In this chapter will be discussed some of the items of the cost of track construction and maintenance, which are so large and important that they should be studied with great care, in order to discover any possible economies. Chief among these items are the costs of rails and ties. A very brief study of the subject will show that variations in the weight and character of the rolling-stock, the rate of grade, the amount and sharpness of curvature, etc., will modify the expenditure which may, with the best economy, be made on these two items.

## Rails. 99. Rail Wear - Theoretical

Definite information on this subject is very difficult to obtain. If rails were only renewed when a certain proportion of their total weight had been worn away - say one-quarter of the head or about 10% of the total weight - then it would be a comparatively simple matter to estimate the effect of aline-ment on rail wear. But it frequently, if not generally, happens that rails on tangents are removed, not on account of wear on the head, but on account of failure at the joints. When the steel of a rail is comparatively soft and ductile, the effect of concentrated wheel-pressure is to cause an actual flow of the metal, so that it will spread outside of its original outline, as is shown in the figure. The burr on the inside of the head will generally be worn off by the occasional pressure of a wheel-flange against the rail. The top of the rail will be worn with a slight slope to the inside, which corresponds somewhat with the coning of the wheels. Fig. 11 shows the usual outline of a worn rail on the outside of curves. The wear is largely on the inner side of the head, the side of the head being practically gone before the top of the rail is much worn. The inside rail of a curve will wear to about the same form as a rail on a tangent, as shown in Fig.12, but the wear is much faster.

Fig. 11.

Fig. 12.

Fig. 13.

Rail wear on curves is due chiefly to two causes: slipping due to unequal length of the rails and grinding of the side of the head by the wheel-flanges.

(a) Longitudinal slipping. When a pair of wheels which are not rigidly attached to their axle run around a curve (see Fig. 13), the outer wheel must roll a distance 2ãào/360or2and the inner wheel will roll a distance of 2ãào/360or1

The difference equals 2ãào/360o(r2-r1) or 2ãào/360og. This shows that when the wheels are fixed for any one gauge (g), the slipping is proportional to the number of degrees of central angle, equals cà°, and is independent of the radius. This slipping must be accomplished by the inner wheel slipping forward or the outer wheel slipping backward, or by a combination of the two which will give the same total amount of slipping. It is quite probable that the most of the slipping occurs on the inner rail, and that this accounts for the great excess of rail wear on the inner rail of a curve over that on a tangent.

(b) Lateral slipping. The two (or three) axles of car-trucks and the two or more driving-axles of a locomotive are always set exactly parallel to each other. This is done so that each pair of wheels shall mutually guide the other and maintain each axle approximately perpendicular to the rails. If the two axles of a truck are not exactly parallel, the truck has a constant tendency to run to one side, producing additional track resistance, rail wear, and wheel-flange wear. When two pairs of wheels with parallel axles are on a curve, the planes of at least one pair of wheels must make an angle with the tangent to the rails. When the radius of the curve is very short compared with the length of the wheel-base (as generally occurs at the street-corners of street-railways), then both axles will make angles with the normals to the curve, as shown in Fig. 14. The normal case for ordinary railroad work with easy curvature is that shown in Fig. 15, in which the rear axle stands nearly or quite normal to the curve, while the front axle makes an angle à° with the normal, and the plane of the wheel makes an angle of à° with the rail. The relative position of the outer front wheel and the rail is shown more clearly, although in an exaggerated way, in Fig. 16. The wheel tends to roll from a to b. Therefore, in moving along the track from a to c, it rolls the distance ab and slides laterally the distance bc, which equals ac sin à. In the usual case (Fig. 15) sin à = tör. When t = 5' and r=5730', the radius of a 1° curve, à=0° 03'. For the usual radii of railroad curves à will vary almost exactly with the degree of the curve. For example, on a 6° curve, using a 5-foot wheel-base, à=0°18/ and sin à = .0052. For each 100 feet traveled along a 6° curve, the lateral slip of the front wheels is 0.52 foot, or about 6¬ inches. If the rear axle remains radial there is no lateral slipping of the rear wheels.

Fig. 14.

Fig. 15.

Fig. 16.

It can readily be seen that when the angle à is large, the wheel-flange continually grinds the side of the head of the rail. The larger the angle the more direct and destructive is the grinding action.