Monument Mythos Calculation: Dark Alaska.

Okay, this is basically a repost of my calculations here, just cleaned up, showing my data, and incorporating the first calculation I made into the fold.

So, the basic idea for the calc is that in The Monument Mythos, during the events of THE MISSSING EYE OF JESUS CHRIST, it was revealed the Last Son of Alcatraz tried to return to Alaska after his interference during the Korean War. However, in response, the US sent a wave of nuclear missiles all targeting him to try and capture him. They succeeded in capturing him, and this attack reduced Alaska to an uninhabitable wasteland known as Dark Alaska. I'm going to be calculating how strong the total explosive power of the warheads would need to be in order to spread enough radiation to reduce Alaska to said wasteland (Note: I'm aware of the stardestroyer.net tool, but it didn't have what I needed)

Presumptions/Assumptions

• All the missiles hit simultaneously rather than piecemeal
• The radiation spread evenly throughout Alaska
• The nukes were surface blasts rather than air blasts
• For Some Calcs: The area of effect was a perfect circle

Settings used for Nukemap.org (The website which I used for this calc)

• Nuclear Warhead Power: 10-100 megatons of TNT, using only multiples of 10 on that line (10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 megatons)
• Detonation Site: about 226 km northwest of Fairbanks at 169.67642 degrees with due east being 0 and due north being 90, nearby Tanana. This is about the center of the state.
• Height of Burst: Surface (I figured that the blasts were specifically targeting him, so they would likely be trying to directly hit and obliterate him, hence I picked a surface blast rather than an airburst)
• Other Effects: Show Radioactive Fallout
• Area used: Approximate Area Affected (km^2)
• Dosage per Hour Used: 1000 rads/hour, 4709 rads/hour, 10000 rads/hour, and 15832 rads/hour
• Designated Areas: 2010 Census for Alaska's Land Area (1,477,953 km²), and four different circular Areas, each with a radius equal to the distance between the blast site and one of four specific points listed below. The points are:
  • Barrow, Alaska (radius 823.26 km, area 2129236.5 km²)
  • Shinshaldin Volcano (radius 1161.62 km, area 4239142.7 km²)
  • Prince of Wales Island (radius 1401.7 km, area 6172484.7 km²)
  • Attu Island (radius 2017.26 km, area 12784202.1 km²)

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I decided to use 1000 rads/hour, 4709 rads/hour, 10,000 rads/hour, and then 15,832 rads/hour for this calculation. 1000 rads/hour is the default baseline for the top tier of Nukemap, 4709 is the absolute maximum for a 10 kiloton surface blast which is the minimum blast power used beside 0 kilotons here, 10,000 rads is similar to the radiation of a criticality incident at a nuclear power plant (Namely the one in Wood River Junction in 1964), and 15,832 rads is the upper limit of radiation for a surface blast according to Nukemap.org.

For the areas, I used the land census data for Alaska because it was the closes thing to an official area, but I used the radii to take into account that the affected area is likely going to be similar to a circle (Assuming no wind). I chose four different points to represent possible radii which could match up with the idea of "All of Alaska was nuked into uninhabitability." These points were: The town of Barrow (the northernmost town in Alaska), Mount Shinshaldin (a notable landmark in the Aelutian Islands), Prince of Wales Island (The southernmost island in Alaska to not be part of the Aelutian Islands), and Attu Island (the westernmost island which is a part of Alaska).

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Process for the calculation

1. Find and record the area of each of the designated radiations for every nuclear blast tier.
2. Use dCode to find an exponential relation to determine the radiation-affected area (A) from the blast power (x) (link to dCode here).
3. Invert the equation to get the formula for x based on A.
4. Find the radii between the blast zone and the four designated points.
5. Plug in the areas stipulated below into the formulas, and find the explosive power needed for the warhead to irradiate the area.

Blast Power (megatons of TNT)	Area (1000 rads/hour) (km^2)	Area (4709 rads/hour) (km^2)	Area (10000 rads/hour) (km^2)	Area (15832 rads/hour) (km^2)
0	0	0	0	0
10	11260	237	-	-
20	19610	1460	-	-
30	26,230	2740	-	-
40	32,590	4110	-	-
50	38,900	5550	784	-
60	45,220	7050	1340	-
70	51,620	8610	1950	-
80	58,100	10240	2600	-
90	64,700	11390	3290	-
100	71,410	13680	4020	479

Here are the formulas derived from the areas, with A being the area of the radiation and x being the explosive power of the warheads.

1000 rads/hour: $A=23338.7+(5.79809\times10^{-39})\times e^{0.982232x}$, $x=\frac{\ln(10^{39}\times\frac{A-23,338.7}{5.79809})}{0.982232}$

4709 rads/hour: $A=5138.62+(2.23504\times10^{-39})\times e^{0.980489x}$, $x=\frac{\ln(10^{39}\times\frac{A-5138.62}{2.23504})}{0.980489}$

10000 rads/hour: $A=660.63+(4.84944\times10^{-40})\times e^{0.980489x}$, $x=\frac{\ln(10^{40}\times\frac{A-660.63}{4.84944})}{0.980489}$

15832 rads/hour: $A=1+0.99134\times e^{0.134018x}$, $x=\frac{\ln(\frac{A-1}{0.99134})}{0.134018}$, Note: I only had one point to go off of, so this is why the equation looks so different from the rest

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So, for the radii, I took the map I used, screenshotted it, and then used some pixel measurements along with the scale to measure the distance between the designated points and the blast epicenter. Below are the measurements I used.

The image used for the calculations, along with markers to determine the radii.

White Box: The scale, it measured 89 pixels wide, and matches up to the scale of 300 km, so that's the conversion rate that'll be used here.

Process for finding the respective areas of the circles needed using the boxes

1. Find height and width of the rectangles.
2. Find distance by finding the hypotenuse of the triangles formed inside the boxes ($Distance^2 = Height^2 + Width^2$).
3. Convert distance from pixels to kilometers ($Radius = Distance(px) \times \frac{300}{89} (\frac{km}{px})$)
4. Find the area of the circle ($Area = \pi \times Radius ^2$)

Barrow/Green Box

• Height: 237 px
• Width: 59 px
• Distance: 244.23 px
• Radius: 823.26 km
• Circular Area: 2129236.5 km²

Shinshaldin/Red Box

• Height: 301 px
• Width: 161 px
• Distance: 341.35 px
• Radius: 1161.62 km
• Circular Area: 4239142.7 km²

Prince of Wales Island/Blue Box

• Height: 301 px
• Width: 291 px
• Distance: 418.67 px
• Radius: 1401.7 km
• Circular Area: 6172484.7 km²

Attu Island/Yellow Box

• Height: 485 px
• Width: 345 px
• Distance: 244.23 px
• Radius: 2017.26 km
• Circular Area: 12784202.1 km²

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And the final results are:

1000 rad/hour

• Alaska Land Area: 104.08 megatons of TNT
• Radius between blast & Barrow: 104.46 megatons of TNT
• Radius between blast & Shinshaldin: 105.16 megatons of TNT
• Radius between blast & Prince of Wales Island: 105.55 megatons of TNT
• Radius between blast & Attu Island: 106.29 megatons of TNT

4709 rad/hour

• Alaska Land Area: 105.25 megatons of TNT
• Radius between blast & Barrow: 105.63 megatons of TNT
• Radius between blast & Shinshaldin: 106.33 megatons of TNT
• Radius between blast & Prince of Wales Island: 106.71 megatons of TNT
• Radius between blast & Attu Island: 107.46 megatons of TNT

10000 rad/hour

• Alaska Land Area: 106.81 megatons of TNT
• Radius between blast & Barrow: 107.19 megatons of TNT
• Radius between blast & Shinshaldin: 107.89 megatons of TNT
• Radius between blast & Prince of Wales Island: 108.27 megatons of TNT
• Radius between blast & Attu Island: 109.02 megatons of TNT

15832 rad/hour

• Alaska Land Area: 106.06 megatons of TNT
• Radius between blast & Barrow: 108.79 megatons of TNT
• Radius between blast & Shinshaldin: 113.93 megatons of TNT
• Radius between blast & Prince of Wales Island: 116.73 megatons of TNT
• Radius between blast & Attu Island: 122.17 megatons of TNT

So, the final result is that all of the calcs are all on the low end of Mountain Level for the US' nuclear arsenal directed at the Last Son. But how does the Last Son's durability compare? Also, from here, I will be using the 122.17 Megaton calc, as it is the most likely to produce a "Dark Alaska" (aka a charred and uninhabitable nuclear wasteland).

As mentioned above, the nuclear missiles were specifically targeting him, so it was likely the explosions were near-point blank. Knowing that, I will use 1 meter for the calc.

Starting with Intensity, we have $I=\frac{P}{A}=\frac{1.2217\times10^{8}}{\frac{4\pi r^2}{2}}$.

The power, as mentioned above, is 122.17 Megatons, or 122170000 tons of TNT. The area meanwhile is a hemisphere due to the surface blast. Using the radius of 1 meter, the final radius is 2π. Doing the division, the intensity of the blast is 19,443,959.3975 tons of TNT per square meter.

Now we find the actual energy the Last Son was hit by using the formula $E=I\times CA$

I, which is the intensity, is 19,443,959.3975 tons of TNT per $m^2$. For Cross-sectional Area, it's a bit trickier. Now, it is mentioned the Last Son can grow to be significantly larger than a normal man, but he does prefer to be human-sized. Using THE LAST SON OF ALCATRAZ, we can get a rough estimate that he could grow up to (Calced the Chumlea equation with this image to get an an assumption of 20 years to get a rough estimate) 4.1551 meters tall. Scaling up the area assuming the average man is 0.68 $m^2$ and 1.7526 m tall, the Last Son's CA should be about 1.6121 $m^2$. This is the highball. The lowball is an average man, while the highball is the giant.

Plugging it all in, the results are

• Lowball: 13,221,892.3903 tons of TNT, or 13.222 Megatons of TNT
• Highball: 31,345,606.9447 tons of TNT, or 31.346 Megatons of TNT

Assuming the lowball is the more accurate guess, the most likely durability for the Last Son to have is 13.222 Megatons of TNT, or City Level.

Final Result: 13.222 Megatons, City Level