Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

OF THE AVERAGE HAUL.

117. To find the cost of the movement of earth on any section, we must have, the total amount of earth to be moved, and the average haul; the latter being the distance through which, if the whole amount were moved, the cost would be the same as the sum of the costs of moving the partial amounts their respective distances. To find the average haul proceed as follows: First, find the distance between the centres of gravity of each mass both before and after moving, which may be done with sufficient accuracy for practice by inspection of the profile. Next,

118. Divide the sum of the products of the partial amounts by their respective hauls, by the total amount; the result is the average haul in feet. Or algebraically, representing the partial amounts by m, m′, m″, m‴, the respective hauls by d, d′, d″, d‴, the total amount by S, and the average haul by D, we have

md + m′d′ + m″d″ + m‴d‴
S = D.

Example.—Let column 1 show the partial amounts in cubic yards. Column 2 the corresponding hauls.

1,000	× 200 =	200,000
2,000	× 300 =	600,000
5,000	× 400 =	2,000,000
8,000	× 600 =	4,800,000
16,000		7,600,000

and 7,600,000
16,000 = 475 feet average haul.

Proof.—Assume the cost of moving 1,000 yards one foot as ten cents, the costs of the separate masses are

1,000 yards 200 feet is	$20.00
2,000 yards 300 feet is	60.00
5,000 yards 400 feet is	200.00
8,000 yards 600 feet is	480.00
Sum,	$760.00

also the cost of moving 16,000 yards 475 feet is

16 × 475 × 10 = $760.00.

119. The movement of earth is effected by shovels, barrows, horses and carts, or by cars. In round numbers we can move earth

By shovels alone	10 to	20 feet,
By barrows alone	20 to	100 feet,
By carts	100 to	500 feet,
By cars	500 to	5,000 feet,

As the haul increases, the number of vehicles of transport remaining the same, the number of excavators must decrease. Earths easily removed do not admit of so large a haul, with a given number of excavators, as hard earths. The nature of the ground, form of carts, kind of horses, season of the year, and price of labor are some of the elements entering the problem of transport. The best illustration of the matter will be found among the very able writings of Ellwood Morris, Esq., C. E., in the Journal of the Franklin Institute. Knowing the value of wages, the nature of the earth and length of haul, it is easy to see what mode of transport must have the preference.

CONTRACTOR’S MEASUREMENTS.

120. The price of executing any piece of work is paid to the contractor at stated intervals, generally once each month. The amount of work done at these partial payments is obtained by instrumental reference to the ground. Towards the completion of operations the most correct and easiest method of finding the rate of progress is to deduct the amount already done from the total as given by primary measurement. The full price is not paid to the contractor, but a percentage is kept back, which insures a faithful performance of work. It is impossible to establish a pro rata price at first, owing to the uncertain nature of the work; what appears to be earth may be rock. By deducting a maximum price estimate for all but one of the items, an approximate pro rata value for that one may be determined. An analysis of cost will define the minimum limit for advantage to the contractor; and the pro rata value less the percentage, the maximum for the company’s benefit.