Viewing blog entries in category: Magi Calculation
So,I have finally gotten around to read Magi spin-off Sinbad no Bouken. There are few feats there that caught my eye. This is one of them.
Falan is a Magician of the Parthevia Empire & also a member of Al-Thamen. She joined Draken & entered the second dungeon expedition with him. On the way she froze a lake to cross it. Lets calc the energy to do it.
First we need the diameter of the lake. I have got two different diameter so I will be using the average to make it simple.
Hinahoho = 46 pixel = 2.4 meter
Lake diameter = (574+265)/2 = 419.5 pixel = 21.8869 meter
Now we need the depth. Now,for depth I will be angsizing. When Sinbad & Hinahoho were swimming a giant sea creature which resided in the lake pulled Sinbad with its tentacle. From the scan we can clearly see the creature at the bottom of the lake & Hinanoho floating inside the lake which in turns makes it possible to do it.
Now I will be using a single scan for two scaling. First I will be using bottom panel to calc Anemone's mouth.
Sinbad = 67.4273 pixel = 1.60 meter
Anemone's mouth = 153.6879 pixel = 3.501366 meter.
Now I will use Anemones's mouth size to determine how far deep it was from our pov. I will be using first panel of the scan here.
Anemone's mouth = 46 pixel = 3.501366 meter.
Anemone's diameter = 181 pixel = 13.7771 meter.
Panel Height = 695 pixel
object degree size = 20.66936
Now, putting object degree size & earth size in angular calculator we will find the distance.
Distance = 37.775 meter
Now that we have got our depth lets get to work the volume.If it wasn't already obvious I am going to model the lake as a cylinder.
Lake Volume = pi*r^2*h = 14212.324169 meter^3
We know,water density = 1000 kg/m^3
p = m/V
p*V = m = 1000*14212.324169 = 14212324.169348 kg
Specific Heat of water C = 4186 J/kg
Latent Heat of Water L = 334880 J/kg
Assuming the water was in room temperature. The temperature change is 20 degree celcius
Q1 = 14212324.169348*4186*20
Q1 = 1189855779457.83132900 Joules
The matter changed phase so latent energy as well.
Q2 = 14212324.169348*334880
Q2 = 475828613189.7777460 Joules
Total Energy = Q1+Q2 = 1665684392647.609075007 Joules
Total Energy = 398.108124438 tons of TNT.
Thalg Hajar = 398.108124438 tons of TNT
Yeah I found a scan to scale the crater more accurately.Its going to lower the energy a lot but still.Anyway do I need to explain the attack? I don't think so. Its pretty straight forward.Lets get to it,
Human = 14 pixel = 1.7 meter
Crater Diameter = 659 pixel
Crater Radius = D/2 = 329.5 pixel = 40.01071 meter
Crater Depth = 106 pixel = 12.87142
Modeling the crater as cylinder cause that's what its shape look like.
Volume = pir^2h
Volume = pi*40.01071^2*12.87142
Volume = 64733.521449 meter^3
Judging from the panel it seems the whole volume was pulverized.Pulverizarion of rock is 214.35 joules/cc.
Energy [Pulverization] = 13875630322746.173557 Joules
Energy [Pulverization]= 3.31635524 kiloton
High Multi-block to Small Town level attack.
Kouha's Lelazzo Madraga = 3.3163 kilotons of TNT
In latest chapter we saw Jader destroying the island where the summit was taking place. Now he didn't destroy the entire island. The place in the island where the summit was spared. He just wanted to show his power.
First I am going to calc the island volume.Then the volume of the exiting part & subtract it from the whole island volume to get the destroyed part volume. Lets start,
First I am going to use Kouen's height to scale the ship's sail length.
Ren Kouen = 14 pixel = 1.85 meter
Sail Length = 216 pixel = 28.5428 meter.
Now I am going to use the ship length to scale the island diameter. Now there are many ships on the shore.Not sure which one is Kouen's.So I randomly scaled few & weirdly enough got same pixel size for all of them.
Sail Length = 6 pixel = 28.5428 meter
Island Diameter = 295.97 pixel = 1407.9715 meter
Island Radius = D/2 = 703.9857 meter
Now Island height is not same in all part.So again I randomly scaled in different places & used average pixel size for island height above sea level.
Island Height = 16.66 pixel = 79.2825 meter
Island is cylinder shaped so that's what I am going to use here.
Whole Island Volume = pi*r^2*h
Whole Island Volume = pi*703.9857^2*79.2825
Whole Island Volume = 123439804.2411 meter^3
Now I am going to calc the remaining island volume.First I am going to scale the place where meeting took place.Lets call it convention center.
Random Human = 23 pixel = 1.7 meter
Convention Center Diameter = 662 pixel = 48.93043 meter
Now I am going to use this to scale remaining island diameter & height.
Convention Center Diameter = 20 pixel = 48.93043 meter
Existing Island Diameter 1 = 150 pixel
Existing Island Diameter 2 = 135 pixel
Existing Island Average Diameter = (150+135)/2 pixel = 142.5 pixel
Existing Island Average Radius = 142.5/2 pixel = 71.25 pixel= 174.3146 meter
Existing Island Height = 28 pixel = 68.5026 meter
Existing Island Volume = pi*r^2*h
Existing Island Volume = pi*174.3146^2*68.5026
Existing Island Volume = 6539203.8913 meter^3
Now I am going to subtract this volume from whole to get volume of destroyed island.
Destroyed part volume = 123439804.2411-6539203.8913 = 116900600.3497 meter^3
Now I am not quite sure what happened here. Either violent fragmentation or total pulverization cause I don't see any fragmented part anywhere near the island. I am going to use both for low end & high end.
Violent fragmentation of rock is 120 j/cc
Low End Energy = 116900600.3497*1000000*120
Low End Energy = 14028072041975437.059314442 Joules
Low End Energy = 3.352789685 megatons.
Pulverization Energy is 214.35 j/cc
High End Energy = 116900600.3497*1000000*214.35
High End Energy = 25057643684978624.447200 Joules
High End Energy = 5.988920575 megatons
Judar DC [ Low End] = 3.3527 megatons of TNT
Judar DC [High End] = 5.9889 megatons of TNT
In her [Can't remember the name] battle against David she fired Ala Raqesa at him. David easily repelled the attack. The attack made contact with the ground & made a huge explosion.Lets calc its energy.
To scale the diameter of the explosion first I need the diameter of Cathedral city first.Here,
Window = 3 pixel = 1 meter.
The windows here are very small that's what I am using 1 meter for its length which is lower than average window length.
Main Tower Width = 84 pixel = 28 meter.
In this scan I am going to scale the Cathedral diameter via main tower width.
Tower Width = 31 pixel = 28 meter
Cathedral Diameter (Green)= 541 pixel = 488.6451 meter
Now I am going to use Cathedral Diameter to scale the explosion diameter.
Cathedral Diameter = 28.16 pixel = 488.6451 meter
Crater Diameter = (69+75)/2 = 72 pixel = 1249.3768 meter
Crater Radius = 1249.3768/2 = 624.6884 meter
There is no way to scale the depth so I am going to use 1/4 of the diameter as depth.From top down view in earlier scan it looks pretty deep so it should be okay.
Crater Depth = 1249.3768/4 meter = 312.3442 meter
Crater Volume = .5*(4/3)*pi*r^3
Crater Volume = .5*(4/3)*pi*312.3442*624.6884 meter^3
Crater Volume = 255281284.66293 meter^3
From the explosion it looked like the rocks were violently fragmented.That's what I am going to use. Violent fragmentation of rock is 120 j/cc.
Ala Raqesa Energy = 255281284.66293*1000000*120 Joules
Ala Ragesa Energy = 30633754159551834.98861 Joules
Ala Ragesa Energy = 7.321642964 megatons
DC of Ala Ragesa = 7.3216 megatons of TNT
All right.Lets get down to business.
The Kingdom of Sindria has two barrier. One is defensive barrier & other is to track & transport anything within the range of 200 kilometers around the island.Sinbad used the transfer magic circle to track the banker.In the scan below you can see both kind of barrier around the island.Its going to help us calc the diameter of the island.
Now,Barrier diameter = 176 px
As stated its 200 km around the island.So the radius of barrier is range around the island.
Barrier Radius = 86 px = 200 km
Island Diameter = 42 px = 97.6744 km
Now,in the scan you can see the world map of Magi World.You can see a white dot in Black space. The edge of the arrow in the whiter space is Sindria.
Sindria Diameter = 4 px = 97.6744 km
World Circumference = 569 px = 13894.1860 km.
We know Circumference =/= Diameter.
So,putting circumference size in this calculator I get,
Diameter = 4422.6567 kilometer
Pretty small for my test.
Magi World Diameter = 4422.6567 kilometer
Spoiler:Koumei teleports the top of a mountain & drops it on top of the medium in hope of destroying medium but upon contact the mountain fragmented in thousand pieces.
First we need to calc the size of mountain top. For that I am going to use the crater diameter the medium is standing on. Generally I would use Medium but after taking Rukh from sea he became countless time bigger.
Here,in this scan
Crater Diameter = 307 px = 787.122608 meter
Mountain Top Height = 377 px = 966.596818 meter.
Mountain Top Base = 780 px = 1999.855486 meter.
Distance from Sea level to Mountain Top = 113 px = 289.722653758 meter
Mountain Volume = 1/3*pi*r^2*h
Mountain Volume = 1012071546.874965 m^3
Density = 2800 kg/m^3
Mass = 2833800331249.902 kg
The mountain fell full distance so medium was crushed to the ground.You can see it in the right lower panel of the scan.
Velocity = 75.36 m/s
K.E = .5*m*v^2
K.E = 8046759670845561.7226496 Joules
K.E = 1.923221719 Megaton
It fragmented upon contact with Medium so
Fragmentation Energy = 1012071546.874965*1000000*8
Fragmentation Energy = 8096572374999722.9977385291 Joules
Fragmentation Energy = 1.935127241 megaton
Almost identical result.
Mountain K.E or Fragmentation ~ 1.9232-1.9351 megaton
Amol Al-Bador Saiqa
This is the combined extreme magic of two fire user Ren Kouen & Aladin.Most of the power was contributed by Kouen anyway.
Distance from C to G = 610 px = 2734.05826 meters
Blast Diameter = 586 px = 2626.488754 meter.
For 1313.244 radius inSD.net I got
Air blast radius (near-total fatalities) = 110 kilotons
Needless to mention here Ren Koumei transferred the potential damage from city pretty easily.
Combined Extreme Magic [Everyone]
So all of them used their magic on the medium. Which dispersed a large amount of water.First water amount.
Here Mediums hand = 166 px = 116.767071557 meter.
Water Diameter = 1119 px = 787.122608 meter.
Again here Water Diameter = 161 px = 787.122608 meter
Water Depth = 139 px = 679.565482 meter.
Volume [Cylinder] = pi*(787.122608/2)^2*679.565482
Volume [Cylinder] = 330678504.039187689 m^3
Sea water density = 1026 kg/m^3
Mass = 339276145144.2065696 kg
Now in this scan you can see the water was already dispersed after the beam went through him.He didn't even fall that much after getting hit. To be safe I am going to say he at best fall 10 meter before water dispersed.
Free Fall Distance = 10 meters
T = sqrt(2d/g)
g = 9.8 m/s^2
d = 10 meters
Free Fall Time = 1.428571 second.
Water dispersed speed = 787.122608/1.428571 = 550.9858255 m/s
K.E = .5*339276145144.2065696*550.9858255^2
K.E = 51499638726324481.416823 Joules
K.E = 12.3087 Megatons
Amol Al-Bador Saiqa = 110 kilotons
Combined Extreme Magic [Everyone] = 12.3087 Megatons
Now from the very start. Just from the medium just started forming.There has been a series of events so far & most of them in recent chapters.
First I am going to calc the size of Black Medium. It will help us to figure how far above the cloud is from ground which is important here cause I am going to need it in at least two calc I presume.
So,this is the first scan,
Human = 5 px = 1.7 meter.
Black Medium = 347 px = 117.98 meter.
Now I am going to calc distance from cloud to ground.
Black Medium = 23 px = 117.98 meter.
Distance from Cloud to Ground = 533 px = 2734.05826 meters
While we are at it lets also calc City Diameter.
City Diameter = 692.491304 meters.
A bit small for my test but whatever.
This was all scalling but now starts the real calc.
From our previous scalling we know Distance from Cloud to Ground 2734.05826 meters.
In here,Distance [C 2 G] = 960 px = 2734.05826 meter.
Tornado Height = (960+147) = 1107 px = 3152.710932 meter.
Tornado Diameter = (187+178+353)/3 = 239.333 px = 681.615818 meter.
Medium's Hand = 116.767071557 meter.
Tornado Volume = pi*(681.615818/2)^2*3152.710932
Tornado Volume = 1150411871.7832144 m^3
Density of Air = 1.29 kg/m^3
Mass = 1484031314.6003465 kg
The equation for rotational kinetic energy of Tornado is
Now for angular velocity I am going to use 318 mph or 142.15861 m/s
So,KE = 1484031314.6003465*(142.15861)^2/4
KE = 7497723444281.074053 Joules
So lets start the second part.Dark cloud,looks like Nimbosters.
Cloud Diameter = 544 px = 1549.299680 meter
Cloud Height = 2000 meter.
Volume [cylinder] = pi*(1549.299680/2)^2*2000
Volume [cylinder] = 3770428759.25971 m^3
Cloud Density = 1.003 kg/m^3
Mass = 3781740045.53749 kg
I am going to use same velocity I used for Tornado which is 142.15861 m/s.
Cloud Dispersion = 38212725999301.3559869 Joules
Total Energy = 7497723444281.074053 + 38212725999301.3559869
Total Energy = 45710449443582.4300399 Joules = 10.92505 kilotons
The result would be higher if there was an accurate way to calc speed.
Medium's Hand = 245 px = 116.767071557 meter
Water Base = 668 px = 318.3689951 meter
Water Height = 816 px = 388.90583833 meter.
Water Volume = (1/3)*pi*(318.3689951/2)^2*388.90583833
Water Volume = 10319879.4174168 m^3
Density of Sea Water = 1026 kg/m^3
Water Mass = 10588196282.26971119 kg
PE = mg(h/2) = 20177275622637.58759647 Joules
PE = 4.822484613 kilotons
Ren Hakuei PA'IR AL-HAZARD" = 10.92505 kilotons
Ren Kougyoku VAINEL GANEZZ = 4.82248 kilotons
Ren Kouen using his Djinn equip Agares digs a hole into the ground,stimulated the veins of the earth & pulled out a lava flow. He basically created a volcano here.
This entire feat has two part. First digging the hole into the ground & second is raising the lava flow. Lets calc the first one now.
First I need to know the height of Black Djinns.Their height is important here why I will show a bit later.All of their height is in same ballpark so there shouldn't be any problem.
In this scan,Random humans 16 px = 1.5 meter.
Black Djinn's height = 565 px = 52.96875 meter.
Now I need the the diameter of the hole.I am going to assume the diameter of the attack will be the diameter of the hole.Its a reasonable assumption.
Black Djinn's height = 31 px = 52.96875 meter.
Diameter of hole = 15 px = 25.630040 meter.
Now question is how far did he dig.According to this article minimal depth range for volcanic reservoirs between 2-6 kilometers.So he at least dig a hole of 2 km depth.
Using 2 kilometer depth,
Volume [Cylinder] = pi*(25.630040/2)^2*2000
Volume [Cylinder] = 1031854.484340 m^3
Energy [Pulverization] = 221178008718316.3640068 Joules
Energy [Pulverization] = 52.862812791 kilotons
Using average 4 kilometer
Volume [Cylinder] = pi*(25.630040/2)^2*4000
Volume [Cylinder] = 2063708.96868 m^3
Energy [Pulverization] = 442356017436632.728013 Joules
Energy [Pulverization] = 105.725625582 kiloton
Using 6 kilometer as depth
Volume [Cylinder] = pi*(25.630040/2)^2*6000
Volume [Cylinder] = 3095563.453020522 m^3
Energy [Pulverization] = 663534026154949.092020 Joules
Energy [Pulverization] = 158.588438374 kiloton
Raising Lava Flow
Now this is the important part. The volcanic eruption was pretty damn big.Its far bigger than diameter of the hole.
Here in this scan I scaled the diameter using Black Djinn that's closest to the diameter. But all Djiins wasn't same size so I scaled 4 djinns & used average.
Black Djinns = (18+24+12+17)/4 = 17.75 px = 52.96875 meter
Volcanic Eruption Diameter = 237 px = 707.244718 meter.
Now how much lava was risen above ground.
Volcanic Eruption Diameter = 247 px = 707.244718 meter.
Here the diameter of volcanic eruption is not same all around as you can see from the scalling.Average will give you 249.333333333 px the difference is negligible so I am going to use 247 px instead since its the exit point of lava in the surface.
So Volcanic Eruption Height = 391 px = 1119.56552 meter.
So Lava Volume above surface = pi*1119.56552*(707.244718/2)^2
Lava Volume above surface = 439823898.80409 m^3
We now need total volume of lava.That means from depth under ground to highest peak of eruption.
Using 2 km depth
Lava volume under surface = pi*2000*(707.244718/2)^2
Lava volume under surface = 785704611.84182191 m^3
Total Volume = 1225528510.6459119 m^3
For mass I am going to use Basalt which is a common extrusive igneous (volcanic) rock formed from the rapid cooling of basaltic lava exposed at or very near the surface of a planet.
Density of Basalt is 2800-3000 kg/m^3.I am going to use 2800 kg/m^3
Mass = 3431479829808.5533616 kg.
So here,P = mgh
P = 3431479829808.5533616*9.8*(2000+1119.56552)/2
P = 52453158182266533.212844 Joules
P = 12.536605684 megaton
Using 4 km depth
Lava volume under surface = pi*4000*(707.244718/2)^2
Lava volume under surface = 1571409223.6836438 m^3
Total Volume = 2011233122.487733829 m^3
Mass = 5631452742965.6547212 kg
P = mgh
P = 5631452742965.6547212*9.8*(4000+1119.56552)/2
P = 141269896771059934.61828142914 Joules
P = 33.764315672 megaton
Using 6 km depth
Lava volume under surface = pi*6000*(707.244718/2)^2
Lava volume under surface = 2357113835.525465 m^3
Total Volume = 2796937734.3295557 m^3
Mass = 7831425656122.75596
P = mgh
P = 7831425656122.75596*9.8*(6000+1119.56555)/2
P = 273206104794017541.778903362 Joules
P = 65.297826194 megaton
So,Total Energy [Low End] = 0.052862813+12.536605684 megaton
Total Energy [Low End] = 12.589468497 megaton
Total Energy [Mid End] = 33.764315672+0.105725626 megaton
Total Energy [Mid End] = 33.870041298 megaton
Total Energy [High End] = 0.158588438+65.297826194 megaton
Total Energy [High End] = 65.456414632 megaton
Low End- 12.589468497 megaton
Mid End -33.870041298 megaton
High End -65.456414632 Megaton
Well I have no idea how to calc it so I asked CT123 & he suggested I calc the GBE of the planet.Well here goes nothing.
The diameter of the planet is 4422.6567 kilometer
Using this we can find it's GBE.
Magi planet GBE is = 9.350E+30 Joules or 2.2347 zettatons of TNT
Value is within small planet level according to OBD criteria.
Magi planet GBE is = 2.2347 zettatons of TNT
Spoiler:All right first we need the distance Mu's fired his shot from. I thought of various way to find that but I conclude using angsize is the best approach.
Now Mu's Barbados charged through enemy line like nothing.First we are going to calc how far away he was from enemy line.Then how far he went into enemy line.That wy we will get total lengh.
Now here in this scan the old man was standing at front line of their army & looking at enemy army's movement .
Panel Height = 200 px.
Random Human in distance = 4 px = 1.7 meter.
As we know,
=>object degree size = 1.604652574916
Using angular calculator I get Distance = 60.696 meter
Again in this scan
Random Magician in crater = 17 px = 1.7 meter.
Crater Diameter = 211 px = 21.1 meter
Crater Radius = 10.55 meter
Crater Depth = 220 px = 22 meter.
Now,in this scan it shows how much Mu advanced after entering enemy line.
Panel Height = 433 px
Crater Diameter in Far = 27 px = 21.1 meter
object degree size = 2*atan(27/(433/tan(70/2)))
object degree size = 5.000109685608
Distance = 241.63
Total Length = 241.63+60.696 = 302.326 meter
I believe this should work fine for finding the volume:
Volume = 105 654 990 082 cm^3
Energy Pulverization = 22647147124076.7 Joule
Energy Pulverization = 5.41279807 kilotons
Mu's Barbados DC = 5.412 kilotons
Titus Great Flash
Aladin = 498 px = 1.38 meter
Magic Stick = 397 px = 0.8839759036144586 meter.
Magic Stick = 20 px = 0.8839759036144586 meter.
Crater Diameter = 376 px = 16.61874698795182168 meter.
To get Crater depth I will use Angsize.Its possible because of Cylinder nature.But I will have to do it in two part.
Using angsize Distance from POV-Crater= 18.4 meter
So POV to Crater Depth = 30.886 meter
So,Crater Depth = 30.886-16.61874698795182168 = 14.267 meter
Volume = 3094.758726893 m^3
Energy [Pulverization] = 663361533109.521475 J = 158.547211546 tons.
Magic Water Bullet-Sharrl Rasars
Spoiler:Basically its a fodder magic but Aladin took one in the back so why not calc it?
Odd prospective,odd angle to calc it.
So Random Human = 46 px = 1.5 meter [ Because Odd prospective using 1.5 instead of 1.7 meter]
Crater Diameter = 273 pixel = 8.90217391304241 meter.
Crater Depth = D/4 = 2.2255434782606025 meter.
Crater Volume = 92.35 m^3
Energy [Pulverization] = 4.731171726 tons
Not bad Durability for Pre-TS Aladin.
Hakuryuu Ren Half Dijjun Equip DC
Alibaba = 171 px = 1.68 meter
Crater Diameter = 410 px = 4.0280701754391 meter.
Crater Depth = 210 px = 2.0631578947371 meter
Crater Volume = 17.53 m^3
Energy [Sedan Crater] = 0.289094168 tons.
Wasted my time on this one.
Kougyoku Ren-Vainel Ganezza
Spoiler:For this calc I need the height of Sinbad's palace but I have no idea how big it is. I am going to assume 15 meter just eyeballing it.
Here Palace Height = 109 px = 15 meter.
Water Column Height = 486 px = 66.88073394495288 meter.
Water Column Width = 366 px = 50.36697247706328 meter.
From this scan,
Water Column Height = 359 px = 66.88073394495288 meter
Water Column Depth = 19 px = 3.539648871738453259 meter.
So Water Column Volume = 11923.59070024 m^3
Mass = 12245527.64915052 kg [1027 kg/m^3 for Ocean Water]
Potential Energy = 4017145345.3037554 Joules or 0.96012078 Tons.
Titus Great Flash = 158.547211546 tons
Kougyoku Ren-Vainel Ganezza = 0.96012078 Tons
Sharrl Rasars = 4.731171726 tons
Hakuryuu Ren Half Dijjun Equip DC = 0.289094168 tons.
Spoiler:Will do it very briefly.
Dark Nimbostratus Cloud with Average height 2000 meter & Stays 2400 meter above surface.
Panel Height = 607 px
Panel Width = 244 px
Cloud Diameter = 153 px
Now,2*atan(tan(70/2)*(244/607) = 31.44034773307649
2*atan(153/(244/tan(31.44034773307649/2))) = 20.01854219910909600892
Cloud Diameter Using Angsize= 847.17 meter
Height = 2000 meter.
Volume = 1127355825.331804227 m^3
Mass = 1130737892.80779964008926112 kg
Now after Masrur kicked the Banker cloud already parted in the time it took for him to go flying.
Banker = 19 px. = 1.7 meter
He went 49 px in the air = 4.38421052631597 meter.
The shit about height actually how far he went into the sky is pretty inconsistant.
This one,this one or this one to calc the distance.
I personally think this one is more accurate.
Panel Width = 326 px
Panel Height = 424 px.
Island Diameter = 181 px. = 67.32 meter.
Now,2*atan(tan(70/2)*(326/424) = 56.59312326358403
2*atan(181/(326/tan(56.59312326358403/2))) = 33.2837941879889681667
Using Angsize= 112.61 meter.
Initial Speed = 46.85 m/s
Timeframe = (4.38421052631597/46.85) = 0.09357973375274215582 second
Cloud parting Speed = (847.17/2)/0.09357973375274215582
KE = .5x4526.46083733474758973547997094^2x1130737892.80779964008926112
= 2.768584666 Megaton
Masrur's Kick = 2.768584666 Megaton