Calc Fate/Stay Night Feat - Fate Route Excalibur Yield and Speed

Did this years ago, but imageshack killed the images

Because fuck imageshack

Anyway, standards for things like cloud parameters were still in their infancy (and I failed to completely consider the fact the moon is a constant angular size related measuring stick to simplify that bullshit), so it doesn't really hurt to redo it in some capacity.

So here's a bit feat, redone with polish~

The Feat from Ufotable's opening and it framebyframe

The feat from the Visual Novel and the let's play archive that houses the text.

So, let's first pick apart how it moves in Ufotable's intro

The first 8 frames involves Excalibur beginning to shine and propagate a comparatively slow climb with an initial burst of Excalibur.

I'm vaguely aware of others elsewhere thinking I should have used this to derive Excalibur's speed in the scene.

If they continued to watch the animation frame by frame, they'd conclude that's kind of nonsense.

For whatever reason Ufotable animates Excalibur as if it sends multiple bursts of energy into the sky as opposed to being a continuous stream. The first initial burst or shine that peters out before it can even really climb into the sky bears no relevance on the subsequent equally as fast streams of light we see flicker on and off screen later in the animation's sequence.

Didn't think about explaining that when I first posted it because I kind of thought it was obvious, but I've been wrong about less *shrugs*

Anyway, calc and such

So the cloud looks something like an Altostratus.

Japan is temperate, so I'll be using the altitude of 2,000 meters and the thickness of 1,000 meters to 5,000 meters for the different low and high end results.

So, let's first get the speed of Excalibur.

It takes about 0.24 seconds (start and end) for the Excalibur to go from the top of the roof to the top of the cloud (as demonstrated by the fact its began to split entirely by the end frame I linked)

How far away is the top of the cloud? Just add the altitude together with the low end and high end thickness to derive a low and high end vertical travel distance.

Vertical Travel (Low End) = 3,000 meters
Vertical Travel (High End) = 7,000 meters

Cool, but it kind of traveled at an angle, so to find the hypotenuse, I need to know what angle the thing moved at

This scan here tells me at 41 degrees.

Total Travel = Vertical Travel/Sin(Angle)

Total Travel (Low End) = 4,572.759 meters
Total Travel (High End) = 10,669.772 meters

So speed

Excalibur Speed (Low End) = 19,053 m/s or mach 55.99
Excalibur Speed (High End) = 44,457 m/s or mach 130.664

Could be higher, but we can't tell beyond what we can see, so anything beyond measuring stick thresholds aren't able to be quantified.

Now for the Dispersion speed and radius.


Cloud Height = 892 pixels
Dispersion Radius = 801 pixels

Dispersion Radius/Cloud Height = 0.898

Cloud Height (Low End) = 1,000 meters
Cloud Height (High End) = 5,000 meters

Dispersion Radius (Low End) = 898 meters
Dispersion Radius (High End) = 4,490 meters

Time Frame = 0.48 seconds (start and end)

Cloud Dispersion Speed (Low End) = 1,870.833 m/s
Cloud Dispersion Speed (High End) = 9,354.167 m/s

So now to find how long the split cloud was

Now with utilization of the moon for degree measuring stick~


That look bizarrely dark to anyone else? Or is that just my screen?

Anyway.

Me elsewhere said:

The purpose is to solve for the distance using the formula yet you're initially finding the angular size

Why?

You already have Angular Diameter (d~) = 29 arcminutes 20 arcseconds - 34 arcminutes 6 arcseconds for the moon's regular position

Which can be converted to degrees by multiplying both by 1/3600 which gives you 0.489 degrees to 0.563 degrees for the regular moon respectively

Click to expand...

Moon = 25 pixels
Cloud Split = 52 pixels
Cloud Split Far/Moon = 2.08

Moon (Low End) = 0.563 degrees
Moon (High End) = 0.489 degrees
Cloud Split Far (Low End) = 1.171 degrees
Cloud Split Far (High End) = 1.017 degrees

Because the moon has a range, the range of low and high ends expands

Wonderful

And because this is about angular size, foreground and background is irrelevant for this comparison.

Calculator

g = real size, r = distance, α = angular diameter or apparent size, parallax

g = Cloud Radius * 2
α = Cloud Split Far

So find "r"

Low End (Degrees)

Cloud Split Distance (Low End) = 87,873.303 meters
Cloud Split Distance (High End) = 219,683.258 meters

High End (Degrees)

Cloud Split Distance (Low End) = 101,180.451 meters
Cloud Split Distance (High End) = 252,951.126 meters

Volume = LWH

L = Cloud Split Distance
W = Dispersion Radius * 2
H = Cloud Height

Low End (Degrees)

Cloud Dispersion Volume (Low End) = 157,820,452,200 m^3
Cloud Dispersion Volume (High End) = 9,863,778,284,000 m^3

High End (Degrees)

Cloud Dispersion Volume (Low End) = 181,720,090,000 m^3
Cloud Dispersion Volume (High End) = 11,357,505,560,000 m^3

Cloud Density = 1.003 kg/m^3

Low End (Degrees)

Cloud Dispersion Mass (Low End) = 158,293,913,500 kilograms
Cloud Dispersion Mass (High End) = 9,893,369,619,000 kilograms

High End (Degrees)

Cloud Dispersion Mass (Low End) = 182,265,250,300 kilograms
Cloud Dispersion Mass (High End) = 11,391,578,070,000 kilograms

KE = 0.5mv^2

m = Cloud Dispersion Mass
v = Cloud Dispersion Speed

Low End (Degrees)

Excalibur Yield (Low End) = 277,015,624,100,000,000 joules or 66.208 megatons
Excalibur Yield (High End) = 432,837,098,700,000,000,000 joules or 103.451 gigatons

High End (Degrees)

Excalibur Yield (Low End) = 318,965,656,500,000,000 joules or 76.235 megatons
Excalibur Yield (High) = 498,384,048,400,000,000,000 joules or 119.117 gigatons