To Aru Kagaku no Railgun 21

Those are bigass fireworks. How do I know? Glad you asked.

Assuming the constellation on the right side is a badly drawn Ursa Major, we can figure out the radial size of the firework by using the radial distance between Merak and Dubhe, which is generally accepted to be 5°.
Using the blue firework at the top as reference, we can see it is approximately 3x the radial distance = 15° in radius.
It appears at 00:12.763, and the sound is heard at 00:14.515, giving us a 1.752 second interval between explosion and when it reaches our ears. (Speed of light is negligible in this case.)
The speed of sound in 25°C summer air at 80% humidity is 347.65m/s, giving us ~609m distance to the firework's center.
Simple trigonometry tells us that its radius is then tan(15°)*609m = ~163m
This means the firework is about 1070 feet wide, or 3 times the length of a football field.
Addendum courtesy of Bored:
At 50 feet per shell inch, this means that this firework had a 21.4" shell. By comparison, the largest naval guns ever mounted were the 18" guns used on Yamato class battleships.

ursa major boom

Here, verify it yourself. And it's a bit harder but you can still see the stars in the XviD too.

Oh, and the timer position has been filled. Thanks to all that inquired about it.

On a different note, did you know?

Comments (80)

Findyat last~
Thank you mazui~
caramellothats pretty much of physics/calculation =v=
thanks for the subss
kousukethanks for the release! and for the unrelated note, i know :D
DetectiveAhh! Thanks very much! Always being consistent makes my life easier and brings less anxiety.
BoredGoogle says a fireworks blast diameter is usually ~50 ft per shell in, so assuming calculations and assumptions are correct, that would be a 21.4 in shell. The largest navel guns ever mounted were 18 in on the Yamato class btw (Wiki)
AzzyThank you.

You're a nerd. And I say that most lovingly. :)
DazzaYou know, having done all that in Maths/Physics in the last year or so.

You are correct, sir!

Why are you not making heaps of money and marrying Japanese chicks?

Btw, thanks for the fast release as always ^_^
mosheeI feel bad for not knowing who that in the last picture is. I have a feeling I do, except I don't.

Forgot to mention, my Friday is now complete :D
DauntaeThank you for the release! ^^
Just curious, what is that anime in the new "MAZUI" banner that has been put up atop of this site (The names of those two characters as well, if possible) if anyone knows?
spazerIt's from Angel Beats, an anime by Key which has not yet aired.
watI'll just leave this here

also, apparently anything above 12" is uncommon even for large shows.

tl;dr: big-ass indeed.
SharmLol, NADEKO-CHAAAAN~~! Wondered when someone will mention that
Geese1Thanks for the release!

Have you made any decision on which shows you'll be subbing next season?
Azure_ShockwaveNadeko!!!! Great episode of it today!!!

Haruhi, Spice and Wolf, Railgun, Katanagatari, and now(Well it seems like it) Angel Beats?
You guys sub like the best animes ever!
エビCirno's Maths class o.O?
DauntaeThank you very much for your feedback. I researched the origins of the show and found myself quite interested with the synopsis. Not to mention it's from those that made Kanon, Clannad and Air. I'll have to bookmark that later, but that might not be necessary if Mazui have plans to sub it... ;)
IronheadKids, this is why you stay in school... math can produce as many laughs as headaches. (^:
methi like meth...
RedI think the question is...As suggested by the new banner, do you, Mazui, plan to sub Angel Beats?R
methnah jk, but thxs for the math
Red^That 'R' is a typo.
i assumed that the anime series may be taking place in the future, maybe near or up to 60 years in advance from present day.
it is likely that given the legal situation and safety concerns of said future, it is likely that that 21 1/2" fireworks could be used, devised and implemented, but however unlikely that any shell of that would be used in regards to safety issues because:

said shell with dimensions of 21.4"d by ~20"z, typical.

v = 3.14(11.2"^2)20"

v ~ 210.168"^3

given 1^3" gunpowder ~ .55oz

210.168(.55) = 115.5924oz of stored gunpowder

the amount of gunpowder used in a 105mm shell casing was roughly 20 kg of gunpowder.

20kg = 705.4792389916082oz
115.5924oz = 3.27698941687425 kg
the 105mm shell had an explosion velocity of roughly 1100 foot pounds per second

55 foot pounds per kilogram of gunpowder

3.27698941687425(55) = 180.23441792808375 foot pounds per second.

1 foot pound = 1.3558179483314 newtons

1.3558179483314(180.23441792808375) =

244.36505873395860759851195475 newtons

why is all this relevant?

a 10 gram bullet to the head at 3.5 newtons is all it takes to kill a person

my point is this: based on the amount of gunpowder inside the charge, considering its potential energy and and the force it inficts within the amount of foot pounds per second equals the same force and energy someone would receive if they were shot 70 times by 10 gram bullets.

or if you wrapped 7 pipe bombs together and threw them down the street and lit them off.

this is the amount of energy we are talking here. there is NO WAY anyone would ever allow such a dangerous BOMB into city limits.

sorry if any of this is going to be easily referenced. I got it mostly from a devil's cookbook.
ThanatosPosts like this are why you guys are such a better sub group than many others.
jonathanasdfyou're forgetting that there's espers there. They don't necessarily have to put gunpowder in the shells. So what if the firework is 300 meters in diameter? That doesn't necessarily mean it had a 21.4" shell. In fact, they don't even necessarily have shells. With different types of espers working together, this thing is not dangerous at all.
my ears.Has anyone else noticed an annoying clicking sound around 02:21 to 03:57, is it only on xvid? maybe just my codecs? Mind you after consistant naggig by somone I finnally upgraded from my "older" codec packs to the latest CCCP pack. Well somone elt me know if I'm not alone in this.
BizounoursBizounours says lol.
Laughed hard when I read the text + nadeko pic :x
Bizounours says thanks.
Nojay Biggest ever aerial firework was a chrysanthemum shell made by a New York company to take the world record previously held by a Japanese manufacturer. It was a bit over 40 inches in diameter. The first attempt prematured in the mortar tube, the second attempt succeeded in getting air. It was fired from a barge in the middle of a river and when it went off it blew in car windscreens half a mile away.
MrTRanCeEviLThank You Mazui~
Huh... Nakedo... NEKEDO-CHAAAAN!!!~ :)
2 thumb up...
GeRo~ GeRo~ (^_^)~
Correction~ N.A.D.E.K.O C.H.A.N~
Azem4144Begin downloading... I got her in my favorite since the first time -nano~ XD Also, I'm just want to ask, after you finished subbing To Aru Kagaku no Railgun, what Anime you're gonna sub then?
Azem4144Wait, don't tell me... Angel Beat? (Judging from seeing the site's banner...)
ehemit's NADEKO-chan in the 2nd pic.
Fenrirwell... i most definitely just got learned.
stothe math made me lol before even watching this ep!
eagle1this anime needs more Touma
OOISHII!#RIt seems all the food in animes are so delicious that after one bite, a person just has to tell the world: IT'S DELICIOUS!

kupiThx a lo!
shinnit would be fun if this will included in my midterms
bobbyhow in the world did misaka know how loliritsu looked like?
flashit looks to me the scene appears to be drawn as if it was emulating film that was shot using an uncorrected wide angle lens. This is common in aerial display filming. The type of lens is used because its design keeps the skyline in normal perspective while distorting object towards the center of the field. Barrel distortion enlarges the center objects like a magnifying glass. The stars off center and closer to the horizon would have a smaller radial distance than the fireworks in the center. The artists in this anime use this style quite a bit. Look at 00:46 the beginning of the OP.
my point was merely to single out the destructive qualities of the firework. all the energy is based on how much gunpwder they would use.

traditionally, fireworks use gunpowder, so i assumed thats what they used. also, just because its a city full of espers doesnt meant they wouldnt consider the amount of explosives they were working with to be considered something dangerous.
i would assume again they would try to prevent property damage, including physical harm, so a charge of that size would have roughly half the same power as what Nojay's reference was, so the city would have to cordon off and reinforce every building, window and anything not tied down within a 32 square block area.
so much work for one firework!
regardless if they did or didnt factor in the destructiveness of the fireworks, the charge size of the one on topic is equal to a small bomb
Even though I haven't watch this episode, but I'm pretty sure that Misaka knows how she looked like because she peeked at Professer's memory which loliritsu was in the memory too. Re-watch episode 11.
rinThanks a lot!
Otakushmm... i'm not sure if this is actually supposed to be part of the video, but at 5:52-5:53 for the xvid, there's some squeaky noise. i think it's either some audio interference or shirai's kissy affection sounds. can someone check this out?
/a/nonI wonder if anyone else analyzes how big the fireworks are in other anime.
IvanTheChemist10x for the ep and the pyromania lessons.
MidgemageI now have motivation to go on to take my AS/A Level in maths...
yubisakimilktea(shiki)I loved reading the comments i feel smarter (lvl up!) now. Maybe i should study more math. XP
bobby@Azem4144: Aah, I remember now. Thanks. I thought "the stripping lady" just had a flashback, but Misaka saw it too. Forgot that x)
Xoleumnow how come none of those brilliant academy city students took note of the size of the fireworks?
NathanCool story bro, but you could also define bigass firework depending on the bang, and you can't find out how much explosive material is compressed in the capacity of the fireworks.

Thanks for the sub.
unfortunately, we can only work with typical numbers here. its very true we cant assume to know what kind of gunpowder they used, how much and how compacted but the numbers do dictate the maximum amount you can physically coalesce inside the volume of the shell. but i digress...the numbers, on my part, are only based on assumptions for typical fireworks, scaled up obviously.
InquirerYou did quite the fine observation of the fireworks. As for the size issue, they (production staff) could well get away with it by the factoring in the setting of the series. They have magic and physic abilities and what have you, not to mention state of the art technology. Making pyrotechnics that leave the average person in awe should be nothing for them.
njamunkynobody is being horror stricken by my observation of how dangerous it is

SnowyNoobYour observations and calculations are quite stunning, but you must also take into account WHO are the people launching the fireworks. Considering that espers are present, perhaps one or more of the crew members handling the fireworks have the ability to alter light waves entering the retina. By using this ability, they could easily make the firework bigger than they actually are, thus pleasing the crowd. That's how I'd like to think about it.
Someone ElseI never thought subbing includes math! Gotta watch out on crazy math geniuses/nerds in any fansub groups as they might kill me of this stuff since math gives me headache, well just a little

By the way, I never knew most of anime lovers are good in science/math, we could make a lab right now with a huge anime banner right now!
johniiireality + anime = wacked ass!

btw, angel's beat! omg! omg!~ finally!!~~
mosheeAll this math is what makes Mazui cool.
Inara963Thank you so much, to the whole team who run and contribute to the site. subbers, encoders, uploaders etc.
Really appreciate all the hard work, keep it up :-)
Shion963Now Railgun just got better.

21.4" fireworks? Academy City is reallu pulling all the stops.
XypherI got a nosebleed just by reading that equation...xD
this is not the place to be racist, im asian too n i hate u ;O
as long ur ON EARTH, bear with it :(
PhantomARFast & Great quality subs, also a XviD encode... what can men what more?!
Thank you, Mazui.
KomidolTakes place in alternate reality. Everything is wrong.
thatthe flower headed thing needs to die.

ShinkuYou mean MY Uiharu.
RedEverybody's Uiharu!

Yes, and that's the reason why I keep coming back to this group. The do great shows and avis you said; What more can we want?^^

Thanks for being this great Mazui, we appreciate you a lot.
EdwardDFMAyay! just a few more hours till they release the 720p of railgun ep 22 xDD
xvid linkcouldn't get this torrent anywhere. Then i found this. Enjoy.
WatcherOops! The mkv link is broken.
SeraphBritish BL 18 Inch Mk1 guns were heavier [151 tons to 147 tons] and fired a heaver shell [1.51 tons vs 1.46 tons] than the Yamato's 46cm Type 94's.

They were deployed on the General Wolfe and Lord Clive towards the end of WW1. 85 rounds were fired in anger.
m3talSeraph, they were talking size of shell, not weight.
skyhackI dunno, "Oh, Edo Rocket" used some REALLY big stuff...