To determine the effect of a delay in clearing Signal No. 47 upon a train approaching this signal, the curves in Figure 7 have been plotted. If Signal 46 indicates "Caution," and Signal 47 "Danger" or "Stop," the following train will require 20 seconds to come to a stop directly opposite Signal 47 from a speed of 26 miles per hour, which is the predetermined speed at which the train should reach Signal 46. If, however, Signal 46 clears so as to allow the train to pass at its maximum speed which is permissible at this point, it will require but 13 seconds for the train to pass through the block preceding Signal 47. In other words, if a clear indication of Signal 47 is delayed 7 seconds (20 seconds minus 13 seconds) then the train will be brought to a full stop at this signal, and as shown by Figure 6 an addition of 142 seconds is made to the running time of the train on account of this full stop. One of the cumulative effects of a delay is thus shown, as by stopping of the train the delay of 7 seconds is at once multiplied into a delay of 141⁄2 seconds, or more than doubled. This diagram shows further the disadvantage of allowing even a small delay to creep into the schedule, and indicates why the operation of the Subway trains upon any single tracks is sensitive to a very slight derangement. In this Figure the small diagrams at the side of the table are intended to illustrate the actual record of seconds shown in the various columns of the table. The first row of figures show that a train entering the Grand Central Station block can come to rest at the station platform in 31 seconds, can then take 62 seconds to unload, load and start, and can then run the length of the platform in 23 seconds, leaving 4 seconds for the signal system to transmit the clear or proceed signal to the following train, the entire cycle of operation having required 120 seconds. The next row of figures shows this same cycle of operation with the exception that the wait at the station platform has been prolonged to 64 seconds, instead of 62 seconds, thus requiring 122 seconds for the complete cycle. The effect of the extra two seconds upon the movement of the following trains is immediate. The third row of figures shows the first effect of the delay. The following train has been delayed 2 seconds and enters the block beginning at signal 47 at a reduced speed; it therefore takes slightly longer than the previous train in coming to rest at the platform (331⁄2 seconds instead of 31 seconds). With the same length of station wait as the original train (62 seconds), the cycle of this third train will require 122 seconds, and the resulting delay of 2 seconds is added to the first delay of 2 seconds, making a total of 4 seconds to be transmitted by means of the signal system to the fourth train. This 4 second delay will cause a corresponding delay in the time of the fourth train, thus making a total delay of 8 seconds, and this delay is sufficient to bring the fifth train to a complete stop at Signal 47. The fifth train starting from a complete stop will require 46 seconds to reach a stop at the station platform, and this time added to 62 seconds platform wait and to the time required to clear the platform and give the proceed signal, will cause this fifth train to occupy the station block for 135 seconds, or 15 seconds over time. The sixth train will thus encounter a delay of 23 seconds (15 seconds plus 8 seconds) which is automatically accumulated from the original delay in the schedule of but 2 seconds. To maintain a headway of 120 seconds with each train stopping at Signal 47 will require that all the platform waits be limited to 47 seconds, and it is absolutely impossible to so limit these station waits to 47 seconds with the present end door cars. Any stop exceeding 47 seconds simply adds to the delay of the following trains. In the next row of figures showing the history of the sixth train, it will be seen that the train starts from a full stop at Signal 47 and reaches a stop at the platform in 46 seconds-the station wait is shown as requiring 47 seconds but the proceed signal to the following train has been given at the time of the starting of the train away from the platform instead of waiting until the train has entirely left the platform; that is, the clearing of Signal 47 has been advanced a full 23 seconds in order to show clearly the benefits to be expected by overlapping one cycle of operations on the following cycle. The time of 4 seconds required for the operation of the signal including the time required for the motorman to act has been retained at 4 seconds as in all previous cases. The elimination of the 23 seconds makes the cycle of operations for the sixth train only 97 seconds long, and the removal of the 23 seconds from the possible delay of the seventh train will allow the seventh train to pass Signal 47 at full speed and to pull into the station and stop in 31 seconds as originally intended. Thus the 120 second headway with the 62 second station wait can be resumed and continued until for some reason a prolonged station wait introduces another delay which by its cumulative action will again derange the regular periodicity of the train movement. The action of the permissive signal system indicated by this diagram shows how the removal of 23 seconds may be compared to the taking out of a link in a chain which has become loose, and the diagrams indicate that if occasionally a train is advanced a number of seconds closer to the preceding train than is now allowed by the inflexibility of the signal system, the disastrous results of the cumulative effects of a delay can be removed. The occasional operation of the suggested permissive signal under the safeguards recommended in the Report upon the Subway Signal System is practically the only method at present known to me by which the trains could be advanced and the schedule straightened out. |