First of all, one must understand that a bicycle is actually an “inverted pendulum” (think of a pendulum, such as one in a clock, except upside-down). In other words, a bicycle will surely fall to one side if it is not balanced. We know this from everyday experience.

So, why is countersteering necessary? The concepts lie in basic mechanics. When riding a bike, turning the front wheel in one direction causes the bike to lean in the opposite direction due to a centripetal force. Therefore, the initial countersteering will cause the bike to lean into the direction of the desired turn. This lean is necessary because when executing the actual turn, there is a centripetal force that acts outward on the bike, and the force of gravity acting on the inward-leaning bike will cancel the outward centripetal force to keep the bike upright during the turn. If there is no inward lean during a turn, then the outward centripetal force will knock the bike over and cause it to fall down to the ground, resulting in a poor cycling experience for both the rider and the bicycle.

Despite being a necessity, countersteering isn’t something that is explicitly taught to a beginning bicyclist. It is something natural that is picked up when one attempts a turn on a bicycle for the first time. This makes countersteering an interesting and subtle phenomenon in bicycle dynamics.

Countersteering is important in bicycle dynamics.

Wheel Imbalance Can Easily Be Detected When Driving on the Highway

Have you ever driven a car that vibrated uncontrollably at certain driving speeds, especially on the highway? If you have, you probably noticed that these large vibrations occur when you drive at one specific speed, as shown on your speedometer, and the vibrations die out when you travel a little lower or higher than that specific speed. Personally, I’ve driven a car that undergoes unusually large vibrations when I’m driving it at around 70 miles per hour. This phenomenon arises from an imbalanced rotor.

Rotors are objects that rotate, like wheels on a car. An imbalanced rotor is one whose center of mass is not in line with its axis of rotation. For a wheel, the axis of rotation would be the axle of the car. Ideally, if a wheel is perfectly circular and uniform, meaning its center of mass is exactly in the center of the wheel, and the axle for the wheel goes through the center of the wheel, then the wheel would be “balanced” because its center of mass and axis of rotation are in line (both at the center of the wheel). However, in the real world, these ideal cases are few and far between. Imbalances on a wheel, if they are drastic, can cause undesired vibrations.

Now, why does an imbalanced rotor tend to have large vibrations at certain speeds? The answer comes from the principles of resonance and resonant frequency. Every object has a resonant frequency at which the object experiences large vibrations or large-amplitude oscillations (resonance). Consider a small wine glass. If you drive the wine glass at its resonance frequency long enough (perhaps by directing sound waves at it), it will shatter due to the resulting resonance. Similarly, for an imbalanced rotor (such as a wheel), there are certain speeds of rotation (called “critical speeds”) that cause large-amplitude vibrations in the rotor (up-and-down and side-to-side). If one changes the speed of rotation away from this critical speed (either higher or lower), then the resonance will die out and the rotor will rotate more smoothly. Interestingly, at very high speeds, an imbalanced rotor will tend to balance itself out and rotate smoothly as if it was balanced to begin with.

When driving a car with imbalanced wheels at its critical speed, you might notice that the resonant vibrations feel uncomfortable to you, especially since you can feel the vibrations  from the steering wheel, which you are probably holding onto if you are moving on the road. Similarly, resonant vibrations are uncomfortable for your car as well (think of the wine glass analogy again). Prolonged periods of driving a car with an imbalanced wheel at its critical speed will subject the car to increased stress and cause it to wear out faster (and potentially break down as a whole due to failure under stress…just like people sometimes do). So, if you ever experience unusually large vibrations from your car when you are driving at particular speeds, you will know what the problem most likely is, and the strategic play would be to get the wheel imbalance fixed as soon as possible to avoid excessively damaging your car.