Calc Eureka Seven - Gekkostate vs Dewey Novak

1. The Ginga bombs Nirvash
(http://imgur.com/6nzLkZ8)
The Ginga drops several charges onto Nirvash Type-Zero, which the later survives in a state where it's so weak it can't even stand up properly. Nirvash's antenne is 1.52507676m long.
65 pixels = 1.52507676m
1 pixel = 1.52507676m/65 = 0.0234627194m
0.0234627194m X 228 = 5.34950002m
28 pixels = 5.34950002m
1 pixel = 5.34950002m/28 = 0.191053572m
0.191053572m X 877 = 167.553983m
0.191053572m X 602 = 115.01425m
115.01425m/2 = 57.507125m

Volume as a cylinder.

V = πr^2h
= π X 57.507125^2 X 167.553983
= 1740796.24m^3

Weight of air per m^3 is 1.003kg/m^3.

M = 1740796.24 X 1.003kg
= 1746018.63kg
Timeframe is 13 frames.

T = 1s/30
= 33.3333333ms
= 33.3333333ms X 13
= 0.433333333s

T = 167.553983m/0.433333333s
= 386.663038m/s

KE = (0.5)mv^2
= (0.5) X 1746018.63 X 386.663038^2
= 1.30522143e11 joules
= 31.1955408699809 tons of TNT

2. Gekko's laser
(http://imgur.com/MduURwB)
The Gekko fires a laserbeam at the Ginga, which blocks it, and one of the smaller beams causes a considerable burst of water. The Ginga has a length of over 1.5km.
(Relevant text)

A boarding ship of the Ageha Corps led by Dewey. She is a huge cone-shaped battleship with a total length of more than 1.5km, equipped with many powerful weapons, and has excellent offensive and defensive performance such as a powerful barrier that repells the main gun of the Moonlight. She carries Tye-THEEND and several Monsoono Type VC-10s.

Click to expand...

1633 pixels = 1.5km (1500m)
1 pixel = 1500m/1633 = 0.918554807m
0.918554807m X 67 = 61.5431721m
78 pixels = 61.5431721m
1 pixel = 61.5431721m/78 = 0.789015027m
0.789015027m X 33 = 26.0374959m
26.0374959m/2 = 13.0187479m
0.789015027m X 106 = 83.6355929m
83.6355929m/2 = 41.8177965m
0.789015027m X 2190 = 1727.94291m
1727.94291m/2 = 863.971455m
0.789015027m X 302 = 238.282538m

Volume of the explosion of water as an ellipsoid (though it's not perfectly accurate, it's a good approximation for a low ball, as there are extra bursts of water beyond that which would make it even higher). The laser splits into 9 beams, so at the end we'll times the result by 9.

V = 4/3πabc
= 4/3 X π X 41.8177965 X 13.0187479 X 13.0187479
= 29688.4954m^3

Mass of water is 1000kg/m^3.

M = 29688.4954 X 1000
= 29688495.4kg

Timeframe is 6 frames.

T = 33.3333333ms X 6
= 0.2s

T = 26.0374959m/0.2s
= 130.187479m/s

KE = (0.5)mv^2
= (0.5) X 29688495.4 X 130.187479^2
= 2.51591884e11 X 9
= 2264326956000 joules

On top of all of this, there's also a complete whiteout, so we can also get luminousity.

M(star) is the apparent magnitude of the light source
m= is the apparent magnitude of the sun (-26.73)
L(star) is the Luminosity
L= Luminosity of the sun (3.486*10^26)
d= Distance to the sun from earth (0.000004731537734207877 parsecs)
d(star)= distance to the light source

Click to expand...

As it's a complete whiteout, I think it's safe to use the luminousity of the Sun (that being 100,000 lux). The conversion factor from lux to apparent magnitude is -2.5 log I - 14.2.

L = -2.5 log I - 14.2
= -2.5 log 100,000 - 14.2
= -26.7

Our formula is as follows...

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(25.553))^2)

Let's go through this step by step.

(146000000000/(863.971455))^2) = 2.8556628e16
-26.7 - -26.73 = 2.8556628e16/((L/3.846*10^26)
0.03 = -2.5Log(2.8556628e16/((L/3.846*10^26))
0.03/-2.5 = (2.8556628e16/((L/3.846*10^26))
10^(-0.012) = (2.8556628e16/((L/3.846*10^26))
0.972747224 = (2.8556628e16/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 2.8556628e16
3.75869527e27/2.8556628e16 = 1.31622518e11 joules

E = 2264326956000 + 1.31622518e11
= 2395949474000 joules
= 572.6456677820267 tons of TNT

3. The Gekko bombards the Ginga
(http://imgur.com/YTzd85e)
The Gekko bombards the Ginga with a ton of powerful bombs.
814 pixels = 238.282538m
1 pixel = 238.282538m/814 = 0.292730391m
0.292730391m X 703 = 205.789465m
205.789465m/2 = 102.894733m

Entering this into nukemap and we get a yield of 1.58 kilotons. Alternatevely, using the MIT nuke calculator (for airburst, as they explode in the air) we get 16.45 kilotons. With our yield in hand, let's times that by the number of missiles.
15 missiles. This means the bombardment has a total energy of 23.7 kilotons for our low end and 246.75 kilotons for our high end.

4. Firepower of the Super Izumo
The Super Izumu has 5 times the firepower of the Gekko.
(Low end)
E = 23.7 kilotons X 5
= 118.5 kilotons

(High end)
E = 246.75 kilotons X 5
= 1.23375 megatons

5. Devilfish vs the Ginga

(http://imgur.com/1PTdDMo)
Holland in the Devilfish rushes the Ginga then bursts into it, then melts a big hole in it.
680 pixels = 10m
1 pixel = 10m/680 = 0.0147058824m
0.0147058824m X 332 = 4.88235296m
55 pixels = 4.88235296m
1 pixel = 4.88235296m/55 = 0.0887700538m
0.0887700538m X 9 = 0.798930484m
593 pixels = 238.282538m
1 pixel = 238.282538m/593 = 0.401825528m
0.401825528m X 34 = 13.662068m
13.662068m/2 = 6.831034m
0.401825528m X 1047 = 420.711328m

That shot is missing the tip though, so let's find another shot where we can scale off the tip of the Ginga (this will be important soon).
2203 pixels = 1500m
1 pixel = 1500m/2203 = 0.680889696m
0.680889696m X 738 = 502.496596m
502.496596m + 420.711328m = 923.207924m

We'll come back to that shortly. Volume as a cylinder.

V = πr^2h
= π X 6.831034^2 X 0.798930484
= 117.120188m^3 (117120188cm^3)

The energy to melt steel is 7309.87 joules/cm.

E = 117120188 X 7309.87
= 8.56133349e11 joules
= 204.620781309751 tons of TNT

Let's get the speed while we're at it.
Timeframe is 2 seconds and 3 frames.

T = 33.3333333ms X 3
= 99.9999999ms + 2s
= 2.1s

T = 923.207924m/2.1s
= 439.622821/340.29
= Mach 1.29190638