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# Resistance to Traction

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RESISTANCE TO TRACTION.

The resistance to traction of a vehicle on a road surface may be divided into three parts: axle friction, rolling resistance, and grade resistance.

Axle friction varies with the nature of the bearing surfaces, and for vehicles of similar construction is directly proportional to the load. It is entirely inde pendent of the nature of the road surface.

Rolling resistance is of two kinds: that due to irregu larities in the surface of the road, and that of a wheel to rolling upon a smooth surface, sometimes called rolling friction.

The resistance due to an inequality in the road face is the horizontal force necessary, at the axle, to raise the weight upon the wheel to the height of the obstacle to be passed. Thus (Fig. I), by the principle of the lever, P = W — • a For small inequalities, this resistance will be approxi mately inversely as the diameter of the wheel. The effect of small irregularities in the surface, however, is due more to the shocks and concussions produced by them than to the direct lifting action of the obstacle, and the resistance due to uneven surface is greater at high than at low velocities.

Rolling friction is probably due for the most part to the compres sibility of the surface of the road, which permits the wheel to indent it to some extent. The wheel is thus always forcing a wave of the surface before it, or climbing an inclination caused by its weight upon the road surface.

Size of Wheels. — The resistance to traction varies for wheels of differing diameters, being less for large than for small wheels. The experiments of M. Morin, in France, seemed to indicate that the resistance varies inversely as the diameter. Other experiments have indicated a less variation, approximately as the square root of the diameter, while Mr. D. K. Clark (Roads and Streets, by Law and Clark; London, 1890) concludes, from a Mathematical discussion based upon the assumption that the material of the surface is homogeneous and the pressure proportional to the depth of penetration, that the resistance to traction is inversely as the cube root of the diameter of the wheel. The experiments of Mr. Mairs (Bulletin, Uni

versity of Missouri Agricultural Experiment Station, 1902) indicate that tractive resistance is somewhat less with large than with small wheels, being nearly inversely as the square root of the diameter, but as might be expected, differing somewhat for different road surfaces.

For practical purposes it may be considered that, for wheels of ordinary sizes used on road vehicles, the rolling resistances are equal to the load multiplied by a coefficient which depends upon the nature and condition of the road surface, although these coefficients are somewhat affected by the sizes of the wheels.

Width of Tire. — The effect upon tractive resistance of the width of tire upon the wagon wheels depends upon the character of the surface upon which the wheel is rolling. In a series of experiments at the University of Missouri Agricultural Experiment Station in 1897, it was found that wide tires considerably diminished tractive resistance upon broken stone and gravel roads, and upon earth roads in good condition, but upon muddy roads or when a hard road is covered with deep dust the resistance is greater for wide tires. The wide tire also has considerable advantage upon plowed land or sod, not cutting in so deeply.

Speed of Travel. — Tractive resistances are somewhat greater at high than at low velocities. This difference is very slight on earth roads in good condition or on smooth pavements; but on rough pavements where con cussions take place the resistance increases rapidly as the speed becomes greater.

Road Surface. — Many experiments have been made for the purpose of determining the • tractive force required for a given load upon various road surfaces. The results show somewhat wide variations, as would be expected when the many elements that may affect them are considered. The following table shows a few average results, which will give some idea of the relative resistances of various surfaces and of the advantage to be•derived from a smooth and well-kept road surface: The resistance upon asphalt is greater at high than at low temperatures.

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