Source: Kaiserwombat of naruto forums. This is the first of what I will imagine to be a fairly sizable compendium of calculations illustrating the physical, technological and supernatural feats and impressions of the multitude of various sci-fi and horror movies underneath the banner of Toho Studios, especially in the genre of tokusatsu (special effects-oriented; including mecha, daikaiju and space opera films, amongst others).
A perfect beginning to this "series" would be with the original entry into tokusatsu for Toho, one of the most critically acclaimed daikaiju films of all time and a personal favourite of mine: the 1954 classic 'Gojira'.
1# - Electrical Durability
Aside from the trend-setting widespread urban destruction that will later represent the majority of the action scenes in succeeding daikaiju flicks, the original '54 Godzilla specimen possesses two standout physical feats: the first of which is related to its durability, as the heading above naturally indicates.
After '54 Godzilla incites pandemonium with a brief foray into Tokyo Bay, the Japanese Self Defense Force begins to initiate a future-commonly-recurring defensive operation: they erect a coastal barbed-wire fence composed of overlaying power lines and transmission towers, designed to transmit 50 kilovolts directly into the target via manual switches, in the hopes of electrocuting the monster to death.
'54 Godzilla pretty much steamrolls through the fence without a hitch, not even being particularly irritated by the voltage. In total, the radioactive dinosaur spends approximately 10 seconds (55:18 - 55:28) experiencing the effects of electrical discharge.
Now, we already have the voltage of the discharge explicitly stated: the hidden ingredient for determining the energy output is electrical current, which is generally a pain in the neck to determine.
The closest result to a solid answer for current figures comes from Yahoo! Answers, of all places: that answer being 10 kilo-amperes (kA). If somebody can provide more valid information of electrical current flowing through transmission lines, I'd greatly appreciate the favour, but I'm so tired now that I don't want to waste more time on this particular sticking point ATM.
With both the amperage and the voltage obtained, I can now use a simple formula to determine the power of the discharge in watts:
W = 50,000*10,000 = 500,000,000 watts
1 watt = 1 joule per second
As mentioned above, the electrical discharge lasted for 10 seconds.
500,000,000*10 = 5,000,000,000 joules or 1.195 tons of TNT equivalent.
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2# - Destructive Firepower
Now, here is the much more ambitious half of this blog entry, mostly down to the rather specific quantity of material affected and the lack of conveniently complete destruction of the object(s), but we'll give it a go.
Basically, after casually stomping through the 50 kV power lines, '54 Godzilla decides to take its anger out on some nearby transmission towers, courtesy of its patented Atomic Breath:
http://i.imgur.com/4IvXP37.png http://i.imgur.com/x5IT7vo.png http://i.imgur.com/MYpJKev.png
So, it heated the towers to at least melting point temperatures, but caused incredibly minimal actual melting, to the point that I found it pretty useless to try and cover that aspect of the destruction, so I'll be focusing purely on the heating of the metal to melting temperatures.
To begin, the height of the transmission towers: we're helpfully provided an exact measurement by the JSDF coordinators of 30 metres. The very blocky shape of these lattice towers also assists majorly in determining actually how much of the structure(s) were heated up.
Scaling http://i.imgur.com/pv70AMC.png
These transmission towers are almost entirely composed of cylindrical "poles", so expect this formula to be making several appearances from this point forward.
I'll be measuring the closer and less damaged transmission tower first, so using the red line as my basis for the vertical pole:
3.14*0.11*0.11*10.41 = 0.40 m^3
Now, there are 4 such vertical shafts at each "corner" of these transmission towers
0.40*4 = 1.6 m^3 in total (vertical poles only)
In addition to the main vertical poles, there are also a multitude of horizontally-aligned poles for further support, forming cube-shaped "levels" of hollow space. From the top of the tower down to the bottom of the red line, I can spy roughly 5 such "levels". The framework of each cubic "level" calls for 4 horizontal poles on the bottom, 4 horizontal poles on the top: at the same time however, one needs to consider that the top 4 horizontal poles of Cube A (at the bottom) = bottom 4 horizontal poles of Cube B (second from the bottom, and so on.
This means that there are 6 "tiles" composed of individual/separate horizontal poles, adding up to a total of 24 separate poles.
Still with me? Because now I need to factor in the diagonally-aligned poles that form an X shape through each "panel" of all the cubic "levels" of the transmission tower. With 4 "panels" per cubic "level", 2 poles required to form the X shape, 5 cubic "levels" affected by the heating and none of the diagonal poles intersecting with each other across different "levels", this leaves us with 40 such poles.
Fortunately, the horizontal and diagonal poles are of the exact same length and width, meaning I can treat them as one in the same.
40 + 24 = 64 poles
Volume of a single horizontal and diagonal pole:
3.14*0.11*0.11*2.66 = 0.10 m^3
0.10*64 = 6.4 m^3 (horizontal and diagonal poles only)
Now adding up the combined volume of the horizontal and diagonal poles with those of the main vertical shafts affected by the heat:
6.4 + 1.6 = 8 m^3 (in total)
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The other affected transmission tower is pretty much the exact same as above, only with an additional cubic "level" to factor in.
So while the affected vertical pole volume is upped to 0.48 m^3, and factoring in all 4 such poles brings us to 1.92 m^3.
Meanwhile, there are now 6 cubic "levels" in the second tower heated up, adding another 4 horizontally-aligned poles (bringing it up to 30) and another 8 diagonally-aligned poles (48), for a total of 78 mini-poles.
0.10*78 = 7.8 m^3 (horizontal and diagonal poles only)
7.8 + 1.92 = 9.72 m^3 (in total)
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8 + 9.72 = 17.72 m^3 of metal heated to melting temperatures in total.
After all that, we now come to the tricky part: obtaining energy output via the heating of this combined volume.
First, we need the density of the heated material: lattice transmission towers (the same type as in this film) are almost always composed of galvanised steel. According to this online shipping website, the density of galvanised steel is 7850 kg/m^3.
At this point, I'd usually go on to determine the mass via volume*density, but the method I'm about to employ does not appear to require the weight of the material.
Namely, I'm experimenting with the formula that willyvereb proposed to Amae in his 00 Gundam 0.49 kJ/kg.K[/B]]), the density (mentioned above to be 7850 kg/m^3) and the temperature difference.
For my final temperature, I'll be using the low-end value of carbon steel's melting point: 1698.2 K(Celsius + 273.2 for conversion purposes).
My initial temperature was more difficult to determine: ultimately I went down the route of using the average of the average monthly low temperatures in Tokyo (285.98 K). I know that counts for more atmospheric temp rather than that of the steel's, but I was unable to discern the latter, so this serves at least as a placeholder.
1698.2 - 285.98 = a difference of 1412.22
1412.22*7.85*0.49 = 5432.10 J/cm^3
5432.10 J/cm^3 = 5,432,100 kJ/m^3
5,432,100*1000*17.72 = 9.625681200e+10 joules or 23 tons of TNT equivalent.
Whew, that's done. Still uncertain about the firepower element, but it looks decently accurate.
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Gojira (1954) Durability: 1.195 tons of TNT equivalent Firepower: 23 tons of TNT equivalent