Calc Madoka Magica - Sad giant lesbian devastates city

Calculations


Homulily's scarves lash about, and wipe out a good chunk of the city. While we're at it, why don't we get Homu;ily's height too (and Oktavias). As per the height chart, Sayaka is at least 158cm tall.
Iwbs8nw.jpg
Now, we can scale Sayaka to Oktavia's helmet...
wawqMY0.jpg
71 pixels = 158cm
1 pixel = 158cm/71 = 2.22535211cm
2.22535211cm X 207 = 460.647887cm (4.60647887m)

Now to scale Homulily's height from Oktavia.
9gXQDKE.png
70 pixels = 4.60647887m
1 pixel = 4.60647887m/70 = 0.065806841m
0.065806841m X 56 = 3.6851831m
0.065806841m X 939 = 61.7926237m

We'll come back for Oktavia's full height in a bit. Now we scale the length of the ribbon.
neTCXyZ.png
35 pixels = 3.6851831m
1 pixel = 3.6851831m/35 = 0.105290946m
89 + 127 + 297 + 120 + 100 + 136 + 170 + 151 + 244 + 455 + 537 = 2426 pixels
244 + 455 + 537 = 1236 pixels
0.105290946m X 2426 = 255.435835m
0.105290946m X 1236 = 130.139609m

Plus there's hands just out of view on the end, so it's a little bit longer than that. Anyway, just to show how fast she's moving, Homulily reaches into the air with her ribbon hands.
gt2qjzY.png

rUs2gtY.png

Timeframe is 5 frames.

T = 1s/24
= 41.6666667ms X 5
= 0.208333333s

T = 130.139609m/0.208333333s
= 624.670124/340.29
= Mach 1.83569933

Next up for her sweep across the city, which we'll calculate using two methods. The first of which is scaling the length of the ribbon hand itself (as per above). Using this calculator (with 90 degrees, and a radius of 255.435835m), we find that the arc is 401.238m long. Getting the timeframe once more...
WeLtPBp.png

eWokblc.png
Timeframe is 21 frames.

T = 41.6666667ms X 21
= 0.875000001s

T = 401.238m/0.875000001s
= 458.557714/340.29
= Mach 1.34754978

Her ribbon hand also curls before hitting the ground, so ultimately this will be somewhat faster in anycase. We're not done yet though. What about the devastation HomuLily wrought on the city?
bDqpmeL.png
93 pixels = 61.7926237m
1 pixel = 61.7926237m/93 = 0.664436814m
0.664436814m X 37 = 24.5841621m
24.5841621m/2 = 12.2920811m
0.664436814m X 75 = 49.8327611m
49.8327611m/2 = 24.9163805m
0.664436814m X 97 = 64.450371m
64.450371m/2= 32.2251855m
0.664436814m X 84 = 55.8126924m
55.8126924m/2 = 27.9063462m
0.664436814m X 213 = 141.525041m
141.525041m/2 = 70.7625205m
0.664436814m X 215 = 142.853915m
142.853915m/2 = 71.4269575m
0.664436814m X 226 = 150.16272m
150.16272m/2 = 75.08136m
0.664436814m X 391 = 259.794794m
259.794794m/2 = 129.897397m
0.664436814m X 70 = 46.510577m
46.510577m/2 = 23.2552885m
0.664436814m X 136 = 90.3634067m
90.3634067m/2 = 45.1817033m
0.664436814m X 241 = 160.129272m
160.129272m/2 = 80.064636m
0.664436814m X 164 = 108.967637m
108.967637m/2 = 54.4838185m
75 + 84 + 213 + 226 + 164 = 762 pixels
0.664436814m X 762 = 506.300852m

Volume of all the segments as ellipsoids.

V = 4/3πabc
= 4/3 X π X 12.2920811 X 12.2920811 X 24.9163805
= 15769.7351m^3

V = 4/3πabc
= 4/3 X π X 32.2251855 X 27.9063462 X 27.9063462
= 105121.123m^3

V = 4/3πabc
= 4/3 X π X 70.7625205 X 70.7625205 X 71.4269575
= 1498157.07m^3

V = 4/3πabc
= 4/3 X π X 75.08136 X 75.08136 X 129.897397
= 3067279.27m^3

V = 4/3πabc
= 4/3 X π X 23.2552885 X 23.2552885 X 45.1817033
= 102351.608m^3

V = 4/3πabc
= 4/3 X π X 80.064636 X 54.4838185 X 54.4838185
= 995553.074m^3

V = 15769.7351 + 105121.123 + 1498157.07 + 3067279.27 + 102351.608 + 995553.074
= 5784231.88m^3

A dust cloud is mostly air, and the weight of air is of air is 1.003kg per m^3.

M = 5784231.88 X 1.003kg
= 5801584.58kg

B81qyVF.png

XaDGdw2.png
Timeframe is 1 second.

T = 506.300852m/1s
= 506.300852m/s

Finally we can get our energy.

KE = (0.5)mv^2
= (0.5) X 5801584.58 X 506.300852^2
= 7.43590699e11 joules
= 177.722442399618 tons of TNT

And because I said earlier I'll return to Oktavia...


Oktavia rams into the Incubator Seal/Labyrinth wall, shattering it's dimensional fabric. The shot does pan up, but thanks to the pattern in the background, we can tell how far she moved.
9COhAsv.jpg
rbWqLFf.jpg
36 pixels = 4.60647887m
1 pixel = 4.60647887m/36 = 0.127957746m
113 + 296 = 409 pixels
0.127957746m X 409 = 52.3347181m
343 + 1494 = 1837 pixels
0.127957746m X 1837 = 235.058379m
Uw2HW4u.png

hU6bqZo.png
Timeframe is 18 frames.

T = 41.6666667ms X 18
= 0.750000001s

T = 235.058379m/0.750000001s
= 313.411172m/s

Final Results
Homulily's height = 61.793m
Homulily reaches into the sky = Mach 1.836
Homulily sweeps her ribbon hand (speed) = Mach 1.348
HomuLily sweeps her ribbon hand (energy) = 177.722 tons of TNT
Oktavia height = 52.335m
Oktavia charges barrier = 313.411m/s

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