Some form of the long jump
was featured in the ancient Olympics after it was introduced in 708
BC as part of the pentathlon. But as vase paintings such as the one
shown in the top photograph attest, there was an intriguing
difference between the way ancient athletes performed their jumps
and the way modern ones do: Ancient Olympians took off holding
halteres, or jumping weights. The weights, made of stone or lead,
improved the jumpers' performance.
A Little Extra Weight Goes a Long Way
One key to understanding that improvement is the relation between
the jumpers' feet and center of mass. Before the takeoff, an athlete
holds the halteres extended backward, then swings them forward. At
takeoff, the jumper's arms are extended up and out, and so the
center of mass of a weighted jumper is further forward and higher
than it would be without halteres. As the jumper prepares to land,
the halteres are swung down and backward so that, on landing, the
feet of the weighted jumper are more forward of the center of mass
than they are for modern, unweighted athletes. Because the initial
position and velocity of the center of mass determine its subsequent
trajectory, halteres improve the jump distance, provided that their
extra weight does not excessively diminish the takeoff speed.
Now, Alberto Minetti and Luca
Ardigó of Manchester Metropolitan University in England have
analyzed the effect of loading athletes with jumping weights.
Assuming an unchanged takeoff speed, they estimated that carrying a
3-kg weight in each hand would allow an athlete to enjoy a 6%
increase in jump distance. They also explored, both with human
subjects and computer simulations, how halteres do affect takeoff
Minetti and Ardigó asked subjects to jump vertically, with and
without halteres. The posture and muscle action associated with a
vertical jump are very similar to those of a standing long jump, but
jumping vertically is a more familiar skill, and one easier to
coordinate with swinging weights. Thus, vertical jumps were more
practical to test than the horizontal sort. They were also easier to
simulate on a computer.
The Manchester experiment determined that takeoff speed actually
increased by 5-7% when jumpers were loaded with halteres weighing
from 2 to 9 kg each. That mass range corresponds well with the range
of archaeological specimens, three of which are pictured above.
Within the 2-9 kg range, the speed was essentially constant, given
experimental uncertainties. The greater takeoff speed achieved by
loaded jumpers led to increases in distances beyond those generated
by using the halteres to shift the position of the feet relative to
the center of mass.
As Minetti explains it, halteres can lead to an increased takeoff
speed because moderately loaded muscles exert greater force than
unloaded muscles, while still contracting at reasonable rates. Thus,
loaded muscles can generate increased power.
Minetti and Ardigó's experimental results were generally
consistent with the results of their computer simulation. In their
model, a jumper was built from a shank, a thigh, a trunk, and an
elbowless arm. Joints at the knee and shoulder were able to generate
torques. The model included physiological measurements relating
muscle forces to contraction distances and speeds, and relating
joint torques to angular displacements and speeds. When holding a
pair of 3-kg halteres, the virtual jumper increased takeoff speed by
2%. Minetti and Ardigó suggest that the simplicity of the model, in
particular its lack of elastic structures such as tendons and
ligaments, could be responsible for the discrepancies between
simulation and experiment.
Few details are known about
how jumping events in the ancient Olympiads were conducted or
judged, according to David Gilman Romano of the University of
Pennsylvania's department of classical studies and Museum of
Archaeology and Anthropology. Written testimonies stipulate that the
foot had to land "properly," and that the halteres were an aid to
proper landing. But it is not known if there was a penalty for
slipping backward, or for allowing the halteres to touch the ground.
Some historians have argued that Olympic athletes could throw the
halteres backward before landing, further increasing their jump
distance. Some vase paintings indicate that ancient Olympic long
jumps commenced from a standing position. Others, though, show
athletes taking off on one foot. The depictions of one-footed
takeoffs and accounts of better than 50-foot jumps suggest to some
scholars that athletes got a running start and that the ancient
Olympic long jump was akin to the modern triple jump. Given the
nearly 1200-year span of the ancient Olympic games, it could be that
the long jump was run differently in various Olympiads. The ancient
Greeks, unfortunately, did not leave us definitive rulebooks.
Steven K. Blau
1. A. E. Minetti, L. P. Ardigó, Nature
420, 141 (2002).
© 2003 American Institute of Physics