The halteres could also help the athletes while they were mid-bound, even though the trajectory of a jumper's center of mass is determined at the instant of launch.
"When you are landing" without halteres, Minetti explained, "your center of mass is close to your lower trunk. But with the hands [and halteres] back you could put your feet more forward." That makes a difference in the long jump, because what counts is where the feet hit the ground.
Furthermore, by enabling competitors to bring their upper-body muscles into play during launch, halteres would have permitted jumpers to propel themselves off the ground with more initial forceat least enough to compensate for the extra weight they bore.
Finally, even the legs can provide more power when working against halteres. "It's much more effective to contract against a load than [to contract muscles] against no load," said Minetti. The ancient Greek philosopher Aristotle recognized this and commented on it in writing about halteres.
The combination of all these small advantages means that the hand-held weights could have contributed an additional seven inches (17 centimeters) to a natural jump of ten feet (three meters), the researchers reported in the November 14 issue of the British science journal Nature.
Best Feet Forward
Long-jump competitors are thought to have first exploited the quirks of physics to boost their performance in 708 B.C., during the 18th Olympic Games, said Minetti. Those Games were the first to include the standing long jump as one of five events in the pentathlon.
Some historians have speculated that airborne athletes may have actually thrown their halteres backward before they themselves hit the ground. "If they did," Minetti said, "flight could be prolonged even more" than his calculations suggest.
He is wary, however, of assuming that this technique was practiced. While lead halteres would have been sturdy enough to sustain a hard impact, he said, stone weights might have broken under the force. Given the careful craftsmanship that went into carving some stone halteres, athletes probably would have been loath to risk breaking them, Minetti said.
Even if halteres were permitted today, he noted, they wouldn't necessarily propel long-jumpers farther. The long-jump event in modern Olympic Games involves a running start, which makes the biomechanics different than those Minetti and Ardigó so carefully modeled.
Should the standing long jumphalteres and allbe reintroduced into the Olympics? Said Minetti: "I would like it to be, in a way."
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