Physics illustrates why a speeding bike can stay upright easier than one moving very slowly. (Bigstock)

When learning to ride a bicycle, one must accept on faith this astonishing fact: The faster a bicycle goes, the less likely it is to fall over.

It’s easy to see why this can strike terror in the hearts of small children being urged on by their parents. Slower is typically safer. Walk, don’t run, in a crowded hallway. Chew your food thoroughly rather than scarfing it down. Obey speed limits. (Imagine if new drivers were told, “Don’t worry; this is going to be a lot easier once you get to 70 miles per hour.”) Experienced bike riders have completely internalized the cycling reality of “speed equals stability.” But, come on, admit it: You have no idea why it’s true.

There’s no shame in your ignorance. More than 300 years after Isaac Newton worked out most of the laws that govern the behavior of medium-size objects (such as a bicycle), physicists still argue over exactly what makes a bicycle so stable.

Several phenomena combine to make a bicycle stand up at speed, but the first one isn’t so hard to understand. Bicycling isn’t fundamentally different from walking.

“As you walk, your brain decides where to put your foot down to correct for mistakes you made when you pushed off with your other foot,” says Hugh Hunt, a lecturer in engineering at the University of Cambridge. “If you walk very slowly, those corrections don’t come in time, and you can wobble or fall.”

“When you ride a bicycle,” Hunt continues, “your brain is making the same calculations. If you begin to lean to the right, let’s say, you steer in that direction to put the wheels back beneath you aided by the centrifugal effect of steering in an arc. When you’re going fast, small steering movements will make that correction. At slow speeds, the steering changes must be more dramatic.”

Simple enough, but it goes only part of the way toward an explanation, because a bicycle’s stability isn’t entirely dependent on the rider. After all, if you push a riderless bicycle straight ahead, it will stay upright for some time before slowing and toppling over. Clearly, a moving bicycle has some inherent stability, independent of human steering.

There are two explanations for this stability. The more obvious but less important is the gyroscopic effect. It takes more force to push over a spinning object than a stationary one; anyone who has seen a spinning top can attest to this. The phenomenon has countless practical applications. Gyroscopes keep pilots informed of a plane’s orientation, and NASA is experimenting with spacesuits that use the gyroscopic effect to mimic the effects of Earth’s gravity, making space feel more Earthlike to astronauts.

On a riderless bike, the gyroscopic effect of the spinning wheel is significant. But put a 200-pound rider tilting this way and that on the bike, and that stabilizing effect is relatively small.

The more significant explanation is that a riderless bicycle steers itself, in a way, because of a largely unnoticed element of bicycle geometry called the trail.

“If you were to draw a straight line from the center of a bicycle’s handlebars through the hub of the front wheel,” notes Hunt, “it would intersect the ground a few inches ahead of the point where the front tire touches the pavement. The distance between those two points is the trail.”

Here’s why the trail is important: The line that Hunt is referring to, between the center of the handlebars and the hub, is the axis around which the front wheel turns during steering. When a riderless bicycle begins to fall over, the front wheel tilts and the ground essentially pushes against the side of the tire. Because of the trail, that push happens at a point away from the steering axis, and that turns the wheel into the direction of the fall — just as a rider would do.

If there were no trail, that push from the ground could not turn the wheel. In order to turn an object, you can’t push right at the axis around which it turns, but only at some point a bit away from it. A good example is a revolving door. The axis sits at the center, where the glass door panels that make up the unit meet. If you push against the axis, the revolving door won’t turn. You have to push against the doors themselves, several inches away from the axis, to get the doors to turn so you can walk through.

The trail has other important effects. The brain seems to have an easier time steering a bicycle when the cyclist leans one way or the other to change course. Lean left to go left, lean right to go right. Riding a bicycle with no trail requires the cyclist to control all movements through assiduous steering with minimal leaning, and those who have tried it say it’s a major challenge.

None of this will convince crying children to pedal faster, of course. Just tell them they’ll understand when they’re older.