LOCATION. 17 



to acquire speed more rapidly. Train stops near the foot of a 

 long grade are most limiting in this respect. 



VIRTUAL GRADES. 



The motion of a train represents stored energy, derived from 

 the engine or gravitation, and, under appropriate conditions, 

 the power of the engine may be in part absorbed in imparting 

 speed to the train, or augmented by the surrendered momen- 

 tum of the train. 



When rolling and grade resistances exceed the applied force, 

 motion is retarded and energy released in definite propor- 

 tions, and conversely, when the applied force is in excess, mo- 

 tion is accelerated and energy imparted in like proportions. 



The moving energy of the train at different speeds is given 

 in Fig. 2 in terms of "Velocity Head," which is the vertical 

 height, through which the train would be lifted, at each 

 degree of speed by its momentum alone. 



The engine tractive power is least at high speed and short 

 "cut off" and greatest at low speed and "full stroke," as 

 shown in Fig. 1. 



The mean tractive power of these engines from different 

 rates of speed to ton miles per hour is given by the table. Fig. 

 1, or may be deduced from the diagram on the same sheet. 



The maximum available power for overcoming rolling and 

 grade resistance is represented by the product of the train 

 weight and its velocity head, added to the product of the mean 

 engine tractive power, and the time or distance over which 

 the power is exerted, illustrated, in short, in the effect pro- 

 duced by "taking a run at the hill." 



Rolling resistance for trains at all speeds is given by Fig. 3, 

 from which mean resistances between different rates of speed 

 may also be readily computed. 



The simplest rule for computing grade resistance is a fol- 

 lows: Resistance (in Ibs. per ton) = rate of grade (in 

 feet) x 20. 



A gradient of equivalent resistance to the force exerted by 

 the engine is the "virtual grade," or real resistance taxing the 

 engine cylinders. The virtual grade line may be plotted with 



