that there is some slipping of the wheel, and for pneumatic tires, there is more flexing of the sidewalls due to the torque. Slip is defined such that a 2% slip means that the circumferential speed of the driving wheel exceeds the speed of the vehicle by 2%. A small percentage slip can result in a slip resistance which is much larger than the basic rolling resistance. For example, for pneumatic tires, a 5% slip can translate into a 200% increase in rolling resistance. This is partly because the tractive force applied during this slip is many times greater than the rolling resistance force and thus much more power per unit velocity is being applied (recall power = force x velocity so that power per unit of velocity is just force). So just a small percentage increase in circumferential velocity due to slip can translate into a loss of traction power which may even exceed the power loss due to basic (ordinary) rolling resistance. For railroads, this effect may be even more pronounced due to the low rolling resistance of steel wheels. It is shown that for a passenger car, when the tractive force is about 40% of the maximum traction, the slip resistance is almost equal to the basic rolling resistance (hysteresis loss). But in case of a tractive force equal to 70% of the maximum traction, slip resistance becomes 10 times larger than the basic rolling resistance. Railroad steel wheels In order to apply any traction to the wheels, some slippage of the wheel is required. For trains climbing up a grade, this slip is normally 1.5% to 2.5%. Slip (also known as creep) is normally roughly directly proportional to tractive effort. An exception is if the tractive effort is so high that the wheel is close to substantial slipping (more than just a few percent as discussed above), then slip rapidly increases with tractive effort and is no longer linear. With a little higher applied tractive effort the wheel spins out of control and the adhesion drops resulting in the wheel spinning even faster. This is the type of slipping that is observable by eye—the slip of say 2% for traction is only observed by instruments. Such rapid slip may result in excessive wear or damage. Pneumatic tires Rolling resistance greatly increases with applied torque. At high torques, which apply a tangential force to the road of