Calc Dragon Ball Feats - Android Cell Collection

Super Saiyan Vegeta's Physical Might and Big Bang Attack

The First Feat

The Second Feat


Android 19 = 345 pixels
Crater Depth = 885 pixels

Android 19/Crater Depth = 2.565

Android 19 = 1.83 meters (Yamcha's Height; they both look vaguely to be like it)
Crater Depth = 4.694 meters


Crater Depth = 27 pixels
Crater Diameter = 207 pixels

Crater Diameter/Crater Depth = 7.667

Crater Diameter = 35.989 meters

Volume = (2/3)PIr1^2r2

r1 = Crater Diameter/2
r2 = Crater Depth

Crater Volume = 3,181.713 m^3

200 j/cc

Android Cell Arc Super Saiyan Vegeta's Physical Might = 636,342,600,000 joules or 152.09 tons

Height of Eye = Crater Diameter = 35.989 meters (given where Vegeta appears to be in the air while firing at any rate)


Distance From Horizon = 21.4 kilometers or 21,400 meters

Panel Width = 1361 pixels
Crater Diameter = 1095 pixels

2*atan(Object_Size/(Panel_Width/tan(FoV/2))) = object degree size

2*atan(1095/(1361/tan(70/2 deg)))

Crater Diameter = 58.79 Degrees


Crater Diameter = 24,112 meters

Now for the depth.

Crater Diameter = 1095 pixels
Hill Height = 18 pixels
Crater Depth = 116 pixels

Hill Height/Crater Diameter = 0.016
Crater Diameter/Crater Depth = 0.106

Hill Height = 385.792 meters (so I can try to get anything out of Goku's feat with treating it like an average height for the region)
Crater Depth = 2,555.872 meters

Volume = (1/3)PIr1r2r3

r1 = Distance to Horizon
r2 = Crater Diameter
r3 = Crater Depth

Crater Volume = 690,183,394,646.357 m^3

200 j/cc
6,147 j/cc (melting, got it using SD.net's calculator)
30342 j/cc (vaporization, got it using SD.net's calculator)

Android Cell Arc Super Saiyan Vegeta's Big Bang Attack Yield (Low End) = 138,036,678,929,271,400,000 joules or 32.992 gigatons
Android Cell Arc Super Saiyan Vegeta's Big Bang Attack Yield (Middle End) = 4,242,557,326,891,156,000,000 joules or 1.014 teratons
Android Cell Arc Super Saiyan Vegeta's Big Bang Attack Yield (High End) = 20,941,544,560,359,760,000,000 joules or 5.005 teratons

Super Saiyan Goku's Physical Might

The Feat


I mean, it would appear that the hill I circled is the one Goku pulverized by sending Android 19 into it?

Hill Height = 86 pixels
Hill Top Diameter = 65 pixels
Hill Bottom Diameter = 190 pixels

Hill Top Diameter/Hill Height = 0.756
Hill Bottom Diameter/Hill Height = 2.209

Hill Height = 385.792 meters (derived above, treating the one gotten before as an average for the area)
Hill Top Diameter = 291.659 meters
Hill Bottom Diameter = 852.215 meters


Hill Volume = 107,049,000 m^3

200 j/cc

Android Cell Arc Super Saiyan Son Goku's Physical Might = 21,409,800,000,000,000 joules or 5.117 megatons

Semi-Perfect Cell's Big Bang Crash

The Feat


I'm lucky Cell stays roughly in a static position between shots. Because I'd otherwise be very put out trying to get a full size for anything here.

2-Lane Road = 8 pixels
Palm Tree 1 = 27 pixels
Palm Tree 2 = 35 pixels
Palm Tree 3 = 36 pixels
Palm Tree 4 = 41 pixels
Palm Tree 5 = 43 pixels
Palm Tree 6 = 51 pixels
Partial Island Distance = 336 pixels

Palm Tree 1/2-Lane Road = 3.375
Palm Tree 2/2-Lane Road = 4.375
Palm Tree 3/2-Lane Road = 4.5
Palm Tree 4/2-Lane Road = 5.125
Palm Tree 5/2-Lane Road = 5.375
Palm Tree 6/2-Lane Road = 6.375
Partial Island Distance/2-Lane Road = 42

2-Lane Road = 7.8 meters (here; this is a city, these are definitely at least 2-lane roads, who the fuck would design such a satanic purely one-way travel means for driving?)
Palm Tree 1 = 26.325 meters
Palm Tree 2 = 34.125 meters
Palm Tree 3 = 35.1 meters
Palm Tree 4 = 39.975 meters
Palm Tree 5 = 41.925 meters
Palm Tree 6 = 49.725 meters
Partial Island Distance = 327.6 meters

I'll be using the Palm Tree 3 later for Piccolo's Makuhoidan because it's the middleish value for the region.


Yeah, this is what I meant, arm and orientation to the camera stayed roughly the same, ergo I can use his arm to mark where that piece of island once was.

Obviously, there's a crater, that's kind of what the water was crashing back into the center to refill and all.

Partial Island Distance = 57 pixels
Crater Diameter = 818 pixels

Crater Diameter/Partial Island Distance = 14.351

Crater Diameter = 4,701.388 meters

Volume = (2/3)PIr1^2r2

r1 = Crater Diameter/2
r2 = Crater Diameter/4

Crater Volume = 13,595,547,132.109 m^3

200 j/cc
2260 j/cc (water vaporization)

Semi-Perfect Cell's Big Bang Impact Yield (Low End) = 2,719,109,426,421,801,000 joules or 649.883 megatons
Semi-Perfect Cell's Big Bang Impact Yield (High End) = 30,725,936,518,566,350,000 joules or 7.344 gigatons

Piccolo Jr's Makūhōidan

The Feat


Obviously, there is no reaction to the large plume of dust the first blast caused, nor is there indication Kame House can be viewed from the vantage 17 takes on either. Would lend to suggest the plume of dust/smoke did not rise high enough to be viewable beyond the horizon.

Thus?

Palm Tree = 36 pixels
Height of Eye (Top of Dust Cloud) = 707 pixels

Height of Eye (Top of Dust Cloud)/Palm Tree = 19.639

Palm Tree = 35.1 meters (derived above; Palm Tree 3)
Height of Eye (Top of Dust Cloud) = 689.329 meters
Height of Eye (Tien) = ~1.7 meters

DBL > 3.57 (sqrt(hb) + sqrt(hl))

hb = Height of Eye (Top of Dust Cloud)
hl = Height of Eye (Tien)

Distance to Explosion Epicenter = 98.385 kilometers or 98,385 meters


Panel Width = 705 pixels
Explosion Diameter = 380 pixels

2*atan(Object_Size/(Panel_Width/tan(FoV/2))) = object degree size

2*atan(380/(705/tan(70/2 deg)))

Explosion Diameter = 41.355 Degrees


Explosion Diameter = 74,265 meters
Explosion Radius = 37,132.5 meters

Surface Area = 4PIr^2

r = Explosion Radius

Explosion Surface Area = 17,318,011,306.5 m^2

Subtract the Explosion Radius from the Distance to Explosion Epicenter to get the distance we will be using to find the size of the debris the explosion was ejecting at its edge into the air.

Distance Debris From Kame House = 61,252.5 meters

Panel Width = 705 pixels
Debris Diameter = 12 pixels

2*atan(Object_Size/(Panel_Width/tan(FoV/2))) = object degree size

2*atan(12/(705/tan(70/2 deg)))

Debris Diameter = 1.366 Degrees


Debris Diameter = 1,460.4 meters

Surface Area = (LW)/2

L and W = Debris Diameter

Cross-sectional Surface Area of Debris = 1,066,384.08 m^2

Now the ratio between the explosion's surface area and the debris'

Explosion/Debris = 16,239.938

Volume = (LWH)/2

L, W, and H = Debris Diameter

Debris Volume = 1,557,347,310.432 m^3
Rock Density = 2,700 kg/m^3
Debris Mass = 4,204,837,738,166.4 kilograms

Now the potential energy of the debris.

Debris Diameter = 12 pixels
Debris Height = 52 pixels

Debris Height/Debris Diameter = 4.333

Debris Height = 6,327.913 meters

PE = MGH

M = Debris Mass
G = 9.8 m/s^2
H = Debris Height

Debris Potential Energy = 260,756,904,385,090,800 joules

Android Cell Arc Piccolo Jr's Makūhōidan Yield = 4,234,675,960,285,803,000,000 joules or 1.012 teratons

Super Vegeta's Final Flash

The Feat


Earth = 1130 pixels
Final Flash = 1009 pixels

Final Flash/Earth = 0.893

Earth = 12,742,000 meters
Final Flash = 11,378,606 meters


If you look here, it would seem the debris kicked up by Vegeta's Final Flash at least reached the height Trunks escaped to.

Krillin = 64 pixels
Height of Debris = 528 pixels

Height of Debris/Krillin = 8.25

Krillin = 1.53 meters (official height; could use Future Trunks, but I'm making the time frame as high as possible)
Height of Debris = 12.623 meters

Time Frame = sqrt(2d/g)

d = Height of Debris
g = 9.8 m/s^2

Time Frame = 1.605 seconds

Android Cell Arc Super Vegeta's Final Flash Speed = 7,089,474 m/s or 0.024C

Perfect Cell's Kiai

The Feat


Kei Truck = 26 pixels
Road = 39 pixels

Road/Kei Truck = 1.5

Kei Truck = 3.3 meters (here; circa the time frame the arc was being released in the 90s)
Road = 4.95 meters


Road = 10 pixels
Pillar Height = 115 pixels
Crater Radius = 190 pixels

Pillar Height = 11.5
Crater Radius/Road = 19

Pillar Height = 56.925 meters (for later)
Crater Radius = 94.05 meters
Crater Diameter = 188.1 meters


Crater Diameter = 1210 pixels
Crater Depth = 455 pixels

Crater Depth/Crater Diameter = 0.376

Crater Depth = 70.726 meters

Volume = (2/3)PIr1^2r2

r1 = Crater Radius
r2 = Crater Depth

Crater Volume = 1,309,589.202 m^3

200 j/cc

Perfect Cell's Kiai Yield = 261,917,840,400,000 joules or 62.6 kilotons

Perfect Cell's Kamehameha

The Feat


Earth = 1100 pixels
Kamehameha Travel = 886 pixels

Kamehameha Travel/Earth = 0.805

Earth = 12,742,000 meters
Kamehameha Travel = 10,257,310 meters

I know IT has a lag between disappearing and reappearing, so I'm going to ignore that in favor of just using the debris the attack kicks up from the air pressure.


So, what height?


Maybe about half the pillar's height?

Pillar Height = 56.925 meters (derived above)

Half Pillar Height = ~Debris Height = 28.423 meters

Time Frame = sqrt(2d/g)

d = Debris Height
g = 9.8 m/s^2

Time Frame = 2.41 seconds

Perfect Cell's Kamehameha Speed = 4,256,145 m/s or 0.014C

Perfect Cell's Perfect Barrier

The Feat


Goku = 15 pixels
Hill Height = 210 pixels

Hill Height/Goku = 14

Goku = 1.75 meters (official height)
Hill Height = 24.5 meters


Hill Height = 67 pixels
Crater Radius = 186 pixels

Crater Radius/Hill Height = 2.776

Crater Radius = 68.012 meters

Volume = (2/3)PIr1^2r2

r1 = Crater Radius
r2 = Crater Depth

Crater Volume = 329,279.756 m^3

200 j/cc
6,147 j/cc (melting, got it using SD.net's calculator)
30342 j/cc (vaporization, got it using SD.net's calculator)

Perfect Cell's Perfect Barrier Yield (Low End) = 65,855,951,200,000 joules or 15.74 kilotons
Perfect Cell's Perfect Barrier Yield (Middle End) = 2,024,082,660,132,000 joules or 483.767 kilotons
Perfect Cell's Perfect Barrier Yield (High End) = 9,991,006,356,552,000 joules or 2.388 megatons

Super Saiyan 2 Son Gohan's Kamehameha

The Feat

Basically, finding how far the attack travels in the time debris falls off Cell.


Goku = 1412 pixels
Cell To Knee = 1186 pixels

Cell To Knee/Goku = 0.84

Goku = 1.75 meters (official height)
Cell To Knee = 1.47 meters


Cell To Knee = 557 pixels
Free Fall Distance = 522 pixels

Free Fall Distance/Cell To Knee = 0.937

Free Fall Distance = 1.377 meters

Time Frame = sqrt(2d/g)

d = Free Fall Distance
g = 9.8 m/s^2

Time Frame = 0.53 seconds


Earth = 2500 pixels
Kamehameha Travel = 539 pixels

Kamehameha Travel/Earth = 0.216

Earth = 12,742,000 meters
Kamehameha Travel = 2,752,272 meters

Android Cell Arc Super Saiyan 2 Gohan's Kamehameha Speed = 5,192,966 m/s or 0.017C

Super Perfect Cell's Solar Kamehameha

The Feat

Weekly ☆ Character Showcase #63: Perfect Cell! said:

Source

Cell launched a Kamehameha powerful enough to destroy the entire Solar System, and a weakened Gohan could only fight back with a one-handed Kamehameha! An epic back-and-forth ensued between the colossal, clashing beams, and just when all hope seemed lost, Gohan, with Goku's spirit supporting him from the afterlife, launched a father-son Kamehameha that not only repelled Cell's attack but completely obliterated him down to the last molecule.

Click to expand...

Weekly ☆ Character Showcase Bonus Content! Technique Compendium—Perfect Cell said:

Source

Kamehameha

Goku's signature technique, the user focuses their energy into the palms of their hands and then releases it in a single, powerful attack. The version of this attack that Cell uses in his final battle against Gohan had enough power to blow away the entire solar system.

Click to expand...

^Take that with a grain of salt, but those are the first and only non-anime related sources released for some kind of official Dragon Ball related material.

Doesn't hurt to model how this works either way. Have fun discussing shit. It's what the hobby exists for.

I mean, unless Cell was pointing the thing at that 0.5 degree slice of the sky the Sun takes up?

Gonna just be the Sun’s GBE multiplied by the ratio of a spherical AU’s surface area and the Sun’s own cross-section.


Gravitational Binding Energy = (3GM^2)/(5R)

G = Gravitational Constant = 6.674×10^−11
M = Sun's Mass = 1.9885 * 10^30 kilograms
R = 695,700,000 meters

GBE of Sun = ~2.276 * 10^41 joules

Next the 1 AU Spherical Explosion Surface Area to Cross-sectional Surface of Sun ratio.

1 AU = ~149,600,000,000 meters

1 AU Spherical Explosion Surface Area = 2.811 m^2 * 10^23 m^2

Cross-sectional Surface Area of Sun = 1.52 * 10^18 m^2

1 AU Spherical Explosion/Sun = 184,934.211

Super Perfect Cell's Solar Kamehameha Yield = 4.209 * 10^46 joules or 420.9 Foe

Not much else here worth considering looking at later. Mecha Freeza's lone feat was a generic AOE explosion. Android 20's Bionic Punisher is a generic set of explosions. Piccolo's Ki Blast vs Imperfect Cell was similarly generic in Ginger Town. Piccolo Jr's Gekiretsu Kōdan is just kind of a flashy explosion with little substance and I'm not really sure how to scale the island anyway? I have no fucking clue how to even try gauging Android 16's Hell's Flash. Like, whatever volume it effected, it was out of sight and underground. Perfect Cell's Kiai vs Gohan was lesser to look at than the one against Goku on account it just broke the rock formation rather than pulverize the ground. No real need to cover Semi-Perfect Cell's Self Destruction either.