Tractive Resistance

Table 5, page 25, gives data on the effect of width of tire upon the tractive power, obtained by the Studebaker Bros. Manufactur ing Co., South Bend, Ind., in 1892, with an ordinary 3k-inch thimble skein wagon. Notice that on a hard and incompressible road sur face, e. g., wood block pavement and gravel, the narrower tire draws the easier; while upon the soft or spongy surface the wider tire draws the easier.

Morin experimented (see § 34) with tires 2i, 41r, and 6i inches wide; and concluded that on a solid road or pavement the resistance was independent of the width of the tire, but on a compressible surface the resistance decreased as the width of the tire increased. the rate depending upon the nature of the surface.

For a further discussion of the relative merits of broad and narrow tires, see § 188-90.

Effect of Speed.

The rolling resistance increases with the velocity, owing to the effect of the shocks or concussions produced by the irregularities of the road surface. This increase is less for vehicles having springs than for those not having them, and is also less for smooth road surfaces than for rough ones.

Table 6, page 26, is a summary of Morin's results (see § 34) showing the effect of a variation of speed for vehicles provided with springs. In a rough way the three speeds are 2i, 5, and 7i feet per second, or about 2, 4, and 6 miles per hour respectively. According to these results the resistance on broken-stone roads in creases roughly as the fourth root of the speed, and on stone-block pavement about as the square root. For springless vehicles the increase would be greater. The above is for metal tires; for pneu matic tires there is very little increase of resistance with increase of speed.* The preceding data refer to the effect of speed upon the tractive power after the load is in motion. It requires from two to six or eight times as much force to start a load as to keep it in motion at 2 or 3 miles per hour. The extra force required to start a load is due in part to the fact that during the stop the wheel may settle into the road surface, in part to the fact that the axle friction at starting is greater than after motion has begun, and further in part to the fact that energy is consumed in accelerating the load.

Effect of Springs.

Springs decrease the tractive resistance by decreasing the concussions due to irregularities of the road sur face, and are therefore more effective at high speeds than at low ones, and on rough roads than on smooth ones. Apparently no experiments have been made upon the effect of springs; but a few data on this subject may be obtained by comparing the last and the sixth columns of 7, page 28.

Different Road Surfaces.

Immediately before and shortly after the introduction of railroads, European engineers made many experiments on the force necessary to draw different vehicles over various surfaces. The experiments by Morin,* made in 1837-41 for the French Government, were much the most elaborate and appear to have been made with great care. Table 7, page 28, is a summary of Morin's results showing the tractive resistance for different vehicles on various road surfaces. The table represents about 700 experi ments. Any vertical column shows the resistance for a particular vehicle on the various road surfaces, and any horizontal line shows the resistance on a particular road surface for different vehicles.

35. Table 8 shows data obtained by the author. The tractive power was determined with a Baldwin dynograph, Fig. 1, page 27. The instrument consists of two long flat springs fastened together at their ends and having their centers slightly farther apart than their ends. One end of the apparatus is attached to the wagon, and the team is hitched to the other. The pull of the team causes the centers of the flat springs to approach each other. One spring supports a graduated disk, and the other is connected to an index arm which is pivoted at the center of the disk. From one end of this index arm, the pull can be read directly from the graduated disk. There are two extra index arms—one to indicate the maxi mum power developed and one to indicate a rough average. The former (the upper one in Fig. 1) is simply pushed around by the main index arm and is left at the highest point. The latter (the middle arm in Fig. 1) has a transverse slot in which plays a stud on the main index arm. When making an experiment the main index arm is continually in motion, and the position of the auxiliary arm roughly indicates the average power exerted. The end of the index arm opposite the graduated arc records the amount of tractive resist ance upon a strip of paper which is wound from one cylinder to another by clock-work located behind the lower right-hand corner of Fig. 1. The autographic record is more accurate than the indi cated reading.

The wagon employed was the usual thimble-skein four-wheel farm wagon with a 2-inch tire. Experiments 3, 4, and 5 were made with wheels averaging 421 inches in diameter, and the remainder with wheels averaging 47 inches.

From a study of the preceding experiments and also others not here described, it is concluded that the average tractive resist ance on different road surfaces is about as in Table 9, page 31, which is given for use in comparing different roads and pavements.

Grade Resistance.

This is the force required on a grade to keep the load from rolling down the slope. It is independent of the na ture of the road surface, and depends only upon its angle of inclination.

In Fig. 2, P is the grade resist ance, and W is the weight of the wheel and its load. From the diagram it is easily seen that P=WXB C÷ A C. For all ordinary cases, A C may be considered as equal to A B, and then P=WXBC÷A B.

The preceding analysis is approximate for three reasons: (1) assuming A C=A B, i. e., assuming the sine of inclination to be equal to the tangent; (2) assuming the normal pressure on the inclined road surface to be equal to the weight, i. e., assuming the cosine of the inclination to be unity; and (3) neglecting the fact that the hind wheels carry a greater proportion of the load on an inclination than on the level. The resulting error, however, is wholly inappreciable.

Grades are ordinarily expressed in terms of the rise or fall in feet per hundred feet, or as a per cent of the horizontal distance. If A B be 100 feet, then the number of feet in B C is the per cent of the grade; and therefore the grade resistance is equal to the load mul tiplied by the per cent of the grade. Or the grade resistance is equal to 20 pounds per ton multiplied by the per cent of the grade.