mile (see § 4-7 and § 20-21), then the cost with the maximum grade will be 10 ÷ = 131 cents per ton-mile; and therefore for each ton going over the road, the maximum grade adds 3.4 cents per ton-mile. In determining the amount of traffic, only full loads should be included; but notice that the full load varies with the speed. A ton may be a full load at 3 miles per hour, while half a ton may be a full load at 6 miles per hour.
Knowing the load on the maximum grade and also the cost per ton-mile for a level road or for a grade less than the maximum, the justifiable expenditure to reduce the maximum grade may be com puted as follows: The difference in cost per ton-mile with and with out the maximum grade may be determined as in the preceding paragraph; and this multiplied by the annual number of loads going over the road gives the sum that may be spent annually to reduce the maximum grade to the lesser value. This sum may be used to pay interest on the cost of cutting down the hill or of filling up the hollow.
The data are so uncertain that the result must be regarded only as a rough approximation; and yet it is worth while to make an investigation as above as a guide to the judgment.
Class B rise and fall is intermediate between Class A and Class C, and its cost is even more difficult to compute than that of Class C. The chief difficulty is in determining the relative cast of developing power on a level and up a grade. Only an estimate can be made, and the estimate will vary greatly with the point of view. For example, farmers usually have a surplus of power (horses) as far as transportation is concerned, and therefore they would con sider a slight increase in the demand for power as a matter of small moment. Again, teamsters differ greatly as to what is a proper or economical load for a horse, and also as to the effect of a tem porary over-load.
There are two methods of computing the cost of this class of rise and fall, neither of which are more than roughly approximate. 1. Assume that the cost of Class B rise and fall bears the same relation to that of Classes A and C, that the grade of B bears to that of A and C. Then if the grade for Class B is only a little greater " than the angle of repose, the cost is only a trifle greater than that of Class A; and if the grade is nearly a maximum, then the cost of the rise and fall closely approximates that of Class C.
2. Assume that the energy developed on a grade over and above that required on the grade of repose, costs the same per unit as that of an equal amount of energy developed on the level. For example, assume that the rise is 1 foot more than the angle of repose; and assume that the cost of drawing a load on a good broken-stone road is 5 cents per ton-mile (see § 5-6), and that the tractive power is 43 lb. per ton. Then, moving a ton one mile will develop 5,280 X 40 = 211,200 foot-pounds of energy, which will cost 5 cents. The cost of one foot-pound of energy, then, is 5+211,200= 0.000,023,7 cents. Drawing a ton over a rise 1 foot high develops 2,000 foot pounds, the cost of which is 0.000,023,7+2 x 2,000= 0.023,7 oents. In going up the above grade, the team must develop enough power to move the load up the grade of repose and in addition must de velop enough to lift the load through 1 foot vertically. Therefore the cost of the 1 foot of rise assumed above is 0.023,7 cents for each ton going over the road.
It was assumed above that the load is retarded in the descent by the application of brakes; but if the grade in question is situated in a flat country where brakes are not usually placed upon vehicles, the team must hold back on the descent an amount equal to the extra energy required on the ascent, and therefore the cost of the foot of rise and fall will be, almost or quite, doubled.
With data similar to the above, and with a knowledge of the amount of traffic, it is a simple arithmetical process to compute the sum that may be spent annually to eliminate one or more feet of rise and fall. Notice that in this case only the full loads should be considered (see the first paragraph of § 71). For example, assume that a broken-stone road has a traffic of 20 tons per day one way for 300 days of the year, or an annual traffic of 20 X 300 = 6,000 tons. The cost of a foot of rise and fall per ton of traffic is 0.023,7 cents, and the annual cost on this particular road is 0.023,7X 6,000- $141.70. This is the amount which, according to the above in vestigation, can be spent annually to cut down the hill or to fill up the hollow sufficiently to eliminate 1 foot of rise and fall.