(This is the fifth in a series of stories about the science behind the Olympics to run daily this week.)
By Sharon Begley
NEW YORK Which long jumpers will leave the London Games with a medal and which with just a memory depends, of course, on the horizontal distance they cover. Paradoxically, however, vertical velocity (the speed at which they jump up from the take-off board) determines success more than horizontal velocity (the speed at which they fly across the sand pit).
As a result, the best long jumpers are those who use their strength to exchange horizontal velocity, generated by their sprint to the take-off board, into the vertical variety.
"The athlete is basically a self-propelled projectile," said biomechanics professor Adrian Lees of England's Liverpool John Moores University, whose scientists have been providing support to British long jumpers and triple jumpers since 1991. "The distance jumped depends on the height, angle and velocity of projection of the center of mass. In practical terms this reduces to the horizontal and vertical velocity at take-off."
The horizontal velocity is determined completely by the speed during the runup. In an analysis of scores of jumps, Lees and his colleagues determined that an approach speed averaging about 10.25 meters per second (m/s) translates into a jump of about 8 meters for men. In Beijing in 2008, Panama's Irving Saladino won with an 8.34 meter jump.
But there is quite a bit of variation, with some 10.25 m/s jumpers stuck at 7 meters and others reaching more than 8. That is more than the difference between medaling and not.
The reason the same horizontal speed translates into different length jumps is vertical velocity. "At high approach speeds, vertical velocity is about three times more important for generating distance than horizontal velocity," said Lees.
The goal then becomes taking off at as steep an angle as possible. In practice, an angle just under 20 degrees is typical; 30 degrees is probably unattainable. Every additional degree of angle adds about 0.3 meter to the jump.
Athletes who under-jump for their velocity, achieving a smaller distance than jumpers with the same speed, are essentially taking off at too flat an angle.
USING THE LEG AS A PIVOT
The reason is strength. "Athletes gain vertical velocity by using the touch-down leg as a pivot," said Lees. "They place the leg in front of them at about 23 degrees to the vertical and pivot over the leg, exchanging horizontal velocity for vertical velocity."
The stiffer they can keep the pivot leg, resisting the tendency to flex the knee and other joints, the better the velocity exchange. Because the force on the knee at the instant of the pivot is about 10 times body weight - compared to three times body weight when running - keeping the knee rigid requires significant strength.
"Good jumpers retain the rigidity of the knee and other joints, while poor ones flex, destroying the effect of the pivot," said Lees. Athletes who fall short for their velocity "have the speed but are not able to convert it into distance," requiring them to improve their strength," he said.
Those who over-jump for their velocity, getting more distance than jumpers with the same speed, do so through their superior ability to keep their leg more rigid than their competitors. They could do even better if they trained for more speed.
Long jumpers tend to peak in their late 20s, once they have maximized their strength, said Lees. American Mike Powell was 27 when he set the current world record of 8.95 meters in 1991.
Technique at the final foot plant on the take-off board is also crucial. The foot should hit perfectly flat: a heel-first plant acts like a brake, while taking off from the toes is unstable and can make the leg buckle, explains Fred Yeadon, professor of computer simulation in sport at Britain's Loughborough University.
The arms and free leg - the one not planted at take-off - can also contribute to a long jumper's distance. "Raising the arms increases the height and velocity of the center of mass," said Lees. That keeps the athlete airborne longer, achieving greater distance.
The upward motion of the arms also "loads" the leg muscles, or applies force to them, pushing them down. The effect is akin to compressing a spring; when it unloads, it does so with more oomph than if it had not been compressed. As a result, said Yeadon, "the double-arm technique gives you more height" and thus distance.
In addition, said Lees, "The forward momentum in the arms can actually pull the body forward, which wasn't recognized scientifically until recently."
(Editing by Michele Gershberg)