User:Geo GeoZ/EVA Calc 2.0

https://youtu.be/gQaafNForNs?t=2m17s

Rei, now having merged with Lilith, grows and expands her wings across the Earth. I'll be calculating the kinetic energy of her expanding her wings at such a speed. I'm not sure if this method is even accepted, but eh, worth a shot.

Basic curvature scaling here. This one is a lot closer than the one I used for my previous calc. It's not perfect but I think it should do. It's also worth noting that in this scene, the Earth is emenating a sort of aura and has waves flowing on top of it so it appears bigger. If you remove those, then the curve should be almost an exact match. Also yadda yadda IRL Earth is flatter at the poles so the shape works out better than you might think.

Radius = 7243 pixels

Radius of Earth = 6371 km

1 px = 0.87960789728 km

Now, for pixel scaling. Note that I only measured the left wings (from the viewer's perspective) for this calc as to avoid losing my sanity. The wings appear to be the same size on both sides anyways, so I doubt it would change anything.

If there are multiple values for some of the wings below, it's just referring to the different segments of some of the more complicated wings in order. I've numbered the wings in order from top to bottom, so wing 1 would the the wing closest to the Earth in this scene, while wing 6 is the last wing sprouting from her back.

Length of wing 1 = 334 pixels = 293.789037692 km, 1453 pixels = 1278.07027475 km

Total = 1571.85931244 km

Length of wing 2 = 1927 pixels = 1695.00441806 km

Left wing 3 = 556 pixels = 489.061990888 km, 1497 pixels = 1316.77302223 km

Total = 1805.83501312 km

Note that the first segment of the third wing also splits off into the fourth wing, that'll be important later on in the calc

Left wing 4 = 1711 pixels = 1505.00911225 km

Total (factoring in segment from third wing) = 1994.07110314 km

Left wing 5 = 1417 pixels = 1246.40439045 km

Left wing 6 = 804 pixels = 707.204749413 km

Now for the widths. If you're wondering about the positioning of some of my lines in the image, it's essentially trying to find a middle ground as the wings tend to be really wide on end and thinner on the other.

Left wing 1 width = 75 pixels = 65.970592296 km, 101 pixels = 88.8403976253 km

Left wing 2 width = 141 pixels = 124.024713516 km

Left wing 3 width = 103 pixels = 90.5996134198 km, 173 pixels = 152.172166229 km

Left wing 4 width = 215 pixels = 189.115697915 km

Left wing 5 width = 122 pixels = 107.312163468 km

Left wing 6 width = 66 pixels  = 58.0541212205 km

I decided to use the size of the bicep for the depth of the wings, as they sprout off from the shoulders like the arm and there isn't any other indication of how far into the background they go.

Average bicep size = 12 inches = 0.3048 m

Average arm length = 25 inches = 0.635 m

Left arm length = 120 pixels= 105.552947674 km, 91 pixels = 80.0443186525 km

Total = 185.597266327 km = 185597.266327 m

Note that midway through I realised I made a mistake while measuring the pixels of her right arm and it was too late to change it, so I just measured her left arm and used that instead. Doesn't change anything since her arms are the same size but I figured I'd mention it.

That's 292279.15957 times greater in length than the average arm, so I'll assume the bicep follows that same proportion

Expanded bicep = 89086.687837 m = 89.086687837 km

Now to find the density. Here's where things might get a bit controversial. I was initially planning on just using the average density of a human for the wings, but I ended up finding a study that gave a density specifically to the arms of humans

https://pdfs.semanticscholar.org/8eda/33ffe8e628c2d058d880e011c3c76c10604b.pdf

Scroll down and you'll find that the density of the forearm is 1.127 g/ml, or 1127 kg/m^3

I decided to use this for the density of the wings. To explain myself, there's no real life basis for something like Lilith's wings, so there's no way to look into how dense they might be themselves. I figured using the density of the arm was safest here. The wings and the arm both sprout from the same places and the wings have no indication otherwise as to what they might be composed of, so there's no way to really know. When Shinji kills Lilith, we see that she actually does have a skeleton and muscles, so she follows real life anatomy to an extent. That's also why I used the density of the forearm specifically. I figured that since it's generally smaller than the upper arm, it might be more reflective of the likely thinner wings. Besides, given Lilith's species and anatomy, and the appearence of the wings, I think it's reasonable to assume that they contain blood and a skeletal structure. Even if you were to use the average density of a human or the upper arm, the difference between the densities is so small that I doubt it would actually affect the results to any notable degree. Feel free to disagree or try these different values on your own.

Moving on to finding the volume, I'm assuming the wings take the form of a cuboid given that generally they can be divided into rectangles length wise.

Left wing 1 volume =1726628012405018 meters cubed, 10115283062057680 meters cubed

Left wing 2 volume = 18728020653267330 meters cubed

Left wing 3 volume = 3947326667236330 meters cubed, 17850852266637335 meters cubed

Left wing 4 volume = 25355928693944783 meters cubed

Left wing 5 volume = 11915732176310888 meters cubed

Left wing 6 volume = 3657556441122802 meters cubed

To get the mass, we just have to multiply these values by the density of 1127 kg/m^3

Left wing 1 mass = 1945909769980455286 kg (first segment), 11399924010939005360 kg (second segment)

Left wing 2 mass = 21106479276232280910 kg

Left wing 3 mass = 4448637153975343910 kg (first segment), 20117910504500276545 kg (second segment)

Left wing 4 mass = 28576131638075770441 kg

Left wing 5 mass = 13429030162702370776 kg

Left wing 6 mass = 4122066109145397854 kg

But remember, there are two sets of wings here. We have to first add the segments' masses together for some of the wings (including wing 4 as the smaller segment goes into both wings 3 and 4) before multiplying these results by two to find the total mass of each set of wings

Total wing 1 mass = 26691667561838921292 kg

Total wing 2 mass = 42212958552464561820 kg

Total wing 3 mass = 49133095316951240910 kg

Total wing 4 mass = 66049537584102228702 kg

Total wing 5 mass = 26858060325404741552 kg

Total wing 6 mass = 8244132218290795708 kg

Now to get a speed. I have a 24 fps version of the series readily available. Looking over the scene, it takes 130 frames from when Rei first starts growing her wings before the scene cuts giving us a timeframe of 5.79166666667 seconds. Luckily for me, none of the wings ever really stop expanding, so I can use the same timeframe for all of them. So to find the speeds at which she grew each wing, we just have to divide the total length of each individual wing by the timeframe.

Left wing 1 speed = 271400 m/s

Left wing 2 speed = 292662.6 m/s

Left wing 3 speed = 311799 m/s

Left wing 4 speed = 344300 m/s

Left wing 5 speed = 215206.5 m/s

Left wing 6 speed = 122107.3 m/s

With both a mass and a speed for each pair of wings, we can finally plug those values into the KE formula to get these results.

KE of wing 1 = 983026890801614395484642160000 joules or 234.9490656791648 Exatons

KE of wing 2 = 2104159137194334233045288865836 joules or 502.9061035359364 Exatons

KE of wing 3 = 2388325773106226101425114082455 joules or 570.8235595378234 Exatons

KE of wing 4 = 3914838324284031302442273990000 joules or 935.6688155554674 Exatons

KE of wing 5 = 621949922648275701628825142886 joules or 148.64959910331802 Exatons

KE of wing 6 = 61460800064279372911848803280 joules or 14.689483762973246 Exatons

Little under half of what I got before for each value, but still small planet level Evangelion. Again, only characters this scales to are Lilith- Rei, duh, and Awakened Unit-01, as it managed to kill her. The total KE of her expanding all her wings at once should be over 2 Zettatons.  Even if she isn't outputting all this energy simultaneously and exerting it all onto her body, she did this all at once, so even a percentage of it should still get small planet results.