Be kind to your bicycle, for you may need it more than it needs you.

Once rolling, bicycles can cover ground just fine on their own—no rider required—thanks to a property known as self-stability. If a bicycle starts to tip over, its front wheel turns into the fall, bringing the bike back into balance, just as a rider would do if he or she were behind the handlebars. Of course, that stability is missing when the bicycle is stationary—bicycles have a limited range of self-stable velocities within which they are able to regain their balance even if knocked sideways [see first video below].


The question of how bicycles work—and what causes self-stability—has been around since the 19th century. Over the years, two main factors have emerged to explain a riderless bicycle's balancing act. One is the gyroscopic motion of the spinning front wheel; the other, a design feature known as trail, is the placement of the bicycle's steering axis so that the axis intersects the ground ahead of the point where the front wheel meets the ground. Both features act to couple the bicycle's steering to its leaning—if the bicycle tips rightward, it will steer to the right—allowing it to turn into a fall and remain upright.

But those two factors are not needed for a self-stable bicycle, as it turns out. In the April 15 issue of Science a team of researchers from the Netherlands and the U.S. describe an experimental bicycle that exhibits self-stability despite having neither trail nor a gyroscopic wheel. "Even though those two effects are important, they're not necessary," says study co-author Andy Ruina, a professor of mechanical engineering at Cornell University. "Just like chocolate cake is important to a nice birthday dinner, it isn't necessary."

The demonstration, Ruina and his colleagues say, shows that a number of parameters contribute to a bicycle's stability, and that more exotic bicycle designs than are typically considered might be surprisingly stable. And the finding serves to underline what complex machines bicycles really are, and how imperfect is the theoretical underpinning of their dynamics.

"Everybody can operate a bicycle, but very few can describe the operations," says study co-author Arend Schwab, a professor of mechanical engineering at the Delft University of Technology in the Netherlands.

"The bicycle has been a perplexing topic for the past century," says Richard Klein, an emeritus professor of mechanical engineering at the University of Illinois at Urbana–Champaign who did not contribute to the new study. "It has so many paradoxes and mysteries and challenges."

One of those challenges, explaining self-stability, even attracted the attention of famed German researchers Felix Klein and Arnold Sommerfeld in the early 20th century. Klein and Sommerfeld advanced the theory that angular momentum from the gyroscopic front wheel keeps the bicycle stable.

The importance of trail was elucidated by British chemist David Jones, who in 1970 recounted in Physics Today his efforts to construct an unrideable bicycle. In his experiments Jones discovered the importance of placing the steer axis so that it points ahead of where the front wheel touches the ground, and built a bicycle with its front wheel extended forward by four inches to demonstrate his finding. The bicycle "crashed gratifyingly to the ground when released at speed," Jones reported.

Schwab says that before undertaking this study, he would not have considered it possible for a bicycle without gyroscopic torque or trail to exhibit self-stability. "Not in a million years," he says. "Before I did this research I was in the group saying, it's the gyroscopic effects and the trail." But by examining the complex mathematical equations that describe a bicycle's motion, the researchers found another route to self-stability. The group designed and built a prototype bicycle (which with its tiny wheels and no place to sit actually resembles a child's scooter more than it does a bike) whose mass distribution causes it to steer toward its direction of tilt in just the right way to stabilize it.

The front of the bicycle, which includes the steering axis, has a lower center of mass in relation to the ground than its rear, so the front falls faster than the rear, much as an upright pencil falls faster than a longer broomstick does. The bicycle's front mass is concentrated forward of its steering axis, so when the bike's front end begins to fall, it turns the bicycle into the fall as needed to stabilize the entire assembly [see video below].


The researchers made sure that gyroscopic torque of the wheels was negated by placing a matching set of wheels on the bike that spin backward, canceling the forward-spinning wheels' angular momentum. And trail effects were eliminated simply by designing the experimental bike so that its steering axis meets the ground behind its front wheel's contact point.

Both of those factors are indeed major contributors to making a rolling bicycle self-stable, and once appeared to be necessary for a bicycle's self-correction. "There were people who said that each of them were essential," says Mont Hubbard, a professor of mechanical and aeronautical engineering at the University of California, Davis, who did not participate in the research. "And they're not."

"It would be very common to presume that if you don't have them you've got nothing," Klein says. "The bicycle won't stay upright."

The demonstration of self-stability without gyroscopic or trail effects does not mean that today's bicycles are somehow flawed. Bikes are highly evolved machines, improved by strategic, incremental advances—as well as trial and error—over the decades, so a new insight into stability is not likely to usurp well-established standards of bicycle design. "If you look at the bicycle they built, it's a bicycle, yes, but it doesn't bring us to any design suggestions about ways to build a bicycle better than the ones we have now, I don't think," Hubbard says.

And Klein, whose own research is focused on applications of bicycle technology, questions whether the findings will ever make an impact on real-life designs. "What they've done is a tremendous piece of work," he says. "If I were in an investor, would I put money in their company? No."

"We're not claiming that this crazy-looking machine is useful in itself," Ruina says. "It's just to prove a point." Still, mass distribution might play a role in designing better cycles outside the standard design realm, such as folding bikes or recumbent bikes. Small-wheel bikes, where gyroscopic torques are minimized, might be especially amenable to increased stabilization. "It gives you sort of a new way to think about what the design possibilities are," Ruina says. "The story is more complicated—there are other design parameters that have effects on stability."

But the long-standing question of what causes a riderless bicycle to balance itself has not been answered—at least not in a clean way. The researchers note that they have found no straightforward set of attributes that are necessary for self-stability.

For Schwab, after years of research and countless international Skype chats with his co-authors, simply adding a new facet to something most people take for granted is gratifying. "Every time I bring this subject up I have the same problem. Everybody shrugs their shoulders and says, 'We have bicycles, we know how to ride bicycles,'" he says. "I still have to fight that now: 'What's new about bicycles?'" Now, he says, he will have something to tell them.