Today, we're going to talk about how in this crazy world that defies physics and logic, Aoi's sword abilities are rather... rational. Weird huh...

First off, let's talk about Aoi's sword, Korokuryu no whatsit. It's a sword that slashes through anything it touches, but really? Anything? Let's take a closer look.

Provided by some microscopes procured through unorthodox means, Kokuryu's sword isn't all that "sharp", if by sharpness you're going for the width of Aoi's blade at it's finest point. See, sharpening a blade can only go so far via the ancient polishing methods that Aoi uses. To put this in comparison, Stitch's scalpels have an edge of 3 nanometers, while Aoi's katana and the Corvat have edge widths nowhere near that. Granted that I made the Corvat for durability, not insane sharpness.

So how does Aoi's sword cut through tables without having the blade even touch them? Well as you might have guessed, the composition of Aoi's blade is what does it. And I'm not talking about just the dragon scale, although that does play a part. Dragon scale accounts for the sheer toughness to withstand impacts that would otherwise bend or chip other swords. However, Eol's punches have been shown to even shatter dragon scale, which I'll cover a lot about much later. I'll let Aoi explain the fine details of smithing.

As with all katanas, the dual material used in the blade provides for its strength and sharpness, durable steel of hochu-tetsu with the scale keratin increases its durability, and the dragon scale edge with tamahagane gives the blade a different kind of sharpness.

You see, actual sharpness of cutting ability in knives and other sharp objects depend on the geometry of the blade and the materials' coefficient of friction. Aoi's smithing style bases itself on sharpness versus durability, which he must compensate with by extending the depth of the slope of the blade, in order to still utilize the full width of the blade for the lo-carbon, durable metal. Thus, as you might have noticed in some photos, the depth of Aoi's blades tends to increase to the very edges of the hilt, here as most katana's blade depths are 3/4 the depth of the hilt.

Photos?

Nevermind that. Here's the interesting point, dragon scale has a very VERY low coefficient of friction at the edges. about 0.049, which has slightly less friction than Diamond-like Carbon. In Aoi's perspective, the scales themselves were rough compared to the edges, like polished wood. thus why only the very edge of the dragon scale is exposed on Aoi's sword, and the other part of the scale exposed is part of the hamon. (See I know my otaku lingo for swords) With this level of sharpness, it's no surprise that Kokakarrot-cake can chip away fucking diamonds.

But that's not even the best part. According to Griffin, Aoi's sword looked as if the air around it was vibrating quickly. It might be due to the weird magic aspect, but here's some fancy sciency stuff. We did a test to observe the effects of Aoi's sword with interaction to other particles by soaking it in water-

Which is poor sword maintenance for those researching on proper cleaning methods.

Yeah yeah, we'll get to that later. Back to the test, a very strange phenomenon happened. The water in contact with the edges of Aoi's sword oscillated to a fine degree, like a chainsaw or a fine frequency power tool. The oscillation was so fine that to the human eye, no ripples would be present, but on the microscopic level, the water was vibrating at around 14 GHz, or 14 billion cycles per second. TL;DR, Kokaburo is a motherfucking atomic chainsaw.

Now the interesting thing of this is that it leads to the next phenomemon of Aoi's sword: the vacuum slash. For starters, let's start with Aoi's average swing. When we measured it, it clocked in at around 180 mph, which, as you might have expected, is a fair bit more than the average human, but then again, most people here, aren't human. On terms of speed, it has nothing to do with the next part, the important part is the acceleration, with fancy mathematics:

a= vf - vi /t

Now the average swing time is about 0.13 seconds, so

80 m/s - 0 m/s / 0.13 = A whopping 615 m/s^2

In comparison, the acceleration of a rifle round is around 21,100 m/s^2. Alright, you might know where I'm going with this. As it stands, Aoi's blade is 9 kilograms and has a length of 78 inches. Really though, you could classify Aoi's blade as a Nodachi if you were comparing it to a human being, but that's beside the point. Now the reason its rather heavy compared to a regular Nodachi is... Why is it so damn heavy?

Well, it needs to be heavy to... balance out the blade.

Oh yeah, I keep forgetting that. But yeah, when you figure in the mass, you get a swing Force of:

F=ma
9 kg * 615m/s^2 = Holy shit! 5535 Neutons

Now here's where the freaky shit comes in. The movement of Aoi's air-chainsaw (shut up, that's what I'm calling it now) causes supercavitation, which is a phenomenon found mostly in water due to it not really being able to happen in the air normally. This happens at a rather minuscule level throughout the entire edge of the blade, and the displacement of the air afterwards. The reason this is freaky is that this shouldn't really happen as the force of Aoi's swing, although great, isn't enough to create a vacuum, and it's not. But it does reduce the air pressure of the air inside the swing arc so much, that it gets to near vacuum conditions, and when that pressure bubble collapses, it collapses hard, generating a shock wave that acts like an extended blade, effectively extending the range of Aoi's blade.

I'm mainly speculating that the ability of making a vacuum in air is cause by all the weird magic stuff happening with Aoi's blade, because according to established physics, cavitation to that degree happens only in water and plants in our natural world, what with animals like the pistol or mantis shrimp being able to execute this due to water being easier to create extreme near instantaneous pressure differences in their environment. Though there have been accidents on submarines that have caused cavitation incidents due to a sudden drop in pressure in one of the compartments. However, cavitations to lesser degrees happen all the time with things like propellers and in cases like aerodynamics.

Alright let's recap. Aoi's sword is a katana that acts like an air-chainsaw. It's not necessarily the sharpest sword on terms of its edge, though it is sharper than most blades except for a few such as Excalibur--said to have a cutting edge of one atom's width--it's sharpness is not its main highlight. It's main highlight is the blade's weird way of oscillating atoms that it comes into contact with in order to cut, while the low coefficient of friction and geometry of the edge makes cuts super clean.

Next time, We'll cover how the fuck Eol can punch through a dragon's scales.

You said we'd get back to sword cleaning techniques.

Oooo... sorry about that, but that's all the time we have for today. I'm Dr. Keith MacGrath, and until next time, don't get eaten by dragons.

I thought you said you lost your medical license.

Shh.......

Author's Notes:

I had this idea for a while, and considering I'm in an AP Physic's class (fuck you AP requirements) I decided to do a spin-off chapter all on the science and magic that goes into the stuff in BSRC to tide you all over until the big update. Science, Motherfuckers, Science!!!