So at this point everyone is aware that in Fairy Tail the new character Brandish has size manipulation magic that she used to make an island grow.
There was a calc here and another on the OBD that both calculated the energy to lift the island. Here I'm trying to revise the OBD calc to work with her newly revealed abilities.
Here is the OBD calc: http://www.narutoforums.com/blog.php?bt=200550
Most of the work has been done there, so I'd recommend reading the first part of it to see if you have any problem with it. There are only a few things I'm actually changing.
The first thing to change is the mass; because if the island was stretched rather than raised the island and the column underneath it must both draw from the island's original mass. In the original calc the mass of the island plus the pillar (if they both had regular densities) has been calculated while what we really need is the mass of the island in it's unstretched state.
So first we're working out volume.
This is the scaling they used in the original, though I've added the blue line myself. Ignore the part where it says 2px; this image is slightly outdated, the red and blue lines are fine but after much deliberation it has been agreed that the green line should measure 3 pixels long.
V=V1+V2
I'm mapping the island as two half cones back to back, one larger than the other.
Red=592px
Red to Blue=366px
Red from Blue=226px
Green=3px
Blue=213px
Now we compare everything to the ship.
Ship=3px=15.6177m
Island height=213px=1104.0500m
Left hand length=366px=1897.1000m
Right hand length=226px=1171.4333m
The equation for volume of a cone uses (1/3), because these are half cones I'm using (1/6). First: for the high end.
V1=(1/6)*3.14*r^2*h
V1=(1/6)*3.14*(1897.1000^2)*1104.0500
V1=2079445717.2619m^3
V2=(1/6)*3.14*r^2*h
V2=(1/6)*3.14*(1171.4333^2)*1104.0500
V2=792870520.2600m^3
And with that we can determine our full volume.
V=V1+V2
V=2079445717.2619+792870520.2600
V=2872316237.5516m^3
Now we can determine our mass. The original calculation uses 2900kgm^-3 as a generic value for unknown stone; I think that's stupid. Most stones are not that heavy, a generic value should be a low end. This is an oceanic island so I should be able to assume igneous rock; I'll use 2400kgm^-3 for the lightest known values for basalt.
m=ρ*V
m=2400*2872316237.5516
m=6893558970123.84kg
The only thing left to determine is the height of the centre of gravity.
E=mgh
The original calculation used (1/2)*h for the centre of gravity of a cylinder but because the column is thicker towards the bottom I'll use the slightly safer (2/5)*h; looking at the image I think (2/5) is low enough to account for the disparity.
h=9808.8116*(2/5)
h=3923.52464m
Now we finally plug our values into our equation.
E=mgh
E=6893558970123.84*9.8*3923.52464
E=265061075070424318.896J
E=63.351Mt
E=6.3351*10^7 tons of TNT
And we have our final result.
See, the thing is that even if she only did so by changing the size, she did raise the centre of gravity, a couple of measures had to be taken to be account for how she did it but gpe should apply, to her and just about anyone.
Thanks to SDZ for recrunching the numbers with the updated size.