The Mystery of Scale: Part Three

Just today, I found this on my Facebook feed.

Source: Isaiah Takahasi

It's an impressive composite water scene of an RX 78-2 towering over what seems to be a Catalina-type sailboat yacht, but something seems off.

Yup, the scale is all wrong. The RX is too big compared to the size of the Catalina, which is about 10m from the base to the tip of the sail, and considering foreshortening, the RX is still rather huge since it's only 18m in 1:1 scale.

But, using the known average height of the Catalina which is around 10m, we can interpolate the height of that RX in the photo/image (proportionate to the GTO kit) to be around 50m, just as tall as the first version of Gojira.

Source: Google Search

So, it really is off scale, almost 3 times its actual height. At that height, the scale of the RX against its 1/1 counterpart is 2.78/1. Rule of thumb: The higher the value of the denominator, the smaller the scale height would be, hence why 1/144 scale of a certain object at 1/1 is smaller than its 1/100 scale counterpart)

Now Someone commented that the boat is 1/144 and that the RX is 1/48. We don't really mix scales when doing dioramas, and I know what the person meant, but sure, let's bite.

Using 1:1 height reference, the scale of the RX would be 1/36, and not 1/48. How did I get that number? Again, by using fractions, ratios and proportions which we learned in grade school and high school. Let's assign xb as the unknown scale we're trying to figure out, knowing the 1:1 height of the RX at 1800cm, the 1:1 height of the boat at 10m, and its estimated height of the RX in the image at 5000cm (1m=100cm), we get

Or, for the mathematically-challenged, here's a visual (which still requires Math to figure out, unfortunately). At 1/144, the height of the boat would be at 7cm (1000/144=6.94444~),  the height of the RX would be 12.5cm (1800/144). At 1/100, the boat and the RX are 10cm and 18cm respectively. At 1/48 (Mega-Size), the height of the RX would be 37.5 cm. At 1/60 (Perfect Grade) the height would be 30cm.

 

Here's where it goes nutty: If we use the 50m height as 1/1, the 1/48 height would be 104cm, while the 1/36 would be a whopping 139cm, almost a meter and a half, which is about the average height of a tall adolescent, or a small adult. I was overthinking this, but, if we interpolate the 1/36 and 1/48 heights into 1:1 relative to the height of the boat of 10m, then we get 50m and 37.5m respectively.

(Sidenote: I did get a little bit confused here earlier because of the 18m and 50m heights, since I thought I made a computation error to get 1/36. As it turns out, the 1/100 scale of 50m and 1/36 scale of 18m are both 50cm).

Now, here's how it should look like when everything is on the same scale.

Where's that rampaging T-Rex when you need it?

So, again, to determine the height of an object based on scale, you need to know one other value: the height of another object you can compare it to. Research comes into play in this case, since the only object I can compare the RX with is the Catalina. Even if you don't know anything about boats, you can simply do a keyword search for sailboat dimensions, which is exactly what I did.

In closing, I'd like to share with you this very nice image that depict the heights of different robots and super robots in relation to one another.

Source: All-over the Internet, but, where the heck is Gurren Lagann?