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Ssj3 Goku's striking energy; Attention: BoG SPOILERS
Topic Started: Aug 10 2013, 10:52 AM (3,548 Views)
Sjk8
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史上最強の孫悟空

Ok guys, for everyone who wants to know it, I can tell you that I've calculated how much energy Ssj3 Goku's punch - which obliterated part of King Kai's planet during BoG - has.
I'm not here to post all the calcs, but if someone wants them, well he can ask. ^_^

In general terms: firstly I figured King Kai's planet diameter, which is below the 100 meters mark, so the actual number doesn't change much the outcome, since the order of magnitude is always 10; then I figured the density of the planet (and obviously it is enormously dense since it is few meters in diameter but it has 10 times the gravitational force of Earth).
After that I've had to find how much quantity of material actually Goku obliterated with his punch, and I've done such a thing by using the mathematical formulas of the spherical cover and such: it turned out that Goku destroyed with his punch around the 15% in volume of the planet (of course, it can't be a perfect value since there's always a margin of error, especially when you do calcs relying on an anime image).
Given the density of the planet and the actual voulme which got destroyed, it has been possible to calculate the actual energy output of Goku's punch, and it turned out that Ssj3 Goku's striking energy is around 6,38*10^16 J, or, if you want, around 64 quadrillions Joules.

BoG punch


1 Megaton is equal to 4,184*10^15 J, so we can say that Ssj3 Goku's punch has an energy of around 15 Megatons, or if you wish, an energy equivalent to around 609 Fat Man atomic bombs.

Since BoG Ssj3 Goku is practically the same as Boo saga Ssj3 Goku, we can thus have a reference value, in physical striking energy (and thus probably also in physical tanking ability) for un-fused Ssj3 tier characters such as Ssj3 Goku himself, Kid Boo, full power Fat Boo and Ssj Gotenks pre Rosat.
Everyone below this level would physically strike with less energy, everyone above this level would strike with more energy.
Edited by Sjk8, Aug 11 2013, 02:40 PM.
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amsmagic
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I don't know, I'm cool with DBZ and real life physics, but I feel your putting WAY to much into it, and most of your calculations weren't proved, you just said them. Like finding the spherical cover of the planet, you can't. Your also assuming the diameter of King Kai's planet. As well as the density.

This is a decent theory, IF you could get actual numbers.
I like your theory.
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Goddess Ultimecia
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Im really interested in looking at Vegito's striking energy.
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Sjk8
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amsmagic
Aug 10 2013, 06:28 PM
I don't know, I'm cool with DBZ and real life physics, but I feel your putting WAY to much into it, and most of your calculations weren't proved, you just said them. Like finding the spherical cover of the planet, you can't. Your also assuming the diameter of King Kai's planet. As well as the density.

This is a decent theory, IF you could get actual numbers.
I like your theory.


As a first thing, I'd like to thank you for appreciating the work; also, since you asked for the actual calcs, I'm going to post them.
Being said that, I immediately have to say that it's impossible to have scentific precision here, especially in reference to the diameter of the planet: indeed, for me it is around 30 meters, but for someone else it could be 35 or 40 meters.
When I got my number, I looked at this picture and got it from the house and the trees dimensions:

King Kais' planet


Anyway, If you look at the image of the planet I posted in my previous post (The "BoG" image), the planet itself seems bigger.
The diameter is therefore the first random variable of the calcs: as said, I assumed 30 meters; if you think that the planet is actually bigger, the actual number, in Joules, of the Goku's feat I posted before would going to simply be a low-end value of Goku's real striking capability.
Given the diameter, I'm going to post the calculations I made in order to find the density of the planet:

the gravitational force of a planet is given by this formula:

F = (G*M*m)/r^2

G is the universal gravitational constant (6,67*10^-11 [m^3/(kg*s^2)];

M is the mass of the planet

m is the generic reference mass

r is the radius of the planet (or distance between the two masses' centers)

Since King Kai's gravitational force is 10 times the Earth gravitational force, we have Fk (gravitational force of King Kai's planet) 10 times bigger than Fe (Earth's gravity).

Fk/Fe = [(G*Mk*m)/rk^2]/[(G*Me*m)/re^2] = 10

G and m are in commons and go away, so we have:

(Mk/rk^2)/(Me/re^2) = 10

Mass is Volume (V)*Density (D), with Volume (of a generical planet) = (4/3)*p*r^3;

back to the formula:

((4/3)*p*rk^3*Dk)/rk^2 = Fk and ((4/3)*p*re^3*De)/re^2 = Fe, so:

Fk/Fe = (Dk*rk)/(De*re) = 10.

The only unknown term is Dk (density of King Kai's planet), while we know De and re of Earth and rk = 15 meters (assuming a diameter of King Kai's planet of 30 m, as previously said).

So, Dk = 2,34*10^10 kg/m^3, while density of Earth (De) is 5,5153*10^3 kg/m^3, thus making the density of King Kai's planet around 4 millions of times higher than the Earth's one.

To know the energy required in order to blow up a planet we need to integrate the radius from the "shell" to the core of the planet itself; we also have to know values such as the mass, the density, Pi, G etc.
For the sake of semplicity, I'm going to post you directly the final formula:

E(p,R) = (16/3)*G*(p^2)*(pi^2)*(R^5) [1]

with p = density, Pi = 3.14159....; R = radius of the planet.
You have to take into account that this formula is surely valid, but yet it has in itself some semplifications due to force majeure: if you are interested in the complete demonstration and in the hypothesis which stand at the basis of such a formula, you can find all you need at this link, which is the original source.

Now, it has to be found how much material Goku actually destroyed with his punch.
If we look at this picture

BoG punch


we can see that the portion of material destroyed is similar to a cone inside the planet, with its tip put in correspondence of Goku's punch and the basis situated in the lower part of the planet (where there is the greatest amount of raised dust, so to speak); then there's the portion of material corresponding to the spherical cap which goes from said basis of the cone to the outer surface of the planet itself.

This one below is a spherical cap:

Spherical cap


The volume of the spherical cap is given by this formula: V = Pi*(h)^2*(r-(h/3)) = ((Pi*h)/6)*(3*(a)^2+(h)^2) [2], while the area of its surface is, on the other hand, given by this other formula: S = 2*Pi*r*h.
"a" is the radius of the basis of the spherical cap.

Anyway, from the image I posted you can see that what we are considering about King Kai's planet isn't exactly a spherical cap, since the sphere (i.e. the planet) is not divided in two caps as instead it is shown by the image of the spherical cap I posted above.
We thus need to consider the concept of "Steradian": the steradian is defined as the solid angle with the vertex at the center of a sphere of radius r, which subtends a spherical cap of area equal to r^2.

Steradian


A spherical cap of area equal to r^2 is extremely similar to what we have as a portion of destroyed material in the case of King Kai's planet.
In this case, r = 15 m (remember, the diameter has be assumed to be equal to 30 m), so, from this equation ----> r^2 = S = 2*Pi*r*h we can find the height h of our spherical cap: if you do the maths, you find h to be equal to a value of around 2,39 m.
Given h, from the previous formula of the volume of a spherical cap, we can indeed find its volume itself: V = 255 m^3; this is the volume of the material content in the spherical cap which got destroyed by Goku.
Knowing this value, from the formula [2] we can find "a", and therefore we have a = 8,12 m.
Now, in order to have the total destroyed volume, we need to find the volume of the cone which has been introduced first:
the volume of a cone is given by the following formula V = (Pi*(r)^2*h)/3, with h being the height of the cone and r being its radius.
"h" of the cone has to be equal to the diameter of King Kai's planet minus the previously found height h = 2,39 m of the spherical cap, while the radius r has to be equal to "a" = 8,12 m; given all these values, we can find that V_cone destroyed is equal to 1906,37 m^3.
We can thus now calculate the total volume destroyed by Goku's punch, which corresponds to the sum of the volumes of the spherical cap and the cone: V_tot = 2161,27 m^3; multiply it by the density of King Kai's planet and you find the mass that got destroyed: M = 5,06*10^13 kg.
Knowing such a total volume, we can now find the radius of the "equivalent planet" that got destroyed by Goku thanks to the formula of the volume of the sphere: the result tells us that Goku destroyed an "equivalent planet" with a radius r of 8,02 m and density obviously equivalent to the one of King Kai's planet, since that is the material we are talking about.
Given all these info, we can now apply the formula [1] and therefore we can find out how much energy is required to blow up such a quantity of material: the result, which it has been written in my first post, is an energy required E = 6,38*10^16 J.

Now, the principal issue with these calcs is the diameter of King Kai's planet, and I personally find obvious that the range of its value has to be between 30 meters and 100 meters: if you choose to use a value of 80 meters, well you'll find, with the same calcs, an higher value of energy for Goku's punch, since, as you can see, the formula of the energy goes with the square of the density and the fifth power of the radius, the latter therefore having much more weight all over the final result.
Because of that, as I said initially, if you want, you can see my result as a low-end value of energy for Goku's punch.
It's usually hard to calculate the physical energy/force of DB character, since they seldom miss their targets (i.e. their opponents), but, in this case, Goku was completely outpaced by Beers, so his "enhanced with Ki-punch" hit the planet, serving me an opportunity of calculation on a silver platter.
Anyway, if somebody finds some issues or ways to improve the calcs, I'd ask to tell me without the slightest problem. ;)

At the end of the analysis, I'd like to tell you that, in order to destroy the Moon, an energy of around 2*10^28 J is required and therefore, as everyone can see, Goku is very far from reaching that level of power, yet BoZ Piccolo destroyed it with a casual blast.
Now, I don't want to state the obvious, but this fact clearly tells us that DBZ characters physical energy, even if enhanced with Ki, is nowhere near the level of power of their energy projection Ki-beams.

TConnor_Demonic
Aug 10 2013, 07:35 PM
Im really interested in looking at Vegito's striking energy.


DB characters striking force, in the same way of their speed, for example, is heavily implied not to grow proportionally to their battle power: indeed, Namek Ssj Goku doesn't probably strike with an energy 50 times bigger than base Namek Goku's.
The best thing to do, is to pick few cases and to use them in order to build an interpolating polynomial and therefore a trend line: the x coordinate o those points is the BP, while the y coordinate is the energy output.
Out of curiosity, I've done such a thing, and the points (x;y) I considered are: the point (0;0) (the origin - dead body), and other two points, one related to Master Roshi, and the other the one I presented in this thread, i.e. related to BoG Ssj3 Goku.
In reference to Master Roshi, I considered his suppressed BP and the energy output of the time he catched 10 machine-gun bullets: a machine-gun bullet has an average weight of 12 g and an average speed of 700 m/s; its energy is given by this formula E = (1/2)*mass*(speed)^2 and the output is equal to around 3000 J, and if you multiply it by 10 (10 bullets) you get around 30000 J of enrgy tanked with ease by Master Roshi.
Since he tanked that energy, he is able to hit with this same energy and above, therefore these 30000 J are a low-end energy feat for Master Roshi.
So, back at the main argument, I used these points (0;0), (Master Roshi's BP; 30000 J), (Ssj3 Goku's BP; 6,38*10^16 J) and I made a trend interpolating line which covers every arc of DB, since it is sufficient that you give a value of a BP as an input, and the formula gives you the corresponding value of striking energy.
It is a reliable method, the only issue with this kind of approach is that it depends on BP, which, as we all know, are not stated anymore after the Freeza's arc; anyway, on this forum practically everyone is very competent and thus the actual DB power-chain is well known: even if the actual numerical value of a BP changes from person to person, everyone knows who is stronger than who in the DB world, so this approach can be still quite trusted.
Accordingly, out of curiosity, I've done such a calc, and it results to me that Ssj Vegetto's striking energy would be in the dimension of 2200 quintillions Joules, or above 520000 Megatons.
Anyway, this still is a guessed number, and not an actual one directly obtainable from manga or anime such as Goku's, so that's why I didn't want to consider it in my previous post.
Edited by Sjk8, Aug 11 2013, 02:54 PM.
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+ Havoc_Wreaker
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Popcorn

Interesting very intersting indeed
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Sjk8
Aug 11 2013, 01:45 PM
amsmagic
Aug 10 2013, 06:28 PM
I don't know, I'm cool with DBZ and real life physics, but I feel your putting WAY to much into it, and most of your calculations weren't proved, you just said them. Like finding the spherical cover of the planet, you can't. Your also assuming the diameter of King Kai's planet. As well as the density.

This is a decent theory, IF you could get actual numbers.
I like your theory.


As a first thing, I'd like to thank you for appreciating the work; also, since you asked for the actual calcs, I'm going to post them.
Being said that, I immediately have to say that it's impossible to have scentific precision here, especially in reference to the diameter of the planet: indeed, for me it is around 30 meters, but for someone else it could be 35 or 40 meters.
When I got my number, I looked at this picture and got it from the house and the trees dimensions:

King Kais' planet


Anyway, If you look at the image of the planet I posted in my previous post (The "BoG" image), the planet itself seems bigger.
The diameter is therefore the first random variable of the calcs: as said, I assumed 30 meters; if you think that the planet is actually bigger, the actual number, in Joules, of the Goku's feat I posted before would going to simply be a low-end value of Goku's real striking capability.
Given the diameter, I'm going to post the calculations I made in order to find the density of the planet:

the gravitational force of a planet is given by this formula:

F = (G*M*m)/r^2

G is the universal gravitational constant (6,67*10^-11 [m^3/(kg*s^2)];

M is the mass of the planet

m is the generic reference mass

r is the radius of the planet (or distance between the two masses' centers)

Since King Kai's gravitational force is 10 times the Earth gravitational force, we have Fk (gravitational force of King Kai's planet) 10 times bigger than Fe (Earth's gravity).

Fk/Fe = [(G*Mk*m)/rk^2]/[(G*Me*m)/re^2] = 10

G and m are in commons and go away, so we have:

(Mk/rk^2)/(Me/re^2) = 10

Mass is Volume (V)*Density (D), with Volume (of a generical planet) = (4/3)*p*r^3;

back to the formula:

((4/3)*p*rk^3*Dk)/rk^2 = Fk and ((4/3)*p*re^3*De)/re^2 = Fe, so:

Fk/Fe = (Dk*rk)/(De*re) = 10.

The only unknown term is Dk (density of King Kai's planet), while we know De and re of Earth and rk = 15 meters (assuming a diameter of King Kai's planet of 30 m, as previously said).

So, Dk = 2,34*10^10 kg/m^3, while density of Earth (De) is 5,5153*10^3 kg/m^3, thus making the density of King Kai's planet around 4 millions of times higher than the Earth's one.

To know the energy required in order to blow up a planet we need to integrate the radius from the "shell" to the core of the planet itself; we also have to know values such as the mass, the density, Pi, G etc.
For the sake of semplicity, I'm going to post you directly the final formula:

E(p,R) = (16/3)*G*(p^2)*(pi^2)*(R^5) [1]

with p = density, Pi = 3.14159....; R = radius of the planet.
You have to take into account that this formula is surely valid, but yet it has in itself some semplifications due to force majeure: if you are interested in the complete demonstration and in the hypothesis which stand at the basis of such a formula, you can find all you need at this link, which is the original source.

Now, it has to be found how much material Goku actually destroyed with his punch.
If we look at this picture

BoG punch


we can see that the portion of material destroyed is similar to a cone inside the planet, with its tip put in correspondence of Goku's punch and the basis situated in the lower part of the planet (where there is the greatest amount of raised dust, so to speak); then there's the portion of material corresponding to the spherical cap which goes from said basis of the cone to the outer surface of the planet itself.

This one below is a spherical cap:

Spherical cap


The volume of the spherical cap is given by this formula: V = Pi*(h)^2*(r-(h/3)) = ((Pi*h)/6)*(3*(a)^2+(h)^2) [2], while the area of its surface is, on the other hand, given by this other formula: S = 2*Pi*r*h.
"a" is the radius of the basis of the spherical cap.

Anyway, from the image I posted you can see that what we are considering about King Kai's planet isn't exactly a spherical cap, since the sphere (i.e. the planet) is not divided in two caps as instead it is shown by the image of the spherical cap I posted above.
We thus need to consider the concept of "Steradian": the steradian is defined as the solid angle with the vertex at the center of a sphere of radius r, which subtends a spherical cap of area equal to r^2.

Steradian


A spherical cap of area equal to r^2 is extremely similar to what we have as a portion of destroyed material in the case of King Kai's planet.
In this case, r = 15 m (remember, the diameter has be assumed to be equal to 30 m), so, from this equation ----> r^2 = S = 2*Pi*r*h we can find the height h of our spherical cap: if you do the maths, you find h to be equal to a value of around 2,39 m.
Given h, from the previous formula of the volume of a spherical cap, we can indeed find its volume itself: V = 255 m^3; this is the volume of the material content in the spherical cap which got destroyed by Goku.
Knowing this value, from the formula [2] we can find "a", and therefore we have a = 8,12 m.
Now, in order to have the total destroyed volume, we need to find the volume of the cone which has been introduced first:
the volume of a cone is given by the following formula V = (Pi*(r)^2*h)/3, with h being the height of the cone and r being its radius.
"h" of the cone has to be equal to the diameter of King Kai's planet minus the previously found height h = 2,39 m of the spherical cap, while the radius r has to be equal to "a" = 8,12 m; given all these values, we can find that V_cone destroyed is equal to 1906,37 m^3.
We can thus now calculate the total volume destroyed by Goku's punch, which corresponds to the sum of the volumes of the spherical cap and the cone: V_tot = 2161,27 m^3; multiply it by the density of King Kai's planet and you find the mass that got destroyed: M = 5,06*10^13 kg.
Knowing such a total volume, we can now find the radius of the "equivalent planet" that got destroyed by Goku thanks to the formula of the volume of the sphere: the result tells us that Goku destroyed an "equivalent planet" with a radius r of 8,02 m and density obviously equivalent to the one of King Kai's planet, since that is the material we are talking about.
Given all these info, we can now apply the formula [1] and therefore we can find out how much energy is required to blow up such a quantity of material: the result, which it has been written in my first post, is an energy required E = 6,38*10^16 J.

Now, the principal issue with these calcs is the diameter of King Kai's planet, and I personally find obvious that the range of its value has to be between 30 meters and 100 meters: if you choose to use a value of 80 meters, well you'll find, with the same calcs, an higher value of energy for Goku's punch, since, as you can see, the formula of the energy goes with the square of the density and the fifth power of the radius, the latter therefore having much more weight all over the final result.
Because of that, as I said initially, if you want, you can see my result as a low-end value of energy for Goku's punch.
It's usually hard to calculate the physical energy/force of DB character, since they seldom miss their targets (i.e. their opponents), but, in this case, Goku was completely outpaced by Beers, so his "enhanced with Ki-punch" hit the planet, serving me an opportunity of calculation on a silver platter.
Anyway, if somebody finds some issues or ways to improve the calcs, I'd ask to tell me without the slightest problem. ;)

At the end of the analysis, I'd like to tell you that, in order to destroy the Moon, an energy of around 2*10^28 J is required and therefore, as everyone can see, Goku is very far from reaching that level of power, yet BoZ Piccolo destroyed it with a casual blast.
Now, I don't want to state the obvious, but this fact clearly tells us that DBZ characters physical energy, even if enhanced with Ki, is nowhere near the level of power of their energy projection Ki-beams.

TConnor_Demonic
Aug 10 2013, 07:35 PM
Im really interested in looking at Vegito's striking energy.


DB characters striking force, in the same way of their speed, for example, is heavily implied not to grow proportionally to their battle power: indeed, Namek Ssj Goku doesn't probably strike with an energy 50 times bigger than base Namek Goku's.
The best thing to do, is to pick few cases and to use them in order to build an interpolating polynomial and therefore a trend line: the x coordinate o those points is the BP, while the y coordinate is the energy output.
Out of curiosity, I've done such a thing, and the points (x;y) I considered are: the point (0;0) (the origin - dead body), and other two points, one related to Master Roshi, and the other the one I presented in this thread, i.e. related to BoG Ssj3 Goku.
In reference to Master Roshi, I considered his suppressed BP and the energy output of the time he catched 10 machine-gun bullets: a machine-gun bullet has an average weight of 12 g and an average speed of 700 m/s; its energy is given by this formula E = (1/2)*mass*(speed)^2 and the output is equal to around 3000 J, and if you multiply it by 10 (10 bullets) you get around 30000 J of enrgy tanked with ease by Master Roshi.
Since he tanked that energy, he is able to hit with this same energy and above, therefore these 30000 J are a low-end energy feat for Master Roshi.
So, back at the main argument, I used these points (0;0), (Master Roshi's BP; 30000 J), (Ssj3 Goku's BP; 6,38*10^16 J) and I made a trend interpolating line which covers every arc of DB, since it is sufficient that you give a value of a BP as an input, and the formula gives you the corresponding value of striking energy.
It is a reliable method, the only issue with this kind of approach is that it depends on BP, which, as we all know, are not stated anymore after the Freeza's arc; anyway, on this forum practically everyone is very competent and thus the actual DB power-chain is well known: even if the actual numerical value of a BP changes from person to person, everyone knows who is stronger than who in the DB world, so this approach can be still quite trusted.
Accordingly, out of curiosity, I've done such a calc, and it results to me that Ssj Vegetto's striking energy would be in the dimension of 2200 quintillions Joules, or above 520000 Megatons.
Anyway, this still is a guessed number, and not an actual one directly obtainable from manga or anime such as Goku's, so that's why I didn't want to consider it in my previous post.
My brain is fried...can you perhaps simplify that to someone who has only taken basic physics.
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Demon Flame
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A 'chunk' of the planet has a certain gravitational potential energy associated with it. In order to free that chunk from the gravity of the planet, at least that much energy has to be put into the matter. In practice this is a minimum bound because it assumes the punch was 100% efficient in putting the energy just into escaping gravity and nothing else. In practice, even more energy was put into breaking the bonds within the material, etc.
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Sjk8
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史上最強の孫悟空

For TConnor: pretty much what Demon Flame said, and that's why that result is only a low-end feat in energy terms.

Also, it's interesting to notice that this is the energy of the exploding planet, i.e. the energy required to blow the planet up, while the energy of Goku's punch is much bigger since what are we talking about is an inelastic collision.
Edited by Sjk8, Aug 20 2013, 10:56 PM.
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GokuBlaze
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Mind = blown
:o
Goku is #1
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