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So I decided to make a manga-based calculation and since Bleach is among the most loved manga these days I'm going to make a calculation of a impressive feat Komamura accomplished through sheer speed and strength alone.

Now the method I'm going to use in this calculation is called the finite element method. I'm using this method for two reasons. Firstly it's a new growing method applicable in all fields of physics ranging from rigid body mechanics to elementary particle movement in dynamic systems and the university I'm is the second most contributing university in terms of development of the method.

Let us begin!

Assumptions:

1. The mountain mainly consists out of granite out of granite.
2. The geometry (drawing) is accurate and consistent.
3. There's no deformation at the foot of the mountain.

Given
Yong's modulus of granite: 40 - 70 ~ Mean value: 55
Poisson's ratio for granite: 0.2 - 0.3 ~ Mean value: 0.25
Ultimate stress for granite: 70 - 280 ~ Mean value: 175

See "Physics handbook: For science and engineering" for reference.

Note: These factors scale linearly with the result meaning that the answer may vary with up to a factor 2 depending on the values chosen above from the actual answer provided here.

Solution

We first examine the geometry (overall shape) used for this problem. Notice the boundaries will effect and structure chosen won't affect the the interesting part is the angle.

http://img10.imageshack.us/img10/5528/geometrym.th.jpg

From the next picture we have that:

http://img832.imageshack.us/img832/9741/rukiaxpillar.th.jpg

From this picture we get the following conditions.

http://img821.imageshack.us/img821/4769/bild11f.png

http://img638.imageshack.us/img638/5567/pillarxcass.th.jpg

http://img683.imageshack.us/img683/5375/bild12i.png

Now from the Rukia's bio we know that she's 1.44 tall, which makes us able to calculate the scaling through the three scans.

So we set up the basis for the shred-spread (note: only the distance from the rift to the edge will affect the energy spread)

Now the question is, how many triangle elements will we use?

http://img233.imageshack.us/img233/867/bild5w.th.png
299 elements? No.

http://img843.imageshack.us/img843/4710/bild6c.th.png
1196 elements?! No.

http://img97.imageshack.us/img97/4334/bild9b.th.png
Try a quoter-million elements (it took my computer about 3 hours to finish this calculation).

We get the following result.

http://img857.imageshack.us/img857/9353/bild10t.th.png

We integrate over all the shredding in order to calculate the energy required at impact.

http://img714.imageshack.us/img714/5567/bild13t.png

And we get the following result (this is done numerically by MATLAB).

http://img251.imageshack.us/img251/2789/bild14y.png

Answer

http://img30.imageshack.us/img30/3355/bild15c.png

Fun fact: In my first calculation I used Dirichlet's boundary condition (instead of Neumann's) and lost 30 minutes luckily I only used around a hundred thousand elements that time.

Oh and feel free to share your thoughts.

Here's a source for the Elastic Modulus of granite, and Poissen's Ratio:

http://www.efunda.com/materials/common_matl/common_matl.cfm?matlphase=solid&matlprop=mechanical



Conclusion: I get the stress and strain but I don't understand the use the Kronecker delta.


Edit - Wait, that's not the symbol I'm thinking of.


Anyway, that system is really complex. His blade is very thin but the damage is very wide. From what we've seen, it appears that there is some sort of "blowing" force that blows materials away like a giant air-compressor. That's going to be reiatsu.




Anyway, please do more of these. I don't have access to MATLAB anymore.


If I give you a scene/image, could you do the calculation?

Sooooooo...... In English?

Originally posted by dadudemon
Here's a source for the Elastic Modulus of granite, and Poissen's Ratio:

http://www.efunda.com/materials/common_matl/common_matl.cfm?matlphase=solid&matlprop=mechanical
Thanks, that works just as well.

Originally posted by dadudemon
Conclusion: I get the stress and strain but I don't understand the use the Kronecker delta.

Edit - Wait, that's not the symbol I'm thinking of.
The ξ (xi) tensor just represent the distance from the impact to all the deformations during the breakdown (crumble).

Originally posted by dadudemon
Anyway, that system is really complex. His blade is very thin but the damage is very wide. From what we've seen, it appears that there is some sort of "blowing" force that blows materials away like a giant air-compressor. That's going to be reiatsu.
That's why I just calculated the energy required at a fix point to cause said damage to the mountain. Just examine the momentum equations for the blade's and wind current's velocity, or whatever you want to get out.

Originally posted by dadudemon
Anyway, please do more of these. I don't have access to MATLAB anymore.
Sure, if I get the time.

Originally posted by dadudemon
If I give you a scene/image, could you do the calculation?
Sure, it may take some time though.

Originally posted by jinzin
Sooooooo...... In English?
It's a brief explanation of how to calculate the energy in Komamura's strike and the result of said strike.

Originally posted by Astner
Thanks, that works just as well.


The ξ (xi) tensor just represent the distance from the impact to all the deformations during the breakdown (crumble).


That's why I just calculated the energy required at a fix point to cause said damage to the mountain. Just examine the momentum equations for the blade's and wind current's velocity, or whatever you want to get out.


Sure, if I get the time.


Sure, it may take some time though.


It's a brief explanation of how to calculate the energy in Komamura's strike and the result of said strike.

Oh, no, dude: everything I typed was not a criticism. You did a great job and are above my head. I was just pointing out how complex the system is.

I actually have no idea how to improve your work to incorporate the "blowing away" effect of the reiatsu, with any sort of sound accuracy on the energy system you've already developed. That "wind" would be a complex system but could still work just nicely with a "flow" system but it's too far into fluid dynamics (with lots of pascals, lol) that I do not have the education to actually address.