Rolling resistance
Rolling resistance, sometimes called rolling friction or rolling drag, is the resistance
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 that occurs when a round object such as a ball
A ball is a round, usually spherical but sometimes ovoid, object with various uses. It is used in ball games, where the play of the game follows the state of the ball as it is hit, kicked or thrown by players. Balls can also be used for simpler activities, such as catch, marbles and juggling...

 or tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

 rolls on a flat surface, in steady velocity straight line motion. It is caused mainly by the deformation of the object, the deformation of the surface, or both. Additional contributing factors include wheel radius, forward speed, surface adhesion, and relative micro-sliding between the surfaces of contact. It depends very much on the material of the wheel or tire and the sort of ground.

For example, rubber
Natural rubber, also called India rubber or caoutchouc, is an elastomer that was originally derived from latex, a milky colloid produced by some plants. The plants would be ‘tapped’, that is, an incision made into the bark of the tree and the sticky, milk colored latex sap collected and refined...

 will give a bigger rolling resistance than steel
Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...

 on some surfaces (polished steel) and a lower rolling resistance on other surfaces (pavement/tarmac). Also, sand
Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...

 on the ground will give more rolling resistance than concrete
Concrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word...

. Any moving wheeled vehicle
A vehicle is a device that is designed or used to transport people or cargo. Most often vehicles are manufactured, such as bicycles, cars, motorcycles, trains, ships, boats, and aircraft....

 will gradually slow down due to rolling resistance including that of the bearings, but a train
A train is a connected series of vehicles for rail transport that move along a track to transport cargo or passengers from one place to another place. The track usually consists of two rails, but might also be a monorail or maglev guideway.Propulsion for the train is provided by a separate...

 car with steel wheels running on steel rails
Rail tracks
The track on a railway or railroad, also known as the permanent way, is the structure consisting of the rails, fasteners, sleepers and ballast , plus the underlying subgrade...

 will roll farther than a bus
A bus is a road vehicle designed to carry passengers. Buses can have a capacity as high as 300 passengers. The most common type of bus is the single-decker bus, with larger loads carried by double-decker buses and articulated buses, and smaller loads carried by midibuses and minibuses; coaches are...

 of the same mass with rubber tires running on tarmac. The coefficient of rolling resistance is generally much smaller for tires or balls than the coefficient of sliding friction.

Primary cause

The primary cause of rolling resistance is hysteresis
Hysteresis is the dependence of a system not just on its current environment but also on its past. This dependence arises because the system can be in more than one internal state. To predict its future evolution, either its internal state or its history must be known. If a given input alternately...


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.

-- National Academy of Sciences

Thus materials that flex more and bounce back slowly,
such as rubber, exhibit more rolling resistance than
materials that flex less, such as steel, or that
bounce back more quickly, such as 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.

Factors that contribute in tires

Several factors affect the magnitude of rolling resistance a tire generates:
  • As mentioned in the introduction: wheel radius, forward speed, surface adhesion, and relative micro-sliding.
  • Material - different fillers and polymers in tire composition can improve traction while reducing hysteresis. The replacement of some carbon black with higher-priced silica–silane is one common way of reducing rolling resistance. The use of exotic nano materials including nano clay has been shown to reduce rolling resistance in high performance rubber tires. Solvents may also be used to swell solid tires, decreasing the rolling resistance.
  • Dimensions - rolling resistance in tires is related to the flex of sidewalls and the contact area of the tire For example, at the same pressure, wider bicycle tire
    Bicycle tire
    A bicycle tire is a tire that fits on the wheel of a bicycle, unicycle, tricycle, quadracycle, bicycle trailer, or trailer bike. They may also be used on wheelchairs and handcycles, especially for racing...

    s flex less in sidewalls as they roll and thus have lower rolling resistance (although higher air resistance).
  • Extent of inflation - Lower pressure in tires results in more flexing of sidewalls and higher rolling resistance. This energy conversion in the sidewalls increases resistance and can also lead to overheating and may have played a part in the infamous Ford Explorer
    Ford Explorer
    The Ford Explorer is a sport-utility vehicle sold in North America and built by the Ford Motor Company since 1990, as a replacement for the smaller but related Ford Bronco II. It is manufactured in Chicago, Illinois...

     rollover accidents.
  • Over inflating tires (such a bicycle tires) may not lower the overall rolling resistance as the tire may skip and hop over the road surface. Traction is sacrificed, and overall rolling friction may not be reduced as the wheel rotational speed changes and slippage increases.
  • Sidewall deflection is not a direct measurement of rolling friction. A high quality tire with a high quality (and supple) casing will allow for more flex per energy loss than a cheap tire with a stiff sidewall. Again, on a bicycle, a quality tire with a supple casing will still roll easier than a cheap tire with a stiff casing. Similarly, as noted by Goodyear truck tires, a tire with a "fuel saving" casing will benefit the fuel economy through many tread lives (i.e. retreading), while a tire with a "fuel saving" tread design will only benefit until the tread wears down.
  • In tires, tread
    The tread of a tire or track refers to the rubber on its circumference that makes contact with the road. As tires are used, the tread is worn off, limiting its effectiveness in providing traction. A worn tire tread can often be retreaded. The word tread is often used incorrectly to refer to the...

     thickness and shape has much to do with rolling resistance. The thicker and more contoured the tread, the higher the rolling resistance Thus, the "fastest" bicycle tires have very little tread and heavy duty trucks get the best fuel economy as the tire tread wears out.
  • Hard steel rails last longer but also have lower static friction (traction) than rubber tires. They may also suffer fatigue
    Fatigue (material)
    'In materials science, fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The nominal maximum stress values are less than the ultimate tensile stress limit, and may be below the yield stress limit of the material.Fatigue occurs...

    Cracking may refer to:* Cracking, the formation of a fracture or partial fracture in a solid material* Fluid catalytic cracking, a catalytic process widely used in oil refineries for cracking large hydrocarbon molecules into smaller molecules...

     because the cracked area is not worn away by the passing trains.
  • Smaller wheels, all else being equal, tend to have higher rolling resistance than larger wheels. However, in some laboratory tests, smaller wheels appeared to have similar or lower losses than large wheels, but these tests were done rolling the wheels against a small-diameter drum, which would theoretically remove the advantage of large-diameter wheels, thus making the tests irrelevant for resolving this issue. Virtually all world speed records have been set on relatively narrow wheels, probably because of their aerodynamic advantage at high speed, which is much less important at normal speeds.
  • temperature: with both solid and pneumatic tires, rolling resistance has been found to decrease as temperature increases (within a range of temperatures: i.e. there is an upper limit to this effect)


There are at least two popular models for calculating rolling resistance.
  1. "Rolling resistance coefficient (RRC). The value of the rolling resistance force divided by the wheel load. The Society of Automotive Engineers (SAE) has developed test practices to measure the RRC of tires. These tests (SAE J1269
    SAE J1269
    SAE J1269 is a standard test defined by the Society of Automotive Engineers to measure the rolling resistance of tires.The rolling resistance coefficient thus measured indicates the proportion of energy that is lost to the hysteresis of the material as the tire rolls....

     and SAE J2452
    SAE J2452
    SAE J2452 is a standard defined by the Society of Automotive Engineers to define the rolling resistance of tires.The rolling resistance coefficient indicates the amount of force required to overcome the hysteresis of the material as the tire rolls...

    ) 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
    In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

    , is approximately (due to the small-angle approximation of ) equal to the value of the rolling resistance force times the radius
    In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

     of the wheel divided by the wheel load.
  3. ISO 8767 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".

Physical formula

The force of rolling resistance, not adjusted for velocity, can be calculated by:
is the rolling resistance force (shown in figure 1),
is the dimensionless rolling resistance coefficient or coefficient of rolling friction (CRF), and
is the normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

 (equal to W, not R, as shown in figure 1).

The power required to overcome this rolling resistance at a given velocity can be expressed as:
is the power required,
is the dimensionless rolling resistance coefficient or coefficient of rolling friction (CRF), and
is the normal force
Normal force
In mechanics, the normal force F_n\ is the component, perpendicular to the surface of contact, of the contact force exerted on an object by, for example, the surface of a floor or wall, preventing the object from penetrating the surface.The normal force is one of the components of the ground...

 (equal to W, not R, as shown in figure 1).
is the forward speed,

The coefficient of rolling friction for a slow rigid wheel, not adjusted for velocity, can be calculated by
is the sinkage depth
is the diameter of the rigid wheel

The force of rolling resistance can also be calculated by:
is the rolling resistance force (shown in figure 1),
is the wheel radius,
is the rolling resistance coefficient or coefficient of rolling friction with dimension of length, and
is the normal force (equal to W, not R, as shown in figure 1).

Equating the above two equations, and solving for b, gives b = Crr·r. Therefore, if a source gives rolling resistance coefficient (Crr) as a dimensionless coefficient, it can be converted to b, having units of length, by multiplying Crr by wheel radius r.

In usual cases, the normal force on a single tire will be the mass of the object that the tires are supporting divided by the number of wheels, plus the mass of the wheel, times the gravitational acceleration
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

 (9.81 m·s−2 on earth). In other words, the normal force is equal to the weight of the object being supported, if the wheel is on a horizontal surface.

The above equations don't include variation of rolling resistance with speed. This is a reasonable simplification but measurements at different speeds show some variation.

Rolling resistance coefficient examples

Table of rolling resistance coefficient examples:
Crr b Description
0.0002 to 0.0010 0.5 mm Railroad steel wheel on steel rail
0.1 mm Hardened steel ball bearings on steel
0.0022 to 0.005 production bicycle tires at 120 psi (8.3 bar) and 50 km/h (31.1 mph), measured on rollers
0.0025 Special Michelin
Michelin is a tyre manufacturer based in Clermont-Ferrand in the Auvergne région of France. It is one of the two largest tyre manufacturers in the world along with Bridgestone. In addition to the Michelin brand, it also owns the BFGoodrich, Kleber, Riken, Kormoran and Uniroyal tyre brands...

 solar car
Solar car
A solar vehicle is an electric vehicle powered completely or significantly by direct solar energy. Usually, photovoltaic cells contained in solar panels convert the sun's energy directly into electric energy. The term "solar vehicle" usually implies that solar energy is used to power all or part...

The Eco-Marathon is an annual competition sponsored by Shell, in which participants build special vehicles to achieve the highest possible fuel efficiency. The Eco-Marathon is held around the world with events in Finland, France, Germany, The Netherlands, Japan, and the USA...

0.005 Tram rails standard dirty with straights and curves
0.0055 Typical BMX bicycle tires used for solar cars
0.0062 to 0.015 Car tire measurements
0.010 to 0.015 Ordinary car tires on concrete
0.3 Ordinary car tires on sand

For example, in earth gravity, a car of 1000 kg on asphalt will need a force of around 100 newtons for rolling (1000 kg × 9.81 m/s2 × 0.01 = 98.1 N).


Rolling friction generates heat and sound (vibrational) energy, as mechanical energy is converted to these forms of energy due to the friction. One of the most common examples of rolling friction is the movement of motor vehicle
Motor vehicle
A motor vehicle or road vehicle is a self-propelled wheeled vehicle that does not operate on rails, such as trains or trolleys. The vehicle propulsion is provided by an engine or motor, usually by an internal combustion engine, or an electric motor, or some combination of the two, such as hybrid...

 tires on a roadway, a process which generates sound
Roadway noise
Roadway noise is the collective sound energy emanating from motor vehicles. In the USA it contributes more to environmental noise exposure than any other noise source, and is constituted chiefly of engine, tire, aerodynamic and braking elements...

 and heat as by-products. The sound generated by automobile and truck tires as they roll (especially noticeable at highway speeds) is mostly due to the percussion of the tire treads, and compression (and subsequent decompression) of air temporarily captured within the treads. The heat generated raises the temperature of the frictional surface; moreover, this temperature increase typically increases the coefficient of friction. This is why automobile racing teams preheat their tires.

See also

  • Coefficient of friction
  • Maglev (Magnetic Levitation
    Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...

    , the elimination of rolling and thus rolling resistance)
  • Rolling element bearing

External links

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