What keeps a bicycle balanced?
Category: Physics Published: April 18, 2013
At first thought, you may think that the human rider is what keeps a bicycle balanced. This ends up not being completely true. If launched properly, a modern bike with no rider balances itself just fine and continues on its path as if a rider were guiding it. This can be easily verified by anyone with a bike, and can make for amusing scenarios such as in this video. Up until a few decades ago, scientists thought a bicycle is self-balancing when in motion because of gyroscopic effects and caster effects alone. "Gyroscopic effect" means that a spinning wheel tends to stay aligned in its original direction. This effect is used in mechanical navigation gyroscopes to maintain a proper sense of direction as a vehicle travels about. The gyroscopic effect is a direct result of the conservation of angular momentum, or spinning motion. In the absence of an external force, the total angular momentum of a system must retain the same strength and orientation. As a result, a small force does little to make a fast-spinning heavy wheel tilt away from its original orientation. Some physicists thought that the spinning wheels of a bicycle create enough angular momentum to resist the tilting that occurs when a bike falls over. Bike designers understood the full physics of bicycles (they have to in order to properly design and optimize bikes), but had a hard time distilling down the huge equations into simple understandable concepts such "gyroscopic effect". Experiments in the last few decades have made more sense of the underlying equations and demonstrate that even if the angular momentum of the wheels is canceled out, the bike is still self-balancing. The angular momentum of a the wheels can be canceled out by adding two more wheels that spin in the opposite direction as the original wheels, and are configured to not touch the ground.
Additionally, some people thought that the caster effect contributes to a bike's self-balancing nature. The caster effect describes what happens when a wheel has its contact point with the ground located at a different point from its steering axis. As the steering axis moves forward, such a wheel's contact point lags behind and the wheel become naturally aligned with the direction of motion. Caster wheels are used on the bottom of office chairs and shopping carts. If you push your office chair in one direction, the wheels naturally line up due to the caster effect. It was thought that having the bicycle's steering axis behind the wheel's contact point with the ground created a reverse caster effect where the bike lines up behind the front wheel and this is what keeps a bicycle upright. While gyroscopic effects and caster effects can contribute to self-balancing, they are not the main effects.
Despite the long-held notions by some that gyroscopic and caster effects are what keep a bike balanced, recent demonstrations have shown clearer than ever that neither is necessary for a self-balancing bike. While gyroscopic and caster effects may contribute to balancing the bicycle, they are not the root cause. J. D. G. Kooijman and his collaborators confirmed that the root cause is a front-loaded steering geometry. A front-loaded steering geometry means that the steering shape of the front wheel and frame on a bicycle is constructed such that the front of the bike falls faster than the back. If the bike starts to tilt to the left after hitting a bump and succumbing to gravity, the front wheel falls to the left faster than the rest of the bike. As a result, the bike turns left. The amazing part is that turning the front wheel to the left causes the momentum of the bike to snap to the right because of centrifugal force (just like you are thrown to the right side of your car when making a quick left turn). The right lurch of the bike compensates for the initial fall to the left and the bike ends up straight again. The fall becomes self-correcting because of the front-loaded steering geometry. (By the way, the centrifugal force is indeed very real in a non-inertial frame, and is not imaginary or fictional.) A riderless bike is not really traveling in a perfectly straight line in a perfectly upright position. It is constantly falling to one side or the other and then lurching back to an upright position under its own momentum. To more effectively demonstrate this concept, which has been known for decades or longer, Kooijman's group built a riderless, gyroscopic-less, caster-less, self-balancing bicycle with front-loaded steering geometry. You can see the results for yourself.