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To calculate the maximum speed at which a person would fall, you need to know that person's weight and their air drag, which depends on their shape, size, position (i.e., spread-eagle, feet-first, etc.), and the density of the air. If you are comfortable with complex equations and integrals, you can calculate this. As a reference, have a look at pages 137 to 139 of Sears and Zemansky's University Physics (10th edition, Volume 1, Chapter 5, published by Addison Wesley).
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Leaving the math aside, here are the important facts, which are drawn from two useful sources: (1) The June 1943 issue of Air Force magazine, page 13 and (2) The Complete Book of Sky Sports by Linn Emrich, pages 40 to 41. (Note: If you can't find Emrich's book, the same tables appear on page 120 of Bud Sellick's The Wild, Wonderful World of Parachutes and Parachuting.)
- With an open parachute, it takes about 24 and a half minutes to descend from 40,000 feet. The landing speed is about 14 miles an hour. Note: This calculation is in reference to a round parachute.
- Without an open parachute, it takes a little over three minutes and the landing speed is about 110 miles per hour. (Air Force magazine did not specify the weight of this person, but presumably it would be a little less than the weight used in the examples from Emrich below.)
- For a 170-pound person wearing two parachutes and using a stable spread position, Emrich calculates that the terminal velocity (i.e, the maximum speed) would be 176 feet per second, or about 120 miles per hour. (Note: In general, the more you weigh, the faster your terminal velocity will be, although your speed will be faster if you fall head down or feet first, because those positions provides the least resistance.)
- Emrich notes that this 170-pound person would reach terminal velocity after about 12 seconds and would fall nearly 10,000 feet in one minute.
- According to Emrich's calculations, this 12-second fall would cover a little under 1,500 feet, which from a terminal velocity perspective means that it doesn't make much difference whether this 170-pound person fell from 2,000 or 20,000 feet. He or she would still be moving at about 120 miles per hour.
- Some living things (ants for example) have terminal velocities that are not fatal, and can survive falls from heights that might be fatal for humans. See more on this in relation to cats and their ability to survive long falls.
- Not used to miles per hour? Prefer another metric? We have recently added the Free Fall Research Page Speed Conversion Table to the site. This is a device that allows you to see comparable values in miles per hour, kilometers per hour, feet per minute (or second), or meters per minute (or second).
- In his marvelous book, The Wild, Wonderful World of Parachutes and Parachuting (Prentice-Hall, 1981), Bud Sellick included a table showing the distance covered by a skydiver in a stable free fall position. We've taken this information and created a graphic that we hope will be useful for anyone wondering how long it takes for someone to fall a given distance. It also shows an approximation of how fast that person was moving.
- Readers of the Free Fall Research Page have submitted explanations of the math for two interesting topics: how acceleration works on the moon and the influence of weight on terminal velocity. Enjoy! (P.S. There are many other math-related questions and answers on our Questions page.
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