The tractive power of a locomotive, and especially the reduction of the effective tractive power with increase in velocity, has already been discussed in previous chapters. It is expected that on ruling grades a train runs slowly if necessary. Fortunately the tractive power of a locomotive is greatest when the speed is slow, and when very nearly the full theoretical adhesion of the drivers to the rails can be counted on. In Table XXVII are given the tractive powers of locomotives of a wide range of types and weights and with various ratios of adhesion. Almost any locomotive will be sufficiently similar to one of these given in this table, so that the tractive force here given may be used for calculations, at least approximately. In Table XXVIII is shown the total train resistance in pounds per ton for various grades and for various values of track resistance. By a combination of these two tables the net train-load on any grade under given conditions may be quickly determined. For example, a consolidation engine weighing 214,000 pounds and having 106,000 on the drivers, will have a tractive power of 23,500 pounds when the effective adhesion is 1/4. When it is moving slowly up a 1.2% grade the grade resistance is 24 pounds per ton, and if the tractive resistance on a level is 6 pounds per ton the total train resistance per ton will be 30 pounds. Dividing 26,500 by 30, we have 883 tons as the gross train-load. Subtracting 107 tons, the weight of the engine and tender in working order, we will have 776 tons as the net load. A much better way of considering this will be on the basis of rating tons, as already explained in Chapter XI (Momentum Grades. 124. Velocity Head), but, whatever the method adopted, Tables XXVII and XXVIII are accurate as long as the velocity is so slow that the boiler capacity is not overtaxed, and as long as the proper ratio of adhesion and the actual tractive resistance on a level are chosen for use in the tables.

Table XXVII. Tractive Power of Various Types OF Standard-gauge Locomotives at Various Rates OF Adhesion.

197. Proportion Of Traffic Affected By The Ruling Grade

Very many light-traffic roads are not fortunate enough to have a traffic which is materially affected by the rate of ruling grade. Passenger-trains are very seldom affected, unless the volume of traffic is so great that the number of cars attached to one engine approaches the limit which one engine is able to haul. The comparatively high speed usually demanded of passenger-trains means that the locomotive must have high steaming power to haul even light loads. Such light loads do not require very great tractive force, and therefore the tax on the adhesion of the drivers is correspondingly small. When a passenger-train reaches an unusually heavy grade, the effect of the grade is usually confined to reducing the speed of the train. On any road but a trunk line such a slight reduction of speed has almost no financial value. We may therefore make the general statement that for all light-traffic roads the passenger-trains need not be considered as being affected by the rate of ruling grade. Local freight-trains may sometimes be considered in the same way. It frequently happens that the local freight is sent out over the line with a far less number of cars than could be hauled by one engine, and therefore the ruling grades cannot be considered as affecting these trains. Whatever business is done by the road in handling bulky freight, such as coal, ore, or timber, is usually handled in train-loads which are made as heavy as the power of the engine on the grades of the road will permit. All such trains are directly affected by the rate of ruling grade. Therefore, in counting the number of trains which are affected by the ruling grade, we must usually count all coal-, lumber-, and ore-trains, and all through freight-trains which are run from one terminus of the division to another, as well as passenger-trains, if any, which are actually limited in length or weight by the grade.

Table XXVIII. Total Train Resistance Per Ton (Of 2000 Pounds) On Various Grades

Grade.

When tractive resistance on a level in pounds per ton is

Rate per cent.

Feet per mile.

6

7

8

9

10

0.00

0.00

6

7

8

9

10

.05

2.64

i

8

9

10

11

.10

5.28

8

9

10

11

12

.15

7.92

9

10

11

12

13

.20

10.56

10

11

12

13

14

025

13.20

11

12

13

14

15

.30

15.84

12

13

14

15

16

.35

18.48

13

14

15

16

17

.40

21.12

14

15

16

17

18

.45

23.76

15

16

17

18

19

0.50

26-40

16

17

18

19

20

.55

29.04

17

18

19

20

21

.60

31.68

18

19

20

21

22

.65

34.32

19

20

21

22

23

.70

36.96

20

21

22

23

24

0.75

39.60

21

22

23

24

25

.80

42.24

22

23

24

25

26

.85

44.88

23

24

25

26

27

.90

47.52

24

25

26

27

28

0.95

50.16

25

26

27

28

29

1.00

52.80

26

27

28

29

30

.05

55.44

27

28

29

30

31

.10

58.08

28

29

30

31

32

.15

60.72

29

30

31

32

33

.20

63.36

30

31

32

33

34

1.25

66.00

31

32

33

34

35

.30

68.64

32

33

34

35

36

.35

71.28

33

34

35

36

37

.40

73.92

34

35

36

37

38

.45

76.56

35

36

37

38

39

1.50

79.20

36

37

38

39

40

.55

81.84

37

38

39

40

41

.60

84.48

38

39

40

41

42

.65

87.12

39

40

41

42

43

.70

89.76

40

41

42

43

44

1.75

92.40

41

42

43

44

45

.80

95.04

42

43

44

45

46

.85

97.68

43

44

45

46

47

.90

100.32

44

45

46

47

48

1.95

102.96

45

46

47

48

49

2.00

105.60

46

47

48

49

50

Grade.

When tractive resistance on a level in pounds per ton is

Rate per cent.

Feet per mile.

6

7

8

9

10

2.00

105.60

46

47

48

49

50

.05

108.24

47

48

49

5C

51

.10

110.88

48

49

50

51

52

.15

113.52

49

50

51

52

53

.20

116.16

50

51

52

53

54

2.25

118.80

51

52

53

54

55

.30

121.44

52

53

54

55

56

.35

124.08

53

54

55

56

57

.40

126.72

54

55

56

57

58

.45

129.36

55

56

57

58

59

2.50

132.00

56

57

58

59

60

.55

134.64

57

58

59

60

61

.60

137.28

58

59

60

61

62

.65

139.92

59

60

61

62

63

.70

142.56

60

61

62

63

64

2.75

145.20

61

62

63

64

65

.80

147.84

62

63

64

65

66

.85

150.48

63

64

65

66

67

.90

153.12

64

65

66

67

68

.95

155.76

65

66

67

68

69

3.00

158.40

66

67

68

69

70

.05

161.04

67

68

69

70

71

.10

163.68

68

69

70

71

72

.15

166.32

69

70

71

72

73

.20

168.96

70

71

72

73

74

3.25

171.60

71

72

73

74

75

.30

174.24

72

73

74

75

76

.35

176.88

73

74

75

76

77

.40

179.52

74

75

76

77

78

.45

182.16

75

76

77

78

79

3.50

184.80

76

77

78

79

80

4.00

211.20

86

87

88

89

90

4.50

237.60

96

97

98

99

100

5.00

264.00

106

107

108

109

110

5.50

290.40

116

117

118

119

120

6.00

316.80

126

127

128

12S

130

6.50

343.20

136

137

138

13S

140

7.00

369.60

146

147

148

149

150

8.00

422.40

166

167

168

169

170

9.00

475.20

186

187

188

189

190

10.00

528.00

2oe

207

208

209

210