All credit goes to Lina Shields.
STEP 1: Dimensions of Dome
First, look at this picture.
Looking at the picture shown above, the bottom of the dome was measured to be about 5.36km, or 5360m.
Now, this picture shows the entire dome, top/bottom and all.
I chose these two pictures because the construction shown in the two pictures look the same, with the square gaps shown at the bottom of the pictures. Now then...
- Dome diameter [bottom] = 163px = 5360m
- Dome diameter [top] = 290px = 9536m
Now look at this picture. Notice that the top of the dome is shown here, but in a different view. Thus the diameter of the top of dome remains the same.
- 721px = Dome diameter [top] = 9536m
- 279px = Field diameter = 3690m
- 12px = Dome thickness = 158m
Seriously, a 9+ km wide dome?
STEP 2: Dome Blows Up
So, the dome blows up, as shown in this picture here. Just the top tho.
We will treat the dome as a spherical bowl, or a dome. Two parts to this calculation; one for the entire diameter of dome, and one for the hollow part of dome.
- Volume of dome [entire diameter] = [4.2*[9536m/2]^3] = 4.55e11 m^3 [1*]
- Volume of dome [hollow] = [4.2*[[9536m-158m]/2]^3] = 4.33e11 m^3 [2*]
Subtract 2 from 1 to get the total volume of dome.
- Total Volume = 2.2e10 m^3, or about 2.2e16 cm^3
I divided the diameter by 2 because of radius and stuff.
STEP 3: Destructive Yield
You see the explosion scattering all the pieces of the dome outwards. Using fragmentation as a low end and violent fragmentation as a high end.
I will use concrete as a baseline material for this calculation.
Btw, cc = cm^3
Low End: Fragmentation
- Fragmentation value of concrete = 6 j/cc
- Energy = [2.2e16 cm^3]*[6j/cc] = 1.32e17 joules, or about 31.55 megatons of TNT
High End: Violent Fragmentation
- VF value of concrete = 20j/cc
- Energy = [2.2e16 cm^3]*[20j/cc] = 4.4e17 joules, or about 105 megatons of TNT
I imagine this would scale to all the people surviving the explosion.
Since it was agreed to use fragmentation of reinforced concrete rather than normal concrete
- Fragmentation value of concrete = 28 j/cc
- Energy = [2.2e16 cm^3]*[28j/cc] = 6.16e+17 joules, or about 147 megatons of TNT