In the third place, the cost of transportation does not necessarily vary proportionally to the distance, as was assumed above. If the difference in distance is sufficient to make a difference of one trip per day, then the value of the saving in distance is tangible; but where the saving in length is insufficient for an additional trip, the value of the difference in distance depends upon the value, for other work, of the small portions of time of men and teams which may be saved by the shorter route,—a value which exists, but which is difficult to estimate.
Therefore any estimate as to the value of a saving of distance is necessarily only a rough approximation ; and at best it should be used only as a guide to the judgment.
The problem to find the value of saving distance is very different for wagon roads than for railroads. In the case of railroads the cost of the various elements has been carefully investigated for many years, and the transportation is all conducted under a single management and by the same party that maintains the road surface; while in the case of wagon roads, a multitude of private parties conduct the transportation under various conditions, and the main tenance of the road is in the hands of public officials.
Grades. A level road is the most desirable; but as it can seldom be obtained, we must investigate the effect of grades upon the cost of constructing and operating the road, and also determine what is the steepest allowable grade.
The grade may be reduced (1) by going round the hill or by zigzagging up the slope, or (2) by cutting down the hill. if the slope to be ascended is a long one, the first method must be em ployed; but if the grade is short, the second is usually the cheaper. Increasing the length adds to the cost of construction and of trans portation, while cutting down the hill adds only to the cost of construction. The maintenance of the longer and flatter line may cost either more or less than the shorter and steeper one according to the circumstances of the case. In a broken or rough country, a proper adjustment of the grades is the most important part of the art and science of road building; and the better the road surface the more necessary is such an adjustment.
All grades are objectionable for two distinct reasons, viz.: because a grade increases the amount of power required to move a load up it. and because a grade may be so steep as to limit the amount of the load that can be moved over the road. The first
applies to all grades whatever their rate or height; while the latter applies only to the steepest grade on the road, and in a measure is independent of its height and depends only on its rate. At present only the first objection to grades will be considered; and subse quently the second objection will be discussed (see § 71).
A horse can occasionally and for a short time exert a pull equal to more than one tenth of his weight. If the grade is not too long, a horse can safely exert a force equal to one quarter of his weight, and in emergencies one half. If the maximum force exerted is equal to one quarter of his weight, up what grade can he pull the ordi nary load? To move a load over an ordinary earth road requires a tractive force of 100 lb. per ton (see Table 9, page 31), and therefore a team of 1200-pound horses exerting a force equal to one tenth of their weight can draw 2.4 tons on the level. The reserve power to take the load up the hill is (0.25— 0.10)X 2= 360 pounds. The total load to be carried up the grade is the wagon and its load plus the weight of the team, or 2.4 + (1200x 2+ 2000) = 3.6 tons. The grade resistance is 20 lb. per ton for each per cent of inclination (see § 37) ; and the grade resistance for this load on a 1 per cent grade is 3.6 X 20 = 72 lb. Therefore, the grade up which a pull of 360 lb. will take the 3.6 tons is 360 + 72 = 5 per cent, which is the maximum permissible grade for an earth road in ordinary condition. The team could probably pull this load up 400 to 500 feet of such a grade.