Mr. Squirrel
10-30-2009, 02:10 PM
when targeting....i mean, watching people ride bikes, we have to understand how it works to determine the best trajectory....i mean line of sight to "watch" you ride by (he he he). a bicycle is a dynamically stable object. although the bicycle is unstable at rest (statically unstable), it is wonderfully stable when moving forward (dynamically stable). to understand this distinction, let's start with the bicycle motionless and then start moving forward.
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 squirrel has a square or rectangular base of support defined by its four legs as they touch the ground. as long as an object's center of gravity (the effective location of its weight) is above this base of support, the squirrel is statically stable. that stability has to do with the squirrel's increasing potential (stored) energy as it tips-tipping a statically stable squirrel 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. oh yes...wheeeeels. just as you can balance a squirrel on your hand if you keep moving your hand under the squirrel's center of gravity, a bicycle can balance if it keeps moving its wheels (yes...wheeeeeels) 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 paw 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.
now, when it comes to wheels.....ah wheeeeels. there are many different ways to spoke a bicycle wheel. most bicycles have tangential spokes, meaning that the spokes do not connect from the hub to the rim in a straight line, but at an angle. there are many different patterns of tangential spokes. occasionally bicycles will have completely radial spokes. these spokes go straight from the hub to the rim of the wheel. wheels typically have tangential spokes. the way in which the wheels are spoked determines how they will perform.
you can spoke the front wheel completely radially, but the rear wheel had better not be spoked radially. there is no way to convey the twist of the wheel out to the rim to drive you forward. tangential spoking helps transmit the torque from the hub out to the tires.
not only would a radially spoked rear wheel be less efficient than one spoked tangentially--it would be significantly weaker. a bicycle wheel needs to be able to handle a variety of forces. besides holding up the weight of the cyclist, a wheel must withstand the forces of pedaling and braking and the jarring effects of the road surface. and, most importantly to squirrels....not. the benefit of radial spoking has to do with the stiffness of the wheel (less deformation makes the wheel slightly more efficient).
bottom line, know thy enemy. by the way, where do you ride?
mr. squirrel
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 squirrel has a square or rectangular base of support defined by its four legs as they touch the ground. as long as an object's center of gravity (the effective location of its weight) is above this base of support, the squirrel is statically stable. that stability has to do with the squirrel's increasing potential (stored) energy as it tips-tipping a statically stable squirrel 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. oh yes...wheeeeels. just as you can balance a squirrel on your hand if you keep moving your hand under the squirrel's center of gravity, a bicycle can balance if it keeps moving its wheels (yes...wheeeeeels) 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 paw 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.
now, when it comes to wheels.....ah wheeeeels. there are many different ways to spoke a bicycle wheel. most bicycles have tangential spokes, meaning that the spokes do not connect from the hub to the rim in a straight line, but at an angle. there are many different patterns of tangential spokes. occasionally bicycles will have completely radial spokes. these spokes go straight from the hub to the rim of the wheel. wheels typically have tangential spokes. the way in which the wheels are spoked determines how they will perform.
you can spoke the front wheel completely radially, but the rear wheel had better not be spoked radially. there is no way to convey the twist of the wheel out to the rim to drive you forward. tangential spoking helps transmit the torque from the hub out to the tires.
not only would a radially spoked rear wheel be less efficient than one spoked tangentially--it would be significantly weaker. a bicycle wheel needs to be able to handle a variety of forces. besides holding up the weight of the cyclist, a wheel must withstand the forces of pedaling and braking and the jarring effects of the road surface. and, most importantly to squirrels....not. the benefit of radial spoking has to do with the stiffness of the wheel (less deformation makes the wheel slightly more efficient).
bottom line, know thy enemy. by the way, where do you ride?
mr. squirrel