How Does a Bicycle Stay Upright? Gyroscopes, Trail and a Century of Wrong Answers
By the BrainSnail editorial team. How these articles are written and checked, and how to tell us when one is wrong.
Push a bicycle down a gentle slope with nobody on it and it will roll for a surprising distance without falling over, steering itself back under its own weight whenever it starts to lean. The machine is self-stabilising, which is why children can learn to ride it, and the explanation that appeared in textbooks for most of the twentieth century, that the spinning wheels act as gyroscopes, turned out on examination to be mostly wrong. The right answer was not settled until 2011, and it involves a bicycle with no gyroscopic effect at all that balanced anyway.
Balance is steering
A stationary bicycle falls over, and a moving one stays up for one reason: when it leans, it steers into the lean, and steering into the lean brings the wheels back under the centre of mass. A rider does this without knowing it, turning the bars a fraction towards whichever side the bike tips, so that the bike curves that way and the outward lean of the turn cancels the fall. The physics is the same as balancing a broom on a hand: the base is moved under the load. What makes a bicycle remarkable is that it does the steering by itself, without a rider, provided it is moving faster than a few kilometres an hour, and the question is what mechanism turns the front wheel into a lean.
The gyroscope, and why it is not enough
A spinning wheel resists having its axis tilted and responds to a tilt by turning at right angles to it, which is precession, and a leaning bicycle's front wheel does precess in the direction that steers into the lean. The effect is real and it helps, and from a 1910 analysis onward it was taught as the reason. It is not sufficient. In 1970 the chemist David Jones built a bicycle with a second front wheel, mounted beside the first and spun backwards to cancel the gyroscopic effect exactly, expecting it to be unrideable, and found it rode almost normally and still balanced when pushed riderless, though a little less well. The gyroscope contributes; something else is doing most of the work.
Trail
The something else is the geometry of the front fork. On every bicycle the steering axis is tilted back, and if it is extended down to the ground it hits the road a few centimetres in front of the point where the tyre touches. That distance is the trail, and it means the front wheel is dragged behind its steering axis like a castor on a shopping trolley. Two things follow. When the bike leans, the weight on the front wheel, acting behind the axis, turns the wheel into the lean, which is the steering the balance needs. And when the wheel is turned, the front of the bike drops slightly, so that gravity itself pulls the steering towards the lean. Trail, with the gyroscopic effect assisting, was the accepted explanation from the 1970s, and the story would have ended there had anyone checked the equations.
The bicycle that broke both rules
In 2011 a team in Delft and Cornell published the results of a decade of working through the full equations of motion of a bicycle, which have 25 parameters and had been derived incorrectly several times since 1899. The equations said that neither gyroscopic effect nor positive trail was necessary, and to prove it the team built a two-mass-skate bicycle: small wheels spun by counter-rotating twins to cancel any gyroscope, a steering axis tilted forward so that the trail was negative, and weights placed so that the front assembly's centre of mass sat ahead of the rear's. Pushed across a gym floor at a jog, it balanced itself and recovered from a sideways shove. The general principle, which the equations reveal and no single mechanism captures, is that a bicycle is stable if a lean causes the front to steer into it faster than the rear falls, and there are several ways to arrange that:
- •Gyroscopic precession of the front wheel, which steers into a lean and matters more at speed
- •Positive trail, which turns a castoring front wheel into a lean under the bike's weight
- •Mass distribution, with the front assembly's centre of mass forward and low so that it falls into the lean first
- •Speed: below a critical speed none of these acts fast enough and the bike falls, above a higher speed it becomes too stable to turn easily, and in between it is self-correcting
What the rider adds
A rider makes the machine stable at speeds where it would not be alone, by steering, and does so with an instinct so fast and unconscious that most riders describe the opposite of what they do. To turn left on a bicycle at speed, the rider first steers briefly right, which leans the bike left, and then steers into the lean; the move is called countersteering, motorcyclists are taught it explicitly, and cyclists do it without believing they do. The learning that takes a child a week is the learning of that reflex, and it is stored in a part of the brain that does not forget, which is why it is the thing one never forgets how to do. The mechanism that keeps the bike up, meanwhile, was designed by trial and error in the 1880s by makers who could not have said why their forks were raked, and their geometry is still what every bicycle uses.
The takeaway
A moving bicycle stays upright because a lean makes the front wheel steer into it, bringing the wheels back under the rider, and it does that by itself through the gyroscopic precession of the front wheel, the castoring effect of trail in the fork geometry, and the forward placement of the front assembly's mass, none of which is essential alone, as a 2011 bicycle with no gyroscope and negative trail proved by balancing anyway. A rider adds steering, including the countersteer that starts every turn.