Rolling resistance

Primary cause

A characteristic of a deformable material such that the energy of deformation is greater than the energy of recovery. The rubber compound in a tire exhibits hysteresis. As the tire rotates under the weight of the vehicle, it experiences repeated cycles of deformation and recovery, and it dissipates the hysteresis energy loss as heat. Hysteresis is the main cause of energy loss associated with rolling resistance and is attributed to the viscoelastic characteristics of the rubber.
This main principle is illustrated in the figure of the rolling cylinders. If two equal cylinders are pressed together then the contact surface is flat. In the absence of surface friction, contact stresses are normal to the contact surface. Consider a particle that enters the contact area at the right side, travels through the contact patch and leaves at the left side. Initially its vertical deformation is increasing, which is resisted by the hysteresis effect. Therefore, an additional pressure is generated to avoid interpenetration of the two surfaces. Later its vertical deformation is decreasing. This is again resisted by the hysteresis effect. In this case this decreases the pressure that is needed to keep the two bodies separate.
The resulting pressure distribution is asymmetrical and is shifted to the right. The line of action of the vertical force no longer passes through the centers of the cylinders. This means that a moment occurs that tends to retard the rolling motion.
Materials that have a large hysteresis effect, such as rubber, which bounce back slowly, exhibit more rolling resistance than materials with a small hysteresis effect that bounce back more quickly and more completely, such as steel or silica. Low rolling resistance tires typically incorporate silica in place of carbon black in their tread compounds to reduce low-frequency hysteresis without compromising traction. Note that railroads also have hysteresis in the roadbed structure.

Definitions

In the broad sense, specific "rolling resistance" is the force per unit vehicle weight required to move the vehicle on level ground at a constant slow speed where aerodynamic drag is insignificant and also where there are no traction forces or brakes applied. In other words, the vehicle would be coasting if it were not for the force to maintain constant speed. This broad sense includes wheel bearing resistance, the energy dissipated by vibration and oscillation of both the roadbed and the vehicle, and sliding of the wheel on the roadbed surface.
But there is an even broader sense that would include energy wasted by wheel slippage due to the [|torque applied from the engine]. This includes the increased power required due to the increased velocity of the wheels where the tangential velocity of the driving wheel becomes greater than the vehicle speed due to slippage. Since power is equal to force times velocity and the wheel velocity has increased, the power required has increased accordingly.
The pure "rolling resistance" for a train is that which happens due to deformation and possible minor sliding at the wheel-road contact. For a rubber tire, an analogous energy loss happens over the entire tire, but it is still called "rolling resistance". In the broad sense, "rolling resistance" includes wheel bearing resistance, energy loss by shaking both the roadbed and the vehicle itself, and by sliding of the wheel, road/rail contact. Railroad textbooks seem to cover all these resistance forces but do not call their sum "rolling resistance" as is done in this article. They just sum up all the resistance forces and call the sum basic train resistance.
Since railroad rolling resistance in the broad sense may be a few times larger than just the pure rolling resistance reported values may be in serious conflict since they may be based on different definitions of "rolling resistance". The train's engines must, of course, provide the energy to overcome this broad-sense rolling resistance.
For tires, rolling resistance is defined as the energy consumed by a tire per unit distance covered. It is also called rolling friction or rolling drag. It is one of the forces that act to oppose the motion of a driver. The main reason for this is that when the tires are in motion and touch the surface, the surface changes shape and causes deformation of the tire.
For highway motor vehicles, there is some energy dissipated in shaking the roadway, the shaking of the vehicle itself, and the sliding of the tires. But, other than the [|additional power required due to torque] and wheel bearing friction, non-pure rolling resistance doesn't seem to have been investigated, possibly because the "pure" rolling resistance of a rubber tire is several times higher than the neglected resistances.

Rolling resistance coefficient

The "rolling resistance coefficient" is defined by the following equation:
where

• is the rolling resistance force,
• is the dimensionless rolling resistance coefficient or coefficient of rolling friction, and
• is the normal force, the force perpendicular to the surface on which the wheel is rolling.

is the force needed to push a wheeled vehicle forward per unit force of weight. It is assumed that all wheels are the same and bear identical weight. Thus: means that it would only take 0.01 pounds to tow a vehicle weighing one pound. For a 1000-pound vehicle, it would take 1000 times more tow force, i.e. 10 pounds. One could say that is in lb/lb. Since this lb/lb is force divided by force, is dimensionless. Multiply it by 100 and you get the percent of the weight of the vehicle required to maintain slow steady speed. is often multiplied by 1000 to get the parts per thousand, which is the same as kilograms per metric ton, which is the same as pounds of resistance per 1000 pounds
of load or Newtons/kilo-Newton, etc. For the US railroads, lb/ton has been traditionally used; this is just. Thus, they are all just measures of resistance per unit vehicle weight. While they are all "specific resistances", sometimes they are just called "resistance" although they are really a coefficient or a multiple thereof. If using pounds or kilograms as force units, mass is equal to weight so one could claim that is also the force per unit mass in such units. The SI system would use N/tonne, which is and is force per unit mass, where g is the acceleration of gravity in SI units.
The above shows resistance proportional to but does not explicitly show any variation with speed, [|loads], torque, surface roughness, [|diameter], tire inflation/wear, etc., because itself varies with those factors. It might seem from the above definition of that the rolling resistance is directly proportional to vehicle weight but [|it is not].

Measurement

There are at least two popular models for calculating rolling resistance.

1. "Rolling resistance coefficient. The value of the rolling resistance force divided by the wheel load. The Society of Automotive Engineers has developed test practices to measure the RRC of tires. These tests are usually performed on new tires. When measured by using these standard test practices, most new passenger tires have reported RRCs ranging from 0.007 to 0.014." In the case of bicycle tires, values of 0.0025 to 0.005 are achieved. These coefficients are measured on rollers, with power meters on road surfaces, or with coast-down tests. In the latter two cases, the effect of air resistance must be subtracted or the tests performed at very low speeds.
2. The coefficient of rolling resistance b, which has the dimension of length, is approximately equal to the value of the rolling resistance force times the radius of the wheel divided by the wheel load.
3. ISO 18164:2005 is used to test rolling resistance in Europe.

The results of these tests can be hard for the general public to obtain as manufacturers prefer to publicize "comfort" and "performance".