04 August 2012

Today's Men's Long-Jump Final

I plan to watch the final of the men's long jump later today.  Ever since hearing stories about Bob Beamon's epic jump in Mexico City on 18 October 1968, nearly two years before I was born, I have been enthralled by the long jump.  I even devoted a full chapter to Beamon and the long jump in my book.

As you watch the long-jump final today, keep an eye out for some great physics.  Just before launching off the ground, athletes achieve sprint speed, nearly 10 m/s (36 km/h or 22 mph).  They want to jump with a large velocity component parallel to the ground so as to maximize jump distance, but they need lots of air time, which happens only with a large vertical component of the launch velocity.  Jump too horizontal and the athlete isn't in the air long enough to go far.  Jump too vertical and the athlete might be able to dunk a basketball, but won't win a long-jump medal.

Basic vacuum kinematics tells us that if launch and landing heights are the same, an angle of 45° will maximize a point particle's horizontal range.  That launch angle represents a perfect balance between launching with plenty of horizontal velocity to get good distance and launching with plenty of vertical velocity to get good hang time.  For a long jumper getting ready to leap from terra firma, launching oneself at 45° to the horizontal is nearly impossible because the athlete has so much forward momentum just before leaping.  Athletes typically jump in the neighborhood of 16°28°.  It turns out that it's more important to achieve as great a launch speed as possible than it is to launch at exactly the optimum angle.

You may be tempted to think that if a jumper launches well below 45° that the jump will be mediocre, but hold on!  That wonderful conservation of angular momentum law that I've discussed before helps athletes make up for a lack of vertical launch velocity.  Notice that athletes land in the pit with their centers of gravity at a height below where they started at the launch.  By landing low in the pit, athletes may add approximately 1 m (~3 feet) to their horizontal distance.  How can they do that if their mechanical energies and angular momenta are essentially fixed at takeoff?

Watch what long jumpers do with their arms while in the air.  By thrusting their arms down and backwards, they rotate their upper bodies in such a way that their heads are rotating toward the ground.  Strong cores and well-conditioned abdominal muscles are crucial for powerful in-air rotations.  Because their angular momenta are conserved, long jumpers' legs and lower bodies have to rotate in the opposite direction, meaning their legs rotate up.  Compared to landing standing up, as they were at takeoff, athletes are able to extend their flight times and land at greater distances.

Pay close attention to what long jumpers do while in flight.  They are not merely flailing their arms and legs in random directions.  There is serious technique involved  and lots of great physics!

My girls and I will root for Will Claye and Marquise Goodwin.  Brits will be pulling for Greg Rutherford and Chris Tomlinson.  Australia's Mitchell Watt was my pre-Olympics pick, so I should stick with him as my pick.  Godfrey Khotso Mokoena of South Africa and Brazil's Mauro Vinicius da Silva could also make some noise.  The latter and Goodwin both jumped 8.11 m (26.6 feet) in qualification.  That's still a long way from Beamon's Olympic record of 8.90 m (29.2 feet) and Mike Powell's world record of 8.95 m (29.4 feet), which he set in Tokyo on 30 August 1991.

Will a long jumper distance himself from his competition with a Beamonesque effort today?  To get close to Beamon and Powell, an athlete will need to jump nearly a first down (10 yards or 9.144 m) in American football!

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