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Olympics: Science of the Sporting Life
Posted 26 JANUARY 2006 (Expanded 2006 based on 1996 story)

Computers on ice
high jumper over barThe triple Axel takes less than a second. Most of us don't even know how the jump got its name. But its the sexiest jump on ice, and one of the most difficult, says Deborah King, assistant professor of exercise and sport sciences at Ithaca College. To do a good triple Axel, you have to speed forward into the jump, drive your arms and leg to create lift, pop up into the air, bring in your arms to speed your spin, then land gracefully with arms spread to slow your rotation.

We hardly need mention that if you're in the Olympics, you're doing this jump before hundreds of millions of potential critics. And King tells us the airborne part takes just 0.6 seconds.

King uses biomechanics, the principles of mechanics applied to the motion of the body, to analyzes these jumps for U.S. Figure Skating and various coaches and skaters. If you remember Physics 101, you recall the motion of fascinating stuff: cannonballs and billiard balls. Human bodies respond to the same mechanical laws, but they are more complicated, since they flex, swing and move their joints with on-board muscles.

Using two or more high-speed video cameras, King films a skater's jumps, and then the tedium begins. "For each view, from approach through landing, we identify key landmarks, hips, shoulder, knee, toe," she said.

A digitally created stick figure completes a complex ice-skating jump.
A wire-frame model shows how a skater performs a triple lutz, triple toe loop combination jump, with no in-between steps. Notice that the center of gravity follows a smooth elliptical arc, which cannot be changed once the skater leaves the ground. Click for 4.3 mb avi movie. Courtesy Deborah King, Ithaca College.

You can't phyght physics
These landmarks show how the entire body is moving, and from data on the movement, a computer assembles the individual views into a three-dimensional picture of the motion, said King. "From the 3-D model, we can calculate the approach velocity, takeoff angle, angular momentum of the skater, and mechanical variables that would be characteristic of success in the jump." Speed, body lean, arm motion and footwork can all be compared to an idealized jump, she says.

Computer models have been used in figure skating in the United States since the 1980s, she says, and while she did not know of research positively crediting biomechanics for the improvement, skaters are certainly introducing ever-more difficult routines. This year, there's even murmur about quad jumps in the Olympics. The models have other purposes, she says, such as "shortening the learning curve." For high-end skills like the triple Axel, "the coach might not have had a previous skater who has gone to that level before, so instead of using trial-error, the coach can learn key points" from the 3D models.

Can a computer help you jump higher?
If computers can help people who jump on ice, what about landlubbers? Jesus Dapena, a professor of kinesiology at Indiana University, uses biomechanics to help high jumpers, although he described himself in a 1996 interview as "not a high jumper. Truthfully, I'm a low jumper."

When a human body moves through the air with some horizontal motion, its center of gravity will follow an elliptical arc, rather like a cannonball. Once the body leaves the ground, the path of the center of gravity cannot be altered. But a high-jumper can alter the relative movement of various parts of the body, as the film clips show.

A woman races towards the high jump fails to turn and hits the bar on her way over the top.A woman  races toward the high jump, rotates clockwise and clears the bar.  Left: click for 1.6 mb QuickTime movie. In a computer-generated image, a jumper touches the bar. She did raise her center of gravity over the bar, but was too extended and failed to rotate enough while passing the bar.

Right: Click for 1.6 mb QuickTime movie. The computer generated a jump with a better mid-air position and more rotation. Note the flexed knees as she starts crossing the bar. The clockwise rotation of the lower legs rotates the upper body counterclockwise, increasing clearance while angular momentum does not change. Flexed knees also reduce the moment of inertia, so the body rotates faster. Both movies courtesy Jesus Dapena, Indiana University.

Because the movement of a non-rigid body is the sum of the movements of its component parts, biomechanic analysis starts by breaking the body into rigid segments. Dapena, for example, uses 16 segments: the upper and lower limbs, the hands and feet, the head, and three parts of the trunk.

Dapena, like King, locates these segments and identifies their movement by looking at the position of various landmarks. Then, from the motion of each segment, he calculates the overall movement of the body, and asks the computer to create stick figures and wire-frame models showing details of A human figure stands ready to hurl a discusthe movement (like computer animation in reverse). Dapena may use the wire-frame models to teach the athlete to optimize acceleration, rotation or body placement.

Biomechanics view the body in 3 dimensions. Courtesy Jesus Dapena.

Jumping to conclusions
A high jumper seems to translate the horizontal velocity of the run-up into vertical motion over the bar, but what actually happens is more related to springs, Dapena says. "The fast run-up makes the muscles of the takeoff leg stretch very quickly after the takeoff foot is planted on the ground, and this stimulates those muscles, which can then make larger forces."

To get the fastest vertical acceleration, your foot must push against the ground for as long as possible. And that requires the runner to, as Dapena says, run with "the butt scraping the ground." Still, there's a tradeoff -- if you run too low, your overly flexed knees will create a puny push-off.

Like King, Dapena says the benefits of biomechanics remain unproven, since athletic performance reflects technique, and physical and mental training, and it's hard to prove the benefit of single input. In some cases, however, the benefits are clear-cut. For example, Dapena examined a discus thrower who did not accelerate the discus fast enough toward the end of the throw. "She went back and concentrated on that, and it made a big difference," he says.

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