Ryuko's final attack in the series
In the Kill la Kill OVA, Ryuko used the tip of her scissors to cut the cylandrical structure below, wider than the arena-like area containing the Honnouji Academy building, which when turned into a mecha, dwarfed the city block length Great Naked Dagger form of the S.S. Naked Sun. The resulting explosion from said cut resulted in the entire city, which is so high that it goes above the clouds (like a really tall mountain), somehow sinking.
Some screenshots of the feat and what it did
A video of the feat:
Kill La Kill OVA - Ryuuko VS Hououmaru
(Low end) Size Scaling 1:
How big was this cylinder, that was snipped to dust? And just how big is the city? Here is one answer.
Scaling from Japan's Tokyo Bay, the Honno city is 11.5 KM accross. And since it also hasa height comparable to it's width, we're practically talking about an artificial Mount Everest.
The cylinder destroyed is nearly two kilometers wide (1.748 KM). Now this scaling may seem questionable, because we're scaling from a satellite picture.. One might question, is the cylinder being inflated to look larger than it actually is, since its over ten kilometers above the ground? However, that actually isn't the high end scaling.
(Higher end) Size Scaling 2:
In Ryuko's fight against Hououmaru, the Honouji Academy mecha picks up the "Great Naked Dagger" and fights Ryuko with it.
The Nudist Beach's trump card, the Great Naked Dagger!
The Great Naked Dagger is the form that S.S. Naked takes when it transforms from a ship back into a giant flying blade by pulling its two sails into a single blade. The next section of the calc will attempt to figure out the Great Naked Dagger's size.
Average Japanese female height: 5'2" = 1.5748 Meters
From this scaling, SS Naked is definitely over a hundred meters wide (105.1 M), and at least MCB in length (706 M) Here's a GIF that pretty much shows SS Naked (and Great Naked Dagger) is on the City Block scale of length.
Great Naked Dagger transforms into the S.S. Naked Sun
Now when we try to scale from it.. the numbers get "Utterly incomprehensible!". Nearly ten times the 550 meter result of the arena's first calculation, and the cylinderical structure below it is even bigger!
It's important to remember that this is a cutting attack, so nothing lower than pulverizaion values are involved for the part of the city that was destroyed
In support of the high end, the Original Life Fiber is the size of mountains, yet can still fit in the arena atop the city
The Original Life Fiber
And finally a relevant feat:
Kill la Kill - Mako & Everyone is Helping-0
- UPDATE 7/21/15*
Scissor Blade Size Calc:
Now I will attempt to find the dimensions of Ryuko's Graduation Ceremony Finale
First, the width:
Now the gigantic one is hard to scale from, so I will use a smaller version
- UPDATE 2 7/22/15*
There's at least two, probably three speed feats in this fight. The first is a casual reaction feat.
Speed feat 1:
Senketsu helps Ryuko "in spirit" by giving her the Scissor Blades so she could fight Hououmaru. First we see the blade at a rather high altitude with the black background of space, then close to a second later its stated to be in the Earth's stratosphere. Ryuko, as she is falling herself (Hououmaru caused a small fissure in the ground, Ryuko fell in) grabs the blade.
The timeframe between when it falls from the stratosphere and arrives to Honnoji Academy is 3;18, which (since the number after the decimal only goes to 29) translates to about 3.6 seconds.
The edge of the stratosphere at moderate latitudes is about 50 kilometers up. However, as calced earlier, Honno City is 11.5 KM in diameter, and similar in height. So this must be subtracted from the distance travelled.
50 - 11.5 = 38.5 KM
38.5 / 3.6 = 10.69 KM/s
or Mach 31.4
Speed feat 2:
Now the second feat is a movement feat. After Ryuko cuts through the Honnoji Academy mecha, there's an explosion, and she immediately appears afterwards on a solid surface in front of the explosion, and the giant Scissor Blades aren't in sight, later revealed to have been changed out of Decomission mode and left on the sinking island. Since this all occurs in less than a second,frame by frame analysis is required to determine the last frame where the Decomission mode Scissors were visible.
The pink substance represents Senketsu's spirit, it follows Ryuko after she performs the feat and flies into her hair. Since the first frame where the Decomission mode Scissors weren't visible was 2:23;01, and the first frame where Senketsu's spirit is visible is 2:23;16, the timeframe is at most about half a second.
Ryuko both took the time to turn her gigantic Scissor Blades into their normal form and return to the sinking Honno City to talk to Hououmaru and Satsuki, so I will use the length of the blade (with its handle) as the minimum distance travelled.
Here's the low and high end size of the Scissor Blade: 14.67+ Kilometers - 69+ Kilometers
14.67 / 0.5 = 29.34 KM/s
Mach 86.29
69 / 0.5 = 138 KM/s
Mach 405.8
Please note that the calc didn't take account for the extensions at the end of the main handle, so the absolute minimum speed should be above Mach 86.3. This is awfully close to Massively Hypersonic, and the low end really contradicts massive objects such as S.S. Naked or the Original Life Fiber even fitting into the Honnoji Academy's arena.
Results:
Size:
S.S. Naked Length: 706 Meters
Honno City Diameter: 11.5 Kilometers - ???
Honnouji Academy Arena: 550 Meters - 5.36 Kilometers
Cylindrical Structure: 1.75 KM - ???
Giant Scissor Blades Tip Width: 1.75+ Kilometers - 8.23 Kilometers (The ratio of this can be used to quickly calculate the lower ends of the length of the blade)
Giant Scissor Blades Length: 7.31+ Kilometers - 34.39 Kilometers
Giant Scissor Blades Length with Handle: 14.67+ Kilometers - 69+ Kilometers EDIT: It's actually a bit longer with the handle
Speed:
OVA Ryuko's Casual Reactions: Mach 31.4
OVA Ryuko's Speed (Likely similar to her actual reactions): Mach 86.29 - Mach 405.8
Key:
Low End - Satellite scaling
High End - S.S. Naked scaling