Sam Rentmeester/FMAX

How do bikes stay upright?

First of all, most people don't realize that bicycles can balance themselves. It's a miracle that bicycles can balance at all, but then there's this second miracle that they can balance by themselves. When you're riding, you think you're going in a straight line. But really you are falling to the right, steering to the right, falling to the left, steering to the left, and constantly making these corrections. The wheels have to be under the bike's center of mass to keep it upright. [But] if there's no person to do that steering, then it has to come from automatic effects. Our paper investigates what causes the bicycle to do this automatic steering.

What did scientists believe about bike self-stabilization up to this point?

There has been a mythology about what makes it. People have locked onto two ideas. One of them is the gyroscope effect and the other is the caster effect. What we've shown is that those two effects aren't actually necessary.

What are the gyro and caster effects?

The front wheel of the bicycle is spinning forward quickly, acting like a gyroscope. Then when you tip the bike to the right, the gyroscope applies the torque, which turns the handlebars to the right and causes the steering, bringing the wheels back under the bicycle and holding it up.

The [caster effect] is a self-aligning effect to keep the steering straight. Look at the bottom of your office chair. If you move your chair around, the wheels reorient themselves to follow the motion. This is because the wheel's ground contact point is behind the chair's steering axis; the wheel trails behind. The front wheel of the bicycle also touches the ground a little [behind] where the steering axis hits the ground. If the bicycle direction changes when it's going forward, the wheel will tend to follow and bring itself back under the rider.

Why did you question these long-held theories about what stabilizes bikes?

If you just solve these big, messy differential equations without thinking about them, they say a bicycle should be stable, but they don't tell you why. [Study co-author] Jim [Papadopoulos] had the idea to see how simple we could make the mathematical model of the bicycle. He started with a model that had 25 parameters and got it down to eight parameters, and that bicycle could still be stable. So about three years ago we convinced [study co-author] Arend Schwab and his students in the Netherlands to build a bike like that and see if it really worked. And it did.

Your group built a bike prototype that included a set of counter-spinning wheels (which canceled out the wheels' angular momentum, eliminating the gyro effect) and a point of ground contact in front of the steering axis (removing any caster effects). Since the bike could still stay upright on its own, this proved the two effects weren't necessary?

Yes. Jim proved it mathematically and then we put it in practice. If we push our self-stable bicycle straight, it goes straight, but it's really self-correcting and weaving back and forth like a regular bike. If it falls to the right, it steers to the right. It doesn't need gyro or caster.

But that doesn't mean that you should get rid of them on bicycles. Just because you can have a good meal without chocolate cake doesn't mean you shouldn't have chocolate cake.

Your experiments showed your bike can stay up without those two effects because its mass distributionhigh in front and low in backcauses the front to fall faster, pulling the wheels into falls and preventing the bike from completely falling over. But could this bike be adapted for riding?

Not the one we built; it's too weird. But we have a bunch of concepts. Once you say, Hey, a stable bicycle doesn't need gyro or caster, you can look around and try all kinds of different designs. What we're interested in now is finding what someone would like to ride.

Where else can this research be used?

The ideas of how bicycles balance, how people balance [on] bicycles and how people balance when they walk are all related. The action of steering right on a bicycle is almost mechanically identical to the action of stepping to the right when you're walking. If you're walking forward and someone on your left shoves you to the right, your next step is forward and to the right. You prevent falling to the right by stepping to the right. You have very good reflexes for that. When you step to the right, you're moving that support point to the right. The act of balance is the same for walking and biking; you're moving the support point back underneath the center of mass in the system.

Then there's this other thought: Maybe you don't learn to walk, but your skeleton is a machine and can balance by itself. So you have this bicycle, which is sort of a bunch of sticks and hinges that balances itself. Then you have the skeleton, which is a bunch of sticks and hinges that balances itself. And so this new idea is that rather than thinking of a person on a bicycle as a person on a machine, think of the person and the bicycle connected together as a bunch of sticks and hinges. It's a more complicated arrangement of sticks and hingessome of them are made out of metal, some of them are made out of calcium and fleshbut maybe you can write equations to show that [this] thing can balance by itself, too. With that idea, we've built some walking robots that balance themselves without computers.

What does this mean for the future of bikes?

People have been stuck in their ways about what bicycles look like and how they can work. We'd like to think that using our ideas, people might make better bicycles, and this certainly opens up the possibilities.

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