The power of Lavos, Queen Zeal and the Mammon Machine keeps the massive Black Omen hovering in the sky for millenia effortlessly. And the Black Omen is so huge that its top reaches into space.
We can find the distance and height from the planet, for which we'll need to get the radius of the planet in pixels so we can then work in kilometers.
R = (h/2) + c^2/(8h)
= (26/2) + 1744^2/(8 X 26)
= 14635.7692 pixels
We'll need the diameter, so double that.
D = 14635.7692 X 2
= 29271.5384 pixels
= 2.96082269 rad
= 169.64264402399212 degrees
The diameter of the Earth at the equator is 12,756km. Put all this information into the angscaler and we have a height of 578.05km. However, it's not sitting directly on the ground but floating in the sky. There is still however, a way in which we can find our height; the heroes arrive at the Black Omen in the clouds.
Looking into cloud heights, they generally range from 6500 feet to 60000 feet, or 1.9812km to 18.28800km.
www.nationalgeographic.com
H = 578.05km - 18.28800km
= 559.76200km
Now for the scaling, which in this case may not be too easy, as it's hard to figure out the dimensions and proper shape of the Black Omen. Thankfully, good people in the Chrono fanbase have pointed out the place where you fight Queen Zeals final form can be seen on the Black Omen sprite.
With that, let's scale the dimensions of the Black Omen!
403 pixels = 559.762km (559762m)
1 pixel = 559762m/403 = 1388.98759m
1388.98759m X 70 = 97229.1313m
1388.98759m X 118 = 163900.536m
163900.536m/2 = 81950.268m
1388.98759m X 84 = 116674.958m
1388.98759m X 688 = 955623.462m
955623.462m/2 = 477811.731m
1388.98759m X 280 = 388916.525m
1388.98759m X 64 = 88895.2058m
1388.98759m X 166 = 230571.94m
1388.98759m X 397 = 551428.073m
551428.073m/2 = 275714.036m
Volume of the connecting part as a cylinder, the bottom-most segment as two triangular pyramids and the top section as two triangular pyramids also.
V=πr^2h
= π X 81950.268^2 X 97229.1313
= 2.05138433e15m^3
A = (0.5)ab
= (0.5) X 477811.731 X 388916.525
= 9.2914439e10m^2
V = Ah
= 9.2914439e10 X 116674.958
= 1.08407883e16m^3
V = 1.08407883e16 X 2
= 2.16815766e16m^2
A = (0.5)ab
= (0.5) X 275714.036 X 230571.94
= 3.17859601e10m^2
V = 3.17859601e10 X 88895.2058
= 2.82561946e15m^3
V = 2.82561946e15 X 2
= 5.65123892e15m^3
V = 2.05138433e15 + 2.16815766e16 + 5.65123892e15
= 2.93841998e16m^3
I'm not able to figure out the proper dimensions of the back of the Black Omen unfortunately, so we'll just stick with the front of it. The light ship mass of container vessel 2700TEU is 102.56kg/m^3 (as with other machine masses, this is honestly probably a huge lowball as the Black Omen looks pretty huge and heavy, although there are also many hollow parts to take into account).
M = 2.93841998e16 X 102.56kg
= 3.01364353e18kg
We will find the energy via GPE.
E = 3.01364353e18 X 9.8 X 18288.00
= 5.40112426e23 joules
All of this is impressive...but it's super important that we watch this sequence as it plays out in the game.
The Black Omen isn't just standing still; it's moving Quite considerably considering the ground below too. As per above, the diameter of the Earth at the equator is 12,756km.
R = 12,756km/2
= 6378km
Once again, we'll refer to the above formula for finding the radius of a sphere...
R = (h/2) + c^2/(8h)
= (11/2) + 633^2/(8 X 11)
= 4558.78409 pixels
4558.78409 pixels = 6378km
1 pixel = 6378km/4558.78409 = 1.39905726km
1.39905726km X 64 = 89.5396646km
Timeframe is 6 seconds.
1.39905726km X 16 = 22.3849162km
89.5396646km - 22.3849162km
67.1547484km
T = 67.1547484km/6s
= 11192.4581/340.29
= Mach 32.8909404
KE = (0.5)mv^2
= (0.5) X 3.01364353e18 X 11192.4581^2
= 1.88761248e26 joules
E = 1.88761248e26 + 5.40112426e23
= 1.8930136e26 joules
= 45.244110898661567433 petatons
Please keep in note this is only the front half of the ship (abet the larger half too); ultimately this would be far higher. And if that's not crazy enough, Lavos's energy sustained it while in it's sleep with no loss at all to its power (in fact it continued to gain power). Infact, we could find out just how much energy Lavos, Queen Zeal and the Mammon Machine spent to sustain the Black Omen in the sky. Without any kind of interference, the Black Omen remains in the skies from 12000 BC to 2300 AD, or over 14300 years.
T = 60 X 60 X 24 X 365 X 14300
= 450964800000s
E = 1.8930136e26 X 450964800000
= 8.536825e37 joules
= 20.403501434034416889 ninatons
Final Results
The Black Omen's height = 559.762km
The Black Omen's speed = Mach 32.891
Energy to sustain the Black Omen (per second) = >45.244 petatons
Total energy spend sustaining the Black Omen = >20.404 ninatons
We can find the distance and height from the planet, for which we'll need to get the radius of the planet in pixels so we can then work in kilometers.
R = (h/2) + c^2/(8h)
= (26/2) + 1744^2/(8 X 26)
= 14635.7692 pixels
We'll need the diameter, so double that.
D = 14635.7692 X 2
= 29271.5384 pixels
= 2*atan(29271.5384/(1257/tan(70/2)))
= 2.96082269 rad
= 169.64264402399212 degrees
The diameter of the Earth at the equator is 12,756km. Put all this information into the angscaler and we have a height of 578.05km. However, it's not sitting directly on the ground but floating in the sky. There is still however, a way in which we can find our height; the heroes arrive at the Black Omen in the clouds.
Clouds tease the mind, protect life on Earth
From thin wisps to threatening thunderheads, clouds come in all shapes, sizes, and types.
www.nationalgeographic.com Just to show how ridiculous this will be, I'm going with the high end of 18.28800 (or 18288.00m).
H = 578.05km - 18.28800km
= 559.76200km
Now for the scaling, which in this case may not be too easy, as it's hard to figure out the dimensions and proper shape of the Black Omen. Thankfully, good people in the Chrono fanbase have pointed out the place where you fight Queen Zeals final form can be seen on the Black Omen sprite.
1 pixel = 559762m/403 = 1388.98759m
1388.98759m X 70 = 97229.1313m
1388.98759m X 118 = 163900.536m
163900.536m/2 = 81950.268m
1388.98759m X 84 = 116674.958m
1388.98759m X 688 = 955623.462m
955623.462m/2 = 477811.731m
1388.98759m X 280 = 388916.525m
1388.98759m X 64 = 88895.2058m
1388.98759m X 166 = 230571.94m
1388.98759m X 397 = 551428.073m
551428.073m/2 = 275714.036m
Volume of the connecting part as a cylinder, the bottom-most segment as two triangular pyramids and the top section as two triangular pyramids also.
V=πr^2h
= π X 81950.268^2 X 97229.1313
= 2.05138433e15m^3
A = (0.5)ab
= (0.5) X 477811.731 X 388916.525
= 9.2914439e10m^2
V = Ah
= 9.2914439e10 X 116674.958
= 1.08407883e16m^3
V = 1.08407883e16 X 2
= 2.16815766e16m^2
A = (0.5)ab
= (0.5) X 275714.036 X 230571.94
= 3.17859601e10m^2
V = 3.17859601e10 X 88895.2058
= 2.82561946e15m^3
V = 2.82561946e15 X 2
= 5.65123892e15m^3
V = 2.05138433e15 + 2.16815766e16 + 5.65123892e15
= 2.93841998e16m^3
I'm not able to figure out the proper dimensions of the back of the Black Omen unfortunately, so we'll just stick with the front of it. The light ship mass of container vessel 2700TEU is 102.56kg/m^3 (as with other machine masses, this is honestly probably a huge lowball as the Black Omen looks pretty huge and heavy, although there are also many hollow parts to take into account).
M = 2.93841998e16 X 102.56kg
= 3.01364353e18kg
We will find the energy via GPE.
E = 3.01364353e18 X 9.8 X 18288.00
= 5.40112426e23 joules
All of this is impressive...but it's super important that we watch this sequence as it plays out in the game.
The Black Omen isn't just standing still; it's moving Quite considerably considering the ground below too. As per above, the diameter of the Earth at the equator is 12,756km.
R = 12,756km/2
= 6378km
R = (h/2) + c^2/(8h)
= (11/2) + 633^2/(8 X 11)
= 4558.78409 pixels
4558.78409 pixels = 6378km
1 pixel = 6378km/4558.78409 = 1.39905726km
1.39905726km X 64 = 89.5396646km
1.39905726km X 16 = 22.3849162km
89.5396646km - 22.3849162km
67.1547484km
T = 67.1547484km/6s
= 11192.4581/340.29
= Mach 32.8909404
KE = (0.5)mv^2
= (0.5) X 3.01364353e18 X 11192.4581^2
= 1.88761248e26 joules
E = 1.88761248e26 + 5.40112426e23
= 1.8930136e26 joules
= 45.244110898661567433 petatons
Please keep in note this is only the front half of the ship (abet the larger half too); ultimately this would be far higher. And if that's not crazy enough, Lavos's energy sustained it while in it's sleep with no loss at all to its power (in fact it continued to gain power). Infact, we could find out just how much energy Lavos, Queen Zeal and the Mammon Machine spent to sustain the Black Omen in the sky. Without any kind of interference, the Black Omen remains in the skies from 12000 BC to 2300 AD, or over 14300 years.
T = 60 X 60 X 24 X 365 X 14300
= 450964800000s
E = 1.8930136e26 X 450964800000
= 8.536825e37 joules
= 20.403501434034416889 ninatons
Final Results
The Black Omen's height = 559.762km
The Black Omen's speed = Mach 32.891
Energy to sustain the Black Omen (per second) = >45.244 petatons
Total energy spend sustaining the Black Omen = >20.404 ninatons
