. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools. By Walter Loring Webb . owering the grade line near that place, and diminishthe cut (and hence the amount of material to be wav^ted) byraising the grade line at or near the ])lace farther on. Whetherthe advantage thus gained would compensate «for the possiblyinjurious effect of these changes on the grade line would requirepatient investigation. But the method outlined shows how the 124 ItAILROAD CONSTRUCTION. 105. mass curve might be used to indicate a possible change in -radelin


. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools. By Walter Loring Webb . owering the grade line near that place, and diminishthe cut (and hence the amount of material to be wav^ted) byraising the grade line at or near the ])lace farther on. Whetherthe advantage thus gained would compensate «for the possiblyinjurious effect of these changes on the grade line would requirepatient investigation. But the method outlined shows how the 124 ItAILROAD CONSTRUCTION. 105. mass curve might be used to indicate a possible change in -radeline which might be demonstrated to be profitable. ^ 105. Limit of free haul. It is sometimes specified in con-tracts for earthwork that all material shall be entitled to freehaul up to some specified limit, say 500 or 1000 feet, and thatall material drawn farther than that shall be entitled to anallowance on the excess of distance. It is manifestly imprac-ticable to measure the excess for each load, as much so as tomeasure the actual haul of each load. The mass diagram alsosolves this problem very readily. Let Fig. 63 represent a pro-. Fig. G3. file and mass diagram of about 2000 feet of road, and supposethat 800 feet is taken as the limit of free haul. Find twopoints, a and h, in the mass curve which are on the same hori-zontal Une and which are 800 feet apart. Project these pointsdown to a and V. Then the cut and fill between a and h willjust balance, and the cut between A and a will be needed forthe fill between h and C. In the mass curve, the area betweenthe horizontal line ah and the curve aBh represents the haula-eof the material between a and V, which is all free. The reel-angle ahnn represents the haulage of the material in the cutAa across the 800 feet from a to h\ This is also free. Thesum of the two areas Aam and hiC represents the haulageentitled to an allowance, since it is the summation of the productsof cubic yards times the excess of distance hauled. § 105. EART


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