Calc Shantae - Risky's lair explodes & Giga Wrench's speed

17:27

Risky Boot's lair exploding causes a volcanic eruption and a colossal explosion which whites out the entire screen. This explosion is seen all the way back in Scuttle Town.
This is important because in the Risky playthrough, we see that Risky survives this explosion at ground zero.

4:25


A massive explosion to be sure, but how do we figure out how big it is? Thankfully, there is a good way we can get a minimum distance; the top of the Tassel Town Tower features a battle where you run in a circle around Wilbur the memory-eating worm, and the view also spins around as you do, showing a desert to the horizon from the very top of this tall tower.


Thus, the distance to the horizon would form the minimum radius of the desert, and the diameter of the desert would be included in the distance over which the light shone. Previously, I estimated Shantae's height to be 158.8cm (or 1.588m) based off an average Arabian woman. Now, how are we going to get the height of the Tassel Town Tower? I couldn't find any ingame version of all of it after a brief search, so we'll have to stitch one together. However, the perspective makes that quite tricky. Will we have to make a massive stitch showing the exact parts which overlap with dozens of screenshots?
154 pixels = 1.588m
1 pixel = 1.588m/154 = 0.0103116883m
0.0103116883m X 24115 = 248.666363m
0.0103116883m X 26937 = 277.765948m

If there's a better way to scale that then please let me know. For now, we'll put all of this into the distance to the horizon calculator to get a distance of 56.3km (or 56300m). With our radius in hand, let's get our diameter.

D = 56300m X 2
= 112600m

Sequin Land is far bigger than just this desert, but for now it's the best way to determine its size (or a size of one of several regions within; it is described as being a continent). As for finding the energy of the explosion, we'll use luminousity. As it's a white out, I think it's fair to use the luminousity of the Sun (the Sun having a luminousity of 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...

-26.7 = -26.73 - 2.5log((L/3.846*10^26)(146000000000/(112600))^2)

Let's go through this step by step.

(146000000000/(112600))^2) = 3330625000000
-26.7 - -26.73 = 1.68123697e12/((L/3.846*10^26)
0.03 = -2.5Log(1.68123697e12/((L/3.846*10^26))
0.03/-2.5 = (1.68123697e12/((L/3.846*10^26))
10^(-0.012) = (1.68123697e12/((L/3.846*10^26))
0.972747224 = (1.68123697e12/((L/3.846*10^26))
0.972747224 X (3.864*10e26) = 1.68123697e12
3.75869527e27/1.68123697e12 = 2.23567251e15 joules = 534.3385540152963813 kilotons

While we're here, there's something else of particular interest, in that Giga-Wrench can maintain his giant form for several seconds, and fly Sky & Shantae anywhere in Sequin Land.
Several, from what I understand is more than a couple, so for a high end we'll use 3 seconds and a mid end we'll use 9 seconds. To play it extra safe, seconds are less than minutes, so for our low end we'll go with 59 seconds.

(Low end)
T = 112600m/59s
= 1908.47458/340.29
= Mach 5.60837691

(Mid end)
T = 112600m/9s
= 12511.1111/340.29
= Mach 36.7660263

(High end)
T = 112600m/3s
= 37533.3333/340.29
= Mach 110.298079

Final Results
Tassel Town Tower's height = 277.766m
Risky Boot's lair explodes = >534.339 kilotons
Giga-Wrench's speed (low end) = >Mach 5.608
Giga-Wrench's speed (mid end) = >Mach 36.766
Giga-Wrench's speed (high end) = >Mach 110.298