. Railroad construction. Theory and practice . expenses. The smallest considerationwill show that the sharper the curvature the greater will bethe tractive force required, also the greater per unit of tracklength will be the rail wear and the general w^ear and tear onroadbed and rolling stock. But it would be inconvenientto use a relation between operating expenses and radius ofcurvature, because even when such a relation was found therewould be two elements to consider in each problem—the radiusand the length of the curve. The method which will be heredeveloped cannot claim to be strictly acc
. Railroad construction. Theory and practice . expenses. The smallest considerationwill show that the sharper the curvature the greater will bethe tractive force required, also the greater per unit of tracklength will be the rail wear and the general w^ear and tear onroadbed and rolling stock. But it would be inconvenientto use a relation between operating expenses and radius ofcurvature, because even when such a relation was found therewould be two elements to consider in each problem—the radiusand the length of the curve. The method which will be heredeveloped cannot claim to be strictly accurate or even strictlylogical, but, as will be sho^^Ti later, the most uncertain elementsof the computation have but a small influence on the finalresult, and the method is in general the only possible method ofsolution. The outline of the method is as follows: (1) For reasons given in detail later, it is found that theexpenses, wear, etc., on the track from A to B will be substan-tially the same whether by the route M or N, The wear, etc.,. Fig. 208. per foot at N is of course greater, but the length of curve isless. Therefore the effect of the curvature depends on thedegrees of central angle J and is independent of the radius. 450 RAILROAD CONSTRUCTION. § 422. (2) At what degree of curvature is the total train resistancedouble its value on a tangent? Probably no one figure wouldbe exact for all conditions. Train resistance varies with thevelocity and with the various conditions of train loading evenon a tangent, and it is b}^ no means certain (or even probable)that the ratio would be exactly the same for all an average figure we may say that a train running at averagevelocity on a 10° curve will encounter a resistance due to cur-vature of about 10 lbs. per ton, which is the average resistancefound on a level tangent. On a 10° curve therefore the resistanceis doubled. (3) A train-mile costs about so much—approximately $ the tractive resistance
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