By Duke of Skibbington Part of the Logopolis Library continuity.

Main Characters Books Battles Locations Updates


The cover page of the thesis.

On Principles of Bending or the Quantitative analysis of Bending or Principles of Bending for short is a thesis published by Philip Hellene. It was considered revolutionary by critics and his findings have been replicated numerous times, passing the peer review and earning Philip his PhD.

Principles of Bending is renowned for being the first quantitative analysis of bending and indeed, what enables bending.


We provide a quantitative means of measuring bending ability, energy consumption of bending moves and the power of a bending move.


Bending requires energy, with higher level and more powerful moves requiring more energy. This energy, referred to by our Asiatic comrades as chi, is a converted form of the chemical energy as derived from the consumption of food. As an energy, it is measured in joules, however, the magnitude is such that it must be measured in kilojoules. It appears that in benders, a certain hereditary trait enables the small intestines to convert chemical energy into bending energy. Those without said trait are unable to bend. Some benders are able to convert even greater amounts of chemical energy into bending energy, thus making it possible to perform greater feats of bending. These people often become masters. Indeed, greater bending energy does not necessarily equate to greater bending ability, rather, it affects the potential ability of the bender.

Bending power is difficult to define, as each state (or element as called in Asia) has different properties. A measure that would perfectly accommodate the great crushing power of earth would have absolutely no relevance in comparison to the heat of fire. Separate measures were defined, with a bench mark for the minimum strength required to kill a man. The respective power of the attack is then formed into a quotient, with 100 as a 50% chance of death.

Airbending power is defined by the product of the mass of the air and its speed, divided by the duration of the stream. Its measure is derived from kinetic energy and is therefore measured in Joules per seconds (J/s). Earthbending power is measured as the product of the mass of the earth and its speed; therefore, it is simply kinetic energy and measured in Joules. The power of waterbending is similar to airbending, being the kinetic energy over the duration. Firebending is totally different; fire has mass, being combusted air, and so is measured as a derivative of kinetic energy. However, fire has another property - it is hot. The measure of firebending is the kinetic energy by the temperature over the duration of the flame; it is therefore measured in Joules kelvin per second (J K/s).

Air/Water = \frac{\frac{mv^2}{2}}{t}

Earth = \frac{mv^2}{2}

Fire = \frac{mv^2}{2}\cdot temp

The power quotient is 100 times the ratio of the power of the attack over the minimum power required for a 50% chance of killing the opponent.

P_q = 100 (\frac{power}{50% kill})

Bending efficiency would be measured as the ratio of the bending power quotient against the energy requirement.

Efficiency = \frac{P_q}{E_r}


Numerous tests were conducted to establish a base line for energy requirements for certain bending moves. The results shown below are the minimum required to conduct the weakest form of the movement. The only specialised elemental subskills known are healing and lightning generation.

Minimum energy requirements
Element Move Energy (kJ)
Air Punch 11
Air Kick 23
Air Slice 43
Water Whip 22
Water Wave 60
Water Freeze 34
Water Healing 9
Earth Levitate 19
Earth Throw 33
Earth Pillars 56
Fire Punch 13
Fire Kick 19
Fire Whip 26
Fire Breath 50
Fire Lightning 123

The table below shows the required bending power for each element to have a 50% chance of killing a human. These experiments were carried out on mathematical models and prisoners of war.

Element Unit Quantity
Air J/s 700
Water J/s 500
Earth J 600
Fire J K/s 900


Bending energy can be classified in terms of raw energy and is measured in Joules. More specialised bending moves require less bending energy. Greater bending energy expended in one use can increase the bending power of the movement.

Bending power for each element has a different measure, owing to the different traits of the elements; however, a ratio in regards to the 50% chance of killing an average human can be used as a reliable measuring system. In terms of bending power to bending energy, earthbending is the least efficient, whereas airbending is the most efficient.

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For the collective works of the author, go here.

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