More calcs from Happy Tree Friends. As per always, keep an eye out for graphic violence.
1. Splendid destroys an oil truck with his laser vision
1:22
Splendid creates a colossal explosion visible from space (which Lumpy somehow survives, abet mortally wounded; infact most of the cast survive this explosion). The radius of the Earth is 6378km.
Timeframe is 3.47 seconds.
R = (h/2) + c^2/(8h)
= (127/2) + 705^2/(8 X 127)
= 552.697835 pixels
552.697835 pixels = 6378km
1 pixel = 6378km/552.697835 = 11.5397593km
11.5397593km X 273 = 3150.35429km
3150.35429km/2 = 1575.17715km (1575177.15m)
11.5397593km X 333 = 3842.73985km
3842.73985km/2 = 1921.36992km (1921369.92m)
11.5397593km X 79 = 911.640985km (911640.985m)
11.5397593km X 73 = 842.402429km
842.402429km/2 = 421.201214km (421201.214m)
11.5397593km X 349 = 4027.376km
Volume as an elipsoid and a cylinder.
V = 4/3πabc
= 4/3 X π X 1575177.15 X 1575177.15 X 1921369.92
= 1.99690959e19m^3
V = πr^2h
= π X 421201.214^2 X 911640.985
= 5.08104385e17m^3
V = 1.99690959e19 + 5.08104385e17
= 2.04772003e19m^3
Weight of a dust cloud/air is 1.003kg/m^3.
M = 2.04772003e19 X 1.003kg
= 2.05386319e19kg
With our mass, let's find the speed of the expansion of the explosion, then get our kinetic energy.
T = 4027.376km/3.47s
= 1160627.09m/s
KE = (0.5)mv^2
= (0.5) X 2.05386319e19 X 1160627.09^2
= 1.38333359e31 joules
= 3.3062466300191206692 zettatons
Way higher than what I expected by several orders of magnitude!
2. Splendid digs through the crust
From the same video above at 2:03
Splendid digs through the planets crust to get rid of a flood, but this brings up a volcanic tide of lava. The average thickness of continental crust is 40km.
Timeframe is 2.32 seconds.
T = 40km/2.32s
= 17241.3793/340.29
= Mach 50.6667234
3. Buddhist Monkey splits a mountain
We've had plently of calcs for the Superman expy, but what about the Aang expy?
1:43
Buddist Monkey sends a Generic Tree Ninja flying into the distance and splits a mountain in half. There are several ways in which we can go about finding the height. The first is scaling from the clouds (using the height of low flying cumulous clouds being between 200m and 2000m) and the second being horizon scaling.
(Low end)
218 pixels = 200m
1 pixel = 200m/218 = 0.917431193m
0.917431193m X 233 = 213.761468m
233 - 31 = 202 pixels
0.917431193m X 202 = 185.321101m
0.917431193m X 31 = 28.440367m
0.917431193m X 142 = 130.275229m
130.275229m/2 = 65.1376145m
0.917431193m X 330 = 302.752294m
302.752294m/2 = 151.376147m
(High end)
218 pixels = 2000m
1 pixel = 2000m/218 = 9.17431193m
9.17431193m X 233 = 2137.61468m
233 - 31 = 202 pixels
9.17431193m X 202 = 1853.21101m
9.17431193m X 31 = 284.40367m
9.17431193m X 142 = 1302.75229m
1302.75229m/2 = 651.376145m
9.17431193m X 330 = 3027.52294m
3027.52294m/2 = 1513.76147m
We'll find our volume as a spherical cap and a conical frustrum.
(Low end)
V = (1/3)πh^2(3R - h)
= (1/3) X π X 28.440367^2 X (3 X 106.880734 - 28.440367)
= 247503.845m^3
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (65.1376145^2 + 65.1376145 X 151.376147 + 151.376147^2) X 185.321101
= 7183987.93m^3
V = 247503.845 + 7183987.93
= 7431491.77m^3
(High end)
V = (1/3)πh^2(3R - h)
= (1/3) X π X 284.40367^2 (3 X 1068.80734 - 284.40367)
= 247503845m^3
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (651.376145^2 + 651.376145 X 1513.76147 + 1513.76147^2) X 1853.21101
= 7.18398793e9m^3
V = 247503845 + 7.18398793e9
= 7431491775m^3
The average weight of the Earth's crusts is 2600 kg per m^3.
(Low end)
M = 7431491.77 X 2600
= 19321878602kg
(High end)
M = 7431491775 X 2600
= 1.93218786e13kg
With that, let's also get our distance to the mountain.
= 0.304293477 rad
= 17.434731965504433 degrees
Using the angscaler, we get a distance of 697.06m and 6970.6m for our low ends and our high ends respectively. Keep that in mind for later. Next up, the splitting of the mountain itself.
Timeframe is 0.44 seconds.
(Low end)
0.917431193m X 41 = 37.6146789m
T = 37.6146789m/0.44s
= 85.4879066m/s
(High end)
9.17431193m X 41 = 376.146789m
T = 376.146789m/0.44s
= 854.879066m/s
Let's get our sweet kinetic energy!
(Low end)
KE = (0.5)mv^2
= (0.5) X 19321878602 X 85.4879066^2
= 7.06039044e13 joules
= 16.874738145315487 kilotons
(High end)
KE = (0.5)mv^2
= (0.5) X 1.93218786e13 X 854.879066^2
= 7.06039044e18 joules
= 1.6874738145315486548 gigatons
That's a lot higher than I was expecting! Finally, let's also ket the speed at which Buddhist Monkey sent the Generic Tree Ninja flying.
Timeframe is 3.28 seconds.
(Low end)
T = 697.06m/3.28s
= 212.518293m/s
(High end)
T = 6970.6m/3.28s
= 2125.18293/340.29
= Mach 6.24521123
4. Ski ya, wouldn't wanna be ya!
1:17, 1:29 and 2:01
Flaky slides down a mountain which took 4 days days straight to reach the top, and its summit was so tall that satellites drifted past (and so high up the pressure cracks her watch), and she reacts to various obstacles on the way down. The Satellite itself is the Sputnik.
The average orbiting height of the Sputnik was 577km. The average speed of a chairlift is 2.5m/s. We'll use those as our low end and our high end.
T = 60 X 60 X 24 X 4
= 345600 X 2.5
= 864000m
Timeframe is 79 seconds.
(Low end)
T = 577km/79s
= 7303.79747/340.29
= Mach 21.4634502
(High end)
T = 864000m/79s
= 10936.7089/340.29
= Mach 32.1393779
With such a speed, we can also get kinetic energy. We'll use the average weight of a 10 year old girl (30kg) for our low end 12 year old girl (40kg) for our high end (both values here).
(Low low end)
KE = (0.5)mv^2
= (0.5) X 30 X 7303.79747^2
= 800181862 joules
= 0.191248054971 tons of TNT
(High low end)
KE = (0.5)mv^2
= (0.5) X 40 X 7303.79747^2
= 1.06690915e9 joules
= 0.2549974067878 tons of TNT
(Low high end)
KE = (0.5)mv^2
= (0.5) X 30 X 10936.7089^2
= 1.79417402e9 joules
= 0.4288178824092 tons of TNT
(High high end)
KE = (0.5)mv^2
= (0.5) X 40 X 10936.7089^2
= 2.39223203e9 joules
= 0.5717571773423 tons of TNT
Final Results
Splendid destroys an oil truck with his laser vision = 3.3067 zettatons
Splendid drills through the planets crusts = Mach 50.667
Buddhist Monkey splits a mountain (low end) = 16.875 kilotons
Buddhist Monkey splits a mountain (high end) = 1.687 gigatons
Buddhist Monkey sends Generic Tree Ninja flying (low end) = 212.518m/s
Buddhist Monkey sends Generic Tree Ninja flying (high end) = Mach 6.245
Flaky ski's down mountain (low end) = Mach 21.463
Flaky ski's down mountain (high end) = Mach 32.139
Flaky's kinetic energy (low low end) = 0.191 tons of TNT
Flaky's kinetic energy (high low end) = 0.255 tons of TNT
Flaky's kinetic energy (low high end) = 0.429 tons of TNT
Flaky's kinetic energy (high high end) = 0.571 tons of TNT
A lot of these where way higher than I thought they were going to be. Very nice.
non
1. Splendid destroys an oil truck with his laser vision
1:22
R = (h/2) + c^2/(8h)
= (127/2) + 705^2/(8 X 127)
= 552.697835 pixels
552.697835 pixels = 6378km
1 pixel = 6378km/552.697835 = 11.5397593km
11.5397593km X 273 = 3150.35429km
3150.35429km/2 = 1575.17715km (1575177.15m)
11.5397593km X 333 = 3842.73985km
3842.73985km/2 = 1921.36992km (1921369.92m)
11.5397593km X 79 = 911.640985km (911640.985m)
11.5397593km X 73 = 842.402429km
842.402429km/2 = 421.201214km (421201.214m)
11.5397593km X 349 = 4027.376km
Volume as an elipsoid and a cylinder.
V = 4/3πabc
= 4/3 X π X 1575177.15 X 1575177.15 X 1921369.92
= 1.99690959e19m^3
V = πr^2h
= π X 421201.214^2 X 911640.985
= 5.08104385e17m^3
V = 1.99690959e19 + 5.08104385e17
= 2.04772003e19m^3
Weight of a dust cloud/air is 1.003kg/m^3.
M = 2.04772003e19 X 1.003kg
= 2.05386319e19kg
With our mass, let's find the speed of the expansion of the explosion, then get our kinetic energy.
T = 4027.376km/3.47s
= 1160627.09m/s
KE = (0.5)mv^2
= (0.5) X 2.05386319e19 X 1160627.09^2
= 1.38333359e31 joules
= 3.3062466300191206692 zettatons
Way higher than what I expected by several orders of magnitude!
2. Splendid digs through the crust
From the same video above at 2:03
T = 40km/2.32s
= 17241.3793/340.29
= Mach 50.6667234
3. Buddhist Monkey splits a mountain
We've had plently of calcs for the Superman expy, but what about the Aang expy?
1:43
218 pixels = 200m
1 pixel = 200m/218 = 0.917431193m
0.917431193m X 233 = 213.761468m
233 - 31 = 202 pixels
0.917431193m X 202 = 185.321101m
0.917431193m X 31 = 28.440367m
0.917431193m X 142 = 130.275229m
130.275229m/2 = 65.1376145m
0.917431193m X 330 = 302.752294m
302.752294m/2 = 151.376147m
(High end)
218 pixels = 2000m
1 pixel = 2000m/218 = 9.17431193m
9.17431193m X 233 = 2137.61468m
233 - 31 = 202 pixels
9.17431193m X 202 = 1853.21101m
9.17431193m X 31 = 284.40367m
9.17431193m X 142 = 1302.75229m
1302.75229m/2 = 651.376145m
9.17431193m X 330 = 3027.52294m
3027.52294m/2 = 1513.76147m
We'll find our volume as a spherical cap and a conical frustrum.
(Low end)
V = (1/3)πh^2(3R - h)
= (1/3) X π X 28.440367^2 X (3 X 106.880734 - 28.440367)
= 247503.845m^3
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (65.1376145^2 + 65.1376145 X 151.376147 + 151.376147^2) X 185.321101
= 7183987.93m^3
V = 247503.845 + 7183987.93
= 7431491.77m^3
(High end)
V = (1/3)πh^2(3R - h)
= (1/3) X π X 284.40367^2 (3 X 1068.80734 - 284.40367)
= 247503845m^3
V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (651.376145^2 + 651.376145 X 1513.76147 + 1513.76147^2) X 1853.21101
= 7.18398793e9m^3
V = 247503845 + 7.18398793e9
= 7431491775m^3
The average weight of the Earth's crusts is 2600 kg per m^3.
(Low end)
M = 7431491.77 X 2600
= 19321878602kg
(High end)
M = 7431491775 X 2600
= 1.93218786e13kg
With that, let's also get our distance to the mountain.
= 2*atan(233/(720/tan(70/2)))
= 0.304293477 rad
= 17.434731965504433 degrees
Using the angscaler, we get a distance of 697.06m and 6970.6m for our low ends and our high ends respectively. Keep that in mind for later. Next up, the splitting of the mountain itself.
(Low end)
0.917431193m X 41 = 37.6146789m
T = 37.6146789m/0.44s
= 85.4879066m/s
(High end)
9.17431193m X 41 = 376.146789m
T = 376.146789m/0.44s
= 854.879066m/s
Let's get our sweet kinetic energy!
(Low end)
KE = (0.5)mv^2
= (0.5) X 19321878602 X 85.4879066^2
= 7.06039044e13 joules
= 16.874738145315487 kilotons
(High end)
KE = (0.5)mv^2
= (0.5) X 1.93218786e13 X 854.879066^2
= 7.06039044e18 joules
= 1.6874738145315486548 gigatons
That's a lot higher than I was expecting! Finally, let's also ket the speed at which Buddhist Monkey sent the Generic Tree Ninja flying.
(Low end)
T = 697.06m/3.28s
= 212.518293m/s
(High end)
T = 6970.6m/3.28s
= 2125.18293/340.29
= Mach 6.24521123
4. Ski ya, wouldn't wanna be ya!
1:17, 1:29 and 2:01
Flaky slides down a mountain which took 4 days days straight to reach the top, and its summit was so tall that satellites drifted past (and so high up the pressure cracks her watch), and she reacts to various obstacles on the way down. The Satellite itself is the Sputnik.
T = 60 X 60 X 24 X 4
= 345600 X 2.5
= 864000m
(Low end)
T = 577km/79s
= 7303.79747/340.29
= Mach 21.4634502
(High end)
T = 864000m/79s
= 10936.7089/340.29
= Mach 32.1393779
With such a speed, we can also get kinetic energy. We'll use the average weight of a 10 year old girl (30kg) for our low end 12 year old girl (40kg) for our high end (both values here).
(Low low end)
KE = (0.5)mv^2
= (0.5) X 30 X 7303.79747^2
= 800181862 joules
= 0.191248054971 tons of TNT
(High low end)
KE = (0.5)mv^2
= (0.5) X 40 X 7303.79747^2
= 1.06690915e9 joules
= 0.2549974067878 tons of TNT
(Low high end)
KE = (0.5)mv^2
= (0.5) X 30 X 10936.7089^2
= 1.79417402e9 joules
= 0.4288178824092 tons of TNT
(High high end)
KE = (0.5)mv^2
= (0.5) X 40 X 10936.7089^2
= 2.39223203e9 joules
= 0.5717571773423 tons of TNT
Final Results
Splendid destroys an oil truck with his laser vision = 3.3067 zettatons
Splendid drills through the planets crusts = Mach 50.667
Buddhist Monkey splits a mountain (low end) = 16.875 kilotons
Buddhist Monkey splits a mountain (high end) = 1.687 gigatons
Buddhist Monkey sends Generic Tree Ninja flying (low end) = 212.518m/s
Buddhist Monkey sends Generic Tree Ninja flying (high end) = Mach 6.245
Flaky ski's down mountain (low end) = Mach 21.463
Flaky ski's down mountain (high end) = Mach 32.139
Flaky's kinetic energy (low low end) = 0.191 tons of TNT
Flaky's kinetic energy (high low end) = 0.255 tons of TNT
Flaky's kinetic energy (low high end) = 0.429 tons of TNT
Flaky's kinetic energy (high high end) = 0.571 tons of TNT
A lot of these where way higher than I thought they were going to be. Very nice.
non
