Rolling resistance

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Rolling resistance, sometimes called rolling friction, is the resistance that occurs when an object (e.g a wheel or tire) rolls. It is much smaller than sliding friction except for special cases like ice skating. It is caused by the deformation of the wheel or tire or the deformation of the ground. It depends very much on the material of the wheel or tire and the sort of ground. For example, rubber will give a bigger rolling friction than steel. Also, sand on the ground will give more rolling friction than concrete. A vehicle rolling will gradually slow down due to rolling friction, but a train with steel wheels running on steel rails will roll much further than a car or truck with rubber tires running on pavement, even when differences in mass and momentum are accounted for.

1 In braking
2 Factors that contribute
3 Physical formula and tables
4 References
5 External links

[edit] In braking

It is worth noting that for all vehicles that travel on wheels (such as cars and bicycles), the sum of rolling friction and static friction is what causes the vehicle to slow when the brakes are applied. The actual force applied in braking (for example, clamps applied to disk brakes) is internal, and by Newton's First Law cannot cause a change in the vehicle's motion. Therefore the slowing is caused by contact between the road and the car's tires; the static friction force between road and tire is the "equal and opposite reaction" specified in Newton's Third Law. Rolling friction can be compared to sliding friction, as when the brakes "lock up", they slide upon the driving surface and do not sufficiently slow the car. Maximum braking force occurs when there is about 11% slip between the wheel's speed and the road - this is used to advantage in ABS braking systems, and cadence braking, a manual technique which achieves something similar.

[edit] Factors that contribute

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

Material - Tires with higher sulfur content tend to have a lower rolling friction. This is one strategy that most hybrid car vendors use to improve fuel efficiency.
Dimensions - rolling friction is related to the flex of sidewalls and the contact area of the tire. For example, at the same pressure wider bicycle tires have less flex in sidewalls and thus lower rolling resistance (although higher air resistance).
Extent of inflation - Lower pressure in tires results in more flexing of sidewalls and higher rolling friction. This friction 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 scarificed, and overall rolling friction may not be reduced as the wheel rotaional speed changes and slipage 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 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. 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 rail steels 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.^[1]

[edit] Physical formula and tables

The force of rolling resistance is given by:

$F = C_{rr} N_f \$

where

F is the resistant force,

C_rr is the rolling resistance coefficient or coefficient of rolling friction (CRF), and

N f

is the normal force.

In usual cases, the normal force on each tire will be the mass of the object (wheels plus what they're supporting) times the gravitational acceleration (9.81 m·s⁻² on Earth) divided by the number of wheels (if the wheels have the same rolling coefficient).

Table of C_rr examples: [1]

C_rr	description
0.001 to 0.0025	train steel on steel with tatz-mounted electric traction
0.0025	low resistance radial tire used for solar cars
0.005	tram-rails standard dirty with straights and curves
0.0055	Typical BMX bicycle tire used for solar cars
0.006 to 0.01	low rolling resistance car tire on a smooth road and truck tires on a smooth road
0.010 to 0.015	ordinary car tires on concrete
0.020	car on stone plates
0.030	car/bus on teer/asphalt