Calc Ultraman Taiga - Woola's path of destruction

3:39


Woola flies into a galaxy and causes several explosions visible from beyond the galaxy before leaving again. For our low end , mid end and high end, we'll use the diameter of the Triangulum Galaxy (61,100 lightyears, or 5.78038286e20m) and the Milky Way (100,000 lightyears, or 9.4605284e20m) for our low end and our high end respectively.
(Low end)

2470 pixels = 61,100LY
1 pixel = 61,100LY/2470 = 24.7368421LY
24.7368421LY X 93 = 2300.52632LY (2.17641946e19m)
2.17641946e19m/2 = 1.08820973e19m

(High end)
2470 pixels = 100,000LY
1 pixel = 100,000LY/2470 = 40.48583LY
40.48583LY X 93 = 3765.18219LY (3.56206131e19m)
3.56206131e19m/2 = 1.78103066e19m

We'll find our energy using luminosity.

M(star) is the apparent magnitude of the light source
m= is the apparent magnitude of the sun (-26.73)
L(star) is the Luminosity
L= Luminosity of the sun (3.486*10^26)
d= Distance to the sun from earth (0.000004731537734207877 parsecs)
d(star)= distance to the light source

Click to expand...

As the area in the flash is near-white and comparable to the core of the galaxy, I think it's safe to use the luminousity of the Sun (that being 100,000 lux). The conversion factor from lux to apparent magnitude is -2.5 log I - 14.2.

L = -2.5 log I - 14.2
= -2.5 log 100,000 - 14.2
= -26.7

Our formula is as follows, for our low end...

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(1.08820973e19))^2)

Let's go through this step by step...

(146000000000/(1.08820973e19))^2) = 1.80003315e-16
-26.7 - -26.73 = 1.80003315e-16/((L/3.846*10^26)
0.03 = -2.5Log(1.80003315e-16/((L/3.846*10^26))
0.03/-2.5 = (1.80003315e-16/((L/3.846*10^26))
10^(-0.012) = (1.80003315e-16/((L/3.846*10^26))
0.972747224 = (1.80003315e-16/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 1.80003315e-16
3.75869527e27/1.80003315e-16 = 2.08812558e43 joules = 4.9907399139579353333 tenakilotons

Now for our high end...

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(1.78103066e19))^2)

(146000000000/(1.78103066e19))^2) = 6.7199017e-17
-26.7 - -26.73 = 6.7199017e-17/((L/3.846*10^26)
0.03 = -2.5Log(6.7199017e-17/((L/3.846*10^26))
0.03/-2.5 = (6.7199017e-17/((L/3.846*10^26))
10^(-0.012) = (6.7199017e-17/((L/3.846*10^26))
0.972747224 = (6.7199017e-17/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 6.7199017e-17
3.75869527e27/6.7199017e-17 = 5.59337835e43 joules = 13.368495100382408142 tenakilotons

With those two in our hands, let's also get another scaling from the middle of the galaxy.

(Low end, again)

R = 61,100LY/2
= 30550LY

1328 pixels = 30550LY
1 pixel = 30550LY/1328 = 23.0045181LY
23.0045181LY X 93 = 2139.42018LY (2.02400454e19m)
2.02400454e19m/2 = 1.01200227e19m

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(1.01200227e19))^2)

(146000000000/(1.01200227e19))^2) = 2.0813386e-16
-26.7 - -26.73 = 2.0813386e-16/((L/3.846*10^26)
0.03 = -2.5Log(2.0813386e-16/((L/3.846*10^26))
0.03/-2.5 = (2.0813386e-16/((L/3.846*10^26))
10^(-0.012) = (2.0813386e-16/((L/3.846*10^26))
0.972747224 = (2.0813386e-16/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 2.0813386e-16
3.75869527e27/2.0813386e-16 = 1.80590283e43 joules = 4.3162113527724666595 tenakilotons

(High end, again)

(Low end, again)

R = 100,000LY/2
= 50000LY

1328 pixels = 50000LY
1 pixel = 50000LY/1328 = 37.6506024LY
37.6506024LY X 93 = 3501.50602 (3.31260972e19m)
3.31260972e19m/2 = 1.65630486e19m

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(1.65630486e19))^2)

(146000000000/(1.65630486e19))^2) = 7.77007408e-17
-26.7 - -26.73 = 7.77007408e-17/((L/3.846*10^26)
0.03 = -2.5Log(7.77007408e-17/((L/3.846*10^26))
0.03/-2.5 = (7.77007408e-17/((L/3.846*10^26))
10^(-0.012) = (7.77007408e-17/((L/3.846*10^26))
0.972747224 = (7.77007408e-17/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 7.77007408e-17
3.75869527e27/7.77007408e-17 = 4.83739953e43 joules = 11.561662356596557617 tenakilotons

With the energy out of the way, let's get the speed.
Timeframe is 19 frames (with 30 frames per second, though almost every video I look at these days has 30 fps, so from now on I'll only post the scans backing that up if I absolutely must).

T = 1s/30
= 33.3333333ms X 19
= 0.633333333s

(Low low end)
560 pixels = 30550LY
1 pixel = 30550LY/560 = 54.5535714LY
54.5535714 X 178 = 9710.53571LY

T = 9710.53571LY/0.633333333s
= 1.4505284e20/299792458
= 483844193000 C

(High low end)
1018 pixels = 61,100LY
1 pixel = 61,100LY/1018 = 60.0196464LY
60.0196464LY X 178 = 10683.4971LY

T = 10683.4971LY/0.633333333s
= 1.59586623e20/299792458
= 532323675000 C

(Low high end)

560 pixels = 50000LY
1 pixel = 50000LY/560 = 89.2857143LY
89.2857143LY X 178 = 15892.8571LY

T = 15892.8571LY/0.633333333s
= 2.37402357e20/299792458
= 791889024000 C

(High high end)

1018 pixels = 100,000LY
1 pixel = 100,000LY/1018 = 98.2318271LY
98.2318271LY X 178 = 17485.2652LY

T = 17485.2652LY/0.633333333s
= 2.61189234e20/299792458
= 871233505000 C

Final Results
Woola arrives in a galaxy (low low end) = 4.316 tenakilotons
Woola arrives in a galaxy (low high end) = 4.991 tenakilotons
Woola arrives in a galaxy (low high end) = 11.562 tenakilotons
Woola arrives in a galaxy (high high end) = 13.368 tenakilotons
Woola flies across the galactic core (low low end) = 483844193000 C
Woola flies across the galactic core (high low end) = 532323675000 C
Woola flies across the galactic core (low high end) = 791889024000 C
Woola flies across the galactic core (high high end) = 871233505000 C

The energy is a bit lower than I expected, but still not far off what I predicted. The speed is just what I expected. It also bears mentioning that Woola caused several explosions like this.