The Mathematics Behind Earthbending in Avatar: The Last Airbender
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Chapter 1: Understanding Earthbending Physics
In a prior article, I delved into the physics that could explain earthbending. Here, I will present some formulas that may help in assessing the energy efficiency of various earthbending methods. By energy efficiency, I mean the proportion of energy that an earthbender inputs into a technique that actually contributes to the intended effect. It would be beneficial to read my previous post on earthbending physics for context.
This video titled The Physics of Earthbending (Avatar Science pt. 3) provides an engaging overview of the scientific principles at play in earthbending.
Moving Earth
The manipulation of earth is possible through the ionization of a thin layer of rock, which allows an electric field to exert forces on charged atoms, thus moving them and the surrounding neutral atoms.
Eo = Change in Kinetic Energy of the Earth
E1 = Energy Required to Generate Electric Field
E2 = Total Energy Needed to Ionize Earth Atoms
eff = Estimated Energy Efficiency of Technique = (Eo / (E1 + E2)) x 100%
R = Electrical Resistance of the Earth Being Manipulated
?t = Duration of Current Flow through the Earth
qi = Initial Charge of the Earth
ei = Average Ionization Energy of Earth Atoms
?q = Change in Charge of a Single Atom of Earth During Ionization
The formula originates from analyzing both the charge of the earth and the voltage change that generates the electric field responsible for moving the charged earth. The energy input from the earthbender is the sum of the energies used to charge the earth and to create the electric field. The energy efficiency is then calculated as the ratio of the total change in kinetic energy of the earth to the combined energy used in charging it and producing the electric field, multiplied by 100%.
This method can also be adapted to apply pressure to the earth, heat it, or even melt it into lava.
Moving Lava
The process for manipulating lava is similar to that of moving solid earth.
Eo = Change in Kinetic Energy of Lava
E1 = Energy Required to Generate Electric Field
E2 = Total Energy Needed to Ionize Lava Atoms
eff = Estimated Energy Efficiency of Technique = (Eo / (E1 + E2)) x 100%
R = Electrical Resistance of Lava Being Manipulated
?t = Duration of Current Flow through the Lava
qi = Initial Charge of the Lava
ei = Average Ionization Energy of Lava Atoms
?q = Change in Charge of a Single Atom of Lava During Ionization
The kinetic energy change in the lava is evaluated similarly to that of the earth. The energy required to charge the lava and generate the electric field must be summed to determine the total energy input by the earthbender, and the efficiency is calculated accordingly.
The video Flat Earth Proof Debunked with 6th Grade Math reinforces the importance of understanding physics, which can help debunk misconceptions surrounding earth science.
Moving Metal
Bending metal utilizes the same principles as moving earth, focusing on the movement of the earth particulates within the metal.
Eo = Change in Kinetic Energy of Metal
E1 = Energy Required to Generate Electric Field
E2 = Total Energy Needed to Ionize Earth Atoms
eff = Estimated Energy Efficiency of Technique = (Eo / (E1 + E2)) x 100%
R = Electrical Resistance of Metal Being Manipulated
?t = Duration of Current Flow through the Metal
qi = Initial Charge of the Earth in the Metal
ei = Average Ionization Energy of Earth Atoms
?q = Change in Charge of a Single Atom of Earth During Ionization
The kinetic energy change in the metal follows the same logic as that used for earth. The total energy required for charging the metal and creating the electric field is essential for calculating efficiency, which again is the ratio of kinetic energy change to the total energy input times 100%.
Works Cited
DiMartino, M. D., & Konietzko, B. (Writers). (2010, June 30). Avatar: The Last Airbender [Television series]. Nickelodeon.
DiMartino, M. D., & Konietzko, B. (Writers). (2012, April 14). The Legend of Korra [Television series]. Nickelodeon.
Nave, Rob. Work and Voltage: Constant Electric Field. hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html.
Libretexts. 6.16: Periodic Trends: Ionization Energy. 14 July 2020, chem.libretexts.org/Bookshelves/Introductory_Chemistry/Book:_Introductory_Chemistry_(CK-12)/06:_The_Periodic_Table/6.16:_Periodic_Trends:_Ionization_Energy.