Rolling resistance

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Diagram of a hard wheel rolling on and deforming a soft surface resulting in the reaction force from the surface having a component that opposes the motion.
Diagram of a hard wheel rolling on and deforming a soft surface resulting in the reaction force from the surface having a component that opposes the motion.

Rolling resistance, sometimes called rolling friction or rolling drag, is the resistance that occurs when a round object such as a ball or tire rolls on a surface. It is caused by the deformation of the object, the deformation of the surface, or both. Additional contributing sources include surface adhesion and relative micro-sliding between the surface of contact. It depends very much on the material of the wheel or tire and the sort of ground. Additional factors include wheel radius, and forward speed.[1]

For example, rubber will give a bigger rolling resistance than steel. Also, sand on the ground will give more rolling resistance than concrete. A vehicle rolling will gradually slow down due to rolling resistance, but a train with steel wheels running on steel rails will roll much farther than a car or truck with rubber tires running on pavement. The coefficient of rolling resistance is generally much smaller for tires or balls than the coefficient of sliding friction.[2]

Contents

[edit] Primary cause

The primary cause of rolling resistance is hysteresis:

"Hysteresis. 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[3]

[edit] Factors that contribute

Several factors affect the magnitude of rolling resistance a tire generates:

  • 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.[3]
  • Dimensions - rolling resistance is related to the flex of sidewalls and the contact area of the tire[4] For example, at the same pressure wider bicycle tires have less flex in sidewalls and thus lower rolling resistance (although higher air resistance).[4]
  • Extent of inflation - Lower pressure in tires results in more flexing of sidewalls and higher rolling resistance).[4] 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 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.[citation needed] 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 casing lives (i.e. retreading), while a tire with a "fuel saving" tread design will only benefit until the tread wears down.
  • Tread thickness has much to do with rolling resistance. The thicker the tread, the higher the rolling resistance)[4] 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 may also have lower static friction. They may also suffer fatigue cracking because the cracked area is not worn away by the passing trains.
  • Smaller wheels, all else being equal, have higher rolling resistance than larger wheels in theory.[5] In some laboratory tests, smaller wheels appeared to have similar or lower losses than large wheels,[6] 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,[citation needed] probably because of their aerodynamic advantage at high speed, which is much less important at normal speeds.

[edit] Measurement

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 and SAE J2452) 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."[3]
  2. The coefficient of rolling resistance a, which has the dimension of length, is approximately (due to the small-angle approximation of cos(θ) = 1) equal to the value of the rolling resistance force times the radius of the wheel divided by the wheel load.[1]

[edit] Physical formula and tables

The force of rolling resistance can be calculated by[3]:

\ F = C_{rr} N_f

where

F is the resistant force,
Crr is the dimensionless rolling resistance coefficient or coefficient of rolling friction (CRF), and
Nf is the normal force.

The force of rolling resistance can also be calculated by[1]:

\ F = \frac{W a}{r}

where

F is the resistant force,
a is the rolling resistance coefficient or coefficient of rolling friction with dimension of length,
W is the weight, and
r is radius.

In usual cases, the normal force on a single tire will be the mass of the object which the tires are supporting divided by the number of wheels, plus the mass of the wheel, times the gravitational acceleration (9.81 m·s−2 on Earth). In other words, the normal force is equal to the weight of the object being supported.

Table of Crr examples: [2]

Crr a description
0.0002 to 0.0010[7][8] 0.5 mm Railroad steel wheel on steel rail
0.0025[9] Special Michelin solar car/eco-marathon tires
0.005 Tram-rails standard dirty with straights and curves[citation needed]
0.0055 Typical BMX bicycle tire used for solar cars[citation needed]
0.006 to 0.01 Low-resistance car tire on a smooth road
  Truck tires on a smooth road
0.010 to 0.015 Ordinary car tires on concrete
0.020 Car on stone[citation needed] plates
0.030 Car/bus on tar/asphalt

For example on the earth a car of 1000 kg on asphalt will need a force of 300 N for rolling.

[edit] Effects

Rolling friction generates heat and sound 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 tires on a roadway, a process which generates sound and heat as by-products.[10] The sound generated by automobile and truck tires as they roll (especially noticeable at highway speeds) is mostly due to the compression (and subsequent decompression) of air temporarily captured within the tire treads. The heat generated raises the temperature of the frictional surface; moreover, this temperature increase typically increases the coefficient of friction itself.[11] This is why automobile racing teams preheat their tires.

[edit] See also

[edit] References

  1. ^ a b c Hibbeler, R.C. (2007). Engineering Mechanics: Statics & Dynamics, Eleventh, Pearson, Prentice Hall, 441-442. 
  2. ^ Peck, William Guy (1859). Elements of Mechanics: For the Use of Colleges, Academies, and High Schools. A.S. Barnes & Burr: New York, 135. Retrieved on 2007-10-09. 
  3. ^ a b c d Tires and Passenger Vehicle Fuel Economy: Informing Consumers, Improving Performance -- Special Report 286. National Academy of Sciences, Transportation Research Board, 2006. Retrieved on 2007-08-11.
  4. ^ a b c d Schwalbe Tires: Rolling Resistance.
  5. ^ VREDESTEIN Bicycle Tires. Retrieved on 2006-08-14.
  6. ^ Greenspeed test results. Retrieved on 2007-10-27.
  7. ^ Gordon, David W. Bicycling Science. Cambridge, Mass. : MIT Press (c. 2004)
  8. ^ Williams, John A. Engineering Tribology. New York : Cambridge University Press (2005)
  9. ^ Roche, Schinkel, Storey, Humphris & Guelden, "Speed of Light." ISBN 0 7334 1527 X
  10. ^ [1] C. Michael Hogan, Analysis of Highway Noise, Journal of Soil, Air and Water Pollution, Springer Verlag Publishers, Netherlands, Volume 2, Number 3 / September, 1973
  11. ^ Gwidon W. Stachowiak, Andrew William Batchelor, Engineering Tribology, Elsevier Publisher, 750 pages (2000) ISBN 0750673044

[edit] External links