Tractive Resistance

TRACTIVE RESISTANCE. The resistance to traction of a vehicle on aroad consists of three independent elements: axle friction, rolling resistance, and grade resistance.

Axle Friction.

The resistance of the hub to turning on the axle is the same as that of a journal revolving in its bearing, and has nothing to do with the condition of the road surface. The co-effi cient of journal friction varies with the material of the journal and its bearing, and with the lubricant. It is nearly independent of the velocity, and according to observations made by the author seems to vary about inversely as the square root of the pressure. For light carriages when loaded, the co-efficient of friction is about 0.020 of the weight on the axle; for the heavier carriages when loaded, it is about 0.015; and for the ordinary thimble-skein Ameri can wagon when loaded, it is about 0.012. The above results are for good lubrication; if the lubrication is deficient, the axle friction is two to six times as much as above. The above figures agree reasonably well with results obtained for journal friction of ma chines. Apparently the value of this co-efficient in Morn's experi ments (§ 34) was 0.065.* The greater axle friction is probably due to the inferior mechanical construction of French carriages and wagons.

The tractive power required to overcome the above axle friction for American carriages of the usual proportions is about 3 to 3i lb. per ton of the weight on the axle; and for truck wagons, which have medium-sized wheels and axles. is about 3i to 4/4 lb. per ton.

Rolling Resistance.

The resistance of a wheel to rolling along on a road is due to the yielding or indentation of the road, which causes the wheel to be continually climbing an inclination. The resistance is measured by the horizontal force necessary at the axle to lift the wheel over the obstacle or to roll it up the inclined surface; and varies with the diameter of the wheel, the width of the tire, the speed, the presence or absence of springs on the vehicle, and the nature of the road surface.

Diameter of

The rolling resistance varies inversely as some function of the diameter of the wheel, since the larger the wheel the less the force required to lift it over the obstruction or to roll it up the inclination due to the indentation of the surface.

Table 3 shows the results obtained by Mr. T. I. Mairs at the Missouri Agricultural Experiment Station,* with three different sized wheels. The 50-inch represents 44-inch front wheels and 56-inch hind wheels; the 38-inch represents 36-inch front and 40-inch hind wheels; and the 26-inch represents 24-inch front and 28-inch hind wheels. The tires were 6 inches wide. The load was practically If tons in each case.

Morin concluded that the resistance varies inversely as the first power of the diameter of the wheel; Dupuit. that it varies as the square root; and Clarke claims that it varies as the cube According to some experiments made in England in 1874,t the tractive resistance varied more rapidly than the first power of the diameter of the wheels. The mean results in Table 3 vary nearly inversely as the square root of the mean diameter—certainly more nearly than as either the first power or the cube root. For obvious reasons, the experiments can not be very exact; and apparently the tractive resistance varies differently for different surfaces. The exact determination of the law of variation is of no great importance.

Width of Tire. If the wheel cuts into the road surface, the tractive resistance is thereby increased; but with surfaces for which there is little or no indentation, the traction is practically inde pendent of the width of tire.

Table 4, page 24, shows the results of an elaborate series of experiments by the Missouri Agricultural Experiment Station.* The load in each case was 1 ton. These results show that on poor macadam, poor gravel, and compressible earth roads, and also on agricultural land, the broad tire gives less resistance except as follows: (1) when the earth road is sloppy, muddy, or sticky on top and firm underneath; (2) when the surface is covered with a very loose deep dust and is hard underneath; (3) when the mud is very deep and so sticky that it adheres to the wheel; or (4) when the road has been rutted with the narrow tire. The last conclusion was established by a large number of experiments not included in Table 4, page 24.