The Laws of Physics in an Animation Universe

Introduction

“My Little Pony: Friendship is Magic,” is an animated TV series that began airing October 2010. It is the fourth animated series based off of Hasbro’s “My Little Pony” toy line. This series has gained wide acclaim for its writing, characters and artistic direction. “Friendship is Magic” focuses on the adventures of the resident ponies of Ponyville, Equestria and the lessons they learn about friendship (Fig.1). 

 Fig.1: Comic-Con 2011 Poster showing the cast of Season 1

And while magic is commonly used in the series, the world of Equestria has patterns that can be called physics and characters also implement scientific methods from time to time, especially in Season 1, Episode 15 (Fig.2). 

Fig.2: Twilight (left) uses various methods of observation to determine if Pinkie (right) has a 6th sense

With this in mind, I will apply the physics known on Earth to the world of Equestria, presenting the argument that the series takes place on a geocentric world, estimating a unit of “wing-power”, and comparing the physical properties of the different types of ponies.

Equestria is Geocentric

Whether Equestria orbits the sun (solar-centric orbit) or if the sun orbits Equestria (geocentric orbit) does not seem like a big deal, but there are occurrences throughout the series that establish that Equestria shares a lot in common with the world we live in, as well as some significant differences that would not be possible in a solar-centric orbit.

In Season 1, Episode 1, it is established that Princess Celestia, a powerful Alicorn (Fig.3), governs the times when the sun rises and sets in the world of Equestria. This establishes that the sun is a body that moves relative to to the sky.

 Fig.3: Princess Celestia (left) and her student Twilight (right)

In Season 1, Episode 14, Twilight is having a custom dress made for her by the town’s top seamstress Rarity. Twilight wants her dress to display the constellations of the night sky, insisting that they must be “technically accurate.” She even goes on to describe the constellations in detail herself (Fig.4).

 Fig.4: Twilight (left) describes the constellation Canis Major to Rarity (right)

In Season 1, Episode 24, the ponies of Ponyville enjoy a night of stargazing. Twilight even brings out a telescope (Fig.5). With all these in mind, it can be assumed that the world of Equestria is in a cosmos with celestial bodies that can be observed and studied.

Fig.5: The ponies enjoy a picnic with stargazing

In multiple scenes of Season 2, Episode 3, the sun moves across the sky in notable increments as if it were attached to the arm of a clock (Fig.6). If the world of the ponies was a planet that rotates as it orbited the sun like our Earth, such an occurrence would be absolutely cataclysmic!

 

Fig.6: The Sun "ticks" across the sky

Using Newtonian physics and taking centrifugal force into account, the forces felt by all the land-dwelling inhabitants in these circumstances would be that of sudden extreme acceleration and sudden extreme deceleration. Such sensations would be comparable to sitting in a train that suddenly hits full speed and then suddenly stops, except such forces of the case originally in question may destroy buildings and cause earthquakes. This would happen regardless of the shape of the planet and regardless if the planet orbited and/or rotated. Because these disasters obviously did not happen in the episode, the sun most likely orbits planet (geocentric orbit). And because this episode focused on Twilight, who was frantically trying to completing a task for Princess Celestia before the day was over, it can be reasonably be assumed that Princess Celestia is cruel and evil (Fig.7).

Fig.7: Princess Celestia, Tyrant and Ruler of Equestria

Determining the Value of the Constant “Wing Power”

In Season 2, Episode 22, the ponies used an anemometer to sample the flight of each pegasus pony and calculate their “Wing-Power” (WP). Assuming that WP is a unit of power (work/time), WP can be compared to Horsepower (HP) with an analysis to this scene (Fig.8).

Fig.8: Two Pegasi ponies ask Twilight about the anemometer

At 8 minutes into the episode, Rainbow Dash flies past the anemometer and was then announced to have 16.5 WP (Fig.9). In estimating Rainbow’s acceleration, mass, time elapsed and distance traveled in passing over the anemometer, her HP can be estimated, allowing a comparison between HP and WP.

Fig.9: The sequence that will be used to analyze the scene for "Wing-Power"

To estimate Rainbow’s acceleration, the formula a = (V2 - V1)/t will be used, where a, V2, V1, and t are acceleration, final velocity, initial velocity, and time elapsed respectively. In this scene, she starts from rest and takes 65 frames to pass the anemometer. At 24 frames per second, t = 2.71 seconds. Her final velocity can be estimated with analysis to the shot of her passing the anemometer (Fig.10).

Fig.10: Estimates on Rainbow's distance traveled

Twilight, the unicorn pony sitting at the anemometer, can be used as reference to the distance Rainbow Travels in the shot. Assuming that the ponies are about the same size as ponies on Earth, which stand at about 1.3 meters tall, Rainbow travels 5.62 meters between frames 64 and 67, giving her a velocity of 44.96 m/s. Rainbow’s acceleration this scene can now be estimated:

a = 44.96 m/s - 0 m/s2.71s

a = 16.59 m/s^2

Assuming that these ponies have the same mass as those on Earth, Rainbow would have a mass of about 350 kg, we can determine the work done in Rainbow’s flight over the anemometer with W=mad, where m, a and d are Rainbow’s mass, acceleration and distance respectively.

W = 350kg x 16.59m/s x 25.62m

W = 32632.53 Joules

To determine Rainbow’s power, the formula P=W/t will be used.

P = 32632.53 Joules / 0.125s

P = 261060.24 Watts

Watts can be converted to Horsepower:

P = 350.08754836 HP

For reference, 350 HP is roughly the power of a modern Ford F-150 (Fig.11)

Fig.11: Ford F-150 (www.ford.com)

Finally, the ratio between WP and HP can be estimated.

WP: HP

 

16.5 WP:350.08754836 HP

1.00 WP:21.2 HP

In this episode, the winged pegasi ponies had to create a tornado to lift the water from a reservoir and send it to Cloudsdale, a city in the sky that creates clouds, rain, and snow. The pegasi would create this tornado by flying in circular formation. The water would then be lifted through the center of the tornado in the form of an extruded column (Fig.12).

Fig.12: An Artificial Tornado created by Pegasi flying in circular formation

 To accomplish this task, the pegasi had to fly at high enough speeds to generate a combined 800 WP, which is 16,880 HP. For comparison, a US Navy C-130A “Hercules” aircraft has a combined 15,000 HP between its four propellers and has a maximum takeoff load of 69,750 kg (Fig.13).

Fig.13: C-130 Aircraft (www.navy.mil)

To determine the volume of the column, we can use a pony on the scene as reference to find the column’s circumference at its widest point. In Fig.14, the width of the column is 16m and the height of the tornado is 46m. The volume of water that would fill the tornado can be found with V=h(c/2)^2, where h and c are height and circumference respectively.

Fig.14: Estimating the measurements of the column

Vol = 46m(16m/2)^2

Vol = 9,200m^3

Given that a cubic meter of pure water has a mass of 1,000 kg, the mass of the volume of water in the tornado would be about 9,000,000 kg. If 1 WP is about 20 HP, and given the comparison of the power and take-off load of an C-130 aircraft, 800 WP is simply not enough to even lift the water past the top of the tornado at its given volume. But because the task was completed with 800 WP, the analysis used to determine wingpower must have been made with bad data (ie, Rainbow Dash should have been portrayed to fly faster or estimated unit values were off significantly).

Pegasi Ponies Have Very Low Mass

            In the world of Equestria, there are three different types of ponies: Earth, Unicorn, and Pegasi. Earth ponies are established to be hardworking and strong, Unicorn ponies are established to be able to perform applicable magic, and Pegasi ponies have wings with which to fly. Although the have the overall same shape and size, they by no means have similar physical properties.

The Pegasi ponies can be assumed to have significantly lower mass than the other two types. In Season 1, Episode 4, AppleJack (Earth type) jumps from a scaffold onto one end of a seesaw-like catapult, with Rainbow Dash (Pegasus type) on the other end. For this, Rainbow Dash is sent hurtling off into the distance (Fig.16) Even though Applejack had increased her gravitational potential energy by jumping from a scaffold, there is now way she could have sent Rainbow Dash flying that way if they had comparable mass.

 

Fig.16: AppleJack launches Rainbow Dash

In Season 1, Episode 23, Fluttershy (Pegasus type) is falling from a dangerous height. Her fall is cushioned by landing on a swarm of butterflies (Fig.17). 

 Fig.17: Fluttershy falls to a potentially hazardous landing

This can happen only if either the butterflies have a combined mass significant enough to break the fall of horse weighing a few hundred pounds, or if Pegasi ponies like Fluttershy have low mass; the latter being more likely. Pegasi types could have significantly lower mass than the other types as this may aid them in their ability to fly, which supports the assumption that they indeed have lower mass.

However, if this is the case, would a pegasus pony have a mass low enough where it could not be die from free-fall like a squirrel? Also, the estimated value of Wing Power found in the earlier calculations is significantly greater than this theory would allow. A lower mass with all other variables unchanged would result in a lower power output.

Conclusion

         Many occurrences in world of “Friendship is Magic” can be explained with the physics of our universe, though it certainly has rules of its own. The creators of the show do a good job at creating a show believable and enjoyable enough to suspend other disbelief. Entertainment and storytelling can be enhanced with fantasy and by breaking a few rules, but it is important that occurrences “feel” right.