As is indicated by Table VII and Fig. 6, the average cost per train-mile seems to be steadily increasing, while certain of the percentages of the items of cost seem to be regularly increasing (or diminishing) instead of merely fluctuating. On this account the averages for the year 1910 will probably be incorrect as an estimate for immediate future costs. These percentages have been combined in Table XII, page 143. If we assume that the average cost of a train-mile is $1.50, then the operating value of saving the use of the additional engine equals 33% of $1.50 or 50 c. There is, however, one additional item to be considered. Although Items 25-27 includes repairs and renewals of locomotives, it does not include the addition, if any, for the capital cost of the extra locomotive. Perhaps this extra cost may be zero. If we consider that the cost of locomotives is roughly proportional to their tonnage, and that, with locomotives of the same type, the tractive force is nearly proportional to their tonnage, then the four locomotives would cost no more than the three heavier locomotives of equal power. But if the four locomotives cost somewhat more (as is probable), then the extra cost, say $2000, divided by the mileage life of the locomotive, say 800,000 miles, would require 0.25 c. to be charged to the above cost per mile. In this case the addition is almost too small for consideration, but in other cases it should not be neglected.

Table XII. Additional Cost Of Operating A Given Freight Tonnage With (N+1) Light Engines Instead Of N Heavier Engines

No.

Item (abbreviated).

Normal average, per cent.

Per cent affected.

Cost per cent.

1-23

Maintenance of way and structures.

20.09

0

0

24

Supt. of equipment..............

0.64

0

0

25-27

Repairs, etc., locomotives........

8.62

0

0

28-30

Electric locomotives...........

0.01

0

0

31-33

Passenger cars ...............

2.14

0

0

34-36

Repairs, etc., freight cars.........

10.15

-10%

-1.01

37-52

Other equipment ................

1.18

0

0

Maintenance of equipment......

22.74

..........

-1.01

53-60

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

3.08

0

0

61

Supt. of transportation...........

1.20

0

0

62-76

Dispatching, station and yard expenses .......................

16.25

50%

8.12

77-79

Dr. and Cr.; also elec. motormen. .

0.47

0

0

80

Road enginemen................

6.08

76%

4.62

81-85

Enginehouse; fuel and supplies....

13.13

75%

9.85

86-87

Electric power ..............

0.06

0

0

88

Road trainmen..................

6.40

100%

6.40

89

Train supplies.........'.........

1.78

0

0

90-103

Signaling; loss and damage, etc...

5.05

100%

5.05

104-105

Dr. and Cr. - joint facilities.......

0.02

0

0

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

50.44

.........

34.04

106-116

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

3.65

0

0

100.00

..................

33.03

89. Numerical Illustration

Assume that the general manager of a road is considering the justification of employing heavier locomotives to handle a given tonnage. Let us assume that he can depend on a daily traffic which will fill 120 cars per day, having an average gross weight of 70 tons per car. This gives a total weight behind the tender of 8400 tons. A locomotive with a tractive force of 30,000 pounds would probably have a total weight of about 140 tons. When the tractive resistance on the level is six pounds per ton, the total grade resistance on a grade of 35 feet per mile is about 19.5 pounds per ton. If we have a tractive force of 30,000 pounds this would permit the hauling of trains with a gross load of 1540 tons. Subtracting the weight of the engine and tender, about 140 tons, we would have 1400 tons as the permissible weight of cars behind one engine. This will permit the total tonnage to be handled in six trains with this type of engine. To handle this same tonnage in five trains instead of six will require a load of 1680 tons behind each engine. Assume that the heavier engines have the same ratio of tractive power to total weight, which is about 10.7%. On this basis, letting W equal the weight of the locomotive in tons, we may say that (1680+W) 19.5 =2000W X .107. Solving this for W, we find that the weight of the locomotive would be 168.4 tons, or about 337,800 pounds. We would then have as the cost of handling that traffic in five trains, five times $1.50, or $7.50, for each mile of the road. Handling the traffic in six lighter trains with lighter engines will cost a somewhat less price per train-mile, which may be expressed by the figure of five times $1.50 for five trains and 50 c. for the sixth train, which will make $8.00 for the six trains, or $1.33 per mile for the average of the six trains, rather than $1.50 per mile for the five heavier trains. The net difference, however, is the 50 c. per mile of road per day. If the division to which this applies is 100 miles long, it means an added expenditure of $50 per day, or about $18,250 per year.

The student is especially cautioned that the above demonstration should be considered as an outline of a method of investigation, rather than a computation of values to be used. The separate items should be carefully investigated in applying this method to any particular case.