Felix Baumgartner: The Mathematics of Falling Faster than the Speed of Sound

Earlier this month, Felix Baumgartner jumped from 39,045 meters, or 24.26 miles, above the Earth from a capsule lifted by a 334-foot-tall helium filled balloon (twice the height of Nelson’s column and 2.5 times the diameter of the Hindenberg). The jump was equivalent to a fall from 4.4 Mount Everests stacked on top of each other, or falling 93% of the length of a marathon.

At 24.26 miles above the Earth, the atmosphere is very thin and cold, only about -14 degrees Fahrenheit on average. The temperature, unlike air pressure, does not change linearly with altitude at such heights. Jason Martinez, a programmer at Wolfram|Alpha, did a number of calculations to see how Felix’s record-setting jump came to be. It’s a very math-heavy post, but something I have been looking forward to!


Felix Baumgartner’s mach speed at various portions of his free fall.

If you’re into the nitty-gritty mathematical computations, I suggest reading the whole blog post.