Introduction[]
In this blog I will be calculating the minimum energy needed to destroy the surface of the Earth.
Calculation[]
Air-burst Explosion
Earth's Circumference = 40075 km
Explosion Radius = 20037.50 km
Y = ((x/0.28)^3)/1000000000
Y is yield in teratons of tnt, x is radius in kilometers.
Y = ((20037.50/0.28)^3)/1000000000 = 366485.26 Teratons of TNT
Only 50% of the total energy of the explosion is actually from the blast, so we need to halve the result. This part can be ignored if the blast was an actual nuclear explosion.
Y = 366485.26/2 = 183242.63 Teratons of TNT
Ground-burst Explosion
[R^3*((27136*P+8649)^(1/2)/13568-93/13568)^2]/1000000000000000
W is the yield in petatons of TNT, R is the radius in meters, and P is the shockwave pressure in bars, where we generally use 1.37895 bars or 20 psi of pressure.
Explosion Radius = 20037.50 km or 20037500 m
[20037500^3*((27136*1.37895+8649)^(1/2)/13568-93/13568)^2]/1000000000000000 = 646.57 Petatons of TNT
Final Tally[]
Average Surface Destruction (Air-burst) = 183.24 Petatons of TNT (Multi-Continent level)
Average Surface Destruction (Ground-burst) = 646.57 Petatons of TNT (Multi-Continent level)
This scales to characters who have stated that they can destroy the surface of the planet, like Lord Boros.