Estimating the Plot Power levels of the Touhou cast

[Anthony Edward Stark]

The only time Superman won was in the Red Son alternate continuity, and even then Batman wasn't Bruce Wayne.

Dark Knight Returns counts, maybe? Batman faked that heart attack. You'd think he'd learn and instead of fist-fighting the guy, just flash-boiling him from space with heat vision.

[Grefter]

Nah the big ones are X-Men VS Jedi OR ISD vs The Enterprise.  oh snap ISD isn't even strongest in the fleet SSD or gtfo !!!!!!

[Anthony Edward Stark]

SSD is old hat. Gimme a Pellaeon. You know, from Legacy, the only good thing to come out of Star Wars in the past few years?

[Ranmilia]

Suika Ibuki

Control of density and lack of control of sobriety.  Same thing.  Anyhow, her most significant exertion of power seems to be the ability to create black holes of approximately 1 meter in diameter.  She is notably lacking in any create-a-super-black-hole spellcards, so it seems safe to assume that that size is the current limit of her powers.

Formula for mass of a black hole is M=Rc^2/2G, where c is the speed of light and G is the gravitational constant.
R = 0.5 meters
c = ~3.0*10^8 meters/second
2G = ~1.33*10^-10  m^3kg^-1s^-2       

Rc^2 = 4.5*10^16 m^3/s^-2

M ~= 3.4*10^26 kg for a Suika-size black hole.  Now we're talking power!

[metroid composite]

As regards Utsuho, there's a couple things I'd like to bring up.  The first is a simple matter of units.  Namely, you seem to be using kg of destroyed shit as your main unit.  This is notably not equal to kg of TNT.  One kg of TNT can certainly destroy a lot more than one kg of material.

I've been thinking about this again recently, and it's a reasonable point; kilograms probably aren't the best measure; in fact, the best measure of power is probably...Power (kg * m^2 / s^3).

This has a few advantages; for one thing, looking through the topic, a lot of the numbers that have come up have been in Joules--power is just Joules per second.  For another thing, it puts some control on attacks that happen outside of battle; if, for instance Remillia's red mist was released over a period of a week, then you're not getting all of that mist concentrated into one absurd attack.

Of course, the downside of power is that it's not intuitive, so I suppose I should build some intuition:



PUTTING POWER (Watts) INTO PERSPECTIVE

http://en.wikipedia.org/wiki/Orders_of_magnitude_(power)#Between_1_and_1000_Watts
Human: 1,000  (10^3) Watts
Car: 100,000 (10^5) Watts

Lifting of an object can fairly easily be translated into power; let's say a human is able to lift a 100 kg object 1 meter off the ground in 1 second.  The potential energy change is:

E = mgh

Where m = 100, g = 9.8 m/s^2.  So that's 980 Joules, and since it was done in one second, 980 J/s = 980 W.


APPLYING POWER TO TOUHOU CHARACTERS



This also gives us a much simpler measure of Utusho--she seems to be much more like a controlled nuclear reaction than a nuclear bomb, and the average nuclear power plant has a power output of...

10^9 Watts

(Unfortunately that's nuclear Fission power plants, IIRC successful Nuclear Fusion power plants have not been demonstrated).  Granted, maybe I should be looking at this from a miniature-sun perspective.  Power output of the sun is 4x10^26 W.  A 5-meter sun has 10^-8 the radius of the regular sun, so assuming it spits out the same energy per surface area that's...

10^10 Watts.



...And looking at Master Spark, we had about 8x10^6 kg of steel which was going to be melted.  A quick google search says that it takes 750,400 Joules to melt 1kg of steel.  I'm going to be conservative and say that it takes the full 5 seconds to melt the steel.  So we're looking at....

1.2 x 10^12 Watts



...Granted, I'm not sure how this carries over to defence.  After all, a knife might only weigh 1 kg, so stopping/starting it doesn't take much energy.  Might have to think in terms of local pressure as far as blades go.