. Railroad construction. Theory and practice . ^ other case, illustrationsof which will follow) is found by adding to the actual profileat any point an ordinate which represents the velocity headdue to the velocity of the train at that point. As another case, assume that a train is climbing the grade AEand exerting a pull just sufficient to maintain a constant velocity ^ / up that grade. Then AB (parallel to A 5) is the virtual profile, A A*representing the velocity head. Astop being required at (7, steam isshut off and brakes are appliedat 5, and the velocity head BBreduces to zero at C. The
. Railroad construction. Theory and practice . ^ other case, illustrationsof which will follow) is found by adding to the actual profileat any point an ordinate which represents the velocity headdue to the velocity of the train at that point. As another case, assume that a train is climbing the grade AEand exerting a pull just sufficient to maintain a constant velocity ^ / up that grade. Then AB (parallel to A 5) is the virtual profile, A A*representing the velocity head. Astop being required at (7, steam isshut off and brakes are appliedat 5, and the velocity head BBreduces to zero at C. The trainstarts from C, and at D attains a velocity corresponding tothe ordinate DU. At D the throttle may be slightly closedso that the velocity will be uniform and the virtual grade isDE, parallel to DE. From the above it may be seen that a virtual profile has thefollowing properties: (a) When the velocity is uniform, the virtual profile is parallelwith the Fig. 213. § 433. GRADE. 465 (b) When the velocity is increasing the profiles are separating ;when decreasing the profiles are approaching. (c) When the velocity is zero the profiles coincide. 433. Use, value, and possible misuse. The essential featurerespecting grades is the demand on the locomotive. From theforegoing it msLj readily be seen that the ruling grade of a roadis not necessarily the steepest nominal grade. When a grademay be operated by momentum, , when every train has anopportunity to take ^a run at the hill/ it may become a veryharmless grade and not limit the length of trains, while anothergrade, actually much less, which occurs at a stopping-placefor the heaviest trains, will require such extra exertion to gettrains started that it may be the worst place on the road. There-fore the true way to consider the value of the grade at any criti-cal place on the road is to construct a virtual profile for thatsection of the road. The required length of such a profile isvar
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