Introduction[]
In Naruto: The Last, there’s this huge explosion that puts a massive hole in the moon and while it’s on Naruto’s profile, it’s never had a calc for it and as such is in the Unknown tier. I’mma calc it.
Calculation[]
I’m gonna do four different methods: explosion, pulverization, melting, and vaporization. I’ll explain my reasoning for these methods later in this blog, but for now, it’s curvature scaling time.
Moon Diameter = 3474.2 km (apparently with a quick Google search) = 3474200 meters = 1503 px
Panel Height = 232 px
sqrt(1-(tan(35 deg)*(Moon Diameter in Pixels/Panel Height in Pixels))^2/((tan(35 deg)*(Moon Diameter in Pixels/Panel Height in Pixels))^2+1))*Moon Diameter in Meters
sqrt(1-(tan(35 deg)*(1503/232))^2/((tan(35 deg)*(1503/203))^2+1))*3474200 = 1777756.93 meters
1777756.93 / 1503 = 1182.81 meters per px
Explosion Diameter = 173.48 px = 205193.88 meters
Explosion Radius = 205193.88 / 2 = 102596.94 meters
Now’s where things split off into the different methods.
Explosion Method:
I’ll use the ground level explosion formula since it happened on the moon’s surface. Ground level explosion formula is W = R^3*((27136*P + 8649)^(1/2)/13568 - 93/13568)^2, where W is the yield in tons, R is the radius in meters, and P is the standard overpressure of 1.37895 bars.
W = 102596.94^3*((27136*1.37895 + 8649)^(1/2)/13568 - 93/13568)^2
W = 86.79 gigatons
Pulverization, Melting, and Vaporization Methods:
These next methods rely on this next shot. The explosion diameter is being used as the crater diameter.
I’m trying pulverization because all the area was completely destroyed, and melting and vaporization due to the molten-looking rock in the crater. Also, this is a cylinder so there’s that.
Top of Crater Diameter = 205193.88 meters= 1305 px
Bottom of Crater Diameter = 205193.88 meters = 591 px
Panel Height = 768 px
Distance = (Object Size in Meters * Panel Height in Pixels) / [Object Size in Pixels * 2tan(70/2 deg)]
Distance to Top of Crater = (205193.88 * 768) / [1305 * 2tan(70/2 deg)] = 86229.99 meters
Distance to Bottom of Crater = (205193.88 * 768) / [591 * 2tan(70/2 deg)] = 190406.32 meters
Crater Height = 190406.32 - 86229.99 = 104176.33 meters
Crater Volume = pi * radius^2 * height = pi * 102596.94^2 * 104176.33 = 3.4449882e+15 meters^3 = 3.4449882e+21 cc
Pulverization = 3.4449882e+21 cc * 214.35 Joules/cc = 7.3843323e+23 Joules = 176.49 teratons
Melting = 3.4449882e+21 cc * 4358.9475 Joules/cc = 1.5016523e+25 Joules = 3.59 petatons
Vaporization = 3.4449882e+21 cc * 25700 Joules/cc = 8.8536197e+25 Joules = 21.16 petatons
Final Result[]
There’s a Hole in the Moon:
Explosion = 86.79 gigatons; Island level+ (6-C)
Pulverization = 176.49 teratons; Large Country level (High 6-B)
Melting = 3.59 petatons; Continent level+ (6-A)
Vaporization = 21.16 petatons; Multi-Continent level (High 6-A)
Can we get New Era Naruto out of the hell that is Unknown now? He tanked this so he should scale for sure.