Calc The Owl House - Hooty protects Luz and King

Calculations
The giant finger explodes and Hooty protects Luz and King from the explosion. Eda is 7'5'' tall (2.2606m)...
4uMIqUL.png
...which will very much come in handy for any other scaling we need to do. Starting now, scaling Luz & King's heights.
NFsmS6t.png
552 pixels = 2.2606m
1 pixel = 2.2606m/552 = 0.00409528986m
0.00409528986m X 403 = 1.65040181m
0.00409528986m X 95 = 0.389052537m
0.00409528986m X 30 = 0.122858696m
0.00409528986m X 221 = 0.905059059m
lqwselr.png
173 pixels = 0.905059059m
1 pixel = 0.905059059m/173 = 0.00523155525m
0.00523155525m X 825 = 4.31603308m

Now we can scale to the island.
LqSpXtY.png
21 pixels = 4.31603308m
1 pixel = 4.31603308m/21 = 0.205525385m
0.205525385m X 1615 = 331.923497m
0.205525385m X 1266 = 260.195137m
0.205525385m X 330 = 67.8233771m
0.205525385m X 670 = 137.702008m
137.702008m/2 = 68.851004m
0.205525385m X 2232 = 458.732659m
458.732659m/2 = 229.36633m
0.205525385m X 330 = 67.8233771m
67.8233771m/2 = 33.9116886m
0.205525385m X 1020 = 209.635893m
0.205525385m X 1529 = 314.248314m

Volume of the main part of the cloud as an ellipsoid and the hoop as a torus.

V = 4/3πabc
= 4/3 X π X 68.851004 X 229.36633 X 33.9116886
= 2243251.51m^3

V = (πr^2)(2πR)
= (π X 67.8233771^2) X (2 X π X 314.248314)
= 28533925.2m^3

V = 2243251.51 + 28533925.2
= 30777176.7m^3

Weight of air is 1.003kg/m^3

M = 30777176.7 X 1.003kg
= 30869508.2kg

Now to get our timeframe.
kv3D6Tg.png

oSacDVX.png
Timeframe is 20 frames (with a frame rate of 30 frames per second, as visible above).

T = 1s/30
= 33.3333333ms X 20
= 0.666666666s

T = 229.36633m/0.666666666s
= 344.049495m/s

KE = (0.5)mv^2
= (0.5) X 30869508.2 X 344.049495^2
= 1.82701269e12 joules

Hold your applause though; we can also add the wave created too.
BcoxwnL.png
0.205525385m X 51 = 10.4817946m
10.4817946m/2 = 5.2408973m

Volume of the wave as a torus.

V = (πr^2)(2πR)
= (π X 5.2408973^2) X (2 X π X 209.635893)
= 113659.746m^2

Weight of water is 1000kg/m^3.

M = 113659.746 X 1000kg
= 113659746kg

T = 209.635893m/0.666666666s
= 314.45384m/s

KE = (0.5)mv^2
= (0.5) X 113659746 X 314.45384^2
= 5.61940703e12 joules

E = 1.82701269e12 + 5.61940703e12
= 7.44641972e12 joules
= 1.779737026768643 kilotons

With the total energy, let's get the area which Hooty tanked.
B2G7ogj.png
842 pixels = 1.65040181m
1 pixel = 1.65040181m/842 = 0.00196009716m
0.00196009716m X 184 = 0.360657877m

Hooty's body is about as thick as his face.
uRYRwLT.png
219 pixels = 0.360657877m
1 pixel = 0.360657877m/219 = 0.00164683962m
0.00164683962m X 1585 = 2.6102408m
2.6102408m/2 = 1.3051204m
0.00196009716m X 1059 = 2.07574289m

We'll find the surface area as half the area of an ellipsoid (the scaling isn't perfect, but it'll leave some parts out, which I do to make up for the wonky scaling). Using this calculator, we end up with a surface area of 36.56m^2 (double checking with Google's ellipsoid surface area calculator and we get 36.55m^2), half of which is 18.27500m^2. Now we will try for the energy Hooty tanked going by inverse square law.

(Low end)

A = 4πr^2
= 4 X π X 260.195137^2
= 850762.257m^2

A = 18.27500/850762.257
= 2.14807367e-5 X 7.44641972e12
= 159954581 joules
= 0.0382300623805 tons of TNT

(High end)
E = 18.27500/260.195137
= 0.0702357477 X 7.44641972e12
= 5.23004857e11 joules
= 125.00116085086 tons of TNT

Final Results
Explosion on Titan Trapper Island = 1.78 kilotons
Hooty protects Luz & King (low end) = 0.038 tons of TNT
Hooty protects Luz & King (high end) = 125.001 tons of TNT


I feel I've somehow lowballed this. :hm
  • Like
Reactions: Ral

Comments

There are no comments to display.

Blog entry information

Author
Stocking Anarchy
Read time
3 min read
Views
414
Last update

More entries in The Outskirts Battledome (OBD)

More entries from Stocking Anarchy

Share this entry

Back
Top