# The Physics of . . . Walking

#### Why humans move like an imperfect pendulum

By Robert Kunzig|Sunday, July 01, 2001

In what one can only assume is Giovanni Cavagna's funniest home video, Cavagna, a jolly physiologist from the University of Milan, is standing in an aviator suit in the passenger compartment of an Airbus A-300. The plane, operated by the European Space Agency, has been cleared of its seats and filled with scientific gear. Cavagna is grinning and holding a pendulum, which is swinging at a steady pace. Next to him, his friend and longtime collaborator Norman Heglund is pacing steadily back and forth on a 10-foot-long platform. The plane is cruising at 30,000 feet or so over the Bay of Biscay, off Bordeaux, France. NASA has a similar plane called the Vomit Comet.

Abruptly, the Airbus starts to climb— so steeply that the horizon outside goes almost vertical. Normally at this point the pilot would jam the stick forward and throttle the engines way back, sending the plane over the top of its parabola and into a screaming dive. For 20 seconds or so, we would see Cavagna et al. floating around the padded compartment in zero gravity. This time, however, the pilot throttles back gravity to only 40 percent of its terrestrial value— to around what it is on Mars. Cavagna stays on his feet, but his pendulum starts swinging in long, slow, sloppy arcs. On the platform Heglund is now taking long, slow, floating steps. "You feel beautiful at .4 g," Cavagna says. "Walking on Mars would be great."

Walking on Earth, Cavagna says, is a bit of a struggle— and so is trying to understand the physics of it. Cavagna's Airbus experiments are but the latest in a long series; he has been studying our awkward form of locomotion for nearly 40 years. Very early on he figured out our basic strategy: To save energy, we walk like a pendulum. The problem is we do it badly.

A pendulum is a device that transforms kinetic energy of motion into gravitational potential energy and back. As it moves through the bottom of its arc, the pendulum's velocity and thus its kinetic energy— mass times velocity squared divided by two, or mv 2/2— reach a maximum. At the top of its arc, the pendulum slows to a stop, but at that point the potential energy— mass times gravity times height— is at its peak. As the pendulum falls back down, potential energy is converted back to kinetic energy. In a good pendulum the conversion is close to 100 percent, with only a bit of energy lost to the friction of moving through the air and that of the bearing from which it is hung. One nudge, and a pendulum keeps swinging a long time.

With each step you walk, you yourself become an inverted pendulum: You pivot around the foot that's on the ground, as if you were using that leg to pole-vault, and your center of mass, somewhere in the belly, describes an arc. As you plant a foot on the ground in front of you, the ground exerts a force back up your leg that slows you down, and you continue slowing as you rise up on that foot to the top of your arc. At that point your kinetic energy is at a minimum— but your potential energy is at a maximum. As you fall forward into the next step, that stored potential energy is converted back into kinetic energy, and you accelerate again.

"If the body were a perfect pendulum— if it could convert the kinetic energy into potential energy and back without wasting a calorie— walking would be nearly effortless," says Heglund, a physiologist at the University of Louvain in Belgium. "But you're only 65 percent of a perfect pendulum." In other words, 35 percent of the energy for each step has to be supplied afresh from the food you burn. Fish and birds do better: They burn less energy per unit distance than we do, even though birds are fighting gravity all the time, and fish have to fight their way through a dense liquid. "So why are we sweating? Where's the work?" asks Cavagna. "It's work we're doing against ourselves. It's a lack of coordination."

Somewhere in our legs, muscles are pulling against one another, wasting energy as heat. Even after four decades Cavagna is not sure where the waste happens— but he does know at what point in the stride. The tip-off came from some experiments that he, Heglund, and Heglund's Louvain colleague Patrick Willems did with women from Kenya.

Women of the Kikuyu and Luo tribes have a remarkable ability: They can carry on their head a basket of produce that weighs as much as 70 percent of their body. Heglund tried to match the feat, wearing a bicycle helmet filled with lead shot; he only got up to 15 percent of his body weight. "When that much weight gets out of balance, it feels like it's going to rip your head off," he explains.

The African women's most surprising prowess, though, is that they can carry as much as 20 percent of their weight with no extra effort— that is, without using more oxygen and burning more calories than when they carry nothing. Puzzled, the researchers had the women walk on a platform that records the forces exerted by the feet, and thus the kinetic and potential energy at each point of the stride.

There is one point, Cavagna's team found, at which load-bearing Kenyan women do far better than the rest of us. As we move through the top of one stride and start to fall into the next one, most of us pause imperceptibly for a few milliseconds: We're falling and losing potential energy, but we're not yet converting it to increased speed, because muscles in our leg are contracting and fighting the fall. The Kenyan women do the same thing when they're not carrying a load. But put a heavy weight on their head, and somehow they are able to shorten or even eliminate this pause— and thus to convert more of their potential energy into forward motion rather than muscle heat. With no visible change in their gait, their conversion rate rises from 65 percent to as much as 80 percent. In other words, they become better pendulums. Unfortunately, they have no idea how they do it.

For most people, the optimum walking speed— the speed at which our kinetic energy is in balance with our potential energy— is around 3 miles per hour. But short legs slow a walker down, and so does low gravity. On Mars, at .4g, you would glide along, lifting your legs more easily than you do on Earth and thus exerting less at any given speed. But you wouldn't be able to walk as fast because you would be falling much more slowly into each new step. On the moon, at around .17 g, in order for your kinetic energy to balance your minuscule potential energy, you would have to walk so slowly that you would hardly move forward at all. In 1969, when Neil Armstrong and Buzz Aldrin took their giant leaps for mankind, Cavagna wasn't at all surprised to see them bouncing (a kind of running) rather than walking. He had predicted as much in 1964.

The Airbus results teach one potentially useful lesson, Cavagna says: For a manned mission to Mars, spacecraft designers might consider pegging their artificial gravity not at 1 g but at the agreeable .4 g of their destination. Certainly they shouldn't choose 1.5 g's, which the Airbus pilot re-created for Cavagna's group by flying steeply banked circles. You walk faster in 1.5 g's, but you feel, well, surprisingly heavy. "You pick up your foot and start to fall forward, and you think you're going to fall on your nose," Heglund says. The video shows Cavagna jerking along like Charlie Chaplin and looking none too stable.

The next time Cavagna rides the Airbus, he plans to take 1.5 g's at a run; it will be like running with a backpack loaded with half his ample body weight. At age 67 and with a bad back, he is defying doctors to forbid him. "I'm not doing this because it's useful," Cavagna says. "I'm doing it because it's amusing."

For a discussion of earlier research on the walking of Kenyan women, see Biomechanics Watch by Carl Zimmer, in Discover's August 1995 issue; this article is available at www.discover.com.