Springs Could Enable Runners to Smash the Natural Speed Limit

Physics
One of the most captivating aspects of the summer Olympics is watching the world’s best athletes push their bodies to the edge of what is humanly possible. In 2016, the world watched in awe as Jamaican sprinter Usain Bolt won his third consecutive Olympic gold in each of three distances—the 100m, 200m, and 4x100m relay. Bolt is the fastest man in recorded history, reaching a top of speed of 12m/s, more than 27mph.

Usain Bolt (Jamaica) in the lead during the 100 m heat of the 14th IAAF World Championships in Athletics in Moscow, Russia. Credit: Tobi 87 (CC BY-3.0).

His wins left me wondering about the science of it all. How fast is it humanly possible to run? Aside from willingness to get off the couch and train, what ultimately limits running performance?

In new research published in the journal Science Advances, Vanderbilt University’s Amanda Sutrisno and David Braun explored these questions from a fascinating perspective. Braun leads the Advanced Robotics and Control Laboratory within Vanderbilt’s Center for Rehabilitation Engineering and Assistive Technology. He and his students are interested not just in optimizing human performance, but in surpassing that capacity by inventing performance augmentation devices. Sutrisno is a graduate student working with Braun.

As they report in the paper, How to run 50% faster without eternal energy, the team considered the limits of human power generation during running. Then, they used the results to consider what could be possible. The thinking goes something like this.

Untapped Energy

Bicycling and running are both human-powered endeavors, but people on bicycles can reach much higher speeds than runners. This means that cycling is a more efficient way to harnesses human power and turn it into forward motion.

In terms of energy, bikes have three major advantages overrunning.

  • When you run, you lose energy each time your foot collides with the ground. This loss is mitigated by wheels.
  • While running, your legs fully support your body weight. When ridding, the wheels can support your body weight.
  • Pedaling produces a constant flow of energy that helps propel you forward. Running produces that energy intermittently—only when your foot pushes off the ground.

“These three features enable the bicycle to double the top speed of running, despite supplying no external energy and adding weight to the human,” explain the researchers.

This inspired the researchers to consider whether an augmentation device could similarly harness human power for faster running. Could a running shoe somehow mimick the energy advantages of a bicycle? If so, how much speed could you gain? Theoretically, would Bolt be able to smash all of his own records?

The answers turn out to be yes, lots, and yes, they conclude—if you use springs.

Traditional compression springs.

Spring-based shoes might bring to mind DIY mattress spring shoes, kangaroo jumping shoes, or running prosthetics. If so, you’re sort of on the right track. Let’s say you’ve attached mattress springs to the bottom of your shoes and decide to go for a jog. Each time your foot hits the ground, the spring is compressed. The energy that goes into compression is stored in the coil, so you don’t lose as much energy as usual during impact. Then, when you pick up your foot, the spring extends and that energy gives you a nice upward kick. The extra bounce is fun, but not ideal for running. In running you want to go faster, not higher.

Running prosthetics and kangaroo jumping shoes are more sophisticated variations of mattress spring shoes, but all of them have another basic limitation. They only harness energy when you compress the spring against the ground. If you really want to go faster, the researchers say, you should harness energy while your feet are in the air—that’s where they spend most of the time when you’re running, around 80%.

Harnessing Energy for Speed

To really gain an advantage, traditional springs aren’t enough. Instead, the researchers propose using a special kind of spring, variable stiffness springs.

The stiffness of a spring describes how hard it is to deform. A toy slinky is easy to deform compared to a traditional mattress spring, so it has a lower stiffness. Stiffness depends on the length of the uncompressed spring, the material it’s made from, and the diameter of the coils. Typical springs, like those used in mattresses, mousetraps, and pens, have a constant stiffness, which means the stiffness doesn’t change.

This isn’t always the case though. Let’s say you have a spring whose uncompressed length changes, perhaps with temperature or pressure. When you change its length, you also change its stiffness. There are many ways to design such variable stiffness springs.

To get people running at maximum speed, the researchers envision specially designed variable stiffness spring devices that work like this.

  • When a runner’s foot leaves the ground, the spring has a low stiffness (so it’s easy to compress). The runner fully compresses the spring as their leg swings backward and around. Simultaneously, the stiffness of the spring increases.
  • On touchdown, the fully compressed, stiff spring hits the ground vertically and its stiffness remains unchanged. The spring supports the runner’s body weight and redirects the velocity of the body.
  • As the runner’s leg flexes and pushes off the ground, the stiff spring is released and produces a big kick in the forward direction.
  • Then the foot is in the air again, the spring has a low stiffness again, and the cycle repeats.

In this way, you can capture the runner’s energy while their feet are in the air, reduce the energy lost to the ground during touchdown, and redirect the runner’s vertical motion while accelerating their horizontal motion.

Illustration of the augmentation device. (A) Swing: The leg is coupled to the spring. As the leg extends, the spring is compressed and the stiffness of the spring is increased. The large leg extension, small leg force, and small leg stiffness provide small spring compression, large spring force, and large spring stiffness. (B) Ground contact: The leg is decoupled from the spring and the mechanism that changes stiffness is locked. As the leg flexes, the spring extends while the stiffness of the spring stays constant. Credit: Copyright © 2020 Amanda Sutrisno and David J. Braun, (CC BY-NC 4.0).


Bypassing the Natural Speed Limit

The researchers then set up a physics-based computer model of this conceptual idea to explore its theoretical limits. If you consider than a human can supply energy at a rate up to 18 W/kg per leg (which is comparable to what’s produced by a world-class cyclist), the model predicts that a runner like Usain Bolt could reach a top speed 21m/s—that nearly 47mph and not even 3% below the world record cycling speed!

Even if in a less-than-ideal world in which not all of the assumptions in the model hold true, the researchers anticipate that elite runners could reach speeds well above Bolt’s top speed.

Unfortunately, even Bolt can’t try these shoes yet. The researchers calculated that the variable stiffness spring should be able to store 940 J of energy, weigh no more than 1.5 kg, and reach a maximum stiffness 10 times that of the natural running leg. That combination of properties is a technological challenge we haven’t met yet. But maybe the possibility of equipping runners to travel much faster than any human has ever gone before will spur researchers to pick up the pace on this line of research.

Kendra Redmond

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