To determine experimentally the rolling friction of wheels, apart from all journal friction, is a very difficult matter and has never been satisfactorily accomplished. Another practical difficulty is that the rolling resistance on a track is more or less intimately connected with the yielding of the rail, which is due not only to its own elasticity but to the yielding under it of the ties and ballast. Theory as well as practice shows that the higher and more perfect the elasticity of the wheel and of the surface on which it rolls the less will be the rolling friction. The determination, even if it could be made, would be chiefly of theoretic interest. The rolling friction is only a very insignificant part of the total train resistance. From the nature of the case no great reduction of the rolling friction by any device is possible. The use of harder rails with higher elasticity would probably have some effect in reducing it, but this effect would be so very small that it should hardly be considered in comparison with the effect of that added hardness and elasticity on the cost of the rails and the rate of rail wear.
The energy used up in this form of resistance has been studied quite extensively by means of the measurement of the force required to turn an axle in its bearings under various conditions of pressure, speed, extent of lubrication, and temperature. It may be measured quite accurately by loading a pendulum with any desired weight and hanging the pendulum on to the axle. The axle is then turned at any desired speed of rotation, which is easily measured. The deviation of the pendulum from the vertical position gives a measure of the circumferential resistance.
The following laws have been fairly well established: (1) The coefficient of friction increases as the pressure diminishes. (2) It is higher at very slow speed, gradually diminishing to a minimum at a speed corresponding to a train velocity of about 10 miles per hour, then slowly increasing with the speed. (3) It is very dependent on the perfection of the lubrication, it being reduced to 1/6 or 1/10 when the axle is lubricated by a bath of oil rather than by a mere pad or wad of waste on one side of the journal. (4) It is lower at high temperatures and vice versa.
The practical effect of these laws is shown by the observed facts that (1) loaded cars have a far less resistance per ton than unloaded cars. (2) When starting a train the resistance may be as much as 16 or even 20 pounds per ton, notwithstanding the fact that the velocity resistances are practically zero. At a speed of two miles per hour it will drop to about one-half of this figure, and at seven miles per hour the resistance of loaded cars will drop to between 4 and 5 pounds per ton. (3) The journal resistance is so very greatly reduced by higher temperature (which results from the increased velocity) that it largely neutralizes the increase in the velocity resistances, and tends to make the total resistance uniform for a considerable range of low velocities, say between 7 and 35 miles per hour. (4) As a corollary to the above, it is found that the resistance at any given speed, say 20 miles per hour, is less, if the velocity has been reduced to that figure from some higher velocity, than it is if the velocity has been increased to 20 miles per hour from a lower velocity. (5) It has been observed that freight-train loads must frequently be cut down in winter by about 10 or 15% of the loads that the same engine can haul over the same track in summer. This is doubtless due chiefly to the reduction of temperature of the journal-bearings and the consequent addition to the journal resistance, in spite of the fact that the tractive resistance will probably be less over a hard frozen road-bed, provided that the track has been kept in uniform surface.
Roller bearings for cars have been used to some extent. It has been found that they very greatly reduce the starting resistance, but that their advantages grow less and less as the velocity increases. The effect of the adoption of this device on car repairs and maintenance has not yet been determined on a large scale, and the ultimate economy is still uncertain.