Credit for the original Caculations Goes to Amae
Supercell Statement[]
Upon analyzing Amae's calculation I found that the he seems to have lowballed the feat by using nimbustratus thicknessand pixel scaling, something he may not have needed since we had statements from the anime itself calling the storm a supercell, meaning the proportions of the cloud were indeed much larger than what the blog originally assumed.
the statement in question
For reference we have the scene in the picture that comes from episode eleven, around the 15:00 mark, the japanese government issues an evacuation order soon after that.
Storm Dimensions[]
A supercell has the following dimensions according to the wiki page:
"can dominate the local weather up to 32 kilometres (20 mi) away."
This gives us a radius of 16,000m to work with
On further research to get a more accurate height that could be used I stumbled upon this
"The cumulonimbus base may extend several miles across and occupy low to middle altitudes- formed at altitude from approximately 200 to 4,000 m (700 to 10,000 ft). Peaks typically reach to as much as 6,000 m (20,000 ft), with extreme instances as high as 23,000 m (75,000 ft)."
Considering this is a supercell strong enough to warrant a city-wide evacuation order, using the 23,000 m figure isn't far fetched.
Gives us a range of 19,000 m to 22,800 m to use as the height of the cloud, for convenience I'll use the average which is 20,900 m as the height, this also close to the 21,000m peak we have in the supercell wiki page.
Timeframe and Speed[]
https://www.youtube.com/watch?v=hB___qgWEp8
"Timeframe: 41.124-38.079 = 3.045 seconds"
"Velocity: 16000m/3.045s = 5254.5m/s"
Thanks to Crazystarf for figuring it out.
Original Timeframe
"Madoka's arrow takes 16 frames (I'll post them later) to part the cloud."
"Time = 16/24 sec (16 frames)"
Which gives us a speed of 24,024.02 m/s to work with
New Kinetic Energy ver 1.1[]
Volume of the Storm : 3.1415 * 16000^2 * 20900 = 16,808,281,600,000 m^3
Mass: Volume * (1.003 kg/m^3)= 16,858,706,444,800 kg
KE= 0.5 * Mass * Velocity ^2
KE = 0.5*16858706444800*5254.5^2 = 232,732,505,826,561,153,600 joules
or 55.62 Gigatons of TNT
Kinetic Energy (Original timeframe)[]
̶V̶o̶l̶u̶m̶e̶ ̶o̶f̶ ̶t̶h̶e̶ ̶S̶t̶o̶r̶m̶ ̶:̶ ̶3̶.̶1̶4̶1̶5̶ ̶*̶ ̶1̶6̶0̶0̶0̶^̶2̶ ̶*̶ ̶2̶0̶9̶0̶0̶ ̶=̶ ̶1̶6̶,̶8̶0̶8̶,̶2̶8̶1̶,̶6̶0̶0̶,̶0̶0̶0̶ ̶m̶^̶3̶
̶M̶a̶s̶s̶:̶ ̶V̶o̶l̶u̶m̶e̶ ̶*̶ ̶(̶1̶.̶0̶0̶3̶ ̶k̶g̶/̶m̶^̶3̶)̶=̶ ̶1̶6̶,̶8̶5̶8̶,̶7̶0̶6̶,̶4̶4̶4̶,̶8̶0̶0̶ ̶k̶g̶
̶K̶E̶=̶ ̶0̶.̶5̶ ̶*̶ ̶M̶a̶s̶s̶ ̶*̶ ̶V̶e̶l̶o̶c̶i̶t̶y̶ ̶^̶2̶
̶K̶E̶ ̶=̶ ̶0̶.̶5̶*̶1̶6̶8̶5̶8̶7̶0̶6̶4̶4̶4̶8̶0̶0̶*̶2̶4̶0̶2̶4̶.̶0̶2̶^̶2̶ ̶=̶ ̶4̶,̶8̶6̶5̶,̶0̶3̶1̶,̶0̶2̶6̶,̶5̶9̶6̶,̶7̶0̶5̶,̶2̶4̶1̶,̶1̶9̶2̶ ̶j̶o̶u̶l̶e̶s̶
̶o̶r̶ ̶1̶.̶1̶6̶2̶7̶7̶ ̶T̶e̶r̶a̶t̶o̶n̶s̶ ̶o̶f̶ ̶T̶N̶T̶
Note: I originally ommitted this becuase the alleged time frame didn't match up with the video (dead links were also major factor), at this point I'm certain this is not accurate at all and general consensus seems to lean more towards the first result.
New Arrow Speed[]
"After parting the cloud, Madoka arrow scatters into several and crosses the radius of the cloud in a short amount of time".
"Distance = 4702 meters"
"Time = 5/24 (5 frames)"
"Speed = 22,573.6 m/s or Mach 66"
All that's needed to do here is replace distance with the radius of 16,000 meters
Speed 16 000/0.2083s = 76,800 m/s
or Mach 223.9067
Arrow Speed Ver Crazystarf[]
"Distance the arrow moved: (336.7/318)*18990m = 20106.7m (or 24130m if using 22.8km for cloud height)
Velocity: V = 20106.7m/0.667s = 30145m/s, or Mach 88.6; High Hypersonic+ (Mach 106.3 if using 22.8km for cloud height)
Edit: Height of cloud updated to 19000m & 22800m (min & max) instead of 17000m based on the suggestions below."
Note: Crazy's version uses a timeframe ripped straight from the anime as well, considering the links for the frames in Amae's calc are now dead I'm leaning more towards Crazy's result.