User blog:ThePerpetual/Request 6: Another STRW Thing

Feat 1
"Saturn returned to his town that is now a massive crater in the ground, it is so deep it can fit 3 skyscrapers on top of each other, his town that had a area of 21.7 km² was now just a massive spherical crater in the ground, about most of everything in the center of the hole was pulverized expect on the edge where luckily the people left the town to bunkers on the edge of it"

...why we have an exact area for this town- or why it was given to us in narration- escapes me. I guess it makes calcing easy, since I can just plug it into a radius of a circle calculator-

Area of 21.7 km = a Radius of 2.628 km, or 2628 meters, so there's A and B when we get to the volume of an ellipsoid calculator. Now, for C, depth-

While | skyscraper is generally used to describe buildings in excess of 150 meters tall, technically speaking it cuts off at 100 meters- the highest end of the category of building below it, High-Rise Building. I'll use 300 meters (100 *3) as my low-end, and 450 meters as my high-end.

Low End: 8.67882e+9, / 2 = 4.33941e+9 cubic meters,

Or 4.33941e+15 cubic cm

High End: 1.30182e+10, /2 = 6.5091e+9 cubic meters

Or 6.5091e+15 cubic cm

Now, the tricky thing is that the great majority of the land under the city, in all likelihood, not all that dense at all. The average bulk density of the earth is ~1.6 g/cc, and with finer soils being ~1.35 g/cc to (granite) stone's ~2.75 g/cc...

(1.6 -1.35 = 0.25) divided by (2.7 - 1.35 = 1.35) = About 18.5% of the Earth's... well, earth being stone rather than soil (and thus having a Pulverization value of 214.35 Joules/cc, as opposed to on average 0.7 Joules/cc.) I'll round down to one-sixth (16.67%) for the slight lowball...

Low-End
 * 7.2324e+14 cc of stone, * 214.35 = 1.5503e+17 Joules +
 * 3.6162e+15 cc of soil, *0.7 = 2.5315e+15 Joules =
 * Total: 1.5716e+17 Joules

High-End
 * 1.0849e+15 cc of stone, *214.35 = 2.3255e+17 Joules +
 * 5.4243e+15 cc of soil, *0.7 = 3.797e+15 Joules =
 * Total: 2.3635e+17 Joules

But wait! If this was a town, it probably had a bunch of buildings on top of it that also got pulverized.

I'll be making some assumptions, of course, for my purposes here-

For starters, I will say that these city blocks are | roughly average in size (96465 sq. ft): accounting for the streets, I'll round it up to 100000 sq. ft. Using this example from my own home town (a suburban area in a larger town- but still shy of being a city outright- seems appropriate) as a model, I'll assume an average of four buildings in each block, each about one-fourth as wide in each dimension as the city block itself (311 feet = 94.79 meters, /4) = 23.6975 meters except height, which I'll take to be roughly two stories on average (20 feet) = 6.096 meters. Finally, I will assume 90% hollowness for these buildings.

This makes each building (23.6975^2 * 6.096) /10 = 342.334 cubic meters, or 342334000 cubic centimeters (I will assume of stone here.) Times 16 is 5477344000 cubic centimeters, per 100000 square feet of the town destroyed, on average...

So, 54773.44 cc/sq. foot. But how many cubic feet are 21.7 km²? Well, according to the almighty Google,

233580000 sq. feet.

Times 54773.44, = 1.2794e+13 cc of stone pulverized... * 214.35 J/cc,

Equals 2.7424e+15 Joules. ...oh. So, that was basically unimportant, huh.

So, adding that to the other values,


 * Low-End: 1.599e+17 Joules, or 38.22 Megatons of TNT. City level.
 * High-End: 2.3909e+17 Joules, or 57.14 Megatons of TNT. City level+.

Feat 2
So, this happened at some point or another. Fortunately, a gigantic fireball is easily calculable-

3000 meters/21 px = 142.86 m/px

x (518/2) = 29857.74 meters in blast radius, or ~29.86 kilometers.

We can really just use | Nukemap Classic from here to reverse engineer the yield a fireball of the size would likely have-

The long story short is that, after a lot of trial and error, I got 30.48 Gigatons of TNT: Island level: as a final result.

Final Tally
Feat 1 (Low-End): 38.22 Megatons of TNT

Feat 1 (High-End): 57.14 Megatons of TNT

Feat 2: 30.48 Gigatons of TNT