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Rating: 7 votes, 5.00 average.

ToAru - Misaka Mikoto - Energy Projection (2% Level 6)

Posted 09-02-2013 at 02:08 PM by Shiorin
Updated 09-05-2013 at 04:03 AM by Shiorin
Spoiler:

Pixel scaling gives ratio of about 6.8:1.

Assumptions
  • Model AC's Windowless Building with Sears Tower, a fairly standard skyscraper.
  • Model the giant bolt of lightning as having similar properties to positive lightning.
  • Model both real and portrayed lightning bolts as cylindrical channels of current.
  • Mikoto's power manipulates or generates electron movement which would affect the current magnitude but the voltage potential difference is still dominated by natural factors such as distance. If the opposite were true, she would still not be able to pull so much power for her discharges even in base form.

Electromagnetic Terms
Positive Lightning Bolt Current: 300e+3 A 1
Positive Lightning Bolt Voltage: 1e+9 V 1

Dimensional Terms
Width of current channel of lightning bolt: 0.02 m 2
Width of Sears Tower skyscraper: 68.58 m 3
Sustained current duration of negative lightning: 51-210 microseconds (never measured for positive lightning) 4

From the ratio we have width (diameter) of Mikoto's giant bolt at 469 m.

The current density is given by the limit of the conducting area which is constant here:

From the current channel width we have positive lightning current density of approx. 955e+6 A/m^2.

For a cylindrical current channel, the cross sectional shape is a circle:

Now, the cross-sectional area of the giant bolt is about 173e+3 m^2.

Using the real world current density, that gives a current of 165e+12 A.

Using the electrical work relationship:

Which gives a power of 165e+21 W.

A watt is broken down as follows:

Taking the low end of 51 microseconds for flash current time of lightning, we have an energy figure of 8.42e+18 J.

TNT equivalent is 4.184e+15 J/megaton. Therefore, in Michael Bay units: 2 gigatons of TNT, which amounts to small island level.

As an aside, the flash current duration of the bolt is a multiplicative effect on the final power, so only one or two orders of magnitude at most. The width of the Windowless Building is a large effect because it scales for the cross-sectional area of the giant lightning bolt, and is a square effect. Therefore, that measure is very important and we are using a rough assumption for it here.

Original (Obnoxious SI Prefixes):
Spoiler:
Electromagnetic Terms
Positive Lightning Bolt Current: 3 300 kA 1
Positive Lightning Bolt Voltage: 1 GV 1

Dimensional Terms
Width of current channel of lightning bolt: 2 cm 2
Width of Sears Tower skyscraper: 68.58 m 3
Sustained current duration of negative lightning: 51-210 microseconds (never measured for positive lightning) 4

From the ratio we have width (diameter) of Mikoto's giant bolt at 469 m.

From the current channel width we have positive lightning current density of approx. 955 MA/m^2.

Now, the cross-sectional area of the giant bolt is about 173000 m^2.

Using the real world current density, that gives a current of 165 TA. Which gives a power of 165 ZW.

Taking the low end of 51 microseconds for flash current time of lightning, we have an energy figure of 8.42 EJ.

Finally, in Michael Bay units: 2 gigatons of TNT, which amounts to small island level.

______________________________________
1 http://www.srh.noaa.gov/jetstream//l...g/positive.htm
2 http://www.ucar.edu/communications/f...Lightning.html
3 http://www.skyscrapercity.com/showthread.php?t=327978
4 http://en.wikipedia.org/wiki/Lightning
Posted in Tryhard Calcs
Comments 38 Email Blog Entry
Total Comments 38

Comments

Old
Quote:
The "path to leveled 6" is called awakening
Nope.

At no point in the series is "awakening", a fan made term to refer to Kakine and Accel's respective angelmodes, ever connected to Level 6.

Quote:
And yes numbers can relate to power
Also wrong.

The ranks have nothing to do with power. Accel is number one because he's a vital portion of Aleister's plan, and Kakine is the backup so he's number two.

It just so happens to be that the two of them are apparently the strongest Level 5s.

If ranks actually corresponded to strength, which they don't as Mugino will point out, Gunha would not be dead last.
Posted 09-02-2013 at 06:53 PM by Regicide Regicide is offline
Old
Fan made or not thats irrelevant. The mode misaka is in now is similar to the one kakine and accelerator use except that its forced onto her.

"It just happens to" my ass,it proves nothing. gunha is dead last because his powers are still mysterious and are unclassified by academy city so they decided to put him last.

All the level 5 so far are from weaker(5) to stronger(1). Strength is a criteria for classifying and ranking level 5s.
Posted 09-02-2013 at 07:03 PM by steveht93 steveht93 is offline
Old
Quote:
Fan made or not thats irrelevant. The mode misaka is in now is similar to the one kakine and accelerator use except that its forced onto her
Nope. It's not even aesthetically similar.

Dark wings and white wings is connected to the angels, as demonstrated by Accel's ability to interpret and speak the language.

Mikoto's form more resembles a raijin than anything else. It doesn't even have wings.

And even then, you can't still prove "awakening" and Level 6 have anything to do with each other. Because at no point is this ever stated or implied.

Quote:
bring a more respectable argument next time
How about you bring up a quote where it's stated that the ranks are based on strength, even though we're explicitly told otherwise?

Quote:
Strength is a criteria for classifying and ranking level 5s.
It's not.
Posted 09-02-2013 at 07:11 PM by Regicide Regicide is offline
Old
Quote:
Originally Posted by steveht93
The "path to leveled 6" is called awakening. And yes numbers can relate to power. See the fights of the level 5s. Kakine can curb stomp mugino and accelerator is stronger than kakine.
Level 5's aren't ranked by power. Their ranked by how useful they are to Aliester and his plans.

Accelerator (#1) and Kakine (#2) just so happen to be the two strongest espers.


If we were to scale them by power alone, including all forms/modes, The true ranking would be something like this:

1.) Angel Accelerator
2.) Darkwing Accelerator
3.) Dark Kakine / Beetle 05 Kakine
4.) Base Accelerator
5.) Kakine Pre-revival / 2% level 6 Mikoto
6.) Sogiita Gunha / Mugino with meltdowner arm
7.) Base Misaka Mikoto
8.) Base Shizuri Mugino
9.) Shokuhou Misaki (Not combat oriented)


Quote:
Originally Posted by Shiorin
I was hoping there was another calc or just another scan of the Windowless Building that gives us something better to work with.
I'm pretty sure there's a better picture somewhere, but I'm not sure what chapter it was in....
Posted 09-02-2013 at 07:59 PM by ~Greed~ ~Greed~ is offline
Old
Quote:
Originally Posted by Greed
Shizuri Mugino
You got the name order backwards, Greed.
Posted 09-02-2013 at 08:02 PM by Regicide Regicide is offline
Old
your just nitpicking
Posted 09-02-2013 at 08:05 PM by ~Greed~ ~Greed~ is offline
Old
Perhaps.
Posted 09-02-2013 at 08:30 PM by Regicide Regicide is offline
Old
I'm super late, and don't understand what happened in the calc at all, but I like it.

Posted 09-02-2013 at 10:59 PM by Xam Xam is offline
Old
Coincidence my ass. I would accept that argument if it was only Kakine and accelerator but the trend is among all the level 5s except gunha who is a special case.

Mugino should have been the true #3 as was stated by word of god but she became #4 because she can't use her abilities at full power. Misaka is stronger than the number 4 because she doesn't have such limitations.

Kakine can be scaled to 2% misaka and he is probably stronger in awakening.
Posted 09-03-2013 at 07:17 AM by steveht93 steveht93 is offline
Old
Good work.
I thought about using this method before and actually already did for Durindana/Durandal from CSR.
Albeit my numbers were far more conservative (remind me to revisit the calc, should result in teratons of yield)

The calc is nicely done.
My only issue is that this type of method would be under the "scruntized calcs" category.
It works by an assumption which would fall appart if the amount of destruction won't suggest similar yields.
Which I suspect would be the biggest issue here.
Even if the lightning hit the Windowless Building, there's another half which landed on the ground around it.
1 gigatons of energy is enough to vaporize 137 million cubic meters of rock.(d=639m)

The area occupied by this lightning column is about 3600 m^2

Which means:

Surface area = 1800 m^2
This is roughly what hit targets other than the Windowless Building.
Vaped volume = 137000000 m^3
Vaporization depth = 137e6/1800 ~ 76111 m

Or more than 76 freakin' kilometers of depth.
Unless the Windowless Building now has a titannic chasm reaching further than the Earth's crust, there's no way Misaka's lightning strike was 2 gigatons in yield.
Not trying to be anal but the difference between the result and the expected visuals is just huge here.
No way you can explain it away.

Shiorin's calculations are right.
But the result is incorrect given the other details.
Meaning he was wrong with his assumptions.


Oh well, whatever the result I think it'd be hasty to equalize this feat for Kakine.
The power relation between the two is difficult to establish.

On a different note Kihara calls this power "dozens of times above her original output" which means we can reverse-scale this feat for regular Misaka.
So whatever yield this gigantic lightning bolt was at, it was "merely" 12-100 times of what Misaka can normally produce.

Think about it for a while.
Posted 09-03-2013 at 02:44 PM by willyvereb willyvereb is offline
Old
A lightning energy feat calc using current density? Cool.

I'll run through it in detail when I get the chance later - partly to confirm the validity, but mostly just because I want to be able to replicate this calc method for other feats later.
Posted 09-03-2013 at 03:58 PM by feebas_factor feebas_factor is offline
Old
Keep in mind though that the above method is an "indirect" or "predictive" calc.
Direct calculation is when somebody tries to measure the energy yield based on the scale and extend of destruction.

Indirect methods rely on something else, thus their result can become questionable.
The only way they become viable when there's a certain level of ambiguity.
For example when the attack hits a character with fictional durability.
Meaning no matter the extend of energy, he/she/it can tank it.
Of course this only applies if the feat is roughly within the scope of other feats in the verse.
Otherwise we're talking about an outlier.

So yeah, this method is actually less reliable than cloud-parting calcs.
But I'm sure there are at least a few feats where it becomes viable.
Posted 09-03-2013 at 04:12 PM by willyvereb willyvereb is offline
Old
Quote:
Coincidence my ass.
Nah. When we're explicitly told the ranks have nothing to do with strength, it's a coincidence and nothing more. Accel's the centerpiece, Fridge-kun is the backup, and Mikoto is needed for the Misaka Network.

But hey, feel free to keep attempting to scale this way, since Level 6 and awakening do not correlate and have never been implied to.
Posted 09-03-2013 at 04:13 PM by Regicide Regicide is offline
Old
Yeah, there's no way Misaki is above Gunha in power.
Albeit based on feats there's an established order of power with Mikoto being at the center.

Misaka = Mugino
Misaka < Mugino (high output)
Mugino < Kakine (base)
Kakine (base) < Kakine (Awakened)
Misaka < Gunha
Misaki < Everyone
Everyone < Accelerator


The actual difference in power is rarely defined but we can more or less position them this way.
The problem is that Majin Misaka is a whole new character.
Without more feats we can't really tell where she stands in relation to awakened Kakine or his resurrected form.
Albeit since according to Kihara Gensei this feat was "only" a dozen times of Misaka's original output, we can reverse-scale it.
And like I showed above there are a fine number of characters who can be scaled to "regular" Misaka.
Posted 09-03-2013 at 04:43 PM by willyvereb willyvereb is offline
Old
Just found this looking through NT 5, thought I would share.

Quote:
“There is no official diagram of the building, but the foundation of the windowless building is 15 meters below the surface and it spreads out for quite some distance. The foundation covers something like 3 kilometers in every direction. There are also several thick pillars that head deep underground, so there’s no way that building is falling over. At the very least, burying a nuclear landmine wouldn’t be enough.”
Assuming the foundation is made of the same Calculate Fortress armor as the building itself, it makes sense that the damage shown was less than the output would suggest. The vapor shown rising would presumably be the 15 meters of concrete on top of the foundation.

Of course, this does make the assumption that the foundation is made of the same material, so it's not really an absolute answer.
Posted 09-07-2013 at 09:37 PM by RedSurvivor RedSurvivor is offline
Old
Quote:
Assuming the foundation is made of the same Calculate Fortress armor as the building itself
What's the justification for this?

I don't think it was implied that the Calculate Fortress also extended to the ground around the Windowless Building.
Posted 09-07-2013 at 09:42 PM by Regicide Regicide is offline
Old
Thor did say not even a nuclear landmine would be enough. Also presumably Crowley wouldn't want someone attempting to tunnel in and would make the support structure for his Tower of Plotting as strong as the building itself.

It is an assumption though admittedly, but one that explains the lack of destruction.
Posted 09-07-2013 at 09:46 PM by RedSurvivor RedSurvivor is offline
Old
Pretty sure the nuclear landmine comment was referring to the fact that the foundation is fuck huge.

Regardless, I think we should to see what the collateral damage is actually like when the next chapter is out.
Posted 09-07-2013 at 09:48 PM by Regicide Regicide is offline
 
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