|MLA Citation:||Bloomfield, Louis A. "Bicycles Home Page" How Everything Works 22 Jul 2018. 22 Jul 2018 <http://www.howeverythingworks.org/prints.php?topic=bicycles&page=0>.|
At rest, the bicycle is unstable because it has no base of support. A base of support is the polygon formed by an object's contact points with the ground. For example, a table has a square or rectangular base of support defined by its four legs as they touch the floor. As long as an object's center of gravity (the effective location of its weight) is above this base of support, the object is statically stable. That stability has to do with the object's increasing potential (stored) energy as it tips-tipping a statically stable object raises its center of gravity and gravitational potential energy, so that it naturally accelerates back toward its upright position. Since a bicycle has only two contact points with the ground, the base of support is a line segment and the bicycle can't have static stability.
But when the bicycle is heading forward, it automatically steers its wheels underneath its center of gravity. Just as you can balance a broom on you hand if you keep moving your hand under the broom's center of gravity, a bicycle can balance if it keeps moving its wheels under its center of gravity. This automatic steering has to do with two effects: gyroscopic precession and bending of the bicycle about its steering axis.
In the gyroscopic precession steering, the spinning wheel behaves as a gyroscope. It has angular momentum, a conserved quantity of motion associated with spinning, and this angular momentum points toward the left (a convention that you can understand by pointing the curved fingers of your right hand around in the direction of the tire's motion; your thumb will then point to the left). When the bicycle begins to lean to one side, for example to the left, the ground begins to twist the front wheel. Since the ground pushes upward on the bottom of that wheel, it tends to twist the wheel counter-clockwise according to the rider. This twist or torque points toward the rear of the bicycle (again, when the fingers of your right hand arc around counterclockwise, your thumb will point toward the rear). When a rearward torque is exerted on an object with a leftward angular momentum, that angular momentum drifts toward the left-rear. In this case, the bicycle wheel steers toward the left. While I know that this argument is difficult to follow, since angular effects like precession challenge even first-year physics graduate students, but the basic result is simple: the forward moving bicycle steers in the direction that it leans and naturally drives under its own center of gravity. You can see this effect by rolling a coin forward on a hard surface: it will automatically balance itself by driving under its center of gravity.
In the bending effect, the leaning bicycle flexes about its steering axis. If you tip a stationary bicycle to the left, you see this effect: the bicycle will steer toward the left. That steering is the result of the bicycle's natural tendency to lower its gravitational potential energy by any means possible. Bending is one such means. Again, the bicycle steers so as to drive under its own center of gravity.
These two automatic steering effects work together to make a forward moving bicycle surprisingly stable. Children's bicycles are designed to be especially stable in motion (for obvious reasons) and one consequence is that children quickly discover that they can ride without hands. Adult bicycles are made less stable because excessive stability makes it hard to steer the bicycle.
To reduce the upward acceleration that the rider experiences, the direct connection between the bicycle wheels and the frame can be replaced by a spring suspension. When the wheel of a bicycle with a spring suspension encounters a bump, the springs compress and the force on the frame and rider is much smaller. The rider still accelerates upward, but not as rapidly as the wheel and without the abrupt jolt of a suspensionless bicycle. In fact, by the time the rider has begun to rise much, the wheel will probably have rolled back off the bump and the spring will return to its original shape. Overall, the rider will barely move at all and will hardly notice the bump.
But a spring suspension isn't perfect by itself. Suppose that the bicycle rolled over a curb and onto a sidewalk. This bump doesn't end—the pavement level rises permanently. When the wheel hits the curb, it rises suddenly and compresses the spring. But since the wheel never drops back to its original height, the only way for the spring to decompress back to its original shape is for the frame and rider to rise. And that's what happens. But the frame and rider don't stop moving once the spring has reached its original shape. They have upward momentum and they continuing rising. The spring begins to stretch upward now. Eventually the frame and rider stop rising and begin to descend again, but they continue to bounce up and down as though they were on a pogo stick. In effect, they are on a pogo stick. When a spring is compressed or stretch, it stores energy. If there is nothing to get rid of the energy stored in the bicycle's compressed or stretched spring, the frame and rider will continue to bounce up and down indefinitely.
To stop the bouncing (and prevent most of it in the first place), a bicycle with a spring suspension also has shock absorbers. These devices waste energy whenever the wheel and frame move relative to one another. Whether the spring is compressing or stretching, the shock absorber extracts energy from the wheel, frame, and spring, and turns that energy into thermal energy. As a result, the frame and rider don't bounce significantly after the wheel rides up and onto the curb. Similar issues occur in cars, where shock absorbers damp out the bouncing that can occur because the car body is suspended above the wheels on springs.
In the other drive systems, there is no possibility of slippage so that any power loss that occurs must be due to internal sliding friction within the components, or from vibrations. Flexing a chain involves some internal sliding friction and wastes some power. I suppose this could be minimized with careful chain construction and I wouldn't be surprised if large change drive systems placed bearings in the chain links to eliminate sliding friction altogether. Flexing a rubber-cogged belt also involves some molecular friction within the belt material so it wastes some power. I'm not sure which system is more efficient, the chain drive or the cogged belt drive. Finally, the gear drive is the least likely to waste significant energy. The only sliding friction that occurs is between the gear teeth. If the teeth are designed well and cut carefully, they should slide very little. In that case, the only significant power loss would be through vibrations. If everything is carefully mounted to prevent vibrations, there should be very little power loss in a gear drive.
For the motorbike to remain upright, you must keep the overall center of gravity (yours and the motorbike's) directly above the wheels (actually the line formed by their contact points on the ground). That's very hard to do when the motorbike is stationary. But when the motorbike is heading forward, it naturally steers itself under the center of gravity. If the motorbike begins to tip to one side, its front wheel automatically steers in the direction of the tip and the forward moving motorbike soon drives its wheels back under the center of gravity. This automatic steering is due to both gyroscopic precession in its spinning front wheel and to the shape and angle of the front wheel fork. If you hold the motorbike (or a bicycle) off the ground, spin its front wheel the right direction, and then tip the motorbike, you'll see its wheel turn toward the direction of the tip because of gyroscopic precession. If you return the motorbike to the ground and then tip it to one side, you'll see that its wheel will automatically turn toward that side because of the fork shape.
With both effects helping the motorbike steer under the center of gravity, the moving motorbike is very stable. A physicist would say that it is dynamically stable. Everything I've said also applies to bicycles and was pointed out by British physicist David Jones in 1970. Bicycles are so dynamically stable that almost anyone can ride them without hands and not tip over!
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