Brake Tests

228 433. In order to obtain the average resistance to the motion of the train, it is necessary to integrate this curve. The shape of the curve at the beginning is determined by the more or less rapid rate of rise of brake cylinder pressure, which depends upon the kind of brake equipment being used. In order to arrive at a relation between the force developed in the brake cylinder or at the brake shoe, and the resulting retarding force, it is advantageous to consider this relation from the standpoint of constant brake cylinder, or shoe pressure throughout the stop. Consequently, it is desirable to replace the effect of the variable press- ures acting during the time the brake is being applied by their equiv- alent effects, had the maximum pressure developed, and held through- out the stop, been realized instantaneously. This can be done by determining the point of equivalent instantaneous application of re- tarding force, which is the point at which the maximum retarding force initially developed could have been applied instantaneously to pro- duce the same effect on the speed of the train, as was realized from the gradual building up of retarding force that actually occurred. The amount of work required to reduce the initial speed of the train to the value which existed at the time the retarding force reached its initial maximum value, is proportional to the area under the distance- resistance curve up to this point. The same amount of work would be represented if the gradually rising resistance curve were replaced by a vertical line, representing the development of the same maximum retarding force instantly, but at a point such that the work done in the two cases is the same. In other words, referring to Fig. 138, the area of the rectangle CDABC is equal to the area of the irregular figure OABO. 434. Having determined the point of equivalent instantaneous application of the retarding force, the average resistance, during the time that the brake may be considered fully applied, can be found by inte- grating the area under the entire distance-resistance curve and dividing this area by the total length of stop minus the distance from the start (o) to the point of equivalent instantaneous application. Referring to Fig. 138, this is equivalent to dividing area CDAEFC by CF. The average resistances in pounds per ton, shown in Figs. 138 to 141, were determined in this manner. 435. The amount of work done during any interval is equal to the corresponding change in kinetic energy. If the change in kinetic energy for consecutive intervals throughout the stop is calculated from data afforded by the speed-time curves, and these values plotted at times corresponding to the average speeds during these intervals, the locus of the points so determined will be a curve representing the rate at which work is being done throughout the stop or, in other words, the power being developed at each unit interval of the stop. Curves so determmed are indicated on Figs. 138, 139 and 140, as power-time