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June 6, 1998World's Fastest Man The 1998 edition of The Guinness Book of World Records features an article about Donovan Bailey, billed as the fastest man alive.
The article begins: "Canadian Donovan Bailey rocketed into the record books when he set a new world mark of 9.84 seconds for the 100-meter dash at the Atlanta Olympics." It briefly recounts Bailey's career and, toward the end, quotes Bailey: "No one has ever run as fast as I have, running 27 mph."
When Roy D. North, a computer programmer and mathematical gadfly now based in Connecticut, came across that passage, something bothered him. When he calculated Bailey's speed from the given time and distance, he obtained 22.7 miles per hour.
"What went wrong here?" North wondered. "Was Bailey misquoted? Was there a typo?"
North had to find out how that apparent mismatch had come about, and his search turned up an article in the Aug. 5, 1996, Sports Illustrated. The account mentioned that Bailey's speed at the 60-meter mark of the race was 27.1 miles per hour.
Mystery solved! One speed was the average over the entire race, and the other was the velocity at a particular point in the race.
There's much more to races and world records than
simple determinations of speed, however. Jonas R. Mureika, a systems
programmer at the University of Southern California in Los Angeles, has been
developing mathematical models of sprinting to find a way to compensate for
wind effects in the 100-m dash.
Wind has long been a confounding factor in the 100-m and 200-m sprints. Indeed, records can be established only if the wind speed is less than 2.0 m/s. Nonetheless, sprinters in a race run with a 1.9 m/s tail wind would undoubtedly have an advantage over competitors racing in still air.
Assuming that a sprinter dissipates about 3 percent of his or her energy in overcoming drag, Mureika developed a formula that compensates for accompanying wind speeds, converting measured times into equivalent times in still air:
t0 = {1.03 – 0.03 [1 – (W tw/100)2]} tw ,
where tw is the recorded race time, W is the wind speed, and t0 is the equivalent time in still air.
Interestingly, because of drag effects, a head wind has a greater effect than a tail wind of equivalent strength. Thus, a 10.00-s run with a 1.5 m/s head wind is roughly equivalent to a 9.91-s run with no wind, while a would-be world record 9.83 s with a 1.5 m/s tail wind also comes to 9.91 s in calm conditions.
The formula enabled Mureika to compare performances in all 100-m races on a more or less equal footing. Thus, Bailey's 9.84-s world-record time, aided by a tail wind of 0.7 m/s, turns into the equivalent of 9.88 s in calm air. A race run in 1996 by Frank Fredericks into a head wind of 0.4 m/s becomes 9.80 s in calm air, surpassing Bailey's world-record performance. If Fredericks had given the same performance in Atlanta, he would have crossed the finish line in roughly 9.81 s, Mureika says.
In 1997, Bailey lost his world sprint crown when he was beaten by Maurice Greene, who clocked 9.86 s at a track meet in Athens. Greene's wind-corrected time was roughly 9.88 s.
Mureika has also developed a simple model that takes into account energy losses when runners in a 200- or 400-m race must negotiate various portions of a curved track. Such efforts have put him into the prognostication game, predicting the outcome of races under various conditions and extrapolating trends to future world records.
Mathematical models only suggest possibilities, however, based on present data and understanding. Athletes set the records.
References:
Guinness Media, Inc. 1998. The Guinness Book of World Records (37th ed.). New York: Bantam.
You can check out the official Donovan Bailey Web page at http://www.donovanbailey.com/.
Jonas R. Mureika describes his mathematical models of sprinting at http://rana.usc.edu:8376/~jonasm/track/index.html.
Comments are welcome. Please send messages to Ivars Peterson at ip@sciserv.org.
Ivars Peterson is the mathematics/computers writer and online editor at Science News. He is the author of *The Mathematical Tourist, Islands of Truth, Newton's Clock, Fatal Defect, and The Jungles of Randomness. His current work in progress is Fragments of Infinity: A Kaleidoscope of Mathematics and Art (to be published in 1999 by Wiley).
*NOW AVAILABLE: The Mathematical Tourist: New and Updated Snapshots of Modern Mathematics by Ivars Peterson. New York: W.H. Freeman, 1998. ISBN 0-7167-3250-5. $14.95 US (paper).