Calculating the power of the explosion

[Frustration]

There has been some dispute regarding the power of the final explosion at the end of the books, so I decided to run a newer calculation, that is(hopefully) more accurate than my previous one.

What we know

• Harmonium is slightly more explosive than dynamite
• Harmonium is often compared to Cesium by Brandon, but is said to not be the same thing
• Telsin put as much as she could into the barrels due to her desperation

What we have to assume

• How much more explosive it is(I'm going to go with 1.3 times for the initial calculations, but if any demolition experts come by with better numbers those would be appreciated)
• density of Harmonium(I'm assuming it's the same as Cesium)
• How much Telsin put in the barrels(This one is the most important and also the most uncertain, there has to be room for the electrolysis arms, and the Trellium, but how much isn't certain. I'm going to run multiple calculations and get those results)

 

Now Dynamite has an explosive force of 190 grams per MJ, meaning that Harmonium would have 1.3MJ per 190 grams

Barrels have a volume of around 158987.3 cm^3,

 

Now the explosion in the books caused large waves to wash over the dockside

In order to create destructive waves Project Seal theorized that 4,400,000 lb bombs would be needed, or roughly the power of the Beirut blast, so our number has to at least get to that point.

 

If 1/3 of the barrel is full of Harmonium:

They can fit roughly 52995.76667 cm^3 of harmonium each, which works out to 99261.07097 grams of Harmonium per barrel.

Which works out to 679.1546961 MJ per barrel, or 2037.464088 MJ overall, which works out to .48 tons of TNT, about the explosive force of the Mark 84

Which is a huge explosion don't get me wrong, but I don't think it matches what we saw.

 

If 1/2 of the barrel was full of Harmonium

They can fit roughly 79493.65 cm^3 in each, which works out to 148891.6064 grams of Harmonium per barrel.

Which works out to 3056.196132 MJ per barrel, or 9168.588397 MJ overall, which works out to 2.19 tons of TNT, with the closest equivalent being the GBU-57A

This is getting closer, but it's only around 30,000 pounds

 

If the entire barrel was full of Harmonium.

Let's assume that the Set had specially made barrels, and can effectively fill the entire thing.

This one's easy as we can just double the last numbers and get 4.38 tons of TNT.

Which isn't even close to amount of force needed, only around 60,000 pounds.

 

So, we must assume that one of our number is off, possibly the barrels are larger, Harmonium is more dense, or Edward is wrong about how powerful Harmonium is.

[alder24]

It's very good math, I like it. 

These calculations seem to be more feasible, yet this time a bit too low. I don't have a book, but Wayne pushed the barrels out of the bubble (by hands or with steel?) so they have to be light enough for him to be able to do it. 100 kg per barrel is enough for pushing by hands, but if steel push was used, it could be higher as he could brace himself using the ship's walls and pewter. 

Difficulty in calculating the correct value is that every number is a variable. Mass, density, explosiveness, volume etc - we know nothing about them. Every number can be vastly different than assumed. And how does ongoing reaction affect remaining Harmonium? I have no idea, but it might blast some of it out of the ship, vaporize it or force it to bond with other elements, reducing the efficiency of the explosion. For now it's like a Drake Equation of Mistborn.

I do agree with the minimum yield comparable to the Beirut explosion - 0.5-1.2 kt. I did it by comparing the damage done by the TLM blast to some other powerful explosions, including nukes (using nuke maps). Powerful nukes quickly had to go out, because the sheer glass-shattering radius would affect the entire city, yet Steris described glass shattering only around the docks, not where she was standing (far side of the city ~10-15 km from the docks). No thermal blast, or blinding power was observed, and they both would be present and would be hard to miss in the scale of mid-large nukes. So it leaves smaller sized explosions, and for this I looked at the Beirut explosion.

We know that some buildings in the docks (docks are outside the outer circle of the city, along the bay) collapsed (judging by the architecture of many buildings in the Basin, I would say they're made with concrete/stone and wood, so they're weaker by today's standards), and windows around the docks were shattered, but not across the whole city. Steris looked right at the explosion and wasn't blinded or burned by it. The biggest damage to the Elendel was expected to be done by the tsunami. We also know that right before Wayne sent Wax into the ocean, the city's lights were visible - that could be somewhere around 10 km from the city, but before the blast occurred the ship would get even closer. Compared to the Beirut explosion, where a hospital less than 1 km away was so damaged that it couldn't function at all, people were being treated outside, and was closed soon after. Homes as far as 10 km were damaged (300 000 people left homeless), and windows were shattered as far as on the airport 10km away.

This damage seems comparable to the damage described by Steris, so the explosion should be on a similar level of power. And with your comparison to Project Seal (2 kt of some explosives) it fits the range. So this is what we should get from math. But you've got 100 times less than we need to reach the low estimate.

[cometaryorbit]

The 'slightly' more explosive than dynamite is based on the Set's early experiments. The Hunters' temple destroying bomb was likely better --their airships are very weight conscious, to the point people need to store weight all the time.

If we assume instead that the early experiments were getting poor yield because the explosion was blowing itself apart before most of the harmonium could react with the water (so the rest of the reaction happened/the energy was released as more dispersed burning rather than one big detonation, like you often see with liquid fueled rocket explosions, for the same reason- the explosion itself keeps fuel and oxidizer from mixing well), it makes more sense.

There's also a WoB that the harmonium water reaction is more energetic than normal chemical, and 1.3x dynamite is less energetic than the best modern solid explosives, and even less than fuel-oxidizer reactions like in liquid fuel rockets.

So I think those early 'slightly better than dynamite' experiments need to have had poor yield.

If the Set's early experiments were getting say 5% yield then it works better, and your 4+ tons of TNT for completely full barrels becomes 80+. That's above the largest conventional weapons and in the range of small tactical nukes (the US Davy Crockett warhead from the 60s had a 25 ton to 500 ton range AFAIK).

It also IMO fits the WoB better since this is clearly beyond the range of normal chemical explosives. Now maybe that WoB just means "more than a normal cesium-water reaction", but "so much more explosive" IMO suggests a major increase, not just 'a bit better than dynamite but worse than other chemical reactions'.

The WoB:

https://wob.coppermind.net/events/117/#e1663

Edited February 5, 2023 by cometaryorbit