Description[]
Hello, everybody! I am back with another calculation! And this time I make my jump to a series I have recently binged and enjoyed to death: Kill La Kill. I will be calculating Ryuko's Tennis Ball feat that she does as early as Episode 2. O_O
Explanation[]
Recently, this calculation has been brought up and discussed about the currently accepted calc. There are two problems with it: weird scaling, seeing as in one of the steps, one of the pixel values is pulled out of nowhere. And two, it was assumed that Omiko hit those balls at the speed of a peak human. However, we see that she hits the tennis balls so fast, she was able to blitz Mako (someone who could block bullets). So, here is this calc to re-work the old one.
Thread in which the changes were agreed on is here.
Context[]
Straight forward: Ryuko slices 220 tennis balls. Tennis balls on average are about 0.0686 in diameter (as stated in the previous calc), and Ryuko Matoi is approximately 5'3" (1.60m).
Calculation[]
Okay, first order of business, finding the distance when Ryuko started to slice the balls to find the time she took to slice them all. We shall do this by first seeing how far Omiko and Ryuko were.
Using head to body ratio: 1.60m / 8 = 0.2m
4974px / 318px = 15.64
15.64 * 0.2m = 3.12m
Neat. So, next shot to see how far the balls are the moment she started slicing them.
Okay... Angsizing:
Distance Ryuko is from the POV = 1.60m * 4890px/[4689px*2*tan(70deg/2)] = 1.2 meters
Distance the farthest Tennis ball is from the POV = 0.0686m * 4890px/[57px*2*tan(70deg/2)] = 4.20 meters
Distance Ryuko is from the Tennis ball = 4.20 meters - 1.2 meters = 3 meters
To find the distance the Tennis balls traveled before they were sliced, we shall subtract the previous 2 distances.
3.12 meters - 3 meters = 0.12 meters
We got our distance. For this calculation, I will assume the balls were traveling as fast as the speed of sound for the reasons in the Context section.
0.12 meters / 343 m/s = 0.00035 seconds
As for the distance Ryuko covered by swinging her Scissor Blade? I will assume she swung the sword 135 degrees everytime. But first, to find the length of the sword and her arm:
5473px / 4689px = 1.17
1.17 * 1.6m = 1.87 meters
C = 1.87m * 2 * 3.141592654 * (135/360) = 4.40 meters
Okay. Seeing as she sliced the balls 5 times, as shown here , I shall do the following:
4.40 meters x 5 = 22 meters
220 balls x 22 meters = 4840 meters
Now that we got both components... Now... For the moment of truth...
4840 meters / 0.00035 seconds = 13,829,324 meters per second.
Conclusion[]
To convert this to Mach and %c... 13,829,324 m/s is Mach 40,318 or 4.6% c. So... Sub-Relativistic.
Very nice upgrade! Almost over 10x faster than before!
Revision[]
Seeing as what Ryukama suggested is deemed as calc-stacking, I guess I shall readjust this using the speed of the tennis ball used in the previous calc instead. So... Back from the top using the same pixelscaling, angsizing, distances and with a sliiiiightly larger angular distance, seeing as her arm was literally to the right of her in the next shot.
0.12 meters / 73.167 m/s = 0.00164 seconds
5473px / 4689px = 1.17
1.17 * 1.6m = 1.87 meters
C = 1.87m * 2 * 3.141592654 * (140/360) = 4.57 meters
4.57 meters x 5 = 22.85 meters
220 balls x 22 meters = 5027 meters
5027 meters / 0.00164 seconds = 3,065,243 meters per second, which is Mach 8,937 or 1% c. Still Sub-Relativistic.
Nice. Under 2 times faster than before.