Homura blasts Walpurgisnacht with magic missiles and sends her flying into an explosive trap. This is going to take a lot of scaling, but thankfully there's a way. Homura is at least 155cm tall (or 1.55cm).
1 pixel = 1.55m/347 = 0.00446685879m
0.00446685879m X 61 = 0.272478386m
Now we scale Homura to the truck's cabin...
1 pixel = 0.272478386m/97 = 0.00280905553m
0.00280905553m X 917 = 2.57590392m
Then we scale the truck's cabin to the tanker...
1 pixel = 2.57590392m/119 = 0.0216462514m
0.0216462514m X 115 = 2.48931891m
Then from the tanker to Walpurgisnacht's horns...
1 pixel = 2.48931891m/56 = 0.0444521234m
0.0444521234m X 1829 = 81.3029337m
Finally, to Walpurgisnacht in all her terrible glory!
1 pixel = 81.3029337m/171 = 0.475455753m
0.475455753m X 827 = 393.201908m
No wonder Walpurgis night is so dreaded! If only it where that easy all the way through...
Walpurgisnacht's cogs have a lot of hollow parts, meaning this is going to be a lot harder. Now the true scaling begins...
283.847085m/2 = 141.923542m
0.475455753m X 40 = 19.0182301m
0.475455753m X 54 = 25.6746107m
0.475455753m X 30 = 14.2636726m
0.475455753m X 396 = 188.280478m
188.280478m/2 = 94.140239m
94.140239m - 14.2636726m = 79.8765664m
0.475455753m X 141 = 67.0392612m
0.475455753m X 118 = 56.1037789m
0.475455753m X 34 = 16.1654956m
Volume of the largest cog as a cylinder, and its teeth as rectangles. The second largest cog also as a cylinder, but with the area of the teeth subtracted from the central hub, and the teeth as rectangles.
V = πr^2h
= π X 141.923542^2 X 19.0182301
= 1203452.22m^3
V = lhw
= 16.1654956 X 56.1037789 X 16.1654956
= 14661.2217m^3
V = πr^2h
= π X 79.8765664^2 X 25.6746107
= 514626.938m^3
V = lhw
= 25.6746107 X 14.2636726 X 14.2636726
= 5223.56004m^3
Pocket the volumes of the teeth for a bit, but to make things easier for later, we'll add the rest up now.
V = 1203452.22 + 514626.938
= 1718079.16m^3
136.455801m/2 = 68.2279005m
0.475455753m X 11 = 5.23001328m
0.475455753m X 329 = 156.424943m
156.424943m/2 = 78.2124715m
0.475455753m X 20 = 9.50911506m
0.475455753m X 189 = 89.8611373m
89.8611373m/2 = 44.9305686m
0.475455753m X 15 = 7.13183629m
0.475455753m X 134 = 63.7110709m
63.7110709m/2 = 31.8555355m
0.475455753m X 95 = 45.1682965m
45.1682965m/2 = 22.5841482m
0.475455753m X 10 = 4.75455753m
0.475455753m X 69 = 32.806447m
Volume of everything in this one as cylinders. For the two cogs cylinders at the top, we'll multiply it, as there's two smaller ones below the central cog too (I also took a bit off the smaller top cogs, as I couldn't make out all the teeth on them). As for the parts we see spinning in the middle. From what I can gather, they seem to be a ring that splits into three segments, then joins together when she closes up her cogwork again, so we'll calculate that as a torus.
R = 32.806447m/2
= 16.4032235m
R = 141.923542m - 16.4032235m
= 125.520319m
V = (πr2) (2πR)
= (π X 16.4032235^2) X (2 X π X 125.520319)
= 666656.595m^3
V = πr^2h
= π X 68.2279005^2 X 5.23001328
= 76485.0719m^3
V = πr^2h
= π X 78.2124715^2 X 9.50911506
= 182743.524m^3
V = πr^2h
= π X 44.9305686^2 X 7.13183629
= 45230.8831m^3
V = πr^2h
= π X 31.8555355^2 X 5.23001328
= 16673.3353 X 2
= 33346.6706m^3
V = πr^2h
= π X 22.5841482^2 X 4.75455753
= 7618.46382 X 2
= 15236.9276m^3
V = 666656.595 + 76485.0719 + 182743.524 + 45230.8831 + 33346.6706 + 15236.9276
= 1019699.67m^3
That's a lot of scaling, so let's take things a bit easier for the next one; we already have the volume of each tooth of the largest cog, so how many teeth are there?
14661.2217 X 36 = 527803.981m^3
5223.56004 X 20 = 104471.201m^3
V = 1055607.96 + 104471.201
= 632275.182m^3
I'll now like to take this moment to point out that just one of the teeth on the largest cog is about as big as Oktavia or Homulily. Almost done with scaling now, just a bit more...
76.5483762m/2 = 38.2741881m
0.475455753m X 52 = 24.7236992m
0.475455753m X 20 = 9.50911506m
The cogs hub as a cylinder, and the teeth as rectangles.
R = 38.2741881m - 9.50911506m
= 28.765073m
V = πr^2h
= π X 28.765073^2 X 24.7236992
= 64267.926m^3
V = lhw
= 9.50911506 X 24.7236992 X 9.50911506
= 2235.59771m^3
There are 6 teeth in view, so to take into account the cogs on the other side, we'll times that by 2, to get 12 teeth.
V = 2235.59771 X 12
= 26827.1725m^3
V = 64267.926 + 26827.1725
= 91095.0985m^3
At long last! There's more to her (her coat, her arms, her head, her central shaft), but I'm not sure how to calc those, so we'll just leave those for now. LEt's add up all the volumes for our total volume!
V = 1718079.16 + 1019699.67 + 632275.182 + 91095.0985
= 3461149.11m^3
Finally that's all out of the way. Now we have the volume, we can get the mass. Cogs & gears are usually made of cast iron, stainless steel, brass and bronze (also plastic, although Walpurgisnacht's cogs look to be metal).
The lightest of these metals, cast iron, weighs 7300kg/m^3.
V = 3461149.11 X 7300
= 25266388503kg (25,266,388.503 tons)
For reference, that makes her far heavier than almost any man-made structure in the world (sans the Great Wall of China). Finally, all we need is the speed, which thanks to the buildings in the background, we can find. As a reminder, Walpurgisnacht's largest cog teeth are 56.1037789m in length.
1 pixel = 56.1037789m/88 = 0.637542942m
0.637542942m X 405 = 258.204892m
T = 1s/24
= 41.6666667ms
0.637542942m X 113 = 72.0423524m
258.204892m - 72.0423524m = 186.16254m
With the distance moved in the timeframe in hand, we can get the speed. May as well get the speed of the rockets while we're at it.
T = 186.16254m/41.6666667ms
= 4467.90096/340.29
= Mach 13.1296863
The moment of truth is here at last! How much energy would sending Walpurgisnacht flying generate?
KE = (0.5)mv^2
= (0.5) X 25266388503 X 4467.90096^2
= 2.5218558e17 joules
= 60.273800191204585985 megatons
Final Results
Walpurgisnacht's height = 393.202m
Homura's missiles = Mach 13.13
Homura blasts Walpurgisnacht = 60.274 megatons
