Tire Rolling resistance

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 & 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 & momentum are accounted for.

In braking
It is worth noting that for all vehicles that travel upon wheels (such as cars & bicycles), the sum of rolling friction & 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, & by Newton's First Law cannot cause a change in the vehicle's motion. Therefore the slowing is caused by contact between the road & the car's tires; the static friction force between road & tire is the "equal & 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 & do not sufficiently slow the car. Maximum braking force occurs when there is about 11% slip between the wheel's speed & the road - this is used to advantage in ABS braking systems, & cadence braking, a manual technique which achieves something similar.


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 & the contact area of the tire. For example, at the same pressure wider bicycle tires have less flex in sidewalls & thus lower rolling resistance (although higher air resistance).
Extent of inflation - Lower pressure in tires results in more flexing of sidewalls & higher rolling friction. This friction in the sidewalls increases resistance & can also lead to overheating & may have played a part in the infamous Ford Explorer rollover accidents.
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]

Units of measure
Rolling resistance is generally measured in Crr, & ranges from 0.0028 for a bicycle with Michelin Ecorun bicycle tires[1] up to around .05 for earth-moving equipment[2].


Physical formula & tables
The force of rolling resistance is given by:


where
F is the resistant force,
Crr is the rolling resistance coefficient or coefficient of rolling friction (CRF), &
Nf 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/sē on Earth) divided by the number of wheels (if the wheels have the same rolling coefficient).

Table of Crr examples: [3]