American made web series created by the late Monty Oum in 2013 and recently began its 6th season or volume. While it is not technically anime, it has certainly been inspired by it and many anime fans do enjoy RWBY. It is a show that I have only gotten into very recently, and I have decided to try and work out some of the physics seen in the show. First off, RWBY takes place on an earth-like planet called Remnant, where men and women called huntsmen and huntresses, respectively, fight creatures that seek to destroy mankind known as Grim. FYI- yes, it also draws heavily from various folktales. The huntsmen and huntresses fight back against the Grim using aura and semblances powered by their souls, which I will not be looking into, and various weapons, like Magnhild, that I will be looking into. These weapons are powered by a fictional substance called dust, which is basically crystalized energy. While I haven’t found out a way to determine just how powerful dust is, I can, however, give you a rough estimate on how powerful their weapons are.
How is this possible
While I can’t give you an exact number on how powerful the projectiles are due to the variable nature of dust and the ammunition they use, I can, however, give you an idea of just how much recoil or kickback the weapons have. This is possible due to how the characters use them to speed up their movements and make long jumps. You see, there is this fun law of motion, specifically Newton’s third law of motion, which states:
To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
This basically means that if I know how a character was moving before and after firing their weapon, I can determine just how much force the weapon exerts when firing.
Nora Valkyrie is part of team JNRP (Juniper) and later team RNJR (Ranger), and she is basically their resident strong woman. Her weapon, Magnhild, is essentially a rotary grenade launcher like the real world Milkor MGL, which can turn into a giant war hammer. She routinely uses Magnhild to help her clear large gaps, and this is used to great effect in volume 1 chapter 8.
This scene also makes it easy to calculate how powerful Magnhild is since Nora Valkyrie uses just the force of the gun firing to clear the gap. All we need to do is find out the distance Nora traveled and the speed she was moving at, which can be done by examining certain scenes in the episode.
In this screenshot we can see team RWBY and JNPR running across the causeway just before the Nevermore crashes into it. According to the RWBY wiki Ren (the one furthest to the right) is 5’9” or 1.75m tall and he is going to be our measuring stick. The Ren in the image is 1cm tall, and the distance between the pillars is 5cm or 5 Ren’s long.
1cm = 1.75m
5cm x 1.75 = 8.75m
Now that we know the distance between pillars it’s time to move onto the distance of the actual jump.
Here we can see that the Nevermore has knocked out 3.5 sections of the causeway. Thus, by using our earlier number of 8.75m for the distance between the pillars it is possible to determine the actual distance.
3.5 x 8.75m = 30.625 meters
The world record for the long jump is 8.95m; no wonder Jaune said he couldn’t make that jump. However, the Death Stalker that Nora hits at the end of her jump is not actually on the causeway but on land, which is another full segment away so her jump is actually 39.375m. I do realize that she didn’t travel in a straight line and was traveling in an arc, but there just isn’t enough information to determine the exact length of the path she traveled. However, we can still make a rather reasonable estimate, nonetheless.
The next piece of information we need is how fast Nora was traveling and that is possible to determine as long as we go with the assumption that the time it takes her to travel the distance in the show is the actual time she took to travel the distance. This time turns out to be 3 seconds, 7:22 to 7:25. The formula for speed or velocity is as follows
Velocity = Distance / Time
Velocity = 39.375meters / 3seconds
Velocity = 13.125 m/s
It was very hard to find just how long gunpowder or any other real-world explosion lasts, and the best number I could come up with was 300 microseconds. This means that Nora went from falling on Magnhild to flying across the gap.
Acceleration = (change in velocity)/ time
Acceleration = (Final velocity – initial velocity) / time
Acceleration = (13.125m/s – 0m/s) / 0.0003s
Acceleration = 13.125m/s / 0.0003s
Acceleration = 43,750m/s^2
This turns out to be 4,464g, which is clearly insane as it is more that the G forces experienced by a baseball when it is struck by a bat. Aura or not, if Nora experienced this, she would probably be turned into chunky salsa. Since I am not a physicist, it is possible that I made a mistake in how I worked out her acceleration. A second method of determining acceleration can be made using the following formula. In this case I use the total distance traveled and the time needed to travel that distance to determine acceleration.
Distance = 0.5 * acceleration * time^2
39.375m = 0.5 * acceleration * 3^2
39.375m = 4.5s^2 * acceleration
8.75m/s^2 = acceleration
This is a much more believable and survivable acceleration number, but there is a problem with it. This formula assumes constant acceleration, and Nora only fires her gun once at the start of her jump, and the blast quickly dissipates, which assumes that the force on her body is not constant. In which case we are still going to use the much larger number from the first calculation.
There is one final piece of information needed before I can determine the force exerted by Magnhild, and that is the mass. In this case it is the combined mass of Nora and Magnhild. We know from the RWBY wiki that Nora is 5’1”, and we can assume that she is healthy given that she is training to become a huntress, so using a BMI chart we can estimate that Nora’s mass is around 55kg. Magnhild was based on a Milkor M32 MGL, which has a mass of 5.3kg. Add in a bit for clothing and I can safely assume Nora’s total mass in the scene is right around 60kg.
Now that we have all of the pieces of the puzzle, namely acceleration and mass, we can calculate the force Magnhild exerts when firing.
Force = Mass * acceleration
F = ma
F = 60kg * 43,750m/s^2
F = 2,625,000 newtons
This means that Magnhild 45% more than that of the space shuttle main engine at lift off. So, yeah, dust and the people of Remnant must be extremely powerful.
I think we all knew this scene was going to be impossible from the beginning. However, as I said earlier, I would love for a physicist to check my work. Thanks for reading and I will be calculating how powerful Crescent Rose is next.