The Physics of RWBY- Ember Celica
I am continuing to march through the physics of the various weapons found in RWBY. This time I am looking at Yang and her weapon Ember Celica, which are a pair of wrist mounted shotgun gauntlets seen above. The physics I will be using is very similar to what I did when I determined the recoil force of Nora’s Magnhild.
Height
The scene I will be using comes from RWBY volume 5 episode 4, where she fights the bandits. During this scene she punches the ground and uses Ember Celica to launch herself over one of her opponents.
In this shot we can see Yang is directly over her opponent and she is 1.73m (5’8”). Using Yang as a measuring stick, we can determine that she is about 3.46m above ground.
Velocity
The velocity is easy to determine at this point as she travels 3.46m in 1s.
Velocity = distance / time
Velocity = 3.46m / 1s
Velocity = 3.46m/s
Acceleration
The acceleration will also be fairly easy to determine using the same gunshot duration that I have been using for the other RWBY physics posts, 0.0003s.
Acceleration = Change in velocity / time
Acceleration = (final velocity – initial velocity) / time
Acceleration = (3.46m/s – 0) / 0.0003s
Acceleration = 3.46m/s / 0.0003s
Acceleration = 11,533 m/s^2
Mass
Using a BMI chart I was able to estimate Yang’s mass to be 82kg. The problem is her weapon, of which there is no real world equivalent. As such I am going to assume that between her clothes, weapon and prosthetic arm that she rounds out at 90kg, which I will admit might be on the heavy side.
Force
Now comes the easy part, determining the recoil force of the gun, which is equal to the force used to launch Yang into the air.
F = m * a
F = 90kg * 11,533m/s^2
F = 1,037,970N
Conclusion
Using just one of the Ember Celica gauntlets puts just over 1 million newtons, and when Yang using both at the same time that’s over 2 million newtons which is a bit more than the 1.8 million newtons put out by the main space shuttle engine at launch.
Biology Bonus
You didn’t think I would just leave it at that, did you, not when there is some biology I can examine? Specifically, I want to see if Yang’s humerus can survive the recoil from firing Ember Celica. To begin with, I am going to assume that the humans of Remnant are the same as humans here on Earth.
Human bones can handle up to 210 mega pascals of compressive pressure before breaking, so it is just a matter of determining how much pressure Yang’s arm experiences when she fires Emerald Celica. While I have covered pressure before in my post on Giant Alien space babes and monsters here is a little refresher. Pressure is simply the force applied over a specific area.
Pressure = force / area
The average human humerus has a diameter of 10-14mm at its narrowest point. In this case I will be using the higher number of 14mm due to Yang’s being a Huntress in training and also that exercise increases bone mass. The humerus also has a somewhat circular shape when examined straight on.
Area of the Humerus
Area = πr^2
Area = 3.14 * 7mm^2
Area = 3.14 * 49mm^2
Area =153.86mm^2
The math to determine pressure is easier if you use square meters instead of square millimeters, so a conversion is in order.
153.86mm^2 = 0.00015386m^2
Pressure exerted on the Humerus
Pressure = Force / Area
Pressure = 1,037,970N / 0.00015386m^2
Pressure = 6,746,197,842 pascals
6,746,197,842 pascals = 6,746 mega pascals
Now this really shouldn’t have come as much of a surprise to anyone, but yes Yang’s humerus would shatter the moment she decided to fire off a blast from Ember Celica as the pressure is 32 times what a human humerus can survive.
Now given that this is a fictional universe, I did want to point out that if Yang uses both gauntlets at the same time, she would generate 13.5 giga pascals which is almost enough pressure to pull off the Superman trick of making diamonds out of coal which takes 18giga pascals (synthetic diamonds). I guess Yang never has to worry about money and is a girl’s best friend. Thanks for reading and leave any comments below.