How did I not find Symphogear sooner, the multimedia Franchise of manga, TV series, video games, and music started in January 2012 and finished its final season in September 2019. It’s basically summed up by magical girl idols combat evil using music, power armor, and the power of awesome. I mean imagine Magical girl Lyrical Nanoha combined with Bubblegum Crisis, and idol singers, you simply can’t beat that. Of course, this also means that there probably isn’t a whole lot of science to examine, but in this case you would be wrong.
Yes, there might be some spoilers, but not too many as I haven’t had to watch much of the series beyond some clips on YouTube at this point. Now onto the science, which is the opening scene or at least I think it is the opening scene of season 3 Symphogear GX.
Is Ulaanbaatar heavily populated?
The season starts with a space shuttle burning up on reentry or crashing into a populated area, Ulaanbaatar. This made me chuckle a bit, because someone does ask if it is a populated area. The reason is I actually lived in Mongolia, specifically Ulaanbaatar for 3 years (2014-2017), and yes, it is a heavily populated area with 1.3 million people as of 2013 according to Wikipedia. It’s actually probably closer to 1.5 million at least according to the Mongolian’s I worked with. What you also need to know is that Mongolia is the worlds least densely populated country outside of a few remote islands, so I can see why it would make sense to ask the question, it’s just that 50% of the country’s population lives in Ulaanbaatar. It also happens to be quite small so a miss of only 5-10 miles from the city center could put you completely outside the city and pretty much in the middle of nowhere.
Either way Ulaanbaatar is saved, due to the timely intervention of Tsubasa, Chris, and Hibiki who were launched into space while riding inside a missile.
Once in space they land on the shuttle using the thrusters on their symphogear suits to slow the shuttle down.
This changes the crash site from Ulaanbaatar to the Karakorum Mountain range the second highest mountain range in the world located on the bord of China, India, and Pakistan.
It is also home to K2 the second highest mountain in the world, which poses a bit of a problem for everyone as mountains tend to be very big and very much not flat, so not the best places to try and land a space shuttle.
Thus, the logical solution is of course shoot tons of missiles at a mountain and blow it up because it is in your way.
Spoiler, between Chris’s missiles, and Hibiki punching it, it works.
Thus, lowering the height of K2 quite a bit.
According to Symphogear, K2 (8,611m) is now somewhere between 8,585m and 8,517m in height, a loss ranging from as little as 26m up to 94m. It is not until the end of the scene that we get a clearer picture of K2 and can calculate its new height. This not exactly the easiest thing to do and I was unsure of how to approach it, but I found someone else has already done the math. (Thanks to ThatAnonGuy)
I can’t find any arguments with the numbers and K2 is a bit shorter than what the anime told us, however now I can determine just how much power Hibiki and Chris used to blast through the mountain. To do the math, I am going to assume that K2 is a cone, and I will be determining the volume of a segment of a cone specifically the segment that Chris and Hibiki destroyed as we can see what looks like a smaller pyramid (the peak of K2), sitting on a plateau (the rest of K2).
Frustrum of a cone
Given the radius of the top of the segment, the bottom of the segment, and the height of the segment, it is possible to calculate the volume.
V = (1/3) * π * h * (r12 + r22 + (r1 * r2))
I’ll save you walking through all the steps but it comes out to 59,300,000 m3 or 23,720 Olympic swimming pools.
Heat of Vaporization
The heat of vaporization is the amount of energy needed to transition a material into a gaseous state. It is a good number to use in our Symphogear scenario given that we see no clouds of dirt in the sky or large mud slides in the aftermath of the event, so we can assume the rock was completely destroyed. Sadly, finding the heat of vaporization numbers for the Earth’s crust, or rocks like granite and slate which make up the bulk of the Karakorum mountains, has proven impossible, at the time of writing. So instead I am going to the numbers from my post on Natsu’s dragon slayer magic in Fairy Tail.
Energy needed to lower K2 by 150 meters
Volume of Meteor crater = 48,694,790m3
Energy used to create meteor crater = 10 megatons
Volume removed from K2 = 59,300,000 m3
Energy used to lower K2 = 12.2 megatons
In other words, the combined force of Chris and Hibiki is roughly 761 Hiroshima bombs. No wonder they needed special permission from the UN to go and rescue the shuttle.
I knew the number I got would be big, but if anything, I think I probably under cut the number a bit since I used Meteor crater as a reference instead of using the heat of vaporization. Either way the girls of Symphogear are extremely strong, as seen here where Hibiki throws the space shuttle over a building.
In this case Hibiki used around 40 million newtons of force to throw the shuttle over the building, or just a little more force than a Saturn V rocket at liftoff. Anyway, I am looking forward to watching Symphogear in the near future.