Calc Fate/Prototype Feat - Excalibur Proto Yield and Speed

Calculations
The Feat

So that's a thing

The building they're fighting near is the Tokyo Metropolitan Government Building standing at 243.4 meters tall

Wish they gave me the floor plan dimensions, but I guess I have to roughly gauge them myself with sub-optimal views of the facade instead *shrugs*

SHdtLtX.jpg

If someone can find the actual dimensions for me to use, that'd be cool, but here's an unofficial gauge within a reasonable margin of error anyway

Height = 299 pixels
Diameter = 138 pixels
Diameter/Height = 0.462

Height = 243.4 meters
Diameter = 112.451 meters

Now the rest

REO7jMj.png

ZK3jNxI.png

tWgqwQB.png

Diameter = 77 pixels
Above Water = 108 pixels

Above Water/Diameter = 1.403

Above Water = 157.8 meters
Remainder = 85.6 meters

Which will be used to calculate the total water volume of the flood later

Initial Diameter = 1090 pixels
Initial Radius = 545 pixels

Initial Radius/Diameter = 7.078

Initial Radius = 795.928 meters

Which is needed later to calculate the speed of Excalibur Proto's streak of light into space

Distance Image 2 = 400 pixels
Distance Image 3 = 160 pixels

Total Expansion = 240 pixels
Diameter/Total Expansion = 3.117

Total Expansion = 350.51 meters
Time Frame = 0.12 seconds (start and end)
Expansion Speed = 2,920.917 m/s

Which is what we'll use to get a KE for the vaporized water later

We need a total AOE for the fallout over which this mass was present and for Excalibur to purge though

ZB6X8Sn.png

AOE = 23 pixels
Travel = 224 pixels
Earth = 2005 pixels

AOE/Earth = 0.0115
Travel/Earth = 0.112

Earth = 12,742,000 meters
AOE = 146,533 meters
AOE Radius = 73,266.5 meters

And seeing as the flood goes well beyond the Horizon in the story board, this seems fair to equate to both the Flood and Excalibur Proto's AOE.

Travel = 1,427,104 meters

Volume = PIr^2*H
r = AOE Radius
H = Remainder

Water Volume = 1,442,827,142,300.444 m^3

Water Density = 1,000 kg/m^3
Water Mass = 1,442,827,142,300,444 kilograms

KE = 0.5mv^2

m = Water Mass
v = Expansion Speed

Excalibur Proto Yield = 6,154,924,651,353,299,000,000 joules or 1.471 teratons

Right, speed though?

I mentioned needing the Initial Radius from earlier to get that

Why?

Because for the first 2 odd seconds or so, the AOE doesn't really hit the top speed the water is propelled at (shown via this sequence), which is the speed we give a shit about for the actual kinetic energy

And knowing the initial expansion distance lets us shave off some horizontal distance the beam's vertical travel time can't be compared to due to the initial speed of the expansion being slower

AOE Radius - Initial Radius = Total Expansion Distance During Top Expansion Speed

Total Expansion Distance During Top Expansion Speed = 72,470.572 meters

Time Frame for Vertical Beam Travel = Total Expansion Distance During Top Expansion Speed/Expansion Speed

Time Frame = 24.811 seconds

Excalibur Proto Speed = 57,519 m/s or mach 169.029

And sans the storyboard having a time frame elaborated upon buried in the moon runes, that's about as exact as I can get for a speed here *shrugs*

Final Tally

Excalibur Proto Speed = 57,519 m/s
Excalibur Proto Yield = 1.471 teratons
About author
ChaosTheory123
I do high school physics for stupid shit because I find it fun for some ridiculous reason.

I'm neither a physicist or engineer. I study psychology.

Before taking me at my word, think for yourself and don't just appeal to the shit I'm posting without evaluating it yourself. That should go without saying. I'm not an expert, do not treat me like one.

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