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TABLE 1-COMPARING ACTUAL TRAIN-HOURS OPERATED WITH THE

THEORETICAL TRAIN-HOUR CAPACITY

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111

17

6.5

.

10.0 11.0 122 0

80.0 3200

60

60

60.

1. Length of Division.

138
124
132

117 2. Miles of double track

11
10
51

56 3. Number of passing sidings.. 24

22
18

14
4. Average miles between sid-
ings..

5.1
5.0
4.3

4.1
5. Maximum miles between
sidings...

8.5
8.8
6.5

5.1 6. Miles of passing sidings.

17.8 17.2 15.0 17.0 7. Total miles of track.

166.8 151.2 198.0 190.0 8. Number of cars per train. 60. 9. Length of train, feet.

2400 2400 2400 2400 11. Theoretical track capacity, train-hours...

*1544 *1460

13485 13854
12. Actual train-hours operated.
Date.

Aug., 1920 Jan., 1920 Aug., 1920 Jan, 1920
Train-hours, freight. 10,000 10,835 10,415 7,793
Train-hours, passenger,
estimated

580
506
846

729
Train-hours, maximum
month.

10,580 11,341 11,261 8,522
Average train-hours per
day...

341
366
363

275
13. Ratio of actual train-hours
to theoretical capacity...

.222
.250
.104

.071
14. Gross ton miles divided by
miles of road..

29,750 34,150 55,100 38,600 15. Ave. train miles divided by miles of road.

27.9 27.7 28.0 24.0

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provided there are no signals spacing trains farther

than one train length apart. On Divisions A and B, Fig. 1, the longest stretch of single track between sidings is 8.5 and 8.8 miles, respectively. If there were but one class of trains operated over these divisions and the speeds were uniform over the entire division the maximum number of trains which could be on the line at any one time would be the same as if all the sidings were the same distance apart, namely 8.5 and 8.8 miles, respectively; that is, from this cause alone the track capacity is reduced from 600 and 528 train-hours per day to 384 and 213 train-hours per day, respectively. Suppose the trains took eight hours to run between terminals and 34 hour to run over the longest section, then there could only be 24 = 34 = 32 trains operated per day, or a capacity of 8 X 32 = 256 train-hours per day.

The actual sidings at each end of the longest sections may be long enough to accommodate two or more trains at a time, in which case we would expect that actual operations could be adjusted to fit the conditions, and a somewhat greater capacity than 256 train-hours could be obtained,

Table I gives a comparison of the actual with the theoretical track capacity, assuming these divisions are operating up to full capacity. The actual train-hours reported cover operations over the single and double track sections because data could not be obtained which would show the actual train-hours operated over each section. It is much better to con

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DIVISION A

Sidings

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50 60

80 go

700
Miles
FIG. 1-TRACK CHARTS OF FIVE ENGINE DISTRICTS.

sider the track capacities of the single and double track sections separately because the capacity of the single track section always limits the capacity of the division. Likewise, if some trains branch off at junction points between terminals the actual train-hours for various sections where the train density is different should be obtained separately.

There is only a light passenger service operated over these divisions and the train-hours consumed by passenger trains on the road are estimated from time-table schedules. On Division A the passenger run is longer than the freight, as indicated by the dotted lines, but the passenger train-hours are estimated to cover only the freight division.

Comparing the actual train-hours per day with the theoretical capacity it will be noted that the single track sections are being operated nearer to capacity than the double track sections. The gross ton-miles per mile of road is greatest for the sections having the greatest amount of double track, but the train-miles per mile of road differs little on any of the sections. There is more passenger service on Division D, particularly on the double track section, than on the other divisions, a fact which no doubt accounts for much of the double track on this division. How much nearer it is possible to approach the theoretical values than are shown by the ratios for the single track sections is problematical. What effect extending the double track will have in reducing the running time of trains would be very interesting to watch, if such plans are being considered.

The comparisons in the above table are based upon the daily average of the maximum month's operation. The maximum movement for a shorter period may show greater utilization of track facilities and it would be interesting to apply these principles to shorter periods of record movements to see what effect limited track facilities have upon train movements under these conditions or how record movements are brought about. On the other hand, the maximum daily movement which can be handled over a given division is of very little value unless nearly equal movement can be repeated day after day without causing congestion.

Usually the best criterion for judging the traffic capacity of a division is the traffic which it can handle regularly for a period of 15 days or a month. In this connection Fig. 2 shows the average road time per train plotted against the average number of trains per day (assuming the number of trains equals train-miles per mile of road per day) for 22 months.

At first glance it would appear that there is no relation between the time taken per train to cover the road and the number of trains on the road per day. However, by symbolizing the various points so as to distinguish between summer and winter operation, Government control period and months of different years, those familiar with the conditions of operation at those times can no doubt explain many of the irregularities.

Without attempting to analyze the charts it will be seen that the road time for 1921 shows improvement over 1920, that operations are appreci

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ably affected by weather conditions, especially by winter temperatures. The important relation it is intended to show by these charts is the tendency for every train to consume more time on the road, the greater the number of trains on the road per day. This tendency is indicated by the slope of the lines drawn through the middle of the group of points. This relation is brought out in the methematical development of the theory of train operation discussed in the Exhibit. Simplification of the Train-Hour Diagrams.

Last year a method of plotting actual train-hour and crew-expense diagrams was discussed. The method of obtaining and asranging the data for these charts is tedious and it is felt that some simpler method can be developed which will make it possible to obtain the data with much less effort and at the same time establish mathematical relationships which can be simplified. The scheme briefly is to find the equation of the train-hour diagram and to ascertain if the results obtained by empirical formulas are close enough to the actual to be of practical value. Similarity Between the Typical Train-Hour Diagrams and

Probability Curve.

Train operations have in them the element of luck, that is, every train-after it leaves a terminal-runs a chance of being delayed from one cause or another. Some trains will be delayed more than others and the time which a train consumes on the road depends largely upon various combinations of circumstances. It is, therefore, logical to assume that an equation in the form of the Probability Curve y = ke-(nr)? will most nearly fit the curve of a train-hour diagram. The origin of coordinates for such a curve is (0,0) and the curve is symmetrical both sides of the y axis, as shown in Fig. 3. The typical train-hour diagram is obtained by using only half of the probability curve and substituting a rectangle for the other half, as indicated.

(ant)2

Y2

FIG. 3—DIAGRAM SHOWING DEVEI OPMENT OF THE TYPICAL TRAIN-HOU'R

DIAGRAM FROM THE PROBABILITY CURVE.

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