Math & Stuff

## Explanation

This page describes all the methods used to achieve the fictional creation evaluation and how to reproduce them.

#### Googling / dedicated Fandom

For the most bare bone of information about a fictional object, all you will need is some keywords in a search engine.

It doesn't get more complicated than unless the subject you are working on is very niche, then you would need to extract the informations yourself if it was officialy stated in narrativr, by word of god or if there is nothing you may need to figure it out yourself.

Either by eyeballing, if the value isn't that important like the height of a minor human character whose age is known.

Or by calculating someone's height with a reference object whose height is consistent across multiple media. (like a standard size door: 203.2 cm tall, 91.44 cm wide, and 3.334 cm thick)

#### Body volume/ Body surface area

The easiest way to find this value is to find a 1:1 scale 3D model of the character from an official release.

Could be the CGI of a movie/anime or a video game, all you need to do after that is open Blender, activate the 3D print Addon. Input the official height of the character and read the volume of the body.

If you know how to utilize the software, you can erase the voxel of the clothes of smooth out the body to get the surface area too.

The other method is to use Square–cube law. Using a reference frame.

In the case of anime-like character, they come in all sort of shape and form.

Some are made to look more realistic, but kept featuring anime-like feature like larger head, eyes and hands.

Others ignore thism and create an abstract figure with clean geometry and body,

    or go into extremely muscular reaching into the absurd. For this reason, and because mainstream anime tend to use a more consistent humanistic style, I like increase the body volume and body surface area of my sample anime character by 1.5.

For reference, the average volume and surface area of a human body with realistic proportions is 0.062 m³ and 1.75 m². So it would 2.625 m² and 0.093 m³.

So how do we use that? By wikipedia, the global average human height is 1,65 m, and weight 62 kg.

So for a 1.68 meter character, like Natsu Dragneel in our example. His body volume and surface area should be :

* (1.68 m/1.65 m)^3\*0.093 m³ = 0.0981 m³.
* (1.68 m/1.65 m)^3\*2.625 m² = 2.77 m².

Now, how the Square–cube law work and how to use it? Because it will be used again on this page.

The formula work like this :

Result = (Object you try to solve/Reference object)^3\*reference value.

##### Square–cube law example

Let's say you have a chicken and next to it you have a giant 5 meter tall chicken. But its running pace is similar to that of a normal chicken, it does not slow down even though it is a giant. You want to solve for the giant Chicken's speed and mass.

On average, Chicken stand less than 70.1 cm tall and weigh approximately 2.58 kg. Chickens can run at an average speed of ≈14.49 km/h

* Reference object-mass : 2.58 kg
* Reference object-speed : 14.49 km/h
* Reference object-size : 70.1 cm
* Object to solve-size : 500 cm

Let's use Square–cube law to solve all of this !

Chicken mass :

* (500 cm/70.1 cm)^3\*2.58 kg = 936.21 kg.

Chicken speed :

* (500 cm/70.1 cm)^3\*14.49 km/h = ≈5,258.04 km/h or 1,460.56 m / s (Mach 4.29)