An inspection of the items under this general heading will show us that we may at once throw out as unaffected all the items except those which concern engine-supplies for road engines, flagmen, and watchmen, and the group which refers to accidents.

173. Items 82, 83, 84, And 85

The required quantities in this calculation are the additions to cost resulting from the introduction of 528° of central angle into a mile of track. We have assumed that this amount of curvature will exactly double the resistance. We found in Chapter XII (§ 142) that the average increase in fuel consumption due to direct hauling amounts to about 44%. We have here assumed that the added curvature exactly doubles the work. We will therefore charge 44% of the average cost of a train-mile for this extra curvature. Since the consumption of water and other engine-supplies is roughly proportional to the consumption of coal, there will evidently be no error worth considering in assigning this same percentage to Items 83, 84, and 85.

174. Flagmen

There are many cases where a dangerous curve justifies and requires the employment of a special flagman to give timely notice of any dangerous condition of the track. Such special cases would, of course, justify a considerable expenditure to eliminate the dangerous features of that particular location, but such a charge should not be made against curvature in general. Ordinarily the elimination or retention of a curve will not involve the question of watchmen and flagmen in any way. We are therefore justified in disregarding this item altogether as a general proposition, if we keep in mind that the item should be included when we are considering the elimination of some particularly dangerous curve.

175. Items 93, 99-103

This group of items, which refer to accidents and the increased danger of accident due to curvature, and therefore the amount of money which might be justifiably spent to avoid this danger, has already been discussed in § 160. It was there shown that, although there might be special cases which would justify considerable expenditure on account of specific dangers in the situation, we cannot ordinarily give any definite financial value to this item as applied to curvature in general. We therefore must eliminate these items as affecting the cost of curvature in general.

General Expenses

Items 106 to 116 will also be unaffected.

176. Estimate Of Total Effect Per Degree Of Central Angle

Compiling the above estimates we have Table XXV. According to the table 528° of curvature in one mile will increase the expenses of each train passing over it by 39.65% of the average cost of a train-mile, and, according to the general principles laid down in § 163, one degree of central angle of any curve, no matter what the radius, will increase the expenses by 1/528 of 39.65%, or .0751% per degree. Therefore, the cost per year per daily train each way, at the average rate of $1.50 per train-mile would be 150 x .0751% x 2 x 365 = 82.23 c.

For a round number we will call this 82 cents.

To forestall one kind of objection to the foregoing course of reasoning, it should be remembered that many of the estimates of additional cost, instead of being actually based on the effects of a continuous 10° curve, were based on the observed effects of lighter curvature, which were then multiplied by a factor to obtain the effect of a continuous 10° curve, as if the effects of curvature were strictly proportional to the curvature; but since we afterward divide our final result by 528 to obtain the effect of one degree of curvature, and then multiply this constant by the number of degrees of central angle, as found in ordinary practice, our calculations are not thereby vitiated because the effect of curvature is not strictly proportional to the rate of curvature. It is probably true that within the ordinary limits of variations in rate of curvature the above calculations are substantially true. In extreme cases they are probably in error, although it is likewise probably true that extreme curvature will have a variable effect on the rate of increase of the various items, and that even in extreme cases the error will not be very large.

Table XXV. Effect On Operating Expenses Of Changes In Curvature

Item number.

Item (abbreviated).

Normal average.

Per cent affected.

Cost per mile, per cent.

2

Ballast......................

0.50

25

0.12

3

Ties........................

3.10

50

1.55

4

Rails.......................

0.92

226

2.10

5

Other track material..........

1.13

25

0.28

6

Roadway and track...........

7.53

25

1.88

(All other items).............

6.91

0

0

Maintenance of way..........

20.09

5.93

25-27

Locomotives.................

8.61

196

16.88

31-33

Passenger-cars...............

2.14

50

1.07

34-36

Freight-cars.................

10.15

100

10.15

43-45

Work-cars...................

0.34

100

0.34

46

Shop machinery; tools........

0.53

50

0.26

(All other items).............

0.97

0

0

Maintenance of equipment.....

22.74

28.70

53-60

Traffic......................

3.08

0

0

82-85

Fuel and other supplies for road engines....................

11.41

44

5.02

(All other items).............

39.03

0

0

Transportation...............

50.44

5.02

106-116

General expenses.............

3.65

0

0

100.00

39.65