I calced this before, but unfortunately, the site hosting the images had a crash. It's one of the best feats in the series though, so it's worth recovering.
Renton & Eureka trigger a Seven Swell, which destroys a mountain and parts the clouds around for miles. There will be a ton of scaling here, so let's get into it.
Final Results
Nirvash Type-Zero destroys a mountain = 4.006 teratons
These results are actually pretty consistent with last time in terms of energy (give or take some), so this bodes well.
Renton & Eureka trigger a Seven Swell, which destroys a mountain and parts the clouds around for miles. There will be a ton of scaling here, so let's get into it.
The Gekko has a wingspan of 232.12m.
146 pixels = 232.12m
1 pixel = 232.12m/146 = 1.58986301m
1.58986301m X 457 = 726.567396m
88 pixels = 726.567396m
1 pixel = 726.567396m/88 = 8.25644768m
8.25644768m X 824 = 6803.31289m
8.25644768m X 938 = 7744.54792m
6803.31289m + 7744.54792m = 14547.8608m
8.25644768m X 39 = 322.00146m
8.25644768m X 232 = 1915.49586m
1915.49586m/2 = 957.74793m
Next we'll need to subtract the height of the part that was blown off, so as to find the length of the area hollowed out, as well as get the bottom length for the area blown off.
8.25644768m X 626 = 5168.53625m
8.25644768m X 571 = 4714.43163m
4714.43163m/2 = 2357.21582m
7744.54792m - 5168.53625m = 2576.01167m
14547.8608m - 2576.01167m = 11971.8491m
938 - 636 = 302 pixels
8.25644768m X 302 = 2493.4472m
Now let's find the diameter (and radius) of the hole in the middle of the mountain.
1227 pixels = 4714.43163m
1 pixel = 4714.43163m/1227 = 3.84224257m
3.84224257m X 767 = 2947.00005m
2947.00005m/2 = 1473.50003m
With all of that in hand, let's finally get the area of the mountain hollowed out (as a cylinder), and the part of the mountain that was blown up (as a conical frustrum and a cone).
V = πr^2h
= π X 1473.50003^2 X 11971.8491
= 2.59933068e10m^3
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (957.74793^2 + 957.74793 X 2357.21582 + 2357.21582^2) X 2493.4472
= 2.27987477e10m^3
V = πr^2h/3
= π X 957.74793^2 X 322.00146/3
= 309306398m^3
V = 2.27987477e10 + 309306398
= 23108054098m^3
For our mass, let's go with a low end of 2.2 tons/m^3 for sandstone (2200kg/m^3).
M = 2.59933068e10 X 2200kg
= 5.7185275e13kg
M = 23108054098 X 2200kg
= 5.0837719e13kg
8.25644768m X 2188 = 18065.1075m
Before we get our timeframe, a reminder that this is 30 frames a second...
Let's find our timeframe!
Total timeframe is 4 seconds and 8 frames, while the timeframe of the top part shattering is 2 seconds.
T = 1s/30
= 33.3333333ms X 8
= 0.266666666s + 4s
= 4.26666667s
T = 11971.8491m/4.26666667s
= 2805.90213m/s
T = 18065.1075m/2s
= 9032.55375m/s
KE = (0.5)mv^2
= (0.5) X 5.7185275e13 X 2805.90213^2
= 2.25112316e20 joules
KE = (0.5)mv^2
= (0.5) X 5.0837719e13 X 9032.55375^2
= 2.07384918e21 joules
We're not done yet though; we can also get the energy for the clouds parting. Scaling from the valley the mountains are sitting in.
199 pixels = 11971.8491m
1 pixel = 11971.8491m/99 = 120.927769m
120.927769m X 2180 = 263622.536m
263622.536m/2 = 131811.268m
The thickness as nimbostratus (nimbostratus are dark clouds that usually have a thickness of 6500 to 10,000 feet, or 2000 to 3000m thick, which is an average of 2500m thick), and they don't seem like cumulonimbi, so we'll go with that. Volume as a cylinder.
V = πr^2h
= π X 131811.268^2 X 2500
= 1.36456729e14m^3
Weigh of air is 1.003kg/m^3.
M = 1.36456729e14 X 1.003kg
= 1.36866099e14kg
Timeframe is 9 seconds and 2 frames
T = 33.3333333ms X 2
= 66.6666666ms + 9s
= 9.06666667s
T = 131811.268m/9.06666667s
= 14538.0075m/s
KE = (0.5)mv^2
= (0.5) X 1.36866099e14 X 14538.0075^2
= 3.11467344e21 joules
We finally have all our values...so let's add them together for our final yield!
E = 2.25112316e20 + 2.07384918e21 + 1.44635756e22
= 1.67625371e22 joules
= 4.0063425191204586895 teratons
1 pixel = 232.12m/146 = 1.58986301m
1.58986301m X 457 = 726.567396m
1 pixel = 726.567396m/88 = 8.25644768m
8.25644768m X 824 = 6803.31289m
6803.31289m + 7744.54792m = 14547.8608m
8.25644768m X 39 = 322.00146m
8.25644768m X 232 = 1915.49586m
1915.49586m/2 = 957.74793m
Next we'll need to subtract the height of the part that was blown off, so as to find the length of the area hollowed out, as well as get the bottom length for the area blown off.
8.25644768m X 571 = 4714.43163m
4714.43163m/2 = 2357.21582m
7744.54792m - 5168.53625m = 2576.01167m
14547.8608m - 2576.01167m = 11971.8491m
938 - 636 = 302 pixels
8.25644768m X 302 = 2493.4472m
Now let's find the diameter (and radius) of the hole in the middle of the mountain.
1 pixel = 4714.43163m/1227 = 3.84224257m
3.84224257m X 767 = 2947.00005m
2947.00005m/2 = 1473.50003m
With all of that in hand, let's finally get the area of the mountain hollowed out (as a cylinder), and the part of the mountain that was blown up (as a conical frustrum and a cone).
V = πr^2h
= π X 1473.50003^2 X 11971.8491
= 2.59933068e10m^3
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (957.74793^2 + 957.74793 X 2357.21582 + 2357.21582^2) X 2493.4472
= 2.27987477e10m^3
V = πr^2h/3
= π X 957.74793^2 X 322.00146/3
= 309306398m^3
V = 2.27987477e10 + 309306398
= 23108054098m^3
For our mass, let's go with a low end of 2.2 tons/m^3 for sandstone (2200kg/m^3).
M = 2.59933068e10 X 2200kg
= 5.7185275e13kg
M = 23108054098 X 2200kg
= 5.0837719e13kg
Before we get our timeframe, a reminder that this is 30 frames a second...
T = 1s/30
= 33.3333333ms X 8
= 0.266666666s + 4s
= 4.26666667s
T = 11971.8491m/4.26666667s
= 2805.90213m/s
T = 18065.1075m/2s
= 9032.55375m/s
KE = (0.5)mv^2
= (0.5) X 5.7185275e13 X 2805.90213^2
= 2.25112316e20 joules
KE = (0.5)mv^2
= (0.5) X 5.0837719e13 X 9032.55375^2
= 2.07384918e21 joules
We're not done yet though; we can also get the energy for the clouds parting. Scaling from the valley the mountains are sitting in.
1 pixel = 11971.8491m/99 = 120.927769m
120.927769m X 2180 = 263622.536m
263622.536m/2 = 131811.268m
The thickness as nimbostratus (nimbostratus are dark clouds that usually have a thickness of 6500 to 10,000 feet, or 2000 to 3000m thick, which is an average of 2500m thick), and they don't seem like cumulonimbi, so we'll go with that. Volume as a cylinder.
V = πr^2h
= π X 131811.268^2 X 2500
= 1.36456729e14m^3
Weigh of air is 1.003kg/m^3.
M = 1.36456729e14 X 1.003kg
= 1.36866099e14kg
T = 33.3333333ms X 2
= 66.6666666ms + 9s
= 9.06666667s
T = 131811.268m/9.06666667s
= 14538.0075m/s
KE = (0.5)mv^2
= (0.5) X 1.36866099e14 X 14538.0075^2
= 3.11467344e21 joules
We finally have all our values...so let's add them together for our final yield!
E = 2.25112316e20 + 2.07384918e21 + 1.44635756e22
= 1.67625371e22 joules
= 4.0063425191204586895 teratons
Final Results
Nirvash Type-Zero destroys a mountain = 4.006 teratons
These results are actually pretty consistent with last time in terms of energy (give or take some), so this bodes well.
