As a practical illustration of the figures in Table XXIX assume that the ruling grade on a given line is 1.4% (73.92 feet per mile). Assume that only 8 trains per day out of a total of 20 trains of all kinds are to be considered as affected by the rate of the ruling grade. Assume that it has been discovered that with the expenditure of $300,000 a change of alinement may be made which will reduce the ruling grade to 1%. Is such an expenditure justifiable under the circumstances? It has been shown in the chapter on Train Resistance that the actual tax on the locomotive depends quite largely on the ratio of live load to tare. Therefore the only comparison which can justifiably be made as the basis for planning construction is to assume the same conditions of loading for both cases. For this comparison we will assume the resistances taken from Mr. Dennis's paper, as already referred to in Chapter XI (Momentum Grades. 124. Velocity Head), §§ 128-133. The grade and tractive resistance for a rating ton on the 1.4% grade would be (28.0 + 2.6), or 30.6 pounds per ton. The tractive power, as given for Mr. Dennis's locomotive at the speed of 7 miles per hour, is 28,200 pounds. The gross rating tons which could be hauled at this speed therefore equals (28,200/30.6), or 922 gross rating tons. The ratio of a tare ton to a rating ton on a 1.4% grade equals 121% (see § 129). The actual weight of the locomotive and tender was 130 tons. On the 1.4% grade the resistance of the locomotive would be that due to (121% x 130) = 157 rating tons. Subtracting this from 922, we have 765 rating tons behind the locomotive. On the basis that the live load is twice the tare, the actual weight of cars with their loading would equal [3/(2+1.21)] x 765 = 715 tons.

Table XXIX. Additional Cost Of Operating A Given Freight Tonnage With (N+1) Engines On Heavy Ruling Grades Instead Of With N Engines On Lighter Grades

Item number.

Item (abbreviated)

Normal average.

Per cent affected.

Cost per mile, per cent.

2

Ballast,

14.89

50

7.46

3

Ties

4

Rails,

5

Other track material,

6

Roadway and track,

9

Bridges, trestles and culverts

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

5.20

0

0

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

20.09

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

7.45

25-27

Steam locomotives ...................

8.61

80

6.89

34-36

Freight cars ....................

10.15

-10

-1.01

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

3.98

0

0

Maintenance of equipment.....

22.74

5.88

53-60

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

3.08

0

0

80

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

6.08

100

6.08

81

Enginehouse expenses, road....

1.72

100

1.72

82-85

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

11.41

80

9.13

88-94

Train service, etc. .......................

9.66

100

9.66

97,98

Stationery, printing etc ...........

0.57

50

0.28

99, 101, 103

Loss, damage, etc............

2.82

50

1.41

104, 105

Operating joint tracks, net.....

0.02

100

0.02

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

18.16

0

0

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

50.44

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

28.30

106-116

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

3.65

0

0

100.00

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

41.63

Since § of this weight consists of live load, the actual weight of live load carried in one train behind such an engine up the 1.4% grade is 477 tons. But, since we are assuming that these cars are loaded to the limit of their capacity, or at least to the same ratio of that limit, we will consider 715 tons as the total weight for both grades of the freight and of the cars which carry it. On a 1% grade the ratio of tare ton to rating ton is 128%. On this grade the locomotive has the equivalent weight of (128% x 130) = 166 rating tons. The eight trains, each of which are assumed to have a gross weight for cars and live load of 715 tons, will therefore weigh 5720 tons. On a 1% grade this will be the equivalent of 5720/[3/(3+128)] = 6254 rating tons.

The grade and tractive resistance for a rating ton on a 1% grade equals (20.0+2.6), or 22.6 pounds per ton.

This locomotive at seven miles per hour can therefore handle 28,200/22.6 = 1248 rating tons.

Subtracting 166 rating tons for the locomotive, we have left 1082 rating tons behind the tender as the capacity of one engine. 'Dividing 6254 by 1082, we have something less than 6, which shows that 6254 rating tons could be handled by six such engines with a margin of 238 rating tons. We may therefore say that, as the effect of reducing the ruling grade from 1.4% to 1%, the eight trains, which are affected by the rate of the ruling grade, can now be handled by six engines, and that there will be the saving due to the reduction of two trains. If these trains were operated 365 days per year, the annual saving on the basis of 62.5 c. per train-mile will be 2 x 0.625 x 365 = $456.25 per mile of length of that division. If the division is 100 miles long, the annual saving is $45,625. Capitalizing this at 5% we have an additional justifiable expenditure of $912,500. Since this is over three times the computed expenditure, which can be readily estimated as the cost of effecting this reduction in ruling grade, it would appear that the improvement is thoroughly justified, especially since future traffic will probably increase rather than diminish the value of the improvement.