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The Physics of Winter Biking

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Bibliography 		There's several things to consider when selecting the appropriate size of wheel for your bicycle. Spinning objects have a property called the moment of inertia, I, that represents its rotational inertia, or how hard it is to start or stop moving. For most objects the moment of inertia is a value that is roughly proportionate to MR2, where M is the object's mass and R is its spinning radius. Thereby, a larger size wheel will have a greater moment of inertia, meaning you have to apply more torque, and thereby more force to it in order to achieve the same angular acceleration. However, it will also retain its angular velocity better than a smaller size wheel, since a greater external force would also be required to slow it down. Traveling up a hill, a larger wheeled bicicly would accelerate more slowly than a smaller one, but it would be more likely to retain that speed. This could be very efficient in the summer, but in the winter snow is always ready to provide additional friction to slow down your cycling.

There are certainly more factors to be considered, however. The idea of moment of inertia assumes a rigid, spinning object, but a tire on the ground does compress when under the weight it supports. This results in a flat part of the wheel, that is touching the ground at any time, often called the tire's "footprint." A larger wheel will have a slower curvature, and thereby a larger footprint. Although we know that the net force of friction is not affected by the contact area, this does still have positive affects for winter biking. For one thing, A larger footprint decreases the likelyhood that the entire contact patch will be on top of an icy patch with less friction. Also, although the net force of friction remains the same, a larger contact patch means that each part of the tire is experiencing less stress to attain that force, meaning that tread and studs will last longer. So although this does not allow you to bike any faster, larger wheels will survive better over extended use.


The force of the wheel pushing back is greater than that of pushing forward. 		Another effect of the larger wheels, however, is the lesser known rolling resistance. As you read above, the tire on the wheel will give under pressure. This can be described as a spring. At the front of the contact patch, when the tire rolls onto the ground and compresses, it pushes forward with a spring force and converts some kinetic energy into potential energy of the spring. At the back end of the footprint, the opposite happens, and the spring of the tire pushes forward, changing the potential energy back into kinetic. In an ideal system, the forces of the spring pushing forward and pulling back would be the same, but in reality, when the energy is converted, some of it is lost to heat, so the rubber at the back of the contact patch does not push forward as hard as the rubber at the front pushes back. This results in a net force opposing the rolling motion, at the bottom of the wheel. The magnitude of the force of rolling resistance is calculated as the magnitude of the normal force times a coefficient of rolling resistance, where the coefficient is calculated as the square root of the sinkage depth (the amount of tire that gives) over the diameter of the rigid wheel. Thereby, a smaller wheel will have a greater rolling resistance.


With these effects considered, most cyclists recommend a larger wheel size.