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The New York Times: Something Strange in Usain Bolt’s Stride

Bolt is the fastest sprinter ever in spite of — or because of? — an uneven stride that upends conventional wisdom.

The New York Times reporter Jeré Longman covered the research of SMU biomechanics expert Peter Weyand and his colleagues Andrew Udofa and Laurence Ryan for a story about Usain Bolt’s apparent asymmetrical running stride.

The article, “Something Strange in Usain Bolt’s Stride,” published July 20, 2017.

The researchers in the SMU Locomotor Performance Laboratory reported in June that world champion sprinter Usain Bolt may have an asymmetrical running gait. While not noticeable to the naked eye, Bolt’s potential asymmetry emerged after the researchers dissected race video to assess his pattern of ground-force application — literally how hard and fast each foot hits the ground. To do so they measured the “impulse” for each foot.

Biomechanics researcher Udofa presented the findings at the 35th International Conference on Biomechanics in Sport in Cologne, Germany. His presentation, “Ground Reaction Forces During Competitive Track Events: A Motion Based Assessment Method,” was delivered June 18.

The analysis thus far suggests that Bolt’s mechanics may vary between his left leg to his right. The existence of an unexpected and potentially significant asymmetry in the fastest human runner ever would help scientists better understand the basis of maximal running speeds. Running experts generally assume asymmetry impairs performance and slows runners down.

Udofa has said the observations raise the immediate scientific question of whether a lack of symmetry represents a personal mechanical optimization that makes Bolt the fastest sprinter ever or exists for reasons yet to be identified.

Weyand, who is Glenn Simmons Professor of Applied Physiology and professor of biomechanics in the Department of Applied Physiology & Wellness in SMU’s Annette Caldwell Simmons School of Education & Human Development, is director of the Locomotor Lab.

An expert on human locomotion and the mechanics of running, Weyand has been widely interviewed about the running controversy surrounding double-amputee South African sprinter Oscar Pistorius. Weyand co-led a team of scientists who are experts in biomechanics and physiology in conducting experiments on Pistorius and the mechanics of his racing ability.

For his most recently published research, Weyand was part of a team that developed a concise approach to understanding the mechanics of human running. The research has immediate application for running performance, injury prevention, rehab and the individualized design of running shoes, orthotics and prostheses. The work integrates classic physics and human anatomy to link the motion of individual runners to their patterns of force application on the ground — during jogging, sprinting and at all speeds in between.

They described the two-mass model earlier this year in the Journal of Experimental Biology in their article, “A general relationship links gait mechanics and running ground reaction forces.” It’s available at bitly, http://bit.ly/2jKUCSq.

The New York Times subscribers or readers with remaining limited free access can read the full story.

EXCERPT:

By Jeré Longman
The New York Times

DALLAS — Usain Bolt of Jamaica appeared on a video screen in a white singlet and black tights, sprinting in slow motion through the final half of a 100-meter race. Each stride covered nine feet, his upper body moving up and down almost imperceptibly, his feet striking the track and rising so rapidly that his heels did not touch the ground.

Bolt is the fastest sprinter in history, the world-record holder at 100 and 200 meters and the only person to win both events at three Olympics. Yet as he approaches his 31st birthday and retirement this summer, scientists are still trying to fully understand how Bolt achieved his unprecedented speed.

Last month, researchers here at Southern Methodist University, among the leading experts on the biomechanics of sprinting, said they found something unexpected during video examination of Bolt’s stride: His right leg appears to strike the track with about 13 percent more peak force than his left leg. And with each stride, his left leg remains on the ground about 14 percent longer than his right leg.

This runs counter to conventional wisdom, based on limited science, that an uneven stride tends to slow a runner down.

So the research team at S.M.U.’s Locomotor Performance Laboratory is considering a number of questions as Bolt prepares for what he said would be his final performances at a major international competition — the 100 meters and 4×100-meter relay next month at the world track and field championships in London.

Among those questions: Does evenness of stride matter for speed? Did Bolt optimize this irregularity to become the fastest human? Or, with a more balanced stride during his prime, could he have run even faster than 9.58 seconds at 100 meters and 19.19 seconds at 200 meters?

“That’s the million-dollar question,” said Peter Weyand, director of the S.M.U. lab.

The S.M.U. study of Bolt, led by Andrew Udofa, a doctoral researcher, is not yet complete. And the effect of asymmetrical strides on speed is still not well understood. But rather than being detrimental for Bolt, the consequences of an uneven stride may actually be beneficial, Weyand said.

It could be that Bolt has naturally settled into his stride to accommodate the effects of scoliosis. The condition curved his spine to the right and made his right leg half an inch shorter than his left, according to his autobiography.

Initial findings from the study were presented last month at an international conference on biomechanics in Cologne, Germany. Most elite sprinters have relatively even strides, but not all. The extent of Bolt’s variability appears to be unusual, Weyand said.

“Our working idea is that he’s probably optimized his speed, and that asymmetry reflects that,” Weyand said. “In other words, correcting his asymmetry would not speed him up and might even slow him down. If he were to run symmetrically, it could be an unnatural gait for him.”

Antti Mero, an exercise physiologist at the University of Jyvaskyla in Finland, who has researched Bolt’s fastest races, said he was intrigued by the S.M.U. findings.

The New York Times subscribers or readers with remaining limited free access can read the full story.

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Cosmos: Painting with light in three dimensions

A new technique uses photoswitch molecules to create three-dimensional images from pure light.

Australia’s quarterly science magazine Cosmos covered the research of SMU organic chemist Alex Lippert, an assistant professor in the Department of Chemistry in SMU’s Dedman College of Humanities and Sciences.

Lippert’s team develops synthetic organic compounds that glow in reaction to certain conditions. He led his lab in developing a new technology that uses photoswitch molecules to craft 3-D light structures — not holograms — that are viewable from 360 degrees. The economical method for shaping light into an infinite number of volumetric objects would be useful in a variety of fields, from biomedical imaging, education and engineering, to TV, movies, video games and more.

For biomedical imaging, Lippert says the nearest-term application of the technique might be in high-volume pre-clinical animal imaging, but eventually the technique could be applied to provide low-cost internal imaging in the developing world, or less costly imaging in the developed world.

Cosmos reporter Joel F. Hooper wrote about the new technology in “Painting with light in three dimensions,” which published online July 14, 2017.

Lippert’s lab includes four doctoral students and five undergraduates who assist in his research. He recently received a prestigious National Science Foundation Career Award, expected to total $611,000 over five years, to fund his research into alternative internal imaging techniques.

NSF Career Awards are given to tenure-track faculty members who exemplify the role of teacher-scholars through outstanding research, excellent education and the integration of education and research in American colleges and universities.

Lippert joined SMU in 2012. He was previously a postdoctoral researcher at the University of California, Berkeley, and earned his Ph.D. at the University of Pennsylvania, and Bachelor of Science at the California Institute of Technology.

Read the full story.

EXCERPT:

By Joel F. Hooper
Cosmos

Those of us who grew up watching science fiction movies and TV shows imagined our futures to be filled with marvellous gadgets, but we’ve sometimes been disappointed when science fails to deliver. We can’t take a weekend trip to Mars yet, and we’re still waiting for hoverboards that actually hover.

But in the case of 3-D image projection, the technology used by R2D2 in Star Wars is making its way into reality. Using advances in fluorescent molecules that can be switched on by UV light, scientists at Southern Methodist University in Dallas have created a method for producing images and animations by structuring light in 3-dimentions.

The technology uses a solution of fluorescent molecules called rhodamines, which have the potential to emit visible light when they are excited by a light beam of the right wavelength. But these molecules are usually in an inactive state, and must be “switched on” by UV light before they can become emitters. When a UV light or visible light beam alone shines through the solution, the rhodamines to not emit light. But where these two beams intersect, the emitting molecules are both switched on and excited, and can produce a small glowing 3D pixel, known as a voxel.

When a number of voxels are produced at once, using two projectors positioned at 90° to a flask containing a solution of the fluorescent molecules, a 3D image is produced.

“Our idea was to use chemistry and special photoswitch molecules to make a 3D display that delivers a 360-degree view,” says Alexander Lippert, lead author of the study. “It’s not a hologram, it’s really three-dimensionally structured light.”

Read the full story.

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Better than Star Wars: Chemistry discovery yields 3-D table-top objects crafted from light

Photoswitch chemistry allows construction of light shapes into structures that have volume and are viewable from 360 degrees, making them useful for biomedical imaging, teaching, engineering, TV, movies, video games and more

A scientist’s dream of 3-D projections like those he saw years ago in a Star Wars movie has led to new technology for making animated 3-D table-top objects by structuring light.

The new technology uses photoswitch molecules to bring to life 3-D light structures that are viewable from 360 degrees, says chemist Alexander Lippert, Southern Methodist University, Dallas, who led the research.

The economical method for shaping light into an infinite number of volumetric objects would be useful in a variety of fields, from biomedical imaging, education and engineering, to TV, movies, video games and more.

“Our idea was to use chemistry and special photoswitch molecules to make a 3-D display that delivers a 360-degree view,” said Lippert, an assistant professor in the SMU Department of Chemistry. “It’s not a hologram, it’s really three-dimensionally structured light.”

Key to the technology is a molecule that switches between non-fluorescent and fluorescent in reaction to the presence or absence of ultraviolet light.

The new technology is not a hologram, and differs from 3-D movies or 3-D computer design. Those are flat displays that use binocular disparity or linear perspective to make objects appear three-dimensional when in fact they only have height and width and lack a true volume profile.

“When you see a 3-D movie, for example, it’s tricking your brain to see 3-D by presenting two different images to each eye,” Lippert said. “Our display is not tricking your brain — we’ve used chemistry to structure light in three actual dimensions, so no tricks, just a real three-dimensional light structure. We call it a 3-D digital light photoactivatable dye display, or 3-D Light Pad for short, and it’s much more like what we see in real life.”

At the heart of the SMU 3-D Light Pad technology is a “photoswitch” molecule, which can switch from colorless to fluorescent when shined with a beam of ultraviolet light.

The researchers discovered a chemical innovation for tuning the photoswitch molecule’s rate of thermal fading — its on-off switch — by adding to it the chemical amine base triethylamine.

Now the sky is the limit for the new SMU 3-D Light Pad technology, given the many possible uses, said Lippert, an expert in fluorescence and chemiluminescence — using chemistry to explore the interaction between light and matter.

For example, conference calls could feel more like face-to-face meetings with volumetric 3-D images projected onto chairs. Construction and manufacturing projects could benefit from rendering them first in 3-D to observe and discuss real-time spatial information. For the military, uses could include tactical 3-D replications of battlefields on land, in the air, under water or even in space.

Volumetric 3-D could also benefit the medical field.

“With real 3-D results of an MRI, radiologists could more readily recognize abnormalities such as cancer,” Lippert said. “I think it would have a significant impact on human health because an actual 3-D image can deliver more information.”

Unlike 3-D printing, volumetric 3-D structured light is easily animated and altered to accommodate a change in design. Also, multiple people can simultaneously view various sides of volumetric display, conceivably making amusement parks, advertising, 3-D movies and 3-D games more lifelike, visually compelling and entertaining.

Lippert and his team in The Lippert Research Group report on the new technology and the discovery that made it possible in the article “A volumetric three-dimensional digital light photoactivatable dye display,” published in the journal Nature Communications.

Some of the 3-D images generated with the new technology are viewable in this video.

Co-authors are Shreya K. Patel, lead author, and Jian Cao, both students in the SMU Department of Chemistry.

Genesis of an idea — cinematic inspiration
The idea to shape light into volumetric animated 3-D objects came from Lippert’s childhood fascination with the movie “Star Wars.” Specifically he was inspired when R2-D2 projects a hologram of Princess Leia. Lippert’s interest continued with the holodeck in “Star Trek: The Next Generation.”

“As a kid I kept trying to think of a way to invent this,” Lippert said. “Then once I got a background in chemistry molecules that interact with light, and an understanding of photoswitches, it finally dawned on me that I could take two beams of light and use chemistry to manipulate the emission of light.”

Key to the new technology was discovering how to turn the chemical photoswitch off and on instantly, and generating light emissions from the intersection of two different light beams in a solution of the photoactivatable dye, he said.

SMU graduate student in chemistry Jian Cao hypothesized the activated photoswitch would turn off quickly by adding the base. He was right.

“The chemical innovation was our discovery that by adding one drop of triethylamine, we could tune the rate of thermal fading so that it instantly goes from a pink solution to a clear solution,” Lippert said. “Without a base, the activation with UV light takes minutes to hours to fade back and turn off, which is a problem if you’re trying to make an image. We wanted the rate of reaction with UV light to be very fast, making it switch on. We also wanted the off-rate to be very fast so the image doesn’t bleed.”

SMU 3-D Light Pad
In choosing among various photoswitch dyes, the researchers settled on N-phenyl spirolactam rhodamines. That particular class of rhodamine dyes was first described in the late 1970s and made use of by Stanford University’s Nobel prize-winning W.E. Moerner.

The dye absorbs light within the visible region, making it appropriate to fluoresce light. Shining it with UV radiation, specifically, triggers a photochemical reaction and forces it to open up and become fluorescent.

Turning off the UV light beam shuts down fluorescence, diminishes light scattering, and makes the reaction reversible — ideal for creating an animated 3-D image that turns on and off.

“Adding triethylamine to switch it off and on quickly was a key chemical discovery that we made,” Lippert said.

To produce a viewable image they still needed a setup to structure the light.

Structuring light in a table-top display
The researchers started with a custom-built, table-top, quartz glass imaging chamber 50 millimeters by 50 millimeters by 50 millimeters to house the photoswitch and to capture light.

Inside they deployed a liquid solvent, dichloromethane, as the matrix in which to dissolve the N-phenyl spirolactam rhodamine, the solid, white crystalline photoswitch dye.

Next they projected patterns into the chamber to structure light in two dimensions. They used an off-the-shelf Digital Light Processing (DLP) projector purchased at Best Buy for beaming visible light.

The DLP projector, which reflects visible light via an array of microscopically tiny mirrors on a semiconductor chip, projected a beam of green light in the shape of a square. For UV light, the researchers shined a series of UV light bars from a specially made 385-nanometer Light-Emitting Diode projector from the opposite side.

Where the light intersected and mixed in the chamber, there was displayed a pattern of two-dimensional squares stacked across the chamber. Optimized filter sets eliminated blue background light and allowed only red light to pass.

To get a static 3-D image, they patterned the light in both directions, with a triangle from the UV and a green triangle from the visible, yielding a pyramid at the intersection, Lippert said.

From there, one of the first animated 3-D images the researchers created was the SMU mascot, Peruna, a racing mustang.

“For Peruna — real-time 3-D animation — SMU undergraduate student Shreya Patel found a way to beam a UV light bar and keep it steady, then project with the green light a movie of the mustang running,” Lippert said.

So long Renaissance
Today’s 3-D images date to the Italian Renaissance and its leading architect and engineer.

“Brunelleschi during his work on the Baptistery of St. John was the first to use the mathematical representation of linear perspective that we now call 3-D. This is how artists used visual tricks to make a 2-D picture look 3-D,” Lippert said. “Parallel lines converge at a vanishing point and give a strong sense of 3-D. It’s a useful trick but it’s striking we’re still using a 500-year-old technique to display 3-D information.”

The SMU 3-D Light Pad technology, patented in 2016, has a number of advantages over contemporary attempts by others to create a volumetric display but that haven’t emerged as commercially viable.

Some of those have been bulky or difficult to align, while others use expensive rare earth metals, or rely on high-powered lasers that are both expensive and somewhat dangerous.

The SMU 3-D Light Pad uses lower light powers, which are not only cheaper but safer. The matrix for the display is also economical, and there are no moving parts to fabricate, maintain or break down.

Lippert and his team fabricated the SMU 3-D Light Pad for under $5,000 through a grant from the SMU University Research Council.

“For a really modest investment we’ve done something that can compete with more expensive $100,000 systems,” Lippert said. “We think we can optimize this and get it down to a couple thousand dollars or even lower.”

Next Gen: SMU 3-D Light Pad 2.0
The resolution quality of a 2-D digital photograph is stated in pixels. The more pixels, the sharper and higher-quality the image. Similarly, 3-D objects are measured in voxels — a pixel but with volume. The current 3-D Light Pad can generate more than 183,000 voxels, and simply scaling the volume size should increase the number of voxels into the millions – equal to the number of mirrors in the DLP micromirror arrays.

For their display, the SMU researchers wanted the highest resolution possible, measured in terms of the minimum spacing between any two of the bars. They achieved 200 microns, which compares favorably to 100 microns for a standard TV display or 200 microns for a projector.

The goal now is to move away from a liquid vat of solvent for the display to a solid cube table display. Optical polymer, for example, would weigh about the same as a TV set. Lippert also toys with the idea of an aerosol display.

The researchers hope to expand from a monochrome red image to true color, based on mixing red, green and blue light. They are working to optimize the optics, graphics engine, lenses, projector technology and photoswitch molecules.

“I think it’s a very fascinating area. Everything we see — all the color we see — arises from the interaction of light with matter,” Lippert said. “The molecules in an object are absorbing a wavelength of light and we see all the rest that’s reflected. So when we see blue, it’s because the object is absorbing all the red light. What’s more, it is actually photoswitch molecules in our eyes that start the process of translating different wavelengths of light into the conscious experience of color. That’s the fundamental chemistry and it builds our entire visual world. Being immersed in chemistry every day — that’s the filter I’m seeing everything through.”

The SMU discovery and new technology, Lippert said, speak to the power of encouraging young children.

“They’re not going to solve all the world’s problems when they’re seven years old,” he said. “But ideas get seeded and if they get nurtured as children grow up they can achieve things we never thought possible.” — Margaret Allen, SMU

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Dallas Innovates: SMU Researchers: Usain Bolt’s Gait is Asymmetrical

The researchers assessed Bolt’s running using a new motion-based method to test how hard and fast each foot hits the ground.

Journalist Lance Murray with D Magazine’s Dallas Innovates covered the research of SMU biomechanics expert Peter Weyand and his colleagues Andrew Udofa and Laurence Ryan for a story about Usain Bolt’s asymmetrical running gait.

The article, “SMU Researchers: Usain Bolt’s Gait is Asymmetrical,” published July 5, 2017.

The researchers in the SMU Locomotor Performance Laboratory reported in June that world champion sprinter Usain Bolt may have an asymmetrical running gait. While not noticeable to the naked eye, Bolt’s potential asymmetry emerged after the researchers dissected race video to assess his pattern of ground-force application — literally how hard and fast each foot hits the ground. To do so they measured the “impulse” for each foot.

Biomechanics researcher Udofa presented the findings at the 35th International Conference on Biomechanics in Sport in Cologne, Germany. His presentation, “Ground Reaction Forces During Competitive Track Events: A Motion Based Assessment Method,” was delivered June 18.

The analysis thus far suggests that Bolt’s mechanics may vary between his left leg to his right. The existence of an unexpected and potentially significant asymmetry in the fastest human runner ever would help scientists better understand the basis of maximal running speeds. Running experts generally assume asymmetry impairs performance and slows runners down.

Udofa has said the observations raise the immediate scientific question of whether a lack of symmetry represents a personal mechanical optimization that makes Bolt the fastest sprinter ever or exists for reasons yet to be identified.

Weyand, who leads the lab and its researchers, he is an expert on human locomotion and the mechanics of running. He is Glenn Simmons Professor of Applied Physiology and professor of biomechanics in the Department of Applied Physiology & Wellness in SMU’s Annette Caldwell Simmons School of Education & Human Development, is director of the Locomotor Lab.

Read the full story.

EXCERPT:

By Lance Murray
Dallas Innovates

When it comes to running, nobody does it faster than Usain Bolt, the eight-time Olympic champion and triple world record holder.

The lanky Jamaican sprinter is known for his explosive acceleration down the track and the famous images of him looking back as he leaves his competitors in his wake.

You’d think Bolt’s powerful legs work as a symmetrical team propelling him at great speed toward the finish line, but according to researchers at Southern Methodist University, Bolt’s gait may, in fact, be asymmetrical.

SMU researchers examined the running mechanics of Bolt, who is considered the world’s fastest man.

The analysis, so far, suggests that his mechanics may vary from his right leg to his left, according to Andrew Udofa, a biometrics researcher in the SMU Locomotor Performance Laboratory.

According to a blog on SMU Research News, most running experts assume that asymmetry impairs performance and slows a runner down. This unexpected asymmetry in Bolt’s mechanics could help scientist better understand the basis of maximal running speeds, according to the university.

“Our observations raise the immediate scientific question of whether a lack of symmetry represents a personal mechanical optimization that makes Bolt the fastest sprinter ever or exists for reasons yet to be identified,” Udofa, a research team member, said in the blog.

Read the full story.

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Does symmetry matter for speed? Study finds Usain Bolt may have asymmetrical running gait

A new method for assessing patterns of ground-force application suggests the right and left legs of the world’s fastest man may perform differently, defying current scientific assumptions about running speed.

World champion sprinter Usain Bolt may have an asymmetrical running gait, according to data recently presented by researchers from Southern Methodist University, Dallas.

While not noticeable to the naked eye, Bolt’s potential asymmetry emerged after SMU researchers assessed the running mechanics of the world’s fastest man.

The analysis thus far suggests that Bolt’s mechanics may vary between his left leg and his right, said Andrew Udofa, a biomechanics researcher in the SMU Locomotor Performance Laboratory.

The existence of an unexpected and potentially significant asymmetry in the fastest human runner ever would help scientists better understand the basis of maximal running speeds. Running experts generally assume asymmetry impairs performance and slows runners down.

“Our observations raise the immediate scientific question of whether a lack of symmetry represents a personal mechanical optimization that makes Bolt the fastest sprinter ever or exists for reasons yet to be identified,” said Udofa, a member of the research team.

The SMU Locomotor Lab, led by Peter Weyand, focuses on the mechanical basis of human performance. The group includes physicist and engineer Laurence Ryan, an expert in force and motion analysis, and doctoral researcher Udofa.

The intriguing possibility of Bolt’s asymmetry emerged after the SMU researchers decided to assess his pattern of ground-force application — literally how hard and fast each foot hits the ground. To do so they measured the “impulse” for each foot.

Impulse is a combination of the amount of force applied to the ground multiplied by the time of foot-ground contact.

“The manner in which Bolt achieves his impulses seems to vary from leg to leg,” Udofa said. “Both the timing and magnitude of force application differed between legs in the steps we have analyzed so far.”

Impulse matters because that’s what determines a runner’s time in the air between steps.

“If a runner has a smaller impulse, they don’t get as much aerial time,” Weyand said. “Our previous published research has shown greater ground forces delivered in shorter periods of foot-ground contact are necessary to achieve faster speeds. This is true in part because aerial times do not differ between fast and slow runners at their top speeds. Consequently, the combination of greater ground forces and shorter contact times is characteristic of the world’s fastest sprinters.”

The researchers didn’t test Bolt in the SMU lab. Instead, they used a new motion-based method to assess the patterns of ground-force application. They analyzed Bolt and other elite runners using existing high-speed race footage available from NBC Universal Sports. The runners were competing in the 2011 Diamond League race at the World Athletics Championships in Monaco.

Udofa analyzed 20 of Bolt’s steps from the Monaco race, averaging data from 10 left and 10 right.

The researchers relied upon foot-ground contact time, aerial time, running velocity and body mass to determine the ground reaction forces using the new method, made possible by the “two-mass model” of running mechanics.

Runners typically run on a force-instrumented treadmill or force plates for research examining running ground-reaction forces. However, the two-mass model method provides a tool that enables motion-based assessments of ground reaction forces without direct force measurements.

“There are new avenues of research the model may make possible because direct-force measurements are not required,” Weyand said. “These include investigations of the importance of symmetry for sprinting performance. The two-mass model may facilitate the acquisition of data from outside the lab to help us better address these kinds of questions.”

Udofa presented the findings at the 35th International Conference on Biomechanics in Sport in Cologne, Germany. His presentation, “Ground Reaction Forces During Competitive Track Events: A Motion Based Assessment Method,” was delivered June 18.

Two-mass model relies on basic motion data
SMU researchers developed the concise two-mass model as a simplified way to predict the entire pattern of force on the ground — from impact to toe-off — with very basic motion data.

The model integrates classic physics and human anatomy to link the motion of individual runners to their patterns of force on the ground.

It provides accurate predictions of the ground force vs. time patterns throughout each instant of the contact period, regardless of limb mechanics, foot-strike type or running speed.

The two-mass model is substantially less complex than other scientific models that explain patterns of ground force application during running. Most existing models are more elaborate in relying on 14 or more variables, many of which are less clearly linked to the human body.

“The two-mass model provides us with a new tool for assessing the crucial early portion of foot-ground contact that is so important for sprinting performance,” said Udofa. “The model advances our ability to assess the impact-phase force and time relationships from motion data only.”

The two-mass model was developed in SMU’s Locomotor Performance Laboratory by Kenneth P. Clark, now an assistant professor in the Department of Kinesiology at West Chester University, West Chester, Pa.; Ryan, a physicist and research engineer at SMU’s Locomotor Performance Laboratory; and Weyand.

The researchers described the two-mass model earlier this year in the Journal of Experimental Biology in their article, “A general relationship links gait mechanics and running ground reaction forces.” It’s available at bitly, http://bit.ly/2jKUCSq.

Support for the research came from the U.S. Army Medical Research and Materiel Command.

Weyand is Glenn Simmons Professor of Applied Physiology and professor of biomechanics in the Department of Applied Physiology & Wellness in SMU’s Annette Caldwell Simmons School of Education & Human Development. — Margaret Allen, SMU