Why is a moving bicycle more stable?

MYSTERY

Sep 20, 2010

Reader Brian writes in to ask "Why can you stay on a bicycle when moving, but not when it's standing still?"

Think of something like a table or a couch. It has four legs that touch the floor and form a base of support (a polygon formed by an object's contact points with the ground) and as long as the table or couch's center of gravity (the mean location of the gravitational force acting on an object, or the effective point at which gravity acts) is above this base of support, it'll be statically stable, or stable when at rest.

A bicycle, on the other hand, is statically unstable because it only has two contact points with the ground (whatever portion of the front and back wheels happen to be touching the ground) and its base of support is a line segment. A good base of support needs at least three contact points with the ground, so bikes are hard to keep upright when they're still. Bikes are, however, dynamically stable, or stable when moving forward, because steering allows a rider to move the bike's points of support around under the center of gravity and keep it balanced, often with steering adjustments small enough that the rider may not even realize they're making them. It's sort of like standing on one foot. If you don't hop around a little, and you start falling sideways, you can't recover and you fall over. If you do hop, though, you can move your foot around to keep your center of gravity above it and keep your balance.

A bike has two features that help this dynamic stability immensely: its wheels. Spinning wheels have angular momentum, and when you're sitting on a bike, you and it and its wheels make up a system that obeys the principle of conservation of angular momentum. Unless torque, or twisting force, is applied from outside the system to change the wheels' angular momentum, that momentum and the direction of the momentum remain constant. In a nutshell, once the wheels line up a certain way, they want to stay lined up like that. It's easy for you to move them, but hard for an outside force to do the same, and so the bike is easy to keep balanced but doesn't topple easily. A non-moving bike has wheels that aren't spinning and zero angular momentum, which makes it very easy for external torque to change the wheels' direction, making the bike harder to balance.

Even when staying relatively motionless, though, a rider can balance a bike with some effort. By steering the front wheel to one side or the other and moving forward and backward slightly, a rider can keep the line between the bike's two contact points with the ground under the bike and rider's combined center of gravity. You can see this physics lesson in action whenever a cyclist is stopped at a red light.
(Image at left from Wikipedia user AndrewDressel.)

That was a short and sweet way to answer Brian's direct question, but there's a lot more to bicycle physics. If you're so inclined, Wikipedia's page on bicycle and motorcycle dynamics is a good starting point to learn about some of the other internal and external forces, motions and dynamics that are involved in a simple bike ride.

by Bill Steele

The 1949 movie "Jour de Fete" shows a postman frantically chasing his bicycle, which rides away on its own. It could happen. Many bicycles, even without a rider, naturally resist tipping over if they are going fast enough.

Almost any bicycle will keep itself upright as long as it's rolling. Mathematical analysis shows that long-accepted explanations are incomplete. See larger image

Scientists and engineers have been trying to explain bicycle self-stability since the 19th century. Now, a new analysis says the commonly accepted explanations are at least partly wrong.

The accepted view: Bicycles are stable because of the gyroscopic effect of the spinning front wheel or because the front wheel "trails" behind the steering axis, or both.

If you try to tilt the axis of a gyroscope in one direction, it will turn in a different direction. When a bike leans, the gyroscopic effect tends to steer the handlebars in the direction of the lean, bringing the wheels back under the bicycle and helping to keep it upright.

Meanwhile, if the front wheel touches the ground behind the steering axis, it will be pulled into alignment with the direction of travel, just as a wheel on a shopping cart turns to follow whichever way you push the cart. This "trail" gives the force of the ground on the front wheel a lever arm to cause steering in a way that can help restore balance.

While gyro and trail effects may contribute to self-stability, they are not the only causes, report Andy Ruina, professor of mechanics at Cornell, and colleagues in the Netherlands and at the University of Wisconsin. To prove it, they built a bicycle without any gyro or trail effects that can still balance itself. Their results were published in the April 15 issue of the journal Science.

An experimental bicycle designed to eliminate the gyroscopic effect of spinning wheels and the "trail" of the front wheel is still stable on its own, disproving conventional theory. See larger image

Using a mathematical analysis that shows how various values for the masses and their position produce stability or instability, the researchers determined that neither gyro nor trail effects are needed for self-stability.

They built a bicycle with two small wheels, each matched with a counter-rotating disk to eliminate the gyro effects, and with the steering axis located behind the front wheel's point of contact, giving the machine a slightly negative trail.

When given a good push, the experimental bike still coasts and balances successfully if it is going fast enough (more than about 5 mph). If you knock it to one side while it's moving, it straightens itself back upright. Like a human rider, the riderless bike turns the handlebars in the direction of a fall, even when gyroscopic and trail effects are eliminated.

The cause is that the center of mass of the front steering assembly of the test bike is lower than that of the rear frame and forward of the steering axis, the researchers explained. In a fall the front tends to fall faster, and this causes it to turn in the direction of the fall.

A bicycle can be modeled mathematically as three masses, each centered on one of the black and white circles. New research shows that the placement of these centers-of-mass is an important part of what makes a bike stable or unstable. See larger image

"There are other ways to distribute the mass and get self-stability without gyro or trail," Ruina notes.

"We have found that almost any self-stable bicycle can be made unstable by mis-adjusting only the trail, only the front-wheel gyro or only the front-assembly center-of-mass position," the researchers said in their paper. "Conversely, many unstable bicycles can be made stable by appropriately adjusting any one of these three design variables."

While their work was intended to gain insight into the nature of bicycle balance, the researchers said, their analysis could lead to further improvements in bicycle design. "The evolutionary process that has led to common present bicycle designs might not yet have explored potentially useful regions in design space," they concluded.