Feat[]
Aokiji frozse a large portion of the ocean so that an old man and his horse could cross the distance between four of the islands (essentially walking on the ice three times).
I'll try to calculate from scratch how large the area was that Aokiji froze, and how much energy is took him to do this in order to calculate his AP.
There are two main horizon shots we can use to determine how far Aokiji froze, so I'll be calcing both of these.
Horizon Shot 1[]
Distance between islands[]
This shot of the horizon from the perspective of the characters on the shore if the first one I'll calc.
Aokiji's Height = 40 px = 2.98 m
Shore Height = 40 px = 2.98 m
So if we combine the height of the shore above sea level with Luffy's height:
Luffy's Height = 1.72 m
Total Height = 4.7 m
Horizon Distance = 3.57 * √(4.7) = 7740 metres
Full length of the ice[]
Kuzan froze over three islands to get the old man to his destination, so multiple the distance by three:
Length = 7740 * 3 = 23220 m
That gets us the length of ice frozen by Aokiji but we don't know exactly how wide the amount of ice is.
Width of the ice[]
Since the ice appears to extend into the distance in each direction we can assume that it extends as far as the horizon for the characters viewing it.
Width = 4682 * 2 = 9364 m
Area of the ice[]
Area = 23220 * 9364 = 217,432,080 m^2
Low End - Melting Rate[]
For the low end, we'll use the depth previously calculated here.
Depth = 1.06 m
Volume of ice = 217,432,080 * 1.06 = 230478004.8 m^3
Mass of ice = 230,478,004.8 * 1025 kg/m^3 = 236,239,954,920 kg
Maximum Mean Monthly Temperature = 30 degrees
Energy to lower the water's temp = (30,000 calories/kg)(236,239,954,920 kg) = 7,087,198,600,000,000 calories
7,087,198,600,000,000 calories = 29,652,838,942,400,000 joules
Energy to convert to ice = (334,000 J/kg)(236,239,954,920 kg) = 78,904,144,900,000,000 joules
29,652,838,942,400,000 joules + 78,904,144,900,000,000 joules = 108,556,984,000,000,000 joules
108,556,984,000,000,000 joules = 25.95 Megatons
Mid End - Average Tidal Range[]
Tidal depth can vary up to 12 m on average, so I'll use that as a mid end depth.
Depth = 12 m
Volume of ice = 217,432,080 * 12 = 2,609,184,960 m^3
Mass of ice = 2,609,184,960 * 1025 kg/m^3 = 2,674,414,600,000 kg
Maximum Mean Monthly Temperature = 30 degrees
Energy to lower the water's temp = (30,000 calories/kg)(2,674,414,600,000 kg) = 80,232,438,000,000,000 calories
80,232,438,000,000,000 calories = 335,692,520,000,000,000 joules
Energy to convert to ice = (334,000 J/kg)(2,674,414,600,000 kg) = 893,254,480,000,000,000 joules
335,692,520,000,000,000 joules + 893,254,480,000,000,000 joules = 1,228,947,000,000,000,000 joules
1,228,947,000,000,000,000 joules = 293.73 Megatons
High End - Extreme Tidal Range[]
The deepest known tidal range is 16.3 m so I'll use that as a high end depth.
Depth = 16.3 m
Volume of ice = 217,432,080 * 16.3 = 3,544,142,904 m^3
Mass of ice = 3,544,142,904 * 1025 kg/m^3 = 3,632,746,500,000 kg
Energy to lower the water's temp = (30,000 calories/kg)(3,632,746,500,000 kg) = 108,982,400,000,000,000 calories
108,982,400,000,000,000 calories = 455,982,341,000,000,000 joules
Energy to convert to ice = (334,000 J/kg)(3,632,746,500,000 kg) = 1,213,337,330,000,000,000 joules
455,982,341,000,000,000 joules + 1,213,337,330,000,000,000 joules = 1,669,319,700,000,000,000 joules
1,669,319,700,000,000,000 joules = 398.98 Megatons
Horizon Shot 2[]
Distance between islands[]
The perspective of the camera is above one of the trees on the Long Ring Long Land island, so I'll calc a tree in relation to one of the flags on the coast to get a rough estimate for how high the camera is up.
Aokiji's Height = 40 px = 2.98 m
Flag Height = 170 px = 12.665 m
Flag's Height = 83 px = 12.665 m
Tree Height = 134 px = 20.45 m
Horizon Distance = 3.57 * √(20.45) = 16144 metres
Full length of the ice[]
Kuzan froze over three islands to get the old man to his destination, so multiple the distance by three:
Length = 16144 * 3 = 48432 m
That gets us the length of ice frozen by Aokiji but we don't know exactly how wide the amount of ice is.
Width of the ice[]
Since the ice appears to extend into the distance in each direction we can assume that it extends as far as the horizon for the characters viewing it.
Width = 4682 * 2 = 9364 m
Area of the ice[]
Area = 48432 * 9364 = 453,517,248 m^2
There is no canon value for the depth to which the ice is frozen, so I'll use
Low End - Melting Rate[]
For the low end, we'll use the depth previously calculated here.
Depth = 1.06 m
Volume of ice = 453,517,248 * 1.06 = 480,728,282.88 m^3
Mass of ice = 480,728,282.88 * 1025 kg/m^3 = 492,746,489,952 kg
Energy to lower the water's temp = (30,000 calories/kg)(492,746,489,952 kg) = 14,782,395,000,000,000 calories
14,782,395,000,000,000 calories = 61,849,540,680,000,000 joules
Energy to convert to ice = (334,000 J/kg)(492,746,489,952 kg) = 164,577,330,000,000,000 joules
61,849,540,680,000,000 joules + 164,577,330,000,000,000 joules = 226,426,871,000,000,000 joules
226,426,871,000,000,000 joules = 54.12 Megatons
Mid End - Average Tidal Range[]
Tidal depth can vary up to 12 m on average, so I'll use that as a mid end depth.
Depth = 12 m
Volume of ice = 453,517,248 * 12 = 5,442,206,976 m^3
Mass of ice = 5,442,206,976 * 1025 kg/m^3 = 5,578,262,200,000 kg
Energy to lower the water's temp = (30,000 calories/kg)(5,578,262,200,000 kg) = 167,347,870,000,000,000 calories
167,347,870,000,000,000 calories = 700,183,471,000,000,000 joules
Energy to convert to ice = (334,000 J/kg)(5,578,262,200,000 kg) = 1,863,139,570,000,000,000 joules
700,183,471,000,000,000 joules + 1,863,139,570,000,000,000 joules = 2,563,323,040,000,000,000 joules
2,563,323,040,000,000,000 joules = 612.65 Megatons
High End - Extreme Tidal Range[]
The deepest known tidal range is 16.3 m so I'll use that as a high end depth.
Depth = 16.3 m
Volume of ice = 453,517,248 * 16.3 = 7,392,331,142.4 m^3
Mass of ice = 7,392,331,142.4 * 1025 kg/m^3 = 7,577,139,400,000 kg
Energy to lower the water's temp = (30,000 calories/kg)(7,577,139,400,000 kg) = 227,314,180,000,000,000 calories
227,314,180,000,000,000 calories = 951,082,537,000,000,000 joules
Energy to convert to ice = (334,000 J/kg)(7,577,139,400,000 kg) = 2,530,764,560,000,000,000 joules
951,082,537,000,000,000 joules + 2,530,764,560,000,000,000 joules = 3,481,847,100,000,000,000 joules
3,481,847,100,000,000,000 joules = 832.18 Megatons
Results[]
Horizon 1
- Low End = 25.95 Megatons (City level)
- Mid End = 293.73 Megatons (Mountain level)
- High End = 398.98 Megatons (Mountain level)
Horizon 2
- Low End = 54.12 Megatons (City level)
- Mid End = 612.65 Megatons (Mountain level+)
- High End = 832.18 Megatons (Mountain level+)
So, all that's left is determining which horizon shot we use - I have reasons for preferring the former - and which end for the depth we use.