Rolling Resistance Coefficient
The "rolling resistance coefficient", is defined by the following equation:
- where
- 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, the force perpendicular to the surface on which the wheel is rolling.
is the force needed to push (or tow) a wheeled vehicle forward (at constant speed on the level with no air resistance) per unit force of weight. It's assumed that all wheels are the same and bear identical weight. Thus: means that it would only take 0.01 pound to tow a vehicle weighing one pound. For a 1000 pound vehicle it would take 1000 times more tow force or 10 pounds. One could say that is in lb(tow-force)/lb(vehicle weight. 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 (kg force) per metric ton (tonne = 1000 kg ) 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 which 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 (ratio)or a multiple thereof. If using pounds or kilograms as force units, mass is equal to weight (in earth's gravity a kilogram a mass weighs a kilogram and exerts a kilogram of force) so one could claim that is also the force per unit mass in such units. The SI system would use N/tonne (N/T) which is and is force per unit mass, where g is the acceleration of gravity in SI units (meters per second square).
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.
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Famous quotes containing the words rolling and/or resistance:
“It is only when we are very happy that we can bear to gaze merrily upon the vast and limitless expanse of water, rolling on and on with such persistent, irritating monotony, to the accompaniment of our thoughts, whether grave or gay. When they are gay, the waves echo their gaiety; but when they are sad, then every breaker, as it rolls, seems to bring additional sadness, and to speak to us of hopelessness and of the pettiness of all our joys.”
—Emmuska, Baroness Orczy (1865–1947)
“The aim of every political association is the preservation of the natural and imprescriptible rights of man. These rights are liberty, property, security and resistance to oppression.”
—French National Assembly. Declaration of the Rights of Man (drafted and discussed August 1789, published September 1791)