Hardly anyone is unable to ride a bicycle and go for a ride. In fact, most people can do it even without using their hands. Yet this strange vehicle only rests on the ground at two points, which, at least in principle, would not be enough to keep its balance. What truth is there in the phrase “easier than riding a bike”?
For more than 150 years, physicists have been occupied solving the problem of the stability of the bicycle. Not even the makers of these contraptions have been able to explain exactly how their product works. For decades they have simply adjusted and improved their features through direct experimentation (the classic trick of “trial and error”), without using mathematical models that would help them design good bicycles. And all cyclists, in an act of faith, simply hop on and don't fall when riding.
The bicycle is probably the only vehicle we learn to ride as children and use for the rest of our lives. However, we rarely stop to think about the physical concepts related to it, even though at first glance it seems impossible for anyone to keep their balance on two wheels. In fact, unlike cars, a bicycle does not stay still without some kind of external support. Obviously, having only two points of contact with the ground does little to help it maintain balance. Yet any child can learn to ride a bike in a very short time. What is the secret?
A good clue is the fact that being in motion helps us not to fall. As you have probably noticed, if you stay still on the bicycle (at “zero kilometers per hour”), you quickly lean to one side or the other and fall. Moving the handlebars wildly or doing stunts with hands and feet does little good: unless you are a consummate tightrope walker, with a stationary bicycle you fall. On the contrary, when you move more or less quickly, keeping your balance is so easy that you can even ride with your hands in your pockets. Obviously, motion helps maintain balance. But... why?
When the bicycle moves forward, its wheels are turning. Obviously, that is the only difference between a stopped bike and one going at full speed. So, to solve our puzzle, we should focus on what happens when a body rotates. Although we don't need to know any physics to enjoy a bike ride, it seems this science is necessary to explain why we don't break a couple of bones doing it. Some of the physical concepts involved in such a simple machine are linear and angular velocities, forces, balance, weight, friction, lever, kinetic and potential gravitational energy, work and power.
In 2007, Arend Schwab, from the Delft University of Technology (Netherlands), published an article in Proceedings of the Royal Society explaining why we can ride a bicycle without breaking our face. His model takes into account no fewer than twenty-five factors that, together, are responsible for the stability and maneuverability of the vehicle. Arend's model can also explain how the bicycle changes its balance conditions at different speeds.
According to this model, a bicycle must travel at a speed between 14 and 20 kilometers per hour to be stable. If it were faster, it would oscillate less, but its tendency to tip over when the rider leans sideways increases. And if it were slower, it would simply fall almost as if it were stopped. Experimental data match the model's results.
One of the key factors for bicycle stability is the so-called “gyroscopic effect”. This can be tested by placing more weight (lead, for example) on the wheel rims. However, this effect is not the only one, since a hypothetical bicycle with massless wheels would still be stable. Nor is it true that bicycles with small wheels are unstable. Arend Schwab's model shows how a combination of forces guarantees the bicycle's stability. For example, it explains why when we want to change direction to the right we have to first turn the handlebars a little to the left, or why we fall if we go too close to the curb: we simply cannot move away from it without hitting it.
The larger the angle the fork forms forward, the more stable the bicycle will be when traveling in a straight line, but the harder it will be to change direction. Normal bicycles have the front wheel slightly displaced forward. This means that when you try to move the bicycle to one side, the wheel tries to turn in that same direction (you can check with a stationary bike: if you lean it, the wheel “falls” to that side). This fact is what makes it possible that, to make a turn, we only need to lean the bicycle slightly.
The bicycles used by circus acrobats have the front wheel installed almost (or completely) vertically. These bicycles don't have that “healthy tendency to turn” when they lean, and they are much harder to keep balanced. However, they allow some tricks that are impossible on a normal bicycle. That is why acrobats can, for example, turn the front wheel a full circle and keep riding normally.
Another important factor is “mass distribution”. If we move the bicycle's center of gravity forward, the vehicle becomes more stable. The cycling industry is very interested in Schwab's model, since it can predict whether a particular design will produce a more “nervous” or more stable bicycle. In bicycle design, three basic parameters are generally taken into account: overall geometry, distance between axles, and the angle of the fork relative to the frame.
The thing is, riding a bicycle is very easy. It's a very effective vehicle over short distances and also helps with the exercise so necessary in modern life. Let's keep enjoying our rides, and let the physicists try to explain why we don't fall.
