Godzilla Math

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godzillasmall.jpgHow much does Godzilla weigh?

A good question. And since the life-size version doesn’t seem to be in New York at the moment, we’ll have to use a smaller replica and then multiply by a scaling factor. Our Godzilla, shown below eating Buffalo-Chicken Dip, lives in our house and occasionally visits Our Best Friend Craig over at Puntabulous (whose Guest Debates and Story of a Snake Wrangler are simply brilliant).

godzillafar.jpg

The first thing we need to do is estimate Godzilla’s volume. Since I was absent the day my geometry teacher covered volumes of giant monsters, we’ll use water displacement. The original plan for this experiment had us using a calibrated beaker, submerging Godzilla, and measuring how much the water level rose, but it turns out that we don’t have any giganto-sized beakers. Instead, we took a 5-gallon cooking pot filled to the absolute top with water, placed it in an emptied toy-container (to catch the water), and then dunked Godzilla in and measured the water that spilled out.

Here’s TwoPi dunking Godzilla.

godzilla_dunk.jpg

Unfortunately, Godzilla didn’t fit completely. So TwoPi carefully added more water to bring the water level back up to the top:

godzilla_1.jpg

And then dunked the part of Godzilla that hadn’t fit originally.

godzilla_dunktail.jpg

The next step was to figure out how much water had overflowed. TwoPi poured it into a measuring up while Godzilla ate an oatmeal cookie to recover from his bath.

godzilla-watchpour.jpg

It turns out that the volume of water was 2.9 liters:

godzilla-watch.jpg

Now we need to calculate the scaling factor. Here’s where things get interesting. Our Godzilla is 37.5 cm tall (head to foot). According to Robert Biodi, the original Godzilla was 50 meters tall.

In the 1984 movie Godzilla, the monster had grown to 80 meters (possibly because the buildings in Tokyo were larger), and for films in the 1990s, including the 1992 Godzilla vs. Mothra, he was 100 meters.

But now, in the 2000s, he’s back to 80 meters. So which height shall we use? Let’s stick with the original of 50 meters. Since our Godzilla is 0.375 meters high, the linear scale is 50/0.375≈133.3. But we are working with volume, so we have to cube this scaling factor to get (50/0.375)3≈2,370,370.37.

We take this number and multiply by the 2.9 liters of water that our Godzilla displaced. The original Godzilla would displace 6,874,074 liters of water!

godzilla_calc.jpgBut how do we translate a volume (liters) to a weight (kilograms, except that’s really a mass, but you know what I mean)? We need to multiply by Godzilla’s density. There aren’t any scientists that mention that in any of the films, so we’ll use the density of a crocodile body: 0.9 kg/liter. So we multiply 6,874,074 by 0.9 and find that Godzilla weighs about 6,186,667 kilograms, or 13,610,667 pounds.

Maybe 13,610,668 after all his snacks.

Thanks to Bill Korth for sharing this method of calculating the weight of dinosaurs during a teacher workshop. He himself got it from Dinosaurs: The Textbook (3rd ed.) by Spencer G. Lucas, which explains that this is in fact the way that scientists estimate dinosaur weights, using very accurate scale models.

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11 Responses to “Godzilla Math”

  1. Craig Says:

    That was great! Informative and funny!

    Thanks for the shout out!

  2. Ξ Says:

    Update: I just found a whole article about the science of Godzilla! In it, Michael Dexter says that the 100-meter Godzilla would weigh about 60,000 tons, which is quite close to what we found. [The 50-meter Godzilla weighs 6820 tons, so the 100-meter Godzilla would weigh 8 times as much, or about 54,560 tons. Except for his probably-too-weak skeleton, his probably-way-too-high blood pressure, and a host of other medical ills. Poor Godzilla!]

  3. How fast was Godzilla running? « 360 Says:

    […] a foot tall. To put it into perspective, if you multiply by the scaling factor of 133.3 (from when we calculated Godzilla’s weight), it’s equivalent to the original 50 meter Godzilla running at just over 54 meters per […]

  4. Dan P Says:

    Hehe, I can’t imagine what your family was thinking as you were dunking the big G in a bucket of water. Mine would have reailized I had finally gone over the edge😀

  5. Kym Says:

    Hello, funny thing to do with Godzilla toy! I was wondering where did you get your Godzilla from? We manufactured this model as a light at our shop, but unfortunately lost contact with the maker of the toy. He mysteriously disapeared…. look forward to hearing from you! Regards, Kym

  6. Ξ Says:

    I really like the lights at your shop Kym! Some of them look like classy version of “the glowing torso” (a mannequin turned into a handmade lamp that we got from friends and that was lost in our move from Madison to Rochester, to our disappointment).

    The Godzilla was a birthday gift to our older son several years ago, and I think it just came from a toy shop in our neighborhood. It looks like the Godzilla himself was made in China in 1997 by Dor Mei. (He’s got U.K.R.D. on the other foot, seems to be another manufacturer of toys, or else Godzilla is part of a media company. I wouldn’t claim to know all the secret lives of Godzilla.)

  7. Sarina Says:

    i loled so hard because my godzilla looks just like that and the fat bastard always eats tooo!

  8. Ξ Says:

    Ah yes, Godzilla does love to eat. I think he has a sweet tooth.

  9. BiGSoph Says:

    I can see a flaw in your technique – your figure has no dorsal spines

    Godzilla has very large dorsal spines, with the largest of them varying in size from about as tall as Godzilla’s head length to almost 1/4 his entire height

    With their rigidity, these would add considerable to big G’s mass

    Now as to mass, Godzilla’s general build is somewhat similar to a tailless Polar Bear. Using cube scaling, we end up with a Polar Bear the size of Godzilla weighing in at 20370 tons

    Adding in 10% for the spines and 20% for the tail, we get around 27,000 tons

  10. David Says:

    The original 40 meter Godzilla was killed at the end of that film. There were a series of new Godzillas, either the son of the previous one or, as in one story in which time past had been changed to where Godzilla never existed and a new line of Godzilla was created to prevent aliens from the future taking over the earth; each incarnation came back larger than before. Some think it was because the new Godzilla was more radioactive and more mutated by radiation than the previous Godzilla. So he went from 40 meters, to 80 meters, to 100 plus meters.

  11. Ξ Says:

    Thanks for the explanation BigSoph! I don’t know if there is a density difference between polar bears and crocodiles — I don’t think there’s a huge one [I talked to Bill Korth about this at the time, and I think I remember his saying that a lot of animals had similar densities, until you got to birds or animals with shells or exoskeletons).

    And also I’m glad to hear the explanation David. I don’t remember all those details, though I’ve seen many of the movies [as a kid, the Top Three movies in our household, from the perspective of my sisters and me, were Wizard of Oz, Godzilla, and the Sound of Music]. It was a happy week indeed when one of those showed up in the TV listings;.

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