newtons for rolling (1000 kg × 9.81 m/s2 × 0.01 = 98.1 N). Dependence on diameter Stagecoaches and railroads According to Dupuit (1837), rolling resistance (of wheeled carriages with wooden wheels with iron tires) is approximately inversely proportional to the square root of wheel diameter. This rule has been experimentally verified for cast iron wheels (8" - 24" diameter) on steel rail and for 19th century carriage wheels. But there are other tests on carriage wheels that do not agree. Theory of a cylinder rolling on an elastic roadway also gives this same rule These contradict earlier (1785) tests by Coulomb of rolling wooden cylinders where Coulomb reported that rolling resistance was inversely proportional to the diameter of the wheel (known as "Coulomb's law"). This disputed (or wrongly applied) -"Coulomb's law" is still found in handbooks, however. Pneumatic tires For pneumatic tires on hard pavement, it is reported that the effect of diameter on rolling resistance is negligible (within a practical range of diameters). Dependence on applied torque The driving torque to overcome rolling resistance and maintain steady speed on level ground (with no air resistance) can be calculated by: where is the linear speed of the body (at the axle), and its rotational speed. It is noteworthy that is usually not equal to the radius of the rolling body as a result of wheel slip. The slip between wheel and ground inevitably occurs whenever a driving or braking torque is applied to the wheel. Consequently, the linear speed of the vehicle differs from the wheel`s circumferential speed. It is notable that slip does not occur in driven wheels, which are not subjected to driving torque, under different conditions except braking. Therefore, rolling resistance, namely hysteresis loss, is the main source of energy dissipation in driven wheels or axles, whereas in the drive wheels and axles slip resistance, namely loss due to wheel slip, plays the role as well as rolling resistance. Significance of rolling or slip resistance is largely dependent on the tractive force, coefficient of friction, normal load, etc. All wheels "Applied torque" may either be driving torque applied by a motor (often through a transmission) or a braking torque applied by brakes (including regenerative braking). Such torques results in energy dissipation (above that due to the basic rolling resistance of a freely rolling, i.e. except slip resistance). This additional loss is in part due to the fact