Calc Voltron: Legendary Defender calcs, part 1

1. Blue Voltron flies to space

(Reaction videos are only versions I could find on Youtube or Dailymotion, sorry)
26:33
35 seconds.

R = (h/2) + c^2/(8h)
= (5/2) + 495^2/(8 X 48)
= 640.585938 X 2
= 1281.17188

That's the diameter of the Earth (12,742km).

object degree size = 2*atan(Object_Size/(Panel_Height/tan(70/2)))

Click to expand...

= 2*atan(1281.17188/(636/tan(70/2)))
= 1.52420618 rad
= 87.3305812219741 degrees

Enter that through the angscaler and we have us 6675km.

T = 6675km/35s
= 190714.286/340.29
= Mach 560.446343

As impressive as that is, it's nothing compared to other feats from the same episode.

2. Blue Voltron flies to the edge of the Solar System
(28:06 in the above video)
Blue Voltron reached Kerberos (one of Plutos moons) in less than a minute. Pluto is 7,500,000,000km away from the Earth at it's closest. It took them 34 seconds (Pidge says 5 seconds, but close enough).

T = 7,500,000,000km/34s
= 2.20588235e11/299792458
= 735.80315 C

Also going by Pidges statement of 5 seconds...

T = 7,500,000,000km/5s
= 1500000000000/299792458
= 5003.46143 C

3. Blue Lions size
Let's scale the size of the Blue Lion. Lance is Cuban...
And the average height of a Cuban is 168cm (1.68m).
902 pixels = 1.68m
1 pixel = 1.68m/902 = 0.00186252772m
0.00186252772m X 490 = 0.912638583m
0.00186252772m X 136 = 0.25330377m
141 pixels = 0.912638583m
1 pixel = 0.912638583m/141 = 0.00647261406m
0.00647261406m X 517 = 3.34634147m
53 pixels = 3.34634147m
1 pixel = 3.34634147m/53 = 0.0631385183m
0.0631385183m X 778 = 49.1217672m

That is one big ass robo lion. Calc should come in handy for the future though. Like right now.

4. Melting/Freezing a tower
(Episode 7, couldn't find footage of this on Youtube sorry)
The Red Lion melts the base of a huge attack, but when it starts falling over (which would hurt the Balmera) the Blue Lion freezes it.
10 pixels = 49.1217672m
1 pixel = 49.1217672m/10 = 4.91217672m
4.91217672m X 98 = 481.393319m
481.393319m/2 = 240.69666m
4.91217672m X 89 = 437.183728m
437.183728m/2 = 218.591864m
4.91217672m X 223 = 1095.41541m
4.91217672m X 245 = 1203.4833m
4.91217672m X 210 = 1031.55711m
4.91217672m X 58 = 284.90625m
284.90625m/2 = 142.453125m
1095.41541m - 1031.55711m = 63.8583m

Volume as the top two parts as cones and the main part as a cylinder.

V = πr^2h
= π X 240.69666^2 X 1203.4833
= 219043348m^3

V = πr^2h/3
= π X 218.591864^2 X 1095.41541/3
= 54811975m^3

V = πr^2h/3
= π X 142.453125^2 X 1031.55711/3
= 21921277.3m^3

V = 54811975 - 21921277.3
= 32890697.7m^3
353 pixels = 1203.4833m
1 pixel = 1203.4833m/353 = 3.40930113m
3.40930113m X 141 = 480.711459m
480.711459m/2 = 240.355729m
3.40930113m X 116 = 395.478931m
395.478931m/2 = 197.739465m

Volume of the tower as a conical frustrum.

V = (1/3)π(r^2+rR+R^2)h
= (1/3) X π X (197.739465^2 + 197.739465 X 240.355729 + 240.355729^2) X 1203.4833
= 181984598m^3

V = 219043348 - 181984598
= 37058750m^3

That's the area of ice surrounding the upper tower, now onto the lower tower, and the hole melted.
416 pixels = 480.711459m
1 pixel = 480.711459m/416 = 1.15555639m
1.15555639m X 100 = 115.555639m
115.555639m/2 = 57.7778195m
1.15555639m X 463 = 535.022609m
535.022609m/2 = 267.511304m
1.15555639m X 378 = 436.800315m
436.800315m/2 = 218.400158m

Volume as a conical frustrum.
V = (1/3) π (r^2 + rR + R^2)h
= (1/3) X π X (57.7778195^2 + 57.7778195 X 218.400158 + 218.400158^2) X 480.711459
= 32044215.4m^3

Specific heat of iron is 450 joules per m^3 (seems like a basic metal to go with) and it's melting point is 1538 °C.

E = 32044215.4 X 450 X 1538
= 2.21778015e13 joules

Heat fusion of iron is 272kj/m^3 (270000j/m^3).

E = 32044215.4 X 270000
= 8.65193816e12 joules

E = 8.65193816e12 + 2.21778015e13
= 3.08297397e13 joules
= 7.36848463193 kilotons

That's a lot lower than I was expecting. Anyway, back to the freezing. The reason we waited is because the part within the melted out part and around it would be super hot.

As for how hot the temperature on the Balmera is..
...it's hard to say, but no one seemed particularly hot or cold, so we'll go with the hottest temperature of a cold or mild desert, that being 25 C, or 298.15 kelvin, which is close to 300Km, which has a specific heat of 1.005. The decrease in temperature is 1513 C. 1538 C is 1811.15K which is close enough to 1500K, or a specific heat of 1.216.

E = 32044215.4 X 1.216X 1513
= 5.89552038e10 joules

We can also add the heat fusion of air/oxygen (13800 joules/kg).

E = 32044215.4 X 13800
= 442210172520 joules

Now the rest of the gun tower.

V = 32890697.7 + 32890697.7 + 37058750
= 102840145m^3

E = 102840145 X 25 X 1.005
= 2.58385864e9

E = 102840145 X 13800
= 1419194001000 joules

E = 5.89552038e10 + 442210172520 + 2.58385864e9 + 1419194001000
= 1922943235960 joules
= 459.594463662 tons of TNT