Dragonball – Calculation List

This post is so people can easily find Dragonball calculations that I’ve done. Before really diving in, I recommend checking out Some Tidbits About Dragonball, while also using Dragonball Character Heights, Explosions, and Energy Required to Destroy Stuff as reference, because I’ll be using those things often for the calcs.

Power and speed calculations will be separated for the sake of simplicity and neatness.

Power Calculations

Pre 21st Budokai

Goku Crushes a Boulder – 61.186 Kg TNT

Yamcha’s Wolf Fang Fist – 2.545 Kg TNT

Roshi’s Max Power Kamehameha – 4.18 Megatons

Oozaru Goku Throws a Building – 460.546 Kg TNT

Goku Pushes Small Boulder (Total Energy) – 22.935 kg TNT

Goku Kicking Strength (Pre-Roshi Training) – 3.888 Kg TNT

Goku Pushes Giant Boulder (Total Energy) – 628 Kg TNT

Goku Kicking Strength (Post Roshi Training) – 420 Kg TNT

Krillin Pushes Giant Boulder/Kicking Strength – 263 Kg TNT 

21st Budokai

Goku vs the Wall – 3.85 Kg TNT

Krillin vs the Wall – 5.89 Kg TNT

Namu’s X-Strike From the Heavens – 336,571,200 N/m^2 or Pascals

Namu’s Jump Power – 1.91 Kg TNT

Roshi Moon Busting Kamehameha – 29.76 Exatons TNT – 1.179 Zettatons

Red Ribbon Army

Goku Underwater Kamehameha – 10.826 Kg of TNT

Blue Crashes – 345.969 Kg of TNT

Blue Knocked to Egypt – 787.495 Kg of TNT

Tao Pai Pai’s Punching Power – 2.448 Tons of TNT

Commander Black Battle Jacket Laser – 92.16 Tons of TNT

Commander Black Battle Jacket Missile – 9.814 Kilotons

22nd Budokai

Yamcha’s Kamehameha – 1.458 Tons of TNT

Chaozu’s Full Power Dodonpa – 543.455 Kg of TNT

Tenshinhan’s Kikoho – 111.062 Tons of TNT

Piccolo Daimao

Piccolo Daimao Hand Wave – 2.76 Kilotons

Piccolo Daimao Punches Goku – 274.29 Tons of TNT

Piccolo Daimao’s Explosive Demon Wave – 550 Kilotons

23rd Budokai

Piccolo’s Ocean Ki Blast – 102.337 Gigatons

Piccolo’s Mountainous Ki Blast Power – 700-800 Kilotons

Piccolo Razes Papaya Island – 11.559 Gigatons of TNT

Saiyan Saga

Piccolo’s Makankosappo Pressure – 378.852 TeraPascals

Piccolo Destroys the Moon – 29.757 Exatons – 1.179 Zetatons TNT

Nappa Raises 2 Fingers – 17.804 – 337.19 Teratons

Vegeta Planet Busting Threat (Theoretical) – 33.009 Petatons – 53.576 Zettatons

Freeza Saga

Vegeta Impact Crater – 723.731 Tons of TNT

Recoome’s Eraser Gun – 778.3 Teratons

Freeza Destroys Planet Vegeta (Speculative) – 615.679 Yottatons

Freeza Destroys Namek’s Core – 33.037 Petatons

Namek Explosion/Freeza Durability – 53.576 Zettatons – 32.186 Yottatons.

Cell + Buu Saga

Cell’s Solar System Busting Claim (Theoretical) – 135,932,591.575 – 6,182,812,457,514.363 Yottatons

Kid Buu Blows up Earth – 8,205,240.342 Yottatons

Speed Calculations

Pre-21st Budokai

Krillin Running Speed – 9.615 m/s

Goku Running Speed – 11.765 m/s

Roshi Running Speed – 17.857 m/s

21st Budokai

Jackie Chun Hand Wave Wind Speed – Mach 1.687

Namu and Goku’s Jump into the Clouds – Mach 1.52

Goku vs Free Fall – Mach 1.83

Red Ribbon Army

Goku Bullet Dodging – 86 – 107.5 m/s

Goku Blocking Bullets – 30.8 – 145.6 m/s

Roshi Catches Bullets – 60.848 – 130.339 m/s

Tao Pai Pai’s Speed – Mach 18.06

22nd Budokai

Goku’s Disappearing Act – Over Mach 10.9

23rd Budokai

Piccolo’s Mountainous Ki Blast Speed – Mach 47.69

Saiyan Saga

Piccolo Ki Blast Speed – Mach 665.854 – 18,843

Freeza Saga

Monster Zarbon Speed – Mach 967.223

Buu Saga

SSJ Gotenks Speed – Mach 1,389.468 – 26,399.885 (3% light speed)… however it could be much faster or slower…

If there end up being any feats I missed for whatever reason, I’ll be sure to come back to Dragonball. I may also attempt some calculations from the anime, or Super if I can work up the desire to re-watch it. Otherwise, that’s about all I have to give for Dragonball calculations. “It’s been a trip” as Kami once said to Popo. 😀

• Cable

Dragonball – End of Series Feats

Yep, it’s already that time! The Cell and Buu sagas do offer plenty of impressive showings, but most are below planet busting and therefore pointless to calculate. I’m only focusing on the most impressive feats in this post.

 

Cell’s Solar System Busting Claim

The Android/Cell saga is almost exclusively about threats to destroy things when it comes to feats. Because the powers have gotten so big that blowing up the planet is trivial… but they kinda need the planet to keep the plot going. SSJ Vegeta says he has to hold back so as not to blow up the planet, and Vegeta’s Final Flash was also a threat to Earth until he concentrated it into a thin stream of sorts. King Cold also mentions that he or Freeza could blow up Earth in one shot because it was such a small planet. Cell does blow up King Kai’s planet which has 10 g, but it’s so small that the minimum required energy is only around 40 Megatons, paltry for this point in the series (Although interestingly it does make the planet hundreds of thousands of times more dense than uranium lol)

However, the ultimate claim to power comes here. Cell comes back more powerful than ever, then makes the claim that he’s gathered enough energy to destroy the solar system. As always, I’m not going to comment on the validity or likelihood of such a claim. I’m instead going to calculate the amount of energy he’d need to do such a thing.

The easiest way to destroy a solar system (It’s not actually easy) is to destroy the sun. For that, we can use Gravitational Binding Energy.

The formula for GBE of a planet differs from a star, however. Instead, it’s expressed as:

3 GM^2 / r (5 – n)

G is the gravity constant, .0000000000667384 m^3 kg s

M is the mass of the sun, 1,989,000,000,000,000,000,000,000,000,000 kg

r is the radius of the sun, 696,340,000 m

n is the polytrope of the star. For our sun, n = 3

3 * .0000000000667384 * 1,989,000,000,000,000,000,000,000,000,000^2 / 696,340,000 (5 – 3) = 568,741,963,149,610,822,299,451,417,411,030,000,000,000 J or 135,932,591.575 Yottatons

As for outright destroying the entire solar system, I’m having trouble figuring out what it would take, energy-wise. My first thought was that, as long as the total energy is enough to destroy the sun and any single planet in the system, perhaps Inverse Square law could work?

You know what my favorite part about calculating this is going to be? Pluto’s going to get the credit it deserves! Back in the 90’s when this chapter came out, Pluto was still considered a planet. So I’m going to use its distance from the Earth as the “radius” of the explosion. Suck on that, NASA! 😀

First and foremost, what’s the GBE of Pluto?

U = 3GM^2 / 5R

Gravity constant remains the same, .0000000000667384 m^3 kg s

Mass of Pluto is 13,090,000,000,000,000,000,000 Kg

Radius of Pluto is 1,188.3 km

3 * .0000000000667384 * 13,090,000,000,000,000,000,000^2 / 5 * 1,188,300 = 5,774,045,966,695,278,969,957,081,545.064 J or 1.38 Exatons

Alright, now for the Inverse Square Law. Cell threatens to destroy the solar system from Earth specifically and if he didn’t simply mean destroying the sun, which would also do the job, then we have to assume that the explosion would reach from Earth all the way to Pluto and still destroy it.

Distance between Earth and Pluto is 4.2 – 7.5 billion Km depending on what part of their orbit each respective planet is in. So, I’ll just take the average of that range to make things easy. 5,850,000,000 Km, which will serve as the radius of the explosion.

If we treat the explosion as a sphere, the surface area would be a whopping 430,050,000,000 Km^2 or 430,050,000,000,000,000 m^2

The surface area of Pluto, meanwhile, is 17,700,000 Km^2 or 17,700,000,000,000 m^2

Using the relation between the surface areas, we can also find the relation in energy…

430,050,000,000,000,000 / 17,700,000,000,000 * 5,774,045,966,695,278,969,957,081,545.064 = 140,289,743,953,520,040,736,160,616,861,850 J or 33.53 Zettatons.

This presents a problem in that it wouldn’t even fully destroy Earth, let alone the other planets. I suppose just because Pluto is the farthest away, doesn’t mean it requires a great source energy, as it is tiny.

So how about we try one more thing? If the blast originates on Earth, I’ve proven that the effects can destroy Pluto if it reaches it. Therefore, a blast originating on Earth that destroys the sun should be able to do the same. So I’m going to use the sun instead.

We already found the GBE of the sun to be 568,741,963,149,610,822,299,451,417,411,030,000,000,000 J, so I need distance for the blast radius, and the two surface areas.

The sun is 148,420,000 Km or 148,420,000,000 m from Earth. The sun’s surface area is 6,090,000,000,000 Km^2 or 6,090,000,000,000,000,000 m^2. The surface area of our theoretic explosion would be 277,000,000,000,000,000 Km^2 or 277,000,000,000,000,015,000,000 m^2

Using the same formula as before…

277,000,000,000,000,015,000,000 / 6,090,000,000,000,000,000 * 568,741,963,149,610,822,299,451,417,411,030,000,000,000 = 25,868,887,322,240,098,862,090,221,222,358,000,000,000,000,000 J or 6,182,812,457,514.363 Yottatons.

That’s about 2.5x stronger than the estimated energy of a hypernova, the much more powerful version of a supernova, pretty much! Consider this a higher-end though, as like I said before, simply destroying the sun would do the trick. There is no solar system without the sun.

 

Gotenks’ Trip Around the World

Gotenks loops around the world 5 times, and even has time to take a nap before Piccolo catches up. According to Piccolo, Gotenks only has 1 minute left in the fusion before he separates, so that would make the elapsed time 29 minutes. However, there’s also the aforementioned “afternoon nap” that Gotenks references. Optimal nap time is 10-20 minutes according to studies. So 10 minute nap would reduce the time frame to 19 minutes, while 20 would make it 9. This would make for a good range, I think, as both are viable and good enough for people to draw their own conclusions.

 

Gotenks obviously moves around the planet in an oval-like circumference, so aside from what I’ve already measured, my assumption for the diameter (smaller) that I can’t measure will be that it’s equal to the diameter of Earth, which does make this lower end in all likelihood.

Sorry for any confusion by the way, but it’s a small panel so be sure to keep an eye on the color coding. Earth measures at 161 pixels here. It’s 12,742 km in diameter. Going from the top text to bottom: Loop 1 measures 247, loop 2 is at 174, loop 3 is 310, loop 4 is 329, and loop 5 is 234.

247 / 161 = 1.534 * 12,742 = 19,546.228 Km, long axis of loop 1.

174 / 161 = 1.081 * 12,742 = 13,774.102 Km, long axis of loop 2.

310 / 161 = 1.926 * 12,742 = 24,541.092 Km, long axis of loop 3.

329 / 161 = 2.044 * 12,742 = 26,044.648 Km, long axis of loop 4.

234 / 161 = 1.453 * 12,742 = 18,514.126 Km, long axis of loop 5.

 

Okay, now using the Earth’s diameter as the short axis of the loop, we can get circumference for each.

Loop 1 = 103,664.331 Km

Loop 2 = 83,365.871 Km

Loop 3 = 122,853.848 Km

Loop 4 = 128,819.263 Km

Loop 5 = 99,854.367 Km

Adding these all together, the total distance comes to 538,557.68 Km.

Alright, for the low-end, we have a time frame of 19 minutes. 19 * 60 = 1,140 s.

538,557.68 / 1,140 =472.419 Km/s or Mach 1,389.468

For a time frame of 9 minutes… 9 * 60 = 540 s.

538,557.68 / 540 = 997.329 Km/s or Mach 2,933.321

And just for the hell of it, if we say that Gotenks took a 28 minute nap and flew around the globe in a minute…

538,557.68 / 60 = 8,975.961 Km/s or Mach 26,399.885 (3% light speed)

I guess the real weakness here is that the time frame can be anything within 29 minutes. It could be a second, 28 minutes and 59 seconds, or even a microsecond. We have no idea. That’s why I’m giving a range of what I think is acceptable. The true result could be higher or lower.

Note: I really wanted to figure out something for Buu and Gotenks creating wormholes to other dimensions, but there is nothing scientifically concrete out there yet. It’s all heavily speculative. The idea, though, is that you can pull apart two black holes to make a wormhole… the issue here of course is that there’s no black hole in sight so it may just be chalked up to a magic wormhole…

 

Kid Buu Blows Up Earth

 

Kid Buu blows up Earth with a single blast, marking the first time in the manga that someone has done this on-panel, believe it or not. What’s nice though is that for once we don’t have to rely on gravitational binding energy. I can get time frame and eventual energy out of this.

So what I didn’t show earlier was that Kibito Kai teleported in, saved everyone, then teleported them back to the Kaioshin home world. It’s instantaneous movement, just liek Goku’s Shunkan-Ido. In the panel after we see the debris shooting out into space, we see Goku and the others landing on the ground at Kaioshin, but Dende hasn’t landed yet. We can use this because…

Little Green is holding on to Mr. Satan’s leg! Satan was held on to by Goku and we see that both have landed while Dende is still in the air. Using these facts, and knowing that Kibito Kai’s teleport accounts for no time at all, we can figure out how long it took for the debris to shoot out like that and get an average speed.

Mr. Satan is 1.88 m tall. Goku is 1.75 m. But Satan is being held on to on his shoulder by Goku’s arm. So for Goku, I’m thinking we shave off 1 m. After all, an outstretched arm should come down to the thighs. So .75 m. Satan is also being held up by his shoulder, so we need to scale…

80 / 283 = .283 * 1.88 = .523 m, distance from top of Satan’s head to shoulder.

1.88 – .523 = 1.357 m.

1.357 + .75 = 2.107 m, distance for Dende to fall.

Goku is at 121 pixels compared to Dende at 78.

78 / 121 = .645 * 1.75 = 1.129 m, Dende’s height.

Dende measures at 48 pixels compared to 61 for distance between where he held on to Satan and the ground.

61 / 48 = 1.27 * 1.129 = 1.434 m, Dende’s height from the ground.

2.107 – 1.434 = .673 m, distance Dende fell between teleportation and the panel.

In free fall, that distance would take .371 s, and that’s our bare minimum time frame for the panel where we see Earth rubble shooting off. Now to scale one more thing…

My biggest assumption here is that the center sphere is still roughly the diameter of Earth and is just beginning to explode. The remaining Earth is 82 pixels compared to the farthest piece of debris at 256. Earth’s diameter is 12,742 km.

256 / 82 = 3.122 * 12,742 = 39,780.524 Km, distance of the furthest rubble.

39,780.524 / .371 = 107,225.132 Km/s, speed of the debris. I am considering this the average speed.

With that in mind, we just do a simple kinetic energy equation. Mass of the Earth is 5,972,000,000,000,000,000,000,000 Kg.

107,225.132 Km/s = 107,225,132 m/s

KE = 1/2mv^2

.5 * 5,972,000,000,000,000,000,000,000 * 107,225,132^2 = 34,330,725,592,198,428,064,000,000,000,000,000,000,000 J or 8,205,240.342 Yottatons

 

This puts Kid Buu in an awkward category. He has 17,000x the power required to destroy Jupiter, but only about 1/17th the power required to destroy our sun. I suppose that makes him small star level here? I’m not sure; I’ll have to put together a list of common energies some day. Especially for series like Dragonball because eventually, I don’t think it’s easy to understand the magnitude of power unless there’s something practical to compare it to.

At any rate, that about does it for Dragonball. I could do Super, but… meh, I haven’t really liked Super enough to re-watch it. lol Maybe some day though, seeing as it is canon. Speaking of which, there may also come a time where I jump into Dragonball anime feats because that’s a whole other beast. Casual planet busters by the Saiyan saga is a game changer. And it goes way beyond that too. Maybe some of the movies will be worth looking into. I will also be compiling a list of Dragonball calculations just to make everything easy to find.

 

TOTALS

Cell’s Solar System Busting Claim (Theoretical) – 135,932,591.575 – 6,182,812,457,514.363 Yottatons

SSJ Gotenks Speed – Mach 1,389.468 – Mach 26,399.885 (3% light speed)… however it could be much faster or slower…

Kid Buu Blows up Earth – 8,205,240.342 Yottatons

Dragonball – Namek Feats

Zarbon Uses Seismic Toss

It’s super-effective!

Because this one is so straight-forward, I want to find not only the energy of this feat, but the speed required as well. That could tell us the speed of Zarbon in his transformed state after all. I know people aren’t big fans of using kinetic energy to find speed, but I think this is a very good example of how it can work out. I mean Zarbon generated the speed and took Vegeta with him so fast that it created such a crater. Let’s see what we get from it, shall we?

 

Vegeta is 1.64 m tall. He’s 25 pixels long here compared to the crater at 778 (Best I could find, but not quite the full crater).

778 / 25 = 31.12 * 1.64 = 51.037 m, diameter of crater.

Assuming that this is half a sphere, the volume would be 34,805.636 m^3

Alright, so this is obviously cratering, which is 87 J/cc.

34,805.636 m^3 = 34,805,636,000 cm^3

34,805,636,000 * 87 = 3,028,090,332,000 J or 723.731 Tons of TNT

Ok, but what about speed? That’s what I’m really interested in here. We got the energy, now we just need the mass of Vegeta. According to the Super Exciting Guide, Vegeta is 56 Kg… kind of a lightweight for a guy who looks as ripped as he does. lol

v = sqrt (KE / 1/2 m)

sqrt (3,028,090,332,000 / .5 * 56) = 328,855.718 m/s or Mach 967.223

Again, this is not a punch, kick, or ki blast. Zarbon literally gains speed and uses it against Vegeta. To me, this is a valid speed feat, but I’ll let you decide for yourself.

 

Recoome’s Eraser Gun

 

Recoome’s Eraser Gun creates a huge explosion and in Krillin’s words “Warps the planet”. Of course, we can’t see to what extent the planet has been altered and nothing ever comes of it, so I guess we can just measure the size of the blast, then?

We can do this by matching the curvature shown of Namek in the scan and then drawing a circle. Most planets are not perfect circles, but they’re close enough. I’ll be assuming that Namek is of a similar size to Earth as it has the same gravity and similar atmospheric conditions.

Based on the curvature, Namek’s assumed full diameter is 1,052 pixels compared to the explosion at 388. Using Earth’s diameter of 12,742 Km here…

388 / 1,052 = .369 * 12,742 = 4,701.798 Km, size of the explosion.

Using SD.net’s nuke calculator, this would be equivalent to 778.3 Teratons

I used near total fatalities for this one, as, unlike the Nappa feat from the previous entry, we can see exactly that this destroyed and warped the environment.

 

Freeza’s Destruction of Planet Vegeta

 

This is yet another speculative feat of sorts. Unlike Vegeta, though, Freeza doesn’t just make the claim that he’ll blow up a planet. He actually did it… off screen. We know nothing about the size of Planet Vegeta or exactly how it was destroyed, so all we can do is speculate.

What we know for sure is that Planet Vegeta had 10x the gravity of Earth. We also know that when Freeza destroyed it, he wiped all of the Saiyans out (Besides the ones who weren’t on the planet at the time). This tells me that it couldn’t have been a core detonation like Namek ended up being. Why would the Saiyans just sit around while a chain reaction eventually destroyed them? The fact that not a single one of them survived tells me that the destruction of the planet happened too quickly for anyone to react and survive by escaping to a pod.

Figuring out how much energy it would take to destroy a planet at an unknown size is not as much a shot in the dark as one might think. SD.net has a handy Planetary Parameter Calculator that can give a Gravitational Binding Energy yield based on a planet’s size and gravity. What’s also handy about the calculator is that it lets you know when the parameters are unrealistic. For instance, an earth-sized planet at 10x gravity would mean that the average density is nearly 3x greater than Uranium. There is no known planet in the universe at such a density. If we input the planet’s size at 40,000 Km, the calculator tells us it would require the planet’s density to be greater than lead on average. This would be incredibly rare. What I’m going to use for Planet Vegeta’s size as a low-end is 61,999 Km. This is the minimum size at 10 g that the average density of the planet wouldn’t be something outrageously rare or impossible. It still makes the planet a rarity, but it’s not as bad as the previous parameters and seeing as we have no visuals whatsoever, I feel the lowest end is safest.

Inputting the Planet Vegeta diameter at 61,999 Km, the GBE is 2,576,000,000,000,000,000,000,000,000,000,000,000 J or 615.679 Yottatons

Jupiter would have a GBE of around 478 Yottatons, for reference.

 

Freeza Destroys Namek’s Core

 

Feeza throws a ki ball that burrows down into Namek’s core and destroys it. This causes a chain reaction that will destroy the planet within 5 minutes. Now in regards to physics and such, I don’t believe that destroying a planet’s core would cause it to explode. I can understand the rationalization behind the idea though. There’s a ton of pressure at the planet’s core. Imagine if it were all released at once? It would be like explosive decompression, except on a planetary scale. Lava would shoot out everywhere and it would be very much like an explosion. However, a planet without its core cannot stay together. In fact, it would crumble apart, gravity would just about cease, and the atmosphere would go away. Dragonball does get the general idea though; the chaos of the environment is pretty accurate. But Goku, Gohan and the others being able to breath and the planet not immediately starting to crumble is what’s inaccurate here.

But anyway, the important part of this feat is the burrowing down and destruction of the core. We already calculated this for Vegeta, but in Feeza’s case, it’s not a hypothetical and the borehole is much larger than what was estimated for Vegeta.

 

My main assumption here is that the “height of eye” in this scan is 1.7 m, standard human viewing height. Based on distance to the horizon, that would make the distance 4.7 Km. I’m going to use angular size and solve for size of the borehole based on distance. We know from the scan after this one that the lightning shooting out of it is about the same size as the hole itself, so that’s what I’m basing it on. The human horizontal visual is 210 degrees.

880 / 210 = 4.191 pixels/degree

211 / 4.191 = 50.346 degrees, size of borehole.

The angular size calculator gives a size of 4,417.9 m, diameter of the borehole.

If you need a refresher on how I did things for a core detonation, refer back to my Vegeta post. I’ll be using most of the same parameters here. The key difference is in the size of the borehole. I will also be treating Namek like it’s Earth, because it is quite similar in terms of atmosphere (Bulma can walk around undeterred) and that’s the best we have to go off of.

Distance before reaching the core is 5,163.99 Km.

Treating the borehole as a cylinder, that would make the volume of destroyed minerals 79,160,228,030,618 m^3

Using 1,500 J/cc like before…

79,160,228,030,618 m^3 = 79,160,228,030,618,009,600 cm^3

79,160,228,030,618,009,600 * 1,500 = 118,740,342,045,927,014,400,000 J

Now just combine that with the previous figure to destroy the core, 138,109,160,691,977,970,300,000,000 J

138,109,160,691,977,970,300,000,000 + 118,740,342,045,927,014,400,000 = 138,227,901,034,023,897,314,400,000 J, or 33.037 Petatons

So the difference is negligible from what I got for Vegeta. It looks like the majority of the energy would be spent on destroying the core and a tiny percentage on the drilling itself.

 

Freeza Planetary Durability

Freeza survives the Namek explosion, and after being cut in half and smacked into the crust of the planet by a Goku ki blast, no less. Naturally, we could assume that he tanked the GBE of Earth/Namek, 53.576 Zettatons. It’s difficult to get any other sort of read on this because we have nothing like a time frame. I can make an assumption that the total debris traveled about twice the radius of Namek based on the top panel of the first scan, and I suppose since the others were pressing King Kai for an update, maybe give it a 1 minute time frame? Those are some lofty assumptions though, so take it with a grain of salt.

Weight of the earth is 5,972,000,000,000,000,000,000,000 kg. Again, we are left with little info about Namek so the best I can do is compare it to Earth. I’ll assume the debris traveled one full diameter of Namek, 12,742 Km.

12,742 / 60 = 212.367 Km/s or 212,367 m/s, speed of debris.

KE = 1/2mv^2

.5 * 5,972,000,000,000,000,000,000,000 * 212,367^2 = 134,667,831,669,354,000,000,000,000,000,000,000 J, or 32.186 Yottatons.

Again, this one is filled with assumptions so treat it as a high-end.

 

If you ever wanted a classic example of how wildly inconsistent Dragonball is in regards to the power of its characters, look no further than the Freeza saga. Zarbon throws Vegeta down at top speed and creates a big old crater in the ground. Recoome does the exact same thing to Vegeta and it barely makes a dent. The characters are like “WHAT??? FREEZA CAN DESTROY THE PLANET? NO WAY!” when Piccolo and Roshi destroyed the moon at power levels well under 1,000 and Vegeta threatened to destroy the Earth at a power level below everyone fighting Freeza toward the end of the saga. Then there’s Freeza destroying a planet with 10 g and is likely several times larger than Namek in his first form. In his final form and at 50%, over 100x higher in battle power than his first form, he “holds back too much” and only destroys Namek’s core. Final form Freeza is incapable of holding back more than his first form because that’s the whole reason he came up with those other forms in the first place; he can’t control his power/lower it enough unless he does that.

So yeah, good luck making any sense of this. lol

 

TOTALS

Vegeta Impact Crater – 723.731 Tons of TNT

Monster Zarbon Speed – Mach 967.223

Recoome’s Eraser Gun – 778.3 Teratons

Freeza Destroys Planet Vegeta (Speculative) – 615.679 Yottatons

Freeza Destroys Namek’s Core – 33.037 Petatons

Namek Explosion/Freeza Durability – 53.576 Zettatons – 32.186 Yottatons.

Dragonball – Saiyan Saga Feats

Piccolo’s Makankosappo

“Makanksapalopogis!”

“Light of Death!”

“Special Beam Cannon!”

Piccolo’s Makankosappo punches a large hole through a mountain. You may be wondering why I’m bothering with this when Piccolo already has a multi-continent level attack under his belt, but I’m specifically looking for pressure here. The Makankosappo is really quite small, and when something small is filled with lots of energy, that generally means a high amount of pressure.

Unfortunately there’s no good way to measure the mountains of the area except by the fact that most of them are taller than clouds. So the best I can do is measure the mountain based on that. I know that there are some who are strictly against using cloud heights because technically they can get as low as the ground (fog), but that’s only when the conditions are overcast. This is obviously a clear day and a cumulus cloud, which has a minimum height of 500 m.

Height of the mountain is 65 pixels compared to the cloud at 26.

65 / 26 = 2.5 * 500 = 1,250 m, height of mountain.

Mountain is 87 pixels tall compared to the diameter of destruction at 46.

46 / 87 = .529 * 1,250 = 661.25 m, diameter of hole.

I’m going to treat this as 1/3rd of a sphere given the shape of the hole and the mountain.

4/3 pi r^3

4/3 * 3.14 * 330.625^3 = 151,324,772.276 * .333 = 50,391,149.168 m^3, volume of destruction.

There is visible debris, but also signs of burning and trace amounts of vapor. So I’m going with cratering here. 87 J/cc.

50,391,149.168 m^3 = 50,391,149,168,000 cm^3

50,391,149,168,000 * 87 = 4,384,029,977,616,000 J

Force = Work / Distance

The Makankosappo penetrated the radius of the destruction, so…

4,384,029,977,616,000 / 330.625 = 13,259,826,019,254.442 N, force.

Now we need to find the area of the Makankosappo itself.

Goku is 1.75 m tall. He’s 692 pixels here compared to the Makankosappo’s tip (Get your mind out of the gutter!) at 58.

58 / 692 = .084 * 1.75 = .147 m, diameter of Makankosappo.

Alright, now I need the surface area of the tip to figure out pressure. I’m treating is as a half-sphere.

4 pi r^2

4 * 3.14 * .074^2 = 0.069 / 2 = .035 m^2, surface area that acted upon the mountain.

P = F / A

13,259,826,019,254.442 / .035 = 378,852,171,978,698.343 N/m^2 or 378,852,171.979 MPa or 378.852 TeraPascals

For comparison, the Earth’s inner core exerts a pressure of 360 GigaPascals.

The pressure of the Makankosappo is comparable in pressure to the inside of hydrogen bombs, and is greater than the minimum pressure required to change solid matter into a molecular state.

Only about 2% of the pressure exerted at the sun’s core, but that’s more than most pressures can say. 😉

 

Piccolo Destroys the Moon

 

Dragonball characters hate the moon, especially Piccolo, so he decides to blow it up. Yep, that’s the canon reason for this happening. It’s right there in the scan. In that panel on the top left, he’s saying “Fuck the moon!” in case you didn’t know. 😀

Anyhow, the low-end for this feat is a rinse and repeat of Roshi’s Moon buster of 29.757 Exatons TNT.

The higher-end is a bit more confusing. We have no real frame of reference for how far the chunks of moon traveled in the second scan despite the fact that they’re visible. There is also no sign of a time frame. The best I can really do is make the same assumption I made for Roshi and give this a 1.179 Zetatons TNT estimate, although that’s not very satisfying, so the least I can do is get a speed for the ki blast.

The moon travels around Earth at 3,683 Km/h or 1,023.056 m/s.

The moon’s radius is 1,737.1 km. If Piccolo is aiming at the center of the moon, that means we can get the max amount of time he would have to hit the moon.

1,737,100 / 1,023.056 = 1,697.952 s, max time frame.

The moon is 384,400,000 m from Earth.

384,400,000 / 1,697.952 = 226,390.381 m/s or Mach 665.854

This is the bare minimum low-end. I should remind everyone that 1,697.952 seconds is roughly 28 minutes and while there is a clear elapsed time (based on the destruction that Gohan caused between panels), I would find it hard to believe that Piccolo stands there in the same pose firing a ki blast for 28 minutes while not drawing the attention of Gohan in any way. I personally don’t believe it could have taken more than a minute for the above reasons, so let’s treat that as our high-end.

384,400,000 / 60 = 6,406,666.667 m/s or Mach 18,843.

 

Nappa Raises Two Fingers

Nappa raises two fingers which creates a ki blast that wipes out East City and presumably anything else nearby. There’s some debate on this one because the news station only ever mentions that East City is destroyed. However, looking at the Dragonball map…

There really isn’t anything within the vicinity of East City. It’s just a bunch of mountains and wasteland. But at any rate, let’s get to the scaling.

Earth’s diameter is 12,742 Km. It measures 186 pixels comapred to the blast at 52.

52 / 186 = .28 * 12,742 = 3,567.76 Km, diameter of blast.

Going by sd.net’s nuke calculator, and using wide-spread destruction as the measuring stick, that would give this blast a yield of 17.804 Teratons of TNT

If we were to base it off of near total fatalities instead, the yield would be 337.19 Teratons of TNT.

I can’t be sure which to choose because most of this blast hit wasteland. Only the city was demolished completely, and we don’t know what happened to the rest of the landscape.

 

Vegeta’s Planet Busting Threat

I’m not really going to give my opinion on whether or not Vegeta could fully destroy Earth in one shot or not. The fact is, it never happened and it doesn’t really matter because moon busting power hitting Earth would still end all life on it anyway.

Still, just as a theoretical, let’s see what he would need to come up with to do such a thing.

The first, most obvious method is with gravitational binding energy. That’s how we figured out the low-end for Roshi’s moon buster.

U = 3GM^2 / 5R

Where G is the gravitational constant, M is the mass of the spherical body, and R is the radius of that spherical body.

G = .0000000000667384 m^3 kg s

M = 5,972,000,000,000,000,000,000,000 kg

R = 6,371,000 m

3 * .0000000000667384 * 5,972,000,000,000,000,000,000,000^2 / 5 * 6,371,000 = 224,160,472,814,842,253,963,271,072,045,200 J or 53.576 Zettatons

 

Another possibility was that Vegeta was planning to pull a Freeza if you will and destroy the planet’s core. That way he would at least have some time to escape to his space pod. Figuring this one out is a little tougher.

First, we have to figure out how much he’d need to burrow down.

The distance from the surface to the center of Earth’s core is 6,371 Km. The Earth’s inner core is  made of solid iron that’s 750 miles/1207.01 Km in diameter. To figure out the distance, I’ll just subtracted the radius of the core from the distance to its center.

6,371 – 1,207.01 = 5,163.99 Km, distance to drill before reaching core.

My assumption will be that the hole is 1 m in diameter based on the size of the ki beam itself. Using the volume of a cylinder…

4,055,788.262 m^3, volume drilled.

For the burrowing itself, I’m going to assume it’s done in the way of thermal spalling, which is 1,500 J/cc.

The main reason for this is speed. The way I see it, treating the blast like a regular rotary bit drill wouldn’t make much sense because that would take a long time and not destroy enough rock/minerals to successfully bore down into the core. This would also be sure to account for the molten metals that are difficult to get figures of destruction for. As for destroying the iron core itself, I’m sticking with the figure, because merely destroying the iron wouldn’t destroy the core. The pressure at the core is so high that fragmenting it would merely make it stick together again under the intense pressure. And knowing that the figure for fragmenting iron is 96 J/cc, I feel that 1,500 isn’t too far off from destroying it enough that the core doesn’t re-form.

4,055,788.262 m^3 = 4,055,788,262,000 cm^3

4,055,788,262,000 * 1,500 = 6,083,682,393,000,000 J

Now for the core itself. As a 1,207,010 m sphere, the volume would be 92,072,773,794,652,000 m^3

92,072,773,794,652,000 m^3 = 92,072,773,794,651,980,200,000 cm^3

92,072,773,794,651,980,200,000 * 1,500 = 138,109,160,691,977,970,300,000,000 J

Adding them together…

138,109,160,691,977,970,300,000,000 + 6,083,682,393,000,000 = 138,109,160,698,061,652,693,000,000 J, or 33.009 Petatons

The assumption that the borehole would be the diameter of Vegeta’s ki blast probably lowered the results here. In the case of Freeza where the borehole was much larger and is something I can potentially measure, we can get more concrete results.

 

TOTALS

Piccolo’s Makankosappo – 378.852 TeraPascals

Piccolo Destroys the Moon – 29.757 Exatons – 1.179 Zetatons TNT

Piccolo Ki Blast Speed – Mach 665.854 – Mach 18,843

Nappa Raises 2 Fingers – 17.804 – 337.19 Teratons

Vegeta Planet Busting Threat – 33.009 Petatons – 53.576 Zettatons

Dragonball – 23rd Budokai feats

Papaya Island Size

Before I get to any feats from the 23rd Budokai, to make life a whole lot easier, I’m going to scale the size of Papaya Island, as it is directly linked to pretty much every major feat we’ll be going over.

During the 22nd Budokai, announcer guy hops on a small jet and flies after Goku and Tenshinhan to see who falls first. In the middle panel on the left, we’re given a view which shows the island ending as a crescent shaped bay. The ending part of the crescent is right on the horizon (See red arrow). We can use that to find out the distance between the Budokai ring and the bay, then use that to get the full island size.

But first, we need to figure out how high up our view is in that panel.

Above are several examples from the page before showing that the palm trees in the area are at least 4 stories tall.

4 stories = 13.2 m.

If we assume that announcer guy has an average male sized head of .24 m, and his head measures 9 pixels compared to difference in height between just under jet stream (Our view height) and the top of the tree is 72 pixels…

72 / 9 = 8 * .24 = 1.92 m.

1.92 + 13.2 = 15.12 m, height of eye.

With the horizon distance calculator, we can figure out how far away that crescent bay is from our view. Inputting the height of eye found earlier, the result is 13.9 Km.

The distance from the blast epicenter (Budokai Ring) to the crescent bay is 400 pixels compared to the diameter of the island at 861.

 

861 / 400 = 2.153 * 13.9 = 29.927 Km, diameter of Papaya Island.

With that out of the way, we can get to the actual feats of the 23rd Budokai.

 

 

Piccolo’s Ocean Ki Blast

Piccolo fires a ki blast, and it creates a huge wave in the water upon exploding. Getting a frame of reference for this one is difficult because there is nothing comparatively close to the water. However, if you look closely, you’ll notice that the explosion of water is just past a crescent shaped bay. 😉

With angular size, we can figure out the size of this water displacement/wave.

Using the vertical field of vision, because in this panel, it’s clearly larger than the horizontal field. The vertical field of vision is 150 degrees.

480 / 150 = 3.2 pixels / degree

208 / 3.2 = 65 degrees, base of the wave.

375 / 3.2 = 117.188 degrees, height of the wave.

With the angular size calculator, we can solve for size based on the minimum distance of 13.9 Km.

Base of wave = 17,711 m

Height of wave = 45,533 m

I’m going to treat this wave as a cone. I need the center of gravity, which luckily this handy calculator can tell me.

Center of gravity = 11,383.250 m

Density of ocean water is 1,027 kg/m^3

Now for volume of the cone…

pi * r^2 h / 3

3.14 * 8,855.5^2 * 45,533 / 3 = 3,737,324,719,769.668 m^3

3,737,324,719,769.668 * 1,027 = 3,838,232,487,203,449.036 Kg of displaced water.

From here we can find the gravitational potential energy.

mgh

Where m is mass of the water, g is gravity (9.8), and h is the center of gravity in this case.

3,838,232,487,203,449.036 * 9.8 * 11,383.250 = 428,177,287,607,594,880,142.661 J or 102.337 Gigatons.

Hot damn Piccolo! And I want to remind everyone that this was undercut by the fact that I have no way of figuring out how far from the crescent bay the explosion happened.

 

Piccolo’s Mountainous Ki Blast

Piccolo fires a deadly ki blast that creates a large mushroom cloud off in the distance. Interestingly enough, we can get both a power and speed from this feat. Let’s start with power.

The ki blast reaches the mountains to the west. Using our previously established scaling, we can figure out the mountain size, and then the mushroom cloud by default.

70 / 400 = .175 * 13,900 = 2,432.5 m, height of the tallest mountain of the cluster.

Tallest mountain of the cluster measures at 79 pixels vs 528 for the mushroom cloud height.

528 / 79 = 6.684 * 2432.5 = 16,258.83 m, height of the mushroom cloud.

Based on this chart, this would mean the blast would be in the 700-800 Kiloton range.

But how about the speed? You may have noticed earlier that the ki beam travels all the way to the cluster of mountains in the time that Goku falls a short distance.

Distance to the mountain cluster is 370 pixels compared to 400 from Budokai grounds to crescent bay.

370 / 400 = .925 * 13,900 = 12,857.5 m, distance to mountain cluster.

Goku is 1.75 m tall. He’s 313 pixels here compared to 176 for the length of his leg.

176 / 313 = .562 * 1.75 = .984 m, length of Goku’s leg.

Goku’s leg is 47 pixels long compared to how much he has fallen from the middle of the ki beam at 147.

147 / 47 = 3.128 * .984 = 3.078 m, distance Goku fell.

Now we just use free fall to figure out the time frame that it took for the blast to reach those mountains.

3.078 = .5 * 9.8 * t^2

t = .793 s, time frame.

12,857.5 / .793 = 16,213.745 m/s or Mach 47.69

 

And now for the big one…

 

Piccolo Razes Papaya Island

Piccolo razes Papaya Island to the most extreme degree. Not only does he destroy all buildings/man-made objects, but the mountains are wiped off the map as well. The blast even creates a tsunami! However, in order to calculate how incredibly powerful this feat is, I’ll only need to measure the size of one mountain despite the fact that the attack destroyed a dozen of them. 😉

Why, you might ask? Because inverse square law will give us the answers we need. From the sheer distance of the furthest away mountain being wiped out, that’s how we’ll know the sheer power behind this attack.

Distance from the Budokai ring to the farthest away mountain is 350 pixels. The mountain itself has a 41 pixel base and a height of 33. As a reminder, the distance from Budokai ring to crescent bay (400 px) is 13,900 m.

350 / 400 = .875 * 13,900 = 12,162.5 m, distance from ring to mountain.

41 / 400 = .103 * 13,900 = 1,431.7 m, base of mountain.

33 / 400 = .083 * 13,900 = 1,153.7 m, height of mountain.

Using this dome calculator, we can find volume.

Volume = 1,732,699,532.74 m^3

There is a decent amount of visible debris and all of the mountains are next to the water. There are, however, also signs of burning. To me, this indicates cratering, 87 J/cc.

1,732,699,532.74 m^3 = 1,732,699,532,740,000 cm^3

1,732,699,532,740,000 * 87 = 150,744,859,348,380,000 J

But we’re not done yet. That is simply the power of the attack after weakening for a whopping 12 Km.

Inverse Square will tell us the point blank power of this attack, which Goku tanked. I also want to point out, for anyone doubting its validity, that ki did not destroy those mountains. The scope of the explosion would be even less than the mushroom cloud, which did not reach the mountains. Rather, a shockwave destroyed them. Interestingly enough, Daizenshuu 7 backs my claims up.

S/4 pi r^2 = I

Where S is the source strength, r is the “radius” or distance from the initial attack, and I is the final intensity. We’re solving for S here.

In addition, we need to know what part of the surface area of the hemisphere struck the surface area of the mountain.

Luckily the surface area of a dome can be found with the same handy dome calculator used earlier. The surface area of this mountain is 5,791,415.83 m^2

The surface area of the explosion is 1,857,955,662.5 m^2

1,393,466,746.875 / 5,791,415.83 * 150,744,859,348,380,000 = 48,360,758,964,719,112,770.348 J or 11.559 Gigatons

Originally I did this and got much higher numbers, but that was because I forgot to relate the surface area of the explosion and surface area of the mountain destroyed to figure out which was needed.

Anyway, that’ll do it for part one of Dragonball. Next up I’ll be handling Z, which will mostly have to do with powerful ki blasts and speed and just about nothing to do with physical strength.

 

RESULTS

Piccolo’s Ocean Ki Blast – 102.337 Gigatons

Piccolo’s Mountainous Ki Blast Power – 700-800 Kilotons

Piccolo’s Mountainous Ki Blast Speed – Mach 47.69

Piccolo Razes Papaya Island – 11.559 Gigatons of TNT

 

Ever notice how it’s always the bad guys who destroy stuff/have the most impressive feats?

 

Dragonball – Piccolo Daimao Feats

Piccolo Daimao’s Hand Wave

Feeling spry and youthful as ever, Piccolo Daimao decides to blow up a chunk of the city to make the king of the world his bitch (Because he’s a dog, get it?). This was also done in his non-powered up state, which makes this a fairly casual feat on his end.

For the longest time I wasn’t sure how to scale this, but that was because I was looking at poor quality scans. With these raw scans, you can actually see people running away after the destruction. They’re small enough to be dots, but there are some people close to our view who we can see fleeing so it makes sense.

I can forgive you if you don’t notice it at first, but I measured near the blast and most of the little specs measure at around 3 pixels tall. The blast diameter of destruction is 726 in comparison. I’ll be assuming an average Japanese male height of 1.70 m.

726 / 3 = 242 * 1.70 = 411.4 m, diameter of destruction.

I’m going to use the Taylor Method to find the power behind the blast, but there’s a slight problem in that I need the size of the fireball. Not simply what the attack destroyed. As we can see above, the fireball is… multiple fireballs? Or at the very least oddly shaped. In the scan of the aftermath, however, it’s almost like a completely uniform spherical explosion. So for now I’m just going to measure it that way.

The building is 5 stories tall, which is around 16.5 m. It measures at 48 Pixels compared to 637 for the fireball.

637 / 48 = 13.271 * 16.5 = 218.972 m, diameter of explosion.

218.972 / 2 = 109.486 m, radius.

No sign of a mushroom cloud or uniform fireball, so I’ll treat it a high explosive. 3,000 m/s.

109.486 / 3000 = .037 s, time frame.

8 * 3.14 * 1.2 * 109.486^5 / [75(1.4 – 1)0.037^2] = 11,546,998,920,537.061 J or 2.76 Kilotons

 

Piccolo Punches Goku

Piccolo punches Goku into the ground,  making a crater. Although this may not seem like anything special at first, I want to apply the inverse square law to see what the original energy of the strike was.

Tenshinhan is 117 pixels compared to 340 for the crater diameter. Tenshinhan is 1.87 m tall.

340 / 117 = 2.906 * 1.87 = 5.434 m, diameter of crater.

That would make the volume 42.01 m^3, assuming a perfect half-sphere.

42.01 m^3 = 42,010,000 cm^3

Obviously this is cratering so we use 87 J/cc.

42,010,000 * 87 = 3,654,870,000 J, or 873.535 Kg of TNT

However, this is only the energy of Goku upon impacting the ground. With inverse square law, I can figure out the energy of the original punch.

If we treat the distance between the initial punch and where Goku landed as a “sphere” (Think of it like a wave of energy), and say that they were 5 m in the air when Piccolo punched…

S/4 pi r^2 = I

Where S is the source strength, r is the “radius” or distance from the initial attack, and I is the final intensity. We’re solving for S here.

S / 4 * 3.14 * 5^2 = 3,654,870,000

S = 1,147,629,180,000 J, or 274.29 Tons of TNT

Now of course I do realize that I made some assumptions, namely how far Goku traveled, but they were high enough to be on-level with a few floors up on a building. And the fact that Tenshinhan thought the punch killed Goku tells me that he thought it was at least as strong as his Ki Ko Ho, if not more.

 

Piccolo Daimao’s Explosive Demon Wave

Piccolo completely wipes out Central City with his Explosive Demon Wave. The way I see it, there are 2 potential ways to scale this. Both involve the fact that the king’s castle is in the middle of the city, according to Daizenshuu 7.

Here is method 1:

The destruction caused by Piccolo’s hand wave is 411.4 m in diameter. It measures 49 pixels here compared to 270 for the distance from that destruction to the king’s castle.

270 / 49 = 5.51 * 411.4 = 2,266.814 m.

2,266.814 * 2 = 4,533.628 m, diameter of Central City

Using the SD.net nuke calculator, imputing for near total fatalities, that would be a nuclear yield of 550 Kilotons.

 

TOTALS

Piccolo Daimao Hand Wave – 2.76 Kilotons

Piccolo Daimao Punches Goku – 274.29 Tons of TNT

Piccolo Daimao’s Explosive Demon Wave – 550 Kilotons

Dragonball – 22nd Budokai Feats

Yamcha’s Kamehameha

 

Tenshinhan reflects Yamcha’s Kamehameha back at him and there’s a fairly large explosion as a result. Since Yamcha has been feat-less for a while now, I thought this would be a nice way to check his progress.

I’m assuming the man knocked back by the explosion is 1.70 m tall, the average Japanese man’s height. We can see here that the explosion is 165 pixels compared to the man at 16.

165 / 16 = 10.313 * 1.70 = 17.532 m, diameter of explosion.

From here we just need to use the Taylor Formula.

E = 8*pi*p*R^5 / [75(y-1)t^2]

Where p is density of the air, t is time after explosion has formed, R is radius of the explosion. y is specific heat ration (Will be using 1.4 here as is common)

For time, I’ll be using the speed of the explosion. A shockwave clearly hits the crowd and bends the trees, but what’s tough is figuring out just how fast it is. Due to the explosion being over 10 m, I’m going to treat this as a smaller high explosive. The minimum detonation velocity of a high explosive is 3,000 m/s.

17.532 / 2 = 8.766 m, radius of explosion.

8.766 / 3000 = .00292 s, time frame.

8 * 3.14 * 1.2 * 8.766^5 / [75(1.4 – 1).00292^2] = 6,099,879,489.548 J or 1.458 Tons of TNT.

 

Chaozu Full Power Dodonpa

Another decent sized explosion at the 22nd Budokai. This one is very similar to Yamcha’s Kamehameha, and I’ll be doing the calculation in the exact same way.

Jackie Chun/Roshi is 1.65 m tall. He’s 31 pixels here compared to the explosion at 237.

237 / 31 = 7.645 * 1.65 = 12.614 m, diameter of explosion.

We see once again that a shockwave smacks several characters in the face. The blast is over 10 m in size, so I’ll use 3,000 m/s for the lowest end high explosive.

12.614 / 2 = 6.307 m, radius of the explosion.

6.307 / 3,000 = .0021 s, time frame.

8 * 3.14 * 1.2 * 6.307^5 / [75(1.4 – 1).0021^2] = 2,273,815,339.074 J or 543.455 Kg of TNT

 

Goku’s Disappearing Act

 

Goku moves back and forth so fast that no one besides Tenshinhan can see him, and even he can only barely make out his image. Roshi and Krillin are unable to see him, and one of those two is a casual bullet timer. With that said, I have no way to calculate based on that. I can only base it off the fact that the normal humans in the crowd see no trace of him at all. They are watching him from all angles, and not even a trace of light of Goku is showing up for their eye to perceive. This means Goku, even under less than ideal conditions, is fooling hundreds of human eyes.

For a human to not see any trace at all of Goku from all angles, Goku would have to be surpassing their vision at over 500 frames per second.

So we use 501 fps as a low end. 1 / 501 = .00199 s

Goku at the time of the 22nd Budokai is 1.12 m tall. He’s 110 pxiels here compared to 362 for the distance he’s jumping back and forth at.

362 / 110 = 3.291 * 1.12 = 3.686 m, distance from which Goku pushes off to.

Now at bare minimum, Goku would need to jump on one side each during the time frame for no one to see him.

3.686 * 2 = 7.372 m, distance traveled.

7.372 / .00199 = 3,705523 m/s or Mach 10.9

While this is below Tao’s feat, I want to stress that this is the bare minimum for Goku to fool the crowd in the way he did. Being able to fool Krillin and especially Roshi means that he is faster than this, there’s just no way to quantify that without stacking calculations (Which is not a road I wish to go down)

Still, it’s yet another casually hypersonic feat under early Dragonball’s belt.

 

Tenshinhan’s Kikoho

 

Tenshinhan’s Kikoho blows away the ring and punches a big hole in the ground underneath. Note: This is the point in the scanlations where it goes back to the crappy quality scans, so for the sake of your eyes, I’m uploading the raw manga scans from here on.

Roshi is 1.65 m tall. He’s 43 pixels here, compared to 473 for the length of destruction, and 254 for width.

473 / 43 = 11 * 1.65 = 18.15 m, length of destruction.

254 / 43 = 5.907 * 1.65 = 9.747 m, width of destruction.

One problem here is that we’re never shown the full depth of the hole. I tried to find a scan that showed the hole as deep as possible, however:

Width of the hole is 193 pixels compared to 82 for the depth.

82 / 193 = .425 * 9.747 = 4.143 m, minimum depth of hole.

 

We also need the ring dimensions. We can easily using the length and width, but we also need the depth of the ring.

My assumption here is that the announcer guy is 1.70 m tall, the average Japanese male’s height. He’s 65 pixels here, compared to the ring height of 29.

29 / 65 = .446 * 1.70 = .758 m, height of ring.

Next we’ll add that to the depth of destruction, just to simplify.

.758 + 4.143 = 4.901 m, total depth of destruction.

 

From here, getting the volume is easy.

4.901 * 18.15 * 9.747 = 867.026 m^3

Another tricky thing about this feat is how the rock was destroyed exactly. We can’t see the bottom of the pit, so we have no idea to what extent the particles were ground up. However, we can see a small cloud of dust come from the pit, and for the hole to be deep without debris outside of the hole, the rock would have to be well ground. Since we can only see a little bit of debris from a large amount of destroyed rock and no large chunks visible, the particle size should be something low, but nothing too crazy.

For this feat, I’m going to use the Kuznetzov Equation with an average particle size of 1 cm.

k50= A(V/Q)^0.8 * Q^1/6

1 = 7(867.026/Q)^0.8 * Q^1/6

Q = 111,062 Kg TNT or 111.062 Tons of TNT

 

Once again I must stress that this isn’t the most reliable method without being able to see the particle size. Instead I’m stuck with relying on guesswork. Still, I can see 111 tons of tnt being a threat since it’s a big step up from previous feats aside from Roshi’s Max. Power Kamehameha.

 

RESULTS

Yamcha’s Kamehameha – 1.458 Tons of TNT

Chaozu’s Full Power Dodonpa – 543.455 Kg of TNT

Goku’s Disappearing Act – Mach 10.9+

Tenshinhan’s Kikoho – 111.062 Tons of TNT

Dragonball – Red Ribbon Army Feats Pt. 3

Tao Pai Pai Goes Cross Country

Tao breaks off a pillar, then throws it (And rides it!) 2,300 Km to pay Goku and the others a visit. This is both a strength and speed feat. A classic in the versus battle community to say the least. It brings back some fun memories. I remember many people denying it’s viability, thinking it made him too strong, but actually? It’s quite in line with the power progression of Dragonball, and more of a landmark speed showing than of strength. The only thing here that would make a physicist roll their eyes is the lack of inertia at play. The pillar being thrown at such a speed should have caught on fire. But if you can get past that, it’s actually a rather cut and dry thing.

Tao is 1.78 m tall. He’s 199 px here compared to the column at 270 tall and its diameter of 47. His arm is 81 pixels, which I’ll be using later.

270 / 199 = 1.357 * 1.78 = 2.416 m, height of the column.

47 / 199 = .236 * 1.78 = .42 m, diameter of the column.

81 / 199 = .407 m, length of Tao’s arm

To me, this looks most like a marble column, based on its shape and coloring. Marble is 2,711 kg/m^3.

3.14 * .21^2 * 2.416 = .335 m^3, volume of column.

2,711 * .335 = 908.185 kg, weight of the column.

With the handy projectile motion calculator, we can plug in the numbers: 2,300,000 m for distance, and 45 degrees for angle.

This gives us an initial velocity of 4749.242 m/s for the pillar. Now to apply the length of Tao’s arm to the distance it acted on the pillar to get acceleration, we need to figure out how much the arm moved and go from there. From what I can tell, Tao appears to have rotated his arm about 1/3rd of a circle. With his arm length at .407 m, this would mean the throw was a total of .853 m.

a =  v^2 / (2 * d)

4749.242^2 / 2 * .853 = 13,221,160.36 m/s^2

f = ma

13,221,160.36 * 908.185  = 12,007,259,521.547 N

w = f * d

12,007,259,521.547 * .853 = 10,242,192,371.88 J or 2.448 Tons of TNT

Like I said, this is a fairly natural progression to what we’ve seen thus far. Tao is a major step up from any of the prior villains in terms of power, and this is just how strong his punch is! More impressive here is his speed. With angular size, I’m going to figure out how fast he moved to catch up with the pillar.

The human horizontal field of vision is 210 degrees. The panel is 355 pixels wide, with the diameter of the column being 10 px from this perspective.

355 / 210 = 1.691 pixels/degree

10 / 1.691 = 5.914 degrees

Knowing that the diameter of the column is .42 m, we can use the calculator to find that the end of the column is 4.065 m away.

However, we need to account for the fact that Tao lands in the middle of the column, so I’m adding half of the column’s height to that distance.

4.065 + 1.208 = 5.273 m, distance between column and Tao before takeoff.

Repeating what we did before… the human field of horizontal vision is 210 degrees. The column measures at just 4 pixels from this view, while Tao is at 120.

680 / 210 = 3.238 pixels/degree

4 / 3.238 = 1.235 degrees, diameter of pillar.

120 / 3.238 = 37.06 degrees, Tao’s height.

Once again, with all the info we have, all we need to do is plug in the numbers and solve for distance to find…

Distance from Red Ribbon HQ = 19.484 m

Now we have to subtract by half the pillar height to account for where Tao eventually lands.

19.484 – 1.208 = 18.276 m, distance traveled of the column.

18.276 – 5.273 = 13.003 m, distance traveled by column since Tao jumped.

Using the angular size calculator, we find that Tao is 2.66 m from our view.

2.66 – 1.208 = 1.452 m, distance between Tao and his destination.

We now have all that is needed to get Tao’s speed. Each of their accelerations are near instantaneous and should be non-factors here. What we need to figure out is how far Tao traveled in the same time that the pillar moved since the jump (13 m). From there we can get Tao’s speed.

Pillar speed = 4,749.242 m/s

13.003 / 4,749.242 = .00274 s, the time frame.

Using how far the column has traveled and Tao’s distance from it in the panel, we can figure out how far he moved during that time frame.

18.276 – 1.452 = 16.824 m, distance traveled by Tao.

16.824 / .00274 = 6,140.146 m/s, or mach 18.06

Impressive… most impressive!

Commander Black Battle Jacket Laser

Commander Black’s battle jacket fires a laser which vaporizes a decent amount of stone. Remember that in the past, we have established that concrete can’t be vaporized unless there’s liquid inside of it; that’s how we know that this is stone.

Conveniently, we have found Goku’s leg length in the past to be .425 m. Even more convenient is that the stone slab length is the same as Goku’s leg. So the stone slab is .425 m.

Unfortunately, the best I can do for the vaporized wall is treat it as a half-circle. That said, I can’t account for the chunk of wall destroyed on the other side, so this calculation will be at least slightly low-end.

We see that the slab is 24 pixels compared to the crater at 199, diameter of the half-circle wall at 183, and the wall thickness at 14.

199 / 24 = 8.292 * .425 = 3.524 m, diameter of crater.

183 / 24 = 7.625 * .425 = 3.241 m, diameter of half-circle wall.

14 / 24 = .583 * .425 = .248 m, thickness of wall.

Assuming that the crater is a perfect half-sphere, the volume of that destruction is 22.91 m^3

The volume of destroyed wall, treated as a half cylinder, would be 2.05 m^3

22.91 + 2.05 = 24.96 m^3 of vaporized stone.

The vaporization point of stone is 1,730 C.

Stone has a density of 2,700 kg/m^3. 2,700 * 24.96 = 67,392 Kg of stone vaped.

Specific Heat of stone is .84 KJ/Kg K or 840 J/Kg C.

Going to assume a stone temperature of 37.5 degrees C before the conversion to vapor.

1,730 – 37.5 = 1,692.5 C

67,392 * 840 * 1,692.5 = 95,811,206,400 J

Now we need to find latent heat of vaporization. Stone has a latent heat of vaporization of 4.3 KJ/g, or 4,300,000 J/Kg

67,392 * 4,300,000 = 289,785,600,000 J

289,785,600,000 + 95,811,206,400 = 385,596,806,400 J, or 92.16 Tons of TNT

Again, there was a chunk of wall that I couldn’t account for, but I would guess the results wouldn’t increase that much from it anyway. The majority of the damage was to the ground.

Goku Kicks a Missile

Goku is able to kick a missile away into the mountains. The top of the mountain is then blown up. Originally I was going to calculate the power of Goku’s kick based on momentum, but then I realized that he merely changed its direction and the rocket continued in with its usual propulsion. lol

The guard is 12 px tall (I’ll assume an average Japanese height of 1.70 m) and the base wall is 48.

48 / 12 = 4 * 1.70 = 6.8 m, height of the wall.

I’m looking for an “Average” tree size here. It’s the only way to get an idea of the mountain size that I can see. Wall is 15 px compared to a taller tree at 29.

29 / 15 = 1.933 * 6.8 = 13.144 m, height of tree.

Tree is 10 pixels compared to the mountain base at 283, and the mountain height at 121.

283 / 10 = 28.3 * 13.144 = 371.973 m, base of mountain.

121 / 10 = 12.1 * 13.144 = 159.042 m, height of mountain.

Base of mountain is 231 pixels, compared to remaining height of 53 and diameter of destruction at 97.

53 / 231 = .229 * 371.973 = 85.182 m, remaining height of mountain.

97 / 231 = .42 * 371.973 = 156.229 m, diameter of destruction.

159.042 – 85.182 = 73.86 m, height of destruction.

Treating the destroyed chunk of mountain as a cone, the volume would be 471,961.742 m^3

Since there is clear debris, signs of burning, and also the fact that it was a nuke, I’ll be using 87 J/cc.

471,961.742 m^3 = 471,961,742,000 cm^3

471,961,742,000 * 87 = 41,060,671,554,000 J or 9.814 Kilotons

TOTALS

Tao Pai Pai’s Punching Power – 2.448 Tons of TNT

Tao Pai Pai’s Speed – Mach 18.06

Commander Black Battle Jacket Laser – 92.16 Tons of TNT

Commander Black Battle Jacket Missile – 9.814 Kilotons

Dragonball – Red Ribbon Army Feats Pt. 2

AKA: “General Blue is Durable as Hell”

 

Goku’s Kamehameha Pushes the Sub

Goku’s Kamehameha pushes the sub out from deep waters and up to the surface. I believe this was done over a long distance and makes for an impressive feat.

First of all, for the submarine itself, which can carry three people as seen above, I am comparing it to the Triton Submarine, which carries the same amount and has a similar shape. Its mass is 4 tons, which I’ll be using for this feat as well.

Now for how deep they were, I’m going to say 200 meters. All we really know for sure was that Goku ran out of breath before he could even see the underwater cave leading to the dragon ball, and considering the human world record for a dive without equipment is over 100 meters, I feel this is more than reasonable. In addition, we see that the waters around the cave are dark. Sunlight becomes less significant in the ocean at depths of 200 m and more.

Finally, for speed at which the sub was pushed, I compare the sub shooting out of the water and up into the air to an orca. They are a similar weight, and shoot up out of the water like that to catch prey from time to time. Orcas swim at a 28 MPH top speed, or 12.5 m/s. This is the presumed velocity of the sub while Goku pushes it with his Kamehameha. We can also see that within just a few meters, they reach a high speed, so for acceleration, I’ll assume they reached top speed within 2 meters.

12.5 * 2 = 25 m/s^2, acceleration.

f = ma

4,000 * 25 = 100,000 N

But there’s more to it than that. We need to take into account the drag of the water pushing back against the sub as Goku pushes it.

Fd = 1/2pu^2 * Cd * A

Where p is density of fluid, u is flow velocity, A is area pushing against fluid, and Cd is a drag coefficient dependent on a shape.

The density of water is 997 kg/m^3

Flow velocity = object velocity = 12.5 m/s

Drag coefficient for a half-sphere is .42

Goku is .97 m tall. He’s 65 px here compared to the front of the sub at 71.

71 / 65 = 1.092 * .97 = 1.059 m, height of the half-sphere.

This would make the surface area about 1.765 m^2

But we should also get the surface area for Goku and the part of Bulma that was dragged (from shoulder up). Surface area of a child’s body on average is 1.07 m^2. Average for a woman is 1.6, but this is only about 1/3rd of Bulma’s body, so let’s just cut that into a third. 1.07 + .533 + 1.765 = 3.368 m^2, total surface area

1/2 * 997 * 12.5^2 * .42 * 3.368 = 110,180.963 N, drag force.

Now that we know the drag, we just need to get net force. This is simple: Add the drag force to normal force, because that’s the amount of thrust the Kamehameha would need to overcome the drag and exert that much force on the submarine.

100,000 + 110,180.963 = 210,180.963 N

Now we can get work. w = d x f

The only problem is that we can’t be sure exactly how far Goku’s Kamehameha pushed the sub. They traveled through an unspecified amount of tunnel before breaking down, and then Goku pushed them out. We at least know that they traveled 200 m up bare minimum. We can also figure out how far out of the cave they traveled in addition.

We have already established that the sub half-sphere is 1.059 m. Here it measures 57 px compared to the height of the tunnel, 292.

292 / 57 = 5.123 * 1.059 = 5.425 m, height of the tunnel.

On the dragon radar, the tunnel diameter is 7 px, and the straight shot that they most likely escaped from is 20 in comparison. I used this because it was a straight away and there’s no evidence that Goku can control the direction of the Kamehameha at this point.

20 / 7 = 2.857 * 5.425 = 15.499 m, distance shot out by the Kamehameha.

That brings total distance to 215.499 m. I get the feeling that it’s more to be honest, but can’t find any direct evidence to show that.

210,180.963 * 215.499 = 45,293,787.35 J, or 10.826 Kg of TNT

My initial calculation inaccurately used kinetic frictional force to get the answer, but underwater there is no friction, so it made no sense and I got an extremely inflated number. To be honest, this was one of those calculations that was reaching to begin with because there are many unknown variables and a lot of guesswork involved.

Blue Crashes

 

There’s a fairly simple way to calculate the energy of that plane crashing. A simple kinetic energy formula, because we know its speed. It is shown to keep up with Goku’s Kinto’un in speed, which has a max velocity of mach 1.5 or 510 m/s.

As for weight, I’ve decided to compare Blue’s jet to a small helicopter, which are generally around 5,000 Kg. We can see after all that the vehicle isn’t very large when Goku is chasing it.

KE = 1/2mv^2

.5 * 5000 * 510^2 = 650,250,000 J or 155.415 Kg or TNT

But that’s just the initial impact. After that came an explosion.

Average Japanese lane size in smaller side streets is 3 meters. I am assuming that these are two lane roads, one going each way. Especially near that mountain because otherwise people wouldn’t be able to turn around. They’d just get stuck. lol

So we use 6 m for the street width. The street closest to the mountain measures 3.2 pixels compared to the explosion at 32.

32 / 3.2 = 10 * 6 = 60 m, explosion size.

Next we use Taylor’s Law to figure out the strength of the explosion.

E = 8*pi*p*R^5 / [75(y-1)t^2]

Where p is density of the air, t is time after explosion has formed, R is radius of the explosion. y is specific heat ration (Will be using 1.4 here as is common)

For time, I’ll be using the speed of the explosion. There is no noticeable shockwave, so I’m using a minimum explosion speed of 171 m/s. The explosion radius is 30 m, so the timing for that would be .175 s

8 * 3.14 * 1.2 * 30^5 / [75(1.4 – 1) .175^2] = 797,278,040.816 J or 190.554 Kg of TNT

Combined, General Blue took 345.969 Kg TNT of energy straight to the face and he was none the worse for wear.

 

Blue Gets Knocked All the Way to Egypt

 

 

Arale is a gag character, so this feat doesn’t concern her so much as it does Blue. The man got knocked very far away. See, we know from Tao Pai Pai’s famous column throwing feat how far 2,300 Km is in the Dragonball world. So if I were to use an official map as reference…

The distance between Red Ribbon HQ and Korin’s Tower is 58 pixels. For Penguin Village, I scaled to where the nearest desert area was. That happens to be where Namu lives. On one side of the globe, it’s 26 px and the other it’s 80 before reaching the desert, for a total of 106 pixels.

106 / 58 = 1.826 * 2,300 = 4,199.8 Km, the minimum distance that Blue was hit.

So now we have to figure out Blue’s weight. We know his official height is 1.81 m, and he’s muscular, so I feel that 80 Kg is reasonable. I am also going to assume that Arale’s big noggin pushed on Blue for .5 m, or the size of Roshi’s gigantic head (Anime, amirite?)

Using this projectile motion calculator, and input a perfect launch angle of 75 degrees (Because she only jumped at a slight angle) and 4,199,800 m, we find that Blue has an initial velocity of 9,075.899 m/s

Now for acceleration…

a =  v^2 / (2 * d)

9,075.899^2 / (2 * .5) = 82,371,942.658 m/s^2

f = ma

80 * 82,371,942.658 = 6,589,755,412.64 N

w = f * d

6,589,755,412.64 * .5 = 3,294,877,706.32 J, or 787.495 Kg of TNT

 

RESULTS

Goku Underwater Kamehameha – 10.826 Kg of TNT

Blue Crashes – 345.969 Kg of TNT

Blue Knocked to Egypt – 787.495 Kg of TNT

 

This should put Blue’s durability around mid-sized building level.

 

Dragonball – Red Ribbon Army Feats Pt. 1

Goku Bullet Dodging

One has to wonder why Goku bothers dodging bullets at this point, seeing as he could tank them as of chapter one. I guess he does it for fun.

I’m not an expert on guns, but after some studying of pictures, this pistol looks to me like a modified Glock 18.

The reason I think it’s an 18 and not a 17 is because of how it fires on panel. The dog looking guy fires three shots in succession at Goku, and the bullets are shown to come one after the other very quickly, almost all at once like an automatic. The Glock 18 can do this. Notice how in the video he talks about the 18 being able to use 17’s magazine if need be. So the magazine size is no problem either.

They have a muzzle velocity of 375 m/s.

Now to use angular size so we can figure out how close Goku dodged from. This time we’re going to use the horizontal field of vision: 210 degrees. The panel width is 745 px and Goku’s height is 235. Goku is .97 m.

745 / 210 = 3.548 pixels/degree

235 / 3.548 = 66.235 degrees, Goku’s size

Solving for distance, we get…

.744 m, distance between gun and Goku.

 

It’s impossible to know which way Goku moved first, so instead I’ll give a general range of motion for him. Dodging to his right was a 36 degree bend, to his left, 40, and I assume bending over would be 45 degrees.

We know that Goku is .97 m tall, and that his legs are .425 m.

.97 – .425 = .545, the length of Goku’s upper body (Hey, I never said Toriyama gave him realistic proportions, did I?)

Now, for each dodge, we can figure out how much Goku moved…

36 degrees = .172 m

40 degrees = .191 m

45 degrees = .215 m

.744 / 375 = .002 s, time frame.

 

.172 / .002 = 86 m/s

.191 / .002 = 95.5 m/s

.215 / .00013 = 107.5 m/s

 

Goku Blocking Bullets

In this panel, Goku upgrades from dodging bullets to blocking them. He also does this to three different attackers at once, and they’re machine guns. Seems impressive to me! Let’s see what we’ve got…

The bear-looking guy is holding what I believe to be an AKSU-74, an assault rifle used by Russia in the 80’s.

Muzzle Velocity = 735 m/s

Goku is 16 px compared to 61 for the distance between him and the bear guy.

61 / 16 = 3.813 * .97 = 3.698 m, distance.

3.698 / 735 = .005 s, time frame.

This gives Goku very little time to maneuver his power pole, and I’m only looking at one guy here when he was actually being fired on by three different men at once. So needless to say this is low-end.

Goku is .97 m, as already established. He’s 213 px here compared to 316 for power pole, and 35 for distance moved to block some bullets. We also see that he’s moved the pole 41 degrees and 58 to make some other blocks.

316 / 213 = 1.484 * .97 = 1.44 m, length of Power Pole

35 / 213 = .164 * .97 = .154 m, distance Power Pole moved

41 degrees = .515 m, distance Power Pole moved

58 degrees = .728 m, distance Power Pole moved

 

.154 / .005 = 30.8 m/s

.515 / .005 = 103 m/s

.728 / .005 = 145.6 m/s

 

Roshi Catches Bullets

Well, it’s that time again! More bullet timing feats! This time featuring Master Roshi, who very casually catches machine gun fire.

The gun shot on panel looks almost exactly like the T-100. Given this is a manga and the gun was used in Japan, it makes even more sense.

Muzzle velocity = 335 m/s

I’m going to make an assumption here and say that Roshi is 2 meters away.

2 / 335 = .0059 s, time to react.

Roshi is 1.65 m tall.  He’s 103 px here compared to 35 for his head.

35 / 103 = .34 * 1.65 = .561 m Ermm, that’s a big ass head. lol

Sorry if it’s a little difficult to read. I’m going to give a range here because there’s no way to know for sure how Roshi moved his hands due to the time lapse. His head measures 108 px here compared to hand motion 1 being 69 and motion 2 148.

69 / 108 = .639 * .561 = .359 m, hand motion one.

148 / 108 = 1.37 * .561 = .769 m, hand motion two.

.359 / .0059 = 60.848 m/s

.769 / .0059 = 130.339 m/s

 

All in all, I had initially expected these results to be higher, because I planned to calculate based on the fire rate of the guns used and not the distance from which they came. In theory this should make the feats more impressive, but ironically, because Goku and Roshi were too close, it made no difference. You see, if the firing rate of a gun isn’t high enough, the bullet reaches a far off distance before the next one comes out. For most of these, the next bullet fired comes out over 20 m after the initial one. Thus, there was no point in basing it off fire rate. Roshi for instance would have had a bunch of extra time (Relatively speaking) to react to the next bullet because the firing rate of the T-100 isn’t that fast.

Next we’ll get to some feats relating to General Blue.

TOTALS

Goku Bullet Dodging – 86 – 107.5 m/s

Goku Blocking Bullets – 30.8 – 145.6 m/s

Roshi Catches Bullets – 60.848 – 130.339 m/s