Name: tire deformation and rolling resistance
Uploaded: 2023-09-22T11:49:30.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Rolling Resistance

Consider a tire rolling at a constant speed. Forces acting on it are its weight and the normal force.
The contact surfaces deform, creating a finite contact area. This results in a distribution of normal forces at each contact point.
The front section of this area experiences deformation, which retards the rolling motion.
In contrast, the rear section undergoes a relatively smaller restoration that pushes the tire forward.
The resultant normal force acting at A is the sum of these forces.
To keep the tire rolling at a constant speed and balance the moment of the weight about A, a horizontal driving force must be applied to the center of the tire. Here all the forces must be concurrent.
The moment equilibrium condition at point A gives the driving force in terms of the coefficient of rolling resistance.
The weight multiplied by the coefficient of rolling resistance upon the radius is usually smaller than the coefficient of kinetic friction times the weight.
So, the rolling frictional force is smaller than the sliding force.

rolling resistance

When a solid cylinder rolls steadily on a rigid surface, the normal force applied by the surface on the cylinder is perpendicular to the tangent at the contact point. However, since no materials are entirely rigid, the surface's reaction to the cylinder involves a range of normal pressures.
For instance, imagine a hard cylinder rolling on a comparatively soft surface. The cylinder's weight compresses the surface beneath it. As the cylinder moves, the material in front of it slows down due to deformation while the material behind it recovers from its deformed state, pushing the cylinder forward. The normal pressures acting on the cylinder in this way are depicted by their resulting forces, Nd and Nr. The deformation force (Nd) and its horizontal component are consistently larger than the restoration force (Nr), necessitating a horizontal driving force to be exerted on the cylinder to maintain its motion.
Rolling resistance primarily occurs due to this effect, although it is also influenced, to a lesser extent, by surface adhesion and relative micro-sliding between the contact surfaces.
To further explain this concept, consider a tire rolling at a constant speed. The main forces acting on it are its weight, acting vertically downward, and the normal force exerted by the ground, acting vertically upward. As the tire rolls, the front section of the contact area experiences deformation, which retards the rolling motion of the tire. In contrast, the rear section undergoes a relatively smaller restoration that pushes the tire forward. The net effect is that the resultant normal force acting at point A (the center of the contact area) is the sum of these opposing forces.
<img alt="Static equilibrium diagram illustrating forces on a wheel, including ΣF=0, torque components." src="/files/ftp_upload/14328/14328_Figure_1v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1761830439000" data-alt="Figure 1">
To keep the tire rolling at a constant speed and balance the moment of the weight about point A, a horizontal driving force (F) must be applied to the center of the tire. For equilibrium, all the forces acting on the tire must be concurrent. Using the moment equilibrium condition at point A, we can determine the driving force needed to maintain constant speed in terms of the rolling resistance coefficient (a).
<img alt="Static equilibrium formula F≈Wa/r, related to balance and load distribution." src="/files/ftp_upload/14328/14328_Equation_1v2.svg" style="text-align: center; height: 28px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
This driving force is usually smaller than the product of the coefficient of kinetic friction and the tire's weight.
<img alt="static equilibrium inequality, Wa/r &lt; μkW, formula, frictional force analysis" src="/files/ftp_upload/14328/14328_Equation_2v2.svg" style="text-align: center; height: 28px;" data-altupdatedat="1761830439000" data-alt="Equation 2">
This relation implies that the rolling frictional force is typically smaller than the sliding force experienced when a tire skids over a surface. As a result, rolling resistance is generally less detrimental to a vehicle's performance than sliding friction.

When a solid cylinder rolls steadily on a rigid surface, the normal force applied by the surface on the cylinder is perpendicular to the tangent at the ...

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Mechanical Engineering

Unit 1

Friction

KEY TERMS AND CONCEPTS

tire deformation and rolling resistance

Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force.

A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact area slows because it is being deformed. The material behind the cylinder begins to recover, and that recovery pushes the cylinder forward.

These effects are often shown as two resultants, N d for the deformation force and N r for the restoration force. The deformation force and its horizontal component are larger than the restoration force. Because of that imbalance, a horizontal driving force must be applied to keep the cylinder moving.

The same idea applies to a tire rolling at constant speed. Its weight acts downward, and the ground provides an upward normal force. The front of the contact patch deforms and slows the tire, while the rear part restores more weakly and pushes it forward. The resultant normal force at point A is the sum of these opposing effects.

To keep the tire in equilibrium and maintain constant speed, a horizontal driving force F must act at the center of the tire. Using moment equilibrium about point A, the needed driving force can be written in terms of the rolling resistance coefficient a. This force is usually smaller than the force from kinetic friction, so rolling resistance is less harmful than sliding when a tire skids.

Rolling resistance is mainly caused by surface deformation, but adhesion and small-scale sliding between surfaces can also play a smaller role. These effects help explain why rolling wheels still lose some energy even when they do not appear to slip.

Tire Deformation and Rolling Resistance

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Tire deformation and rolling resistance explain why a rolling wheel still needs a driving force. When a solid cylinder or tire rolls on a rigid surface, the normal force is perpendicular to the surface at the contact point. But real materials are not perfectly rigid, so the surface pushes back with a spread of normal pressures instead of one single force. A hard cylinder on a softer surface compresses the material under it. As the cylinder moves forward, the material in front of the contact...

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Learn how tire deformation creates rolling resistance, why a driving force is needed, and how it compares with sliding friction in moving wheels.

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Tire Deformation and Rolling Resistance

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