Acceleration Due to Gravity: Super Mario Brothers
I've pointed to nerdy analysis of Super Mario Brothers before. Back in February 2008, I came across a video that discussed Quantum Physics in Super Mario World, in which an anonymous blogger used a hacked Mario game to demonstrate a principal of theoretical quantum physics. Well, today we're moving from quantum physics to good old-fashioned regular physics. Specifically, the physics you learn in high school.
High school physics teacher Glenn Elert's students write something called The Physics Factbook™. Elert describes it as "an exercise in library research methods in which students are sent out in search of a measurement with the intent of having them find more than just a number with a unit." My favorite article is Acceleration Due to Gravity: Super Mario Brothers -- a scholarly approach to the problem of physics in Super Mario Brothers, in an attempt to measure the relative gravity of various Mario games. Here's a snippet of the article and a sample chart:
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 = s0 + v0t + ½ at2
where s is the distance he falls, s0 is his initial distance, which is 0, v0 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 / t2
Read the rest to learn whether gravity is getting more or less realistic as the games have progressed. (And a personal note: my favorite Mario game is SMB 2, in which, playing the Princess, you're able to sort of glide through the air for a few seconds while jumping -- completely bizarre physics, and great fun in the game.)
See also: Five Super Mario Brothers Videos, including various masterful feats of SMB athletics -- playing with feet, playing while not looking at the screen, etc.