Calc Avatar: The Last Airbender Feats - Book Two: Earth Collection Part 2

^The Feats

Because these are the last times Aang won't be using bending, but rather his muscles, for any kind of bullshit.


Image 1

Aang = 426 pixels
Aang Face = 80 pixels
Aang Face/Aang = 0.188

Aang = 1.37 meters
Aang Face = 0.258 meters

Image 2

Aang Face = 112 pixels
Boulder = 521 pixels
Boulder/Aang Face = 4.652

Boulder = 1.2 meters

Volume = (4/3)PIr^3

r = Boulder/2

Boulder Volume = 0.904 m^3
Rock Density = 2,700 kg/m^3
Boulder Mass = 2,440.8 kilograms or 2.441 tons

Image 3

Aang = 262 pixels
Bottom Height (Light Green) = 34 pixels
Middle Height (Blue) = 18 pixels
Top Height (Green) = 43 pixels
Bottom Diameter (Orange) = 73 pixels
Top Diameter (Purple) = 61 pixels

Bottom Height/Aang = 0.13
Middle Height/Aang = 0.069
Top Height/Aang = 0.164
Bottom Diameter/Aang = 0.279
Top Diameter/Aang = 0.233

Aang = 1.37 meters
Bottom Height (Light Green) = 0.178 meters
Middle Height (Blue) = 0.095 meters
Top Height (Green) = 0.225 meters
Bottom Diameter (Orange) = 0.382 meters
Top Diameter (Purple) = 0.319 meters

Bottom/Top Volume = PIr^2*H

r = Bottom or Top Diameter/2

Middle Volume = Conical Frustrum Calculator

Bottom Volume = 0.02 m^3
Middle Volume = 0.009 m^3
Top Volume = 0.018 m^3
Total Volume = 0.047 m^3

8 j/cc

Aang's Physical Might = 376,000 joules or 89.866 grams

^The Feat

Wasn't really sure how to treat this, but this is what I've got.

Given mushroom clouds only continue to be able to grow until they reach a place in the atmosphere with similar density, this seemed like the reasonable route to take.


Aang = 426 pixels
Katara's Head = 85 pixels

Katara's Head/Aang = 0.2

Katara's Head = 0.274 meters


Panel Width = 1440 pixels
Mushroom Cloud Top Diameter 1 = 250 pixels
Mushroom Cloud Top Diameter 2 = 150 pixels
Mushroom Cloud Height = 66 pixels
Mushroom Cloud Bottom Diameter = 65 pixels

Mushroom Cloud Top Diameter 2/Mushroom Cloud Top Diameter 1 = 0.6
Mushroom Cloud Expansion/Mushroom Cloud Top Diameter 1 = 0.06
Mushroom Cloud Height/Mushroom Cloud Top Diameter 1 = 0.264
Mushroom Cloud Bottom Diameter/Mushroom Cloud Top Diameter 1 = 0.26

2*atan(Object_Size/(Panel_Width/tan(FoV/2))) = object degree size

2*atan(250/(1440/tan(70/2)))

Mushroom Cloud Top Diameter = 13.862 degrees

Katara's Head = 40 pixels
Height of Observer = 347 pixels
Height of Observer/Katara's Head = 8.675

Height of Observer = 2.377 meters (as far as I can see, our view of the screen is no lower than the top of Katara's head at any rate)


Distance to Horizon = 5,503.4 meters (seems fair enough looking at the video [like here and here] that the desert looks mostly flat for the most part and all sans the occasional dune and shit)


Mushroom Cloud Top Diameter 1 = 1,338 meters
Mushroom Cloud Top Diameter 2 = 802.8 meters
Mushroom Cloud Height = 353.232 meters
Mushroom Cloud Bottom Diameter = 347.88 meters

Mushroom Top Volume?

Volume = (4/3)PIr1^2r2

r1 = (Mushroom Cloud Top Diameter 1)/2
r2 = (Mushroom Cloud Top Diameter 2)/2

Mushroom Cloud Top Volume = 752,138,792.208 m^3

Bottom Volume?

Volume = PIr^2*H

r = Mushroom Cloud Bottom Diameter
H = Mushroom Cloud Height

Mushroom Cloud Bottom Volume = 33,557,424.353 m^3

Total Mushroom Cloud Volume = 785,696,216.561 m^3

Air Density at 1,000 Meters (here) = 1.112 kg/m^3 (most of the Mushroom Cloud is sitting below this altitude, not splitting hairs over it and doing some kind of gradient)

Mushroom Cloud Mass = 873,694,192.816 kilograms


Once the mushroom forms, it doesn't really grow taller at the bottom or the stalk of it, hence I can reasonably use it to scale how fast the thing expands in general.

Mushroom Cloud Bottom Height = 390 pixels
Start = 651 pixels
End = 705 pixels
Expansion = (End - Start)/2 = 27 pixels

Expansion/Mushroom Cloud Bottom Height = 0.069

Expansion = 24.373 meters
Time Frame = 0.083 seconds (2 Frames, 24 FPS, here and here)
Expansion Speed = 293.651 m/s

KE = 0.5mv^2

m = Mushroom Cloud Mass
v = Expansion Speed

Aang's Airbending Explosion Yield = 37,669,722,567,187 joules or 9.003 kilotons