Calc Dragon Ball Feats - Saiyan Collection

Piccolo Jr's Makankōsappō

The Feat

Think one of the dubs had a line about Raditz needing to be faster than light? Sounds random until you know that its attack name in Japanese literally translates to "魔貫光殺砲/Demon's Penetrating, Killing Light Gun" with the "光" literally just being "light" so that added dub line doesn't quite sound so random with that context I guess


It was work with cloud altitude or quite literally nothing, so fuck it.

Cloud Height = 28 pixels
Mountain Height = 145 pixels

Mountain Height/Cloud Height = 5.179

They look enough like Cumulus and such so, let's reference here and here for a range of 500 meters and 1,500 meters

Cloud Height (Low End) = 500 meters
Cloud Height (High End) = 1,500 meters
Mountain Height (Low End) = 2,589.5 meters
Mountain Height (High End) = 7,768.5 meters


Mountain Height = 284 pixels
Hole Diameter = 102 pixels
Hole Radius = 69 pixels

Hole Diameter/Mountain Height = 0.359
Hole Radius/Mountain Height = 0.243

Hole Diameter (Low End) = 929.631 meters
Hole Diameter (High End) = 2,788.892 meters
Hole Radius (Low End) = 629.249 meters
Hole Radius (High End) = 1,887.746 meters

Volume = (LWH)/2

I don't know, I figure treating it like a triangular prism is about where I should be approximating this odd gouging? I know its not a direct fit, but I'm not sure what percentage of a full sphere I'm actually getting volume wise here.

L = Hole Diametr
W and H = Hole Radius

Hole Volume (Low End) = 184,045,697.791 m^3
Hole Volume (High End) = 4,969,226,793.852 m^3

200 j/cc

Beginning of Saiyan Arc Piccolo Jr's Makankōsappō Yield (Low End) = 36,809,139,558,200,000 joules or 8.798 megatons
Beginning of Saiyan Arc Piccolo Jr's Makankōsappō Yield (High End) = 993,845,358,770,400,000 joules or 237.535 megatons

Son Gohan's Hidden Potential Ki Blast

The Feat


Gohan's training and where they fight Vegeta and Nappa basically take place in the same general area. This is what I have to work with.

Neat...

Vegeta = 45 pixels
Tree = 173 pixels

Tree/Vegeta = 3.844

Vegeta = 1.64 meters (official height)
Tree = 6.304 meters


Tree = 60 pixels
Hill Top Diameter = 294 pixels
Hill Bottom Radius = 310 pixels
Hill Height 1 = 330 pixels
Hill Height 2 = 135 pixels

Hill Top Diameter/Tree = 4.9
Hill Bottom Radius/Tree = 5.167
Hill Height 1/Tree = 5.5
Hill Height 2/Tree = 2.25

Hill Top Diameter = 30.89 meters
Hill Bottom Radius = 32.573 meters
Hill Height 1 = 34.672 meters


Hill Body Volume = 65,451 m^3

Hill Height 2 = 14.184 meters

Volume = (2/3)PIr1^2r3

r1 = Hill Top Diameter/2
r2 = Hill Height 2

Hill Cap Volume = 7,082.93 m^3


Trench Diameter = Hill Bottom Radius * 2 = 65.146 meters

So?

Trench Diameter = 942 pixels
Trench Depth = 166 pixels

Trench Depth/Trench Diameter = 0.176

Trench Depth = 11.466 meters

Now the Trench Length

Panel Height = 1343 pixels
Trench Diameter (Foreground) = 942 pixels
Trench Diameter (Background) = 27 pixels

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

2*atan(942/(1343/tan(70/2 deg)))

Trench Diameter (Foreground) = 52.315 Degrees


Distance to Trench Diameter (Foreground) = 66.321 meters

2*atan(27/(1343/tan(70/2 deg)))

Trench Diameter (Background) = 1.613 Degrees

Distance to Trench Diameter (Background) = 2,313.9 meters

Trench Length = Distance to Trench Diameter (Background) - Distance to Trench Diameter (Foreground) = 2,247.579 meters

Volume = ((PIr1r2)/2)*H

r1 = Hill Bottom Radius
r2 = Trench Depth
H = Trench Length

Trench Volume = 1,317,905.635 m^3

Added all together?

Total Destruction Volume = 1,390,439.565 m^3

200 j/cc

Saiyan Arc Son Gohan's Hidden Potential Ki Blast Yield = 278,087,913,000,000 joules or 66.465 kilotons

Oozaru Son Gohan's Physical Might

The Feat

Going to scale this 2 ways. The first will equate Gohan's armspan to what I got for Goku's at Pilaf's Castle. The second will just use what is available in the area. Neither matter. Just doing the feat for the feat's sake.


Dome Diameter = 161 pixels
Oozaru Goku Height = 265 pixels
Oozaru Goku Armspan = 521 pixels

Oozaru Goku Height/Dome Diameter = 1.646
Oozaru Goku Armspan/Dome Diameter = 3.236

Dome Diameter = 34.41 meters (found here)
Oozaru Goku Height = 56.638 meters
Oozaru Goku Armspan = 111.351 meters (found here)


Oozaru Goku = Oozaru Gohan

Oozaru Gohan Armspan = 174 pixels
Bottom Pillar Diameter = 134 pixels
Top Pillar Diameter = 82 pixels
Pillar Height = 251 pixels

Bottom Pillar Diameter/Oozaru Gohan Armspan = 0.77
Top Pillar Diameter/Oozaru Gohan Armspan = 0.471
Pillar Height/Oozaru Gohan Armspan = 1.443

Bottom Pillar Diameter = 85.74 meters
Top Pillar Diameter = 52.446 meters
Pillar Height = 160.679 meters


Pillar Volume = 614,102 m^3

8 j/cc

Saiyan Arc Oozaru Son Gohan Physical Might (Pilaf Palace Scaled) = 4,912,816,000,000 joules or 1.174 kilotons

And the alternative


Gohan = 64 pixels
Dionsaur Crown = 263 pixels

Dinosaur Crown/Gohan = 4.109

Gohan = 1.023 meters (here, Gohan is 4, ergo I'll use an average height for the age)
Dinosaur Crown = 4.204 meters


Panel Height = 2400 pixels
Dinosaur Crown = 49 pixels
Gohan Armspan = 122 pixels

Gohan = Gohan Armspan

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

2*atan(49/(2400/tan(70/2 deg)))

Dinosaur Crown = 1.638 Degrees


Distance From Dinosaur Crown = 147.04 meters

2*atan(122/(2400/tan(70/2 deg)))

Gohan Armspan = 4.077 Degrees

Distance From Gohan = 14.371 meters

Subtract Distance From Dinosaur Crown from Distance From Gohan to get the Pillar Height

Pillar Height = 132.669 meters

Let's also get the Pillar Bottom Diameter

Dinosaur Crown = 49 pixels
Pillar Bottom Diameter = 545 pixels

Pillar Bottom Diameter/Dinosaur Crown = 11.122

Pillar Bottom Diameter = 46.757 meters


Gohan = 30 pixels
Pillar Top Diameter = 343 pixels

Pillar Top Diameter/Gohan = 11.433

Gohan = 1.023 meters (here, Gohan is 4, ergo I'll use an average height for the age)
Pillar Top Diameter = 11.696 meters


Pillar Volume = 99,678.7 m^3

8 j/cc

Saiyan Arc Oozaru Son Gohan Physical Might (Low End) = 797,429,600,000 joules or 190.59 tons

This is what I mean by Toriyama being ONE if ONE was able to draw anything aesthetically pleasing that isn't just the kinetics of combat/motion. Scale doesn't matter, the background is pretty or cool and he doesn't care.

Oozaru Son Gohan's Mouth Ki Blast

The Feat


Going require an assumption, but let's go with the height of the pillar I scaled being not particularly special compared to the one in the distance on the edge/foreground of the explosion's diameter?

Pillar Height = 51 pixels
Explosion Diameter = 1177 pixels
Debris Height = 219 pixels
Rock Height = 40 pixels
Rock Diameter = 17 pixels

Explosion Diameter/Pillar Height = 23.078
Debris Height/Pillar Height = 4.294
Rock Height/Pillar Height = 0.784
Rock Diameter/Pillar Height = 0.333

Pillar Height (Low End) = 132.669 meters (derived above)
Pillar Height (High End) = 160.679 meters (derived above)
Explosion Diameter (Low End) = 3,061.735 meters
Explosion Diameter (High End) = 3,708.15 meters

Surface Area = 4PIr^2

r = Explosion Diameter/2

Explosion Surface Area (Low End) = 29,435,054.6 m^2
Explosion Surface Area (High End) = 43,176,181.967 m^2

Debris Height (Low End) = 569.681 meters
Debris Height (High End) = 689.956 meters
Rock Height (Low End) = 104.012 meters
Rock Height (High End) = 125.972 meters
Rock Diameter (Low End) = 44.179 meters
Rock Diameter (High End) = 53.506 meters

Surface Area = LW

L = Rock Height
W = Rock Diameter

Rock Cross-sectional Surface Area (Low End) = 4,595.146 m^2
Rock Cross-sectional Surface Area (High End) = 6,740.258 m^2

Surface Area Ratio Time

Explosion/Rock = 6,403.508 to 6,405.717

So, rounding error leads to some difference here given ratio should remain the same.

Volume = LWH

L = Rock Height
W and H = Rock Diameter

Rock Volume (Low End) = 203,008.962 m^3
Rock Volume (High End) = 360,644.236 m^3

Rock Density = 2,700 kg/m^3

Rock Mass (Low End) = 548,124,197.4 kilograms
Rock Mass (High End) = 973,739,437.2 kilograms

PE = mgh

m = Rock Mass
g = 9.8 m/s^2
h = Debris Height

Rock Potential Energy (Low End) = 3,060,108,220,810 joules
Rock Potential Energy (High End) = 6,584,006,197,901 joules

Saiyan Arc Oozaru Son Gohan's Mouth Ki Blast Yield (Low End) = 19,595,427,472,822,600 joules or 4.683 megatons
Saiyan Arc Oozaru Son Gohan's Mouth Ki Blast Yield (High End) = 42,175,280,429,999,800 joules or 10.08 megatons

Explosion diameter is much further in the background, thus muting the result a bit, but not super important either way.

Piccolo Jr's (Night After Raditz Fight) Bakurikimaha

The Feat

Right, before anything else?

I've heard before that supposedly the moon was off panel still in the after scan, so let's put that claim to rest, right?


First Panel

Piccolo = 827 pixels
Distance Between Hill and Moon = 1393 pixels

Distance Between Hill and Moon/Piccolo = 1.684

Second Panel

Piccolo = 573 pixels
New Distance Between Hill and Top of Panel = 1243 pixels

New Distance Between Hill and Top of Panel/Piccolo = 2.169

Which would mean that the "Distance Between Hill and Moon" from the first panel transposed onto the second panel would be a measure of ~965 pixels. The space the moon occupied in the first panel therefore is on the second panel.

Any rate?

First Panel

Moon Diameter = 340 pixels
Moon Expansion Distance (Blue Line + Red Line) = 1563 pixels

Moon Expansion Distance/Moon Diameter = 4.597

Moon Diameter = 3,474,800 meters
Moon Expansion Distance = 15,973,655.6 meters

Distance To Moon = 384,400,000 meters

Time Frame would be the time it takes the light from the moon to no longer be reaching Gohan to keep him transformed, ergo using the speed of light over the distance to the moon.

Rationale?


Let's think about it like this. This transformation is so finicky, even tiny fractions of a sliver in the lunar cycle off from a full moon will not enable the transformation to occur or be retained. By the time the light of moon from that deviation in the moon's ability to reflect reaches back to the surface where the transformed Saiyan is at, the transformation ends. Be it obstruction or obliteration, the transformation will fail. The moment Piccolo's blast engulfed the moon, the light was obstructed and the radiation that would transform Gohan back would have already been in transit. By the time it reaches planet side, the moon's entire mass has fucked off well into all cardinal directions

Ergo?

Speed of Light = ~300,000,000 m/s

Time Frame Moon Expansion and Ki Blast Travel = 1.281 seconds

He's still firing at it while the moon's light that causes Gohan to transform is being obstructed by Piccolo's blast, so the time frame for Piccolo's blast to finish traveling up to where the rest of it would be similar to the expansion that is occurring.

Which would make his attack?

Beginning of Saiyan Arc Piccolo Jr's (Night After Raditz Fight) Bakurikimaha Speed (High End) = ~300,000,000 m/s or 1C

Any rate, need that expansion speed.

So divide the Moon Expansion Distance by the 1.281 seconds and get...

Moon Expansion Speed = 12,469,676.503 m/s

Moon Mass = 7.34767309 × 10^22 kilograms

KE = 0.5mv^2

m = Moon Mass
v = Moon Expansion Speed

Beginning of Saiyan Arc Piccolo Jr's (Night After Raditz Fight) Bakurikimaha Yield (High End) = 5,712,552,490,158,447,000,000,000,000,000,000,000 joules or 1,365.333 yottatons or 1.365 ninatons

We also have our handy dandy low end minimum visual acuity time frame to establish the bog standard low ball.

Namely?

The moon itself is approximately ~0.5 degrees across and covers about that much distance over the course of an hour. The given what we know about the limits of human visual acuity?

Visual acuity, basically the resolution of the naked eye, can perceive upwards of shit as small as 0.02 degrees and perceive it as its own distinct object without them all blurring the fuck together. It's hard to sell the idea that at this range, Piccolo's attack was fired and risked being moved that far off center, there was no real notable deviation in it's placement in the sky, Piccolo did not need to alter the beam's trajectory.

So, a full time frame of 144 seconds for the beams travel and then the expansion. Half the time for the beam to reach (72 seconds), half the time for the mass to expand (72 seconds).

Total Time Frame = 144 seconds

Time Frame Kamehameha Travel = 72 seconds

Distance To Moon = 384,400,000 meters

Beginning of Saiyan Arc Piccolo Jr's (Night After Raditz Fight) Bakurikimaha Speed = 5,338,889 m/s or 0.018C

Time Frame Moon Expansion = 72 seconds

Moon Expansion Distance = 15,973,655.6 meters

Moon Expansion Speed = 221,856.328 m/s

Moon Mass = 7.34767309 × 10^22 kilograms

Beginning of Saiyan Arc Piccolo Jr's (Night After Raditz Fight) Bakurikimaha Yield (Minimum Visual Acuity Time Frame) = 1,808,270,807,326,271,000,000,000,000,000,000 joules or 432.187 zettatons

Bearing a reminder that this is the same attack Raditz chose to face tank.


Nappa's Bakuhatsuha

The Feat

Kind of wonder if I could get a KE for the mass he clearly ejects out of the atmosphere (given the Saiyan Pods used to be in craters and those kind of vanished after Nappa let off his shock wave), but I'll just go with the AOE, because fuck it. It's nothing new, but now its in shiny HQ Color.


Earth = 435 pixels
Shock Wave Diameter = 160 pixels

Shock Wave Diameter/Earth = 0.368

Earth = 12,742,000 meters
Shock Wave Diameter = 4,689,056 meters


Nappa's Bakuhatsuha Yield (Low End; Air blast radius [widespread destruction]) = 40.756 teratons
Nappa's Bakuhatsuha Yield (High End; Air blast radius [near-total fatalities]) = 771.9 teratons

Son Gohan's Physical Might

The Feat

I figure he likely kicked Nappa into the structure Krillin used his Kienzan on, if not at least one of similar stature.

Sent him in roughly the same direction.

All the same a bit feat, but whatever.


Vegeta = 45 pixels
Tree = 173 pixels

Tree/Vegeta = 3.844

Vegeta = 1.64 meters (official height)
Tree = 6.304 meters


Tree = 78 pixels
Hill Top Diameter = 247 pixels

Hill Top Diameter/Tree = 3.167

Hill Top Diameter = 19.965 meters


Hill Top Diameter = 64 pixels
Hill Height = 118 pixels
Hill Bottom Radius = 77 pixels

Hill Height/Hill Top Diameter = 1.844
Hill Bottom Radius/Hill Top Diameter = 1.203

Hill Height = 36.815 meters
Hill Bottom Radius = 24.018 meters


Hill Volume = 35,324.7 m^3

8 j/cc

Saiyan Arc Son Gohan's Physical Might = 282,597,600,000 joules or 67.542 tons

Vegeta Powering Up

The Feat

Kind of like what I did for Bleach?

ME said:

Explanation? For the first bit, Ichigo is our height of eye and Karakura is behind the horizon, thus we can't see the town from where the pair are now located. Here's the deal though, as you can determine from here? The bigass cumulus cloud behind Ichigo (here and here) that's sitting behind the horizon is no where in view of Karakura as Ichigo flies away with Aizen in palm. The gap between the cloud and the ground is hidden behind the horizon and functions as a second height of eye from the direction of Karakura Town as this cloud and the gap between itself and the ground sit outside Karakura town proper. Thus the distance between Ichigo's arena with Aizen compared to this cloud peaking over the horizon is still something of a low ball given I can't determine where Karakura is behind the cloud.

What kind of normalish elevation can you view a cumulus cloud from anyway? Seems like a range of 500-1,500 meters is pretty average for a temperate region here and here.

Height of Eye 2 (Low End) = 500 meters
Height of Eye 2 (High End) = 1,500 meters

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

hb = Height of Eye 1
hl = Height of Eye 2

Click to expand...

I'll be doing the same with Vegeta's creation of that storm and subsequent dispersion of the cloud. I'll get the height of eye from the perspective of Goku and Vegeta, then I'll also need the height of the Cloud Base of the Cumulonimbus that is still hidden well behind the horizon to inform our minimum Storm Radius.


Cloud Base Height (Low End) = 609.6 meters (2,000 feet)
Cloud Base Height (High End) = 1,524 meters (5,000 feet)

Next for the pair's height of eye?


Goku = 70 pixels
Height of Eye = 1093 pixels

Height of Eye/Goku = 15.614

Goku = 1.75 meters (official height)
Height of Eye = 27.325 meters

Going to also use that to derive the time frame as, by the time the storm is fully parted? It looks like similar pillars around the pair have just started to impact the ground and begin to kick up some dust/sand/etc while other chunks od debris are still just starting to fall apart?

Time Frame = sqrt(2d/g)

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

Time Frame = 2.361 seconds

Any rate, on with getting the cloud radius.

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

hb = Height of Eye
hl = Cloud Base Height

Cloud Radius (Low End) = 106.805 kilometers or 106,805 meters
Cloud Radius (High End) = 158.029 kilometers or 158,029 meters

Can derive a dispersion speed for the cloud now then.

Cloud Dispersion Speed (Low End) = 45,237.188 m/s
Cloud Dispersion Speed (High End) = 66,933.079 m/s


Going to use 3,000 meters for cloud thickness because I don't feel like doing another range within a range. The low end is nice and safe anyway.

Volume = PIr^2*H

r = Cloud Radius
H = Cloud Height = 3,000 meters

Cloud Volume (Low End) = 107,456,841,595,500 m^3
Cloud Volume (High End) = 235,247,212,802,220 m^3

Cloud Density = 1.003 kg/m^3 (here, for those wondering where it came from, apparently they long since edited this .gov website? Guess it's fine since it roughly lines up with average density of the atmosphere between altitudes I'm using anyway)

Cloud Mass (Low End) = 107,779,212,120,286.5 kilograms
Cloud Mass (High End) = 235,952,954,440,626.7 kilograms

KE = 0.5mv^2

m = Cloud Mass
v = Cloud Dispersion Speed

Saiyan Arc Vegeta's Powering Up Yield (Low End) = 110,279,861,110,585,500,000,000 joules or 26.358 teratons
Saiyan Arc Vegeta's Powering Up Yield (High End) = 528,538,990,676,734,000,000,000 joules or 126.324 teratons

Neat.

Saiyan Arc Son Goku's Genki-dama Speed
The Feat

Here, here, and here are relevant raw scans.

So, Goku draws in the ki to create the Genki-dama, he needs 10 seconds by his own estimate to accomplish the task. He draws on energy from around the planet.

I don't know what shit Viz was on, but the second raw had nothing that remotely resembled what they said here.

Volume 20 p050 said:

translate from Japanese to English with proper grammar大猿に変身しだ恐るペきベジータを倒すには元気玉しガない!しかし そのだめの精神集中をする時閏がかせげない!悟空は太陽拳でベジー夕の目をくらませだスキに距離をおき精神集中をはじめだ!!

To defeat the fearsome Vegeta, who has transformed into a giant ape, Goku needs the Spirit Bomb! However, he cannot afford to waste time when gathering the necessary energy for that. Goku, taking advantage of the opportunity when Vegeta is temporarily blinded by the Solar Flare, creates distance and begins to concentrate his energy!

Click to expand...

The raws do say he needs 10 seconds and that he does gather the energy from around the planet though. So got a time frame and a distance (the Earth's half circumference) to work with at the low end.

Volume 20 p044 center bottom left panel said:

translate from Japanese to English with proper grammarた たった10秒だけでいいんだっ!!!

Just just
10 seconds
is enough!!!

...

translate from Japanese to English with proper grammar集中する時間がほしいっ

I want time to concentrate.

Click to expand...

Volume 20 p052 bottom right panel said:

translate from Japanese to English with proper grammarで...できた地球じゆうの元気があつまった...!!!

And...It's done.
The energy from all over the Earth has gathered...!!!

Click to expand...

High end? I'll take what North Kaio says about the Sun given that seems to be the upper bound on his expectations on what Goku can drag energy wise?

Time Frame = 10 seconds
Earth's Circumference = ~40,075,000 meters

Halve that for the half circumference and the furthest point the energy can be taken from on Earth.

Distance Genki-dama Travels (Low End) = 20,037,500 meters
Distance Between Earth and Sun/Distance Genki-dama Travels (High End) = ~149,597,870,700 meters

Saiyan Arc Son Goku's Genki-dama Speed (Low End) = 2,003,750 m/s or mach 5888.36
Saiyan Arc Son Goku's Genki-dama Speed (High End) = 14,959,787,070 m/s or 49.866C

So that's neat too.

Nothing much else to discuss. Does anyone really need me to rehash Snake Way? Like, at all? I can, I'll collect those scans later (EDIT - here, enjoy), but literally nothing about that needs me. You can do it yourself with your own calculator and everything. Raditz firing on those mountains wasn't worth the trouble, it's just a pair of explosions without showing us so much as a crater. I barely bothered with the Makankōsappō, and that can be taken or left given it needed fucking cloud altitudes. We also know Raditz can catch bullets, so that's nice I guess. Oozaru Vegeta's Mouth Ki Blast is all AOE and little to go with either. Exhausted and half-dead Vegeta's Chōbakuhatsuha is similar and that crater is honestly pretty shallow. And you have the least of Oozaru Gohan's feats of just chucking a boulder.