LOCATION. 15 



to maximum gradients. This effect occurs oftenest on valley 

 lines with low ruling gradients. 



Train weights may be limited either by ruling gradients 

 which tax adhesion, or by time requirements, which tax the 

 engine boiler. 



The product of speed and train resistance is horse-power, 

 and with fixed conditions of speed and engine horse-power, 

 the train resistance is also fixed. Hence, the train weights 

 over the division may be fixed by the average scheduled speed, 

 and the engine horse-power at limits far below those fixed by 

 ruling gradients. Under such conditions the average and not 

 the maximum resistance controls the train weights. 



Compute engine horse-power by the simple formula 



R x S 



p __ . 



375 



in which P is horse-power; R, resistance of total train in 

 pounds; S, speed in miles per hour; and 375 a constant factor. 

 (See Fig. 1 for horse-power of typical engines in use on the 

 N. P. Ry. in 1898.) 



Vertical curves are required on summits at all grade inter- 

 sections not less than 50 ft. in length for each change of one- 

 tenth in rate of grade. 



In "sags" the rate of change should not exceed 0.05 ft. per 

 station. In theory, the rate of change should be such as to 

 maintain equality between the rolling resistance and the 

 "acceleration of gravity" of each car throughout the varying 

 rates of speed. 



RULING GRADES. 



Grades which limit the maximum weights and length of 

 trains, are termed "Ruling Grades." Maximum grades, which 

 may be operated by heavier engines, or by assistant engines, 

 are not necessarily ruling grades. 



The economic value of changes in rates of grades is deter- 

 mined by the relative total cost and number of trains required 

 on each rate of grade to transport the same number of cars 

 and tons. The practical rule is as follows: Multiply the daily 

 number of trains saved or added by the ascertained cost per 

 train-mile, by the length of the division in miles, and by the 



