# Acceleration Due to Gravity: Super Mario Brothers

## Abstract

The purpose of this analysis is to determine the evolution of gravity in the Mario video game series as video game hardware increases.

## Introduction

Gravity is force which is responsible for keeping us on the ground. It is also the force that prohibits us from jumping 50 feet in the air. However, in Mario's world, gravity does not quite work that way. Mario is able to jump 5 times his height and fall with accelerations that would be deadly to humans.

We will find Mario's acceleration due to gravity by using the formula

s = s_{0} + v_{0}t + ½ at^{2}

where s is the distance he falls, s_{0} is his initial distance, which
is 0, v_{0} is his initial vertical velocity, which is also 0, a is
his acceleration due to gravity, and t is the time it takes for him to fall.
When we solve this formula for a, we get

a = 2s/t^{2}

## Procedure

- Record video clips of Mario falling from a ledge in the following games:
- Super Mario Bros 1, 2 & 3, for NES
- Super Mario World for SNE
- Super Mario 64 for N64
- Super Mario Sunshine GCN
- Super Paper Mario for Wii

- Watch the clip in Quicktime Video Player and use the frame by frame option to determine the number of frames it took Mario to fall. Also using Quicktime, the FPS, or frames per second, of each video must be found.
- Take a screen shot of Mario standing next to the ledge. This Screen shot will be used to determine the distance of the fall.

## Analysis

First, you must find the time it took Mario to fall from the edge of the ledge to the ground in each game. To do this, we opened each clip in Quicktime movie player, and using the frame by frame option, found the total number of frames it took Mario to fall. We then used the formula:

Time = (Number of Frames)/(Frame Rate)

To find the time of each of Mario's falls. Once we knew the time, we needed to figure out the distance Mario fell in each game. We used a screen shot of Mario next to the ledge he fell from in each game, and found the height of Mario and the ledge in pixels. According to Wikipedia, Mario is "a little over five feet tall.", so we used 5 feet, or 1.524 meters, as Mario's height. We used the formula:

Height_{Mario}[m]/Height_{Mario}[pixels] = Distance[m]/Distance[pixels]

Distance = (Height_{Mario}[m]/Height_{Mario}[pixels]) x Distance[pixels]

Once we had the distance Mario fell in each instance, we were able to use the formula

s = s_{0} + v_{0}t + ½ at^{2}

to find Mario's acceleration in each game. Mario was in free fall in each
case, so this acceleration was equal to gravity. His initial velocity was
0, as was his initial position. Our results in m/s^{2} as well
as in multiples of g are outlined in the table below.

Game |
Frames |
Time (s) |
Height of Mario (pixels) |
Distance of Fall (pixels) |
Distance of Fall (m) |
Acceleration (m/s ^{2}) |
Acceleration (g) |
---|---|---|---|---|---|---|---|

Super Mario Bros. | 15 | 0.5 | 39 | 292 | 11.4 | 91.28 | 9.31 |

Super Mario Bros. 2 | 12 | 0.4 | 45 | 255 | 8.6 | 107.95 | 11 |

Super Mario Bros. 3 | 15 | 0.5 | 35 | 265 | 11.5 | 92.31 | 9.42 |

Super Mario World | 15 | 0.5 | 38 | 193 | 7.7 | 61.92 | 6.32 |

Super Mario 64 | 10 | 0.33 | 86 | 217 | 3.8 | 69.22 | 7.06 |

Super Mario Sunshine | 23 | 0.77 | 119 | 988 | 12.7 | 43.05 | 4.4 |

Super Paper Mario | 12 | 0.4 | 288 | 748 | 4 | 49.47 | 5.05 |

Finally, we graphed the acceleration due to gravity in each game as the bit rate of the graphics processor increased. Since Super Mario Bros. 1, 2, and 3 were from the same console, we took an average of the three values. Also, the Nintendo Wii never clearly defined its bit rate, but sources say that it is 96 Bits, which is actually less than that of the Nintendo GameCube. As for the other systems, the NES is an 8 Bit system, the SNES is 16 bit, the N64 is 64 Bit, and the GCN is 128 Bit. We set a power fit to this graph, and the result is shown below.

## Conclusion

We determined that, generally speaking, the gravity in each Mario game, as
game hardware has increased, is getting closer to the true value of gravity
on earth of 9.8 m/s^{2}. However, gravity, even on the newest consoles,
is still extreme. According to Wikipedia, a typical person can withstand 5 g
before losing consciousness, and all but the very latest of Mario games have
gravity greater than this. Also, with gravity that great, it is a wonder Mario
can perform such feats as leaping almost 5 times his own body height!

## Sources of Error

The primary source of error in this experiment would be the assumption that Mario is 5 feet tall, and that his height stays constant in each game. In most Mario games, he can become bigger by consuming mushrooms or other powerup objects, and the 5 foot height may be referring to this state. Also, in the 3D Mario games, the camera angle was always angled down, so when measuring the height of Mario and the ledge, this angle caused the measured distance to be different than the actual distance.

Adam Lefky, Artem Gindin -- 2007

External links to this page:

- Acceleration Due to Gravity: Super Mario Brothers, Chris Higgins, mental_floss, 16 January 2009
- Acceleration Due to Gravity: Super Mario Brothers, physics and physicists, 17 January 2009
- Gravity in Mushroom Kingdom Weakening, Toads Worried, Charge Shot, Craig, 29 January 2009
- Gravity in Super Mario Bros: A Study, Keane Ng, the escapist, 16 January 2009 [Click here to read the article with reader commentary.]
- Mario donne son corps à la science, Laurent Checola, Playtime - Blog, LeMonde, 27 Janvier 2009
- Mario Physics: measuring Mushroom Kingdom gravity, Brandon Boyer, Offworld, 16 January 2009
- Mario's Gravity, inventory is full, 17 January 2009
- Super Mario Gravity, Borat on Autism and the Comic Book Hero of Climate Change, Christopher Mims, GrandUnifiedWeekly, Episode 9, 28 January 2009
- The Physics Factbook, Jorge Pereira, 20 January 2009
- The physics of Mario World show the game has a fundamental flaw, Jessica Orwig, Business Insider 24 February 24 2015
- The Physics of the Mushroom Kingdom Are Worthy of Research, Luke Plunkett, Kotaku, 16 January 2009
- The real-life physics of Super Mario: How could a portly plumber jump that high? Julian Benson, techradar, 29 December 2016
- Visual Math Instruction: Premium Grade, Dan Meyer, 21 January 2009
- Wetenschappelijke paper over zwaartekracht in Mario, SpankmasterC, 18 January 2009
- マリオの世界で“重力”に大異変が!? アメリカ物理教師の発見, 中島理彦, 20 January 2009
- Blog Buzz For Brooklyn HS Science Project, W.J. Levay, edwize.org, 29 January 2009
- Super Mario Gravity, David M. Ewalt, Forbes, 17 April 2009

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