Rolling Resistance

A tire rolling at constant speed requires a driving force because the contact surfaces deform asymmetrically. The front section of the contact area experiences deformation that retards motion, while the rear section undergoes smaller restoration that pushes forward. This imbalance creates a net resistance, necessitating horizontal driving force applied to the tire's center to maintain equilibrium and constant velocity.

Rolling resistance is typically smaller than kinetic friction because the coefficient of rolling resistance multiplied by weight divided by radius is usually less than the coefficient of kinetic friction times weight. This means rolling frictional force is smaller than the sliding force experienced when a tire skids. Consequently, rolling resistance is generally less detrimental to vehicle performance than sliding friction.

Surface deformation creates rolling resistance through asymmetric pressure distribution at the contact area. As a cylinder or tire rolls, material in front deforms and slows motion, while material behind recovers and pushes forward. The deformation force consistently exceeds the restoration force, generating net resistance. This effect, combined with minor contributions from surface adhesion and micro-sliding, constitutes the primary mechanism of rolling resistance.

For constant-speed rolling, weight acts vertically downward, normal force acts upward, and a horizontal driving force must be applied to the tire's center. All forces must be concurrent at point A, the center of the contact area. The moment equilibrium condition at this point determines the required driving force in terms of the rolling resistance coefficient, ensuring balanced moments and sustained constant velocity.

The resultant normal force shifts forward because deformation and restoration forces act asymmetrically across the contact area. The deformation force at the front is larger than the restoration force at the rear, creating a net forward shift in the pressure distribution. This shift is represented by the resultant normal force acting at point A, which is the sum of these unequal opposing forces.

The driving force is determined using the moment equilibrium condition at the contact center point A. The driving force equals the weight multiplied by the coefficient of rolling resistance divided by the tire radius. This relationship shows that rolling resistance depends on both the load and material properties, with the coefficient of rolling resistance quantifying the resistance per unit weight and radius.

When a tire rolls on a deformable surface, the contact area experiences a finite zone of compression and recovery. The front section compresses and resists forward motion, while the rear section recovers and provides forward push. This creates a distribution of normal pressures across the contact zone, with the front pressures exceeding rear pressures, resulting in rolling resistance problem solving applications.