Rolling Resistance - Rolling Resistance Coefficient

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.