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GRADE

HO scale

Gradients, Curves, Train and Locomotive Weight

The following table is a guide to help predict what length train can be hauled up a particular grade and curve on a HO layout. I have been conservative in developing the table so the tractive ability of HO models in practice should be better. Because of the difficulty in measuring grades, curves and other variables on layouts I cannot guarantee the accuracy of the results for trains on curves. Comments on the accuracy of the table would be appreciated.

 

The table uses the following assumptions

  1. All driving wheels on the locomotive support all the weight of the locomotive.
  2. There is a thin layer of oil on the track
  3. The locomotive driving wheels are nickel plated or stainless steel. (Coefficient of friction = 0.2 on nickel silver track)
  4. The train is free rolling and can roll freely down a 1 in 50 grade.

 

Examples of how to use the table.

I wish to design a double deck layout, using a helix to join the different levels. I want to be able to haul 10 wagons with my locomotive. I have limited space. What is the steepest grade I can use?

From experience I decide to run trains which are a maximum length of 3 times longer than the radius of curve. Each of my wagons is 210mm (60ft HO) long, thus my train length is 2100mm. My locomotive (Kato RS4/5) weighs 378g. If I use 0.57g/mm for my wagon weight, then my train weight is 1197g. My train to locomotive ratio is 1197g / 378g = 3.17. From the table looking down the 3 * radius column 3.17 is between a grade of 1 in 45 and 46. Therefore I would choose I in 45. A minimum radius of 700mm could be used. This would give a rise of 97mm per revolution in the helix. Normally I would not design a HO layout with curves sharper than 900mm radius.

Using the above example we can also determine the steepest grade that can be used on a straight section by looking down the Train on straight column. 3.17 lies between 1 in24 and 1 in 25. Therefore I would choose 1 in 25.

My layout has a 1 in 80 grade on a 910mm radius curve. My passenger train is 2127mm long. This train’s total weight is 1000g. What is the minimum weight required for my locomotive?

The train length is between 2 and 3 times the radius of curve, hence we use the 3 * radius column. The train to locomotive weight result for a 1 in 80 grade is 4.58. Therefore the minimum weight for my passenger locomotive is 1000g / 4.58 = 218 g.

Again we can find the steepest grade on the straight this train can negotiate by looking down the Train Straight column. 4.58 is between 1 in 44 and 1 in 45.

 

 

 

 

 

 

 

 

TRAIN TO LOCOMOTIVE WEIGHT RATIO

GRADE

Train on straight

Train Length = Radius

Train length = 2 * radius

Train length = 3* radius

Train length = 4* radius

Train Length = 5 * radius

Train length = 6 * radius
               

20

2.714285

2.314285

1.914285

1.514285

1.114285

0.714285

0.314285

21

2.816901

2.416901

2.016901

1.616901

1.216901

0.816901

0.416901

22

2.916666

2.516666

2.116666

1.716666

1.316666

0.916666

0.516666

23

3.013698

2.613698

2.213698

1.813698

1.413698

1.013698

0.613698

24

3.108108

2.708108

2.308108

1.908108

1.508108

1.108108

0.708108

25

3.2

2.8

2.4

2

1.6

1.2

0.8

26

3.289473

2.889473

2.489473

2.089473

1.689473

1.289473

0.889473

27

3.376623

2.976623

2.576623

2.176623

1.776623

1.376623

0.976623

28

3.461538

3.061538

2.661538

2.261538

1.861538

1.461538

1.061538

29

3.544303

3.144303

2.744303

2.344303

1.944303

1.544303

1.144303

30

3.625

3.225

2.825

2.425

2.025

1.625

1.225

31

3.703703

3.303703

2.903703

2.503703

2.103703

1.703703

1.303703

32

3.780487

3.380487

2.980487

2.580487

2.180487

1.780487

1.380487

33

3.855421

3.455421

3.055421

2.655421

2.255421

1.855421

1.455421

34

3.928571

3.528571

3.128571

2.728571

2.328571

1.928571

1.528571

35

4

3.6

3.2

2.8

2.4

2

1.6

36

4.069767

3.669767

3.269767

2.869767

2.469767

2.069767

1.669767

37

4.137931

3.737931

3.337931

2.937931

2.537931

2.137931

1.737931

38

4.204545

3.804545

3.404545

3.004545

2.604545

2.204545

1.804545

39

4.269662

3.869662

3.469662

3.069662

2.669662

2.269662

1.869662

40

4.333333

3.933333

3.533333

3.133333

2.733333

2.333333

1.933333

41

4.395604

3.995604

3.595604

3.195604

2.795604

2.395604

1.995604

42

4.456521

4.056521

3.656521

3.256521

2.856521

2.456521

2.056521

43

4.516129

4.116129

3.716129

3.316129

2.916129

2.516129

2.116129

44

4.574468

4.174468

3.774468

3.374468

2.974468

2.574468

2.174468

45

4.631578

4.231578

3.831578

3.431578

3.031578

2.631578

2.231578

46

4.6875

4.2875

3.8875

3.4875

3.0875

2.6875

2.2875

47

4.742268

4.342268

3.942268

3.542268

3.142268

2.742268

2.342268

48

4.795918

4.395918

3.995918

3.595918

3.195918

2.795918

2.395918

49

4.848484

4.448484

4.048484

3.648484

3.248484

2.848484

2.448484

50

4.9

4.5

4.1

3.7

3.3

2.9

2.5

51

4.950495

4.550495

4.150495

3.750495

3.350495

2.950495

2.550495

52

5

4.6

4.2

3.8

3.4

3

2.6

53

5.048543

4.648543

4.248543

3.848543

3.448543

3.048543

2.648543

54

5.096153

4.696153

4.296153

3.896153

3.496153

3.096153

2.696153

55

5.142857

4.742857

4.342857

3.942857

3.542857

3.142857

2.742857

56

5.188679

4.788679

4.388679

3.988679

3.588679

3.188679

2.788679

57

5.233644

4.833644

4.433644

4.033644

3.633644

3.233644

2.833644

58

5.277777

4.877777

4.477777

4.077777

3.677777

3.277777

2.877777

59

5.321100

4.921100

4.521100

4.121100

3.721100

3.321100

2.921100

60

5.363636

4.963636

4.563636

4.163636

3.763636

3.363636

2.963636

61

5.405405

5.005405

4.605405

4.205405

3.805405

3.405405

3.005405

62

5.446428

5.046428

4.646428

4.246428

3.846428

3.446428

3.046428

63

5.486725

5.086725

4.686725

4.286725

3.886725

3.486725

3.086725

64

5.526315

5.126315

4.726315

4.326315

3.926315

3.526315

3.126315

65

5.565217

5.165217

4.765217

4.365217

3.965217

3.565217

3.165217

66

5.603448

5.203448

4.803448

4.403448

4.003448

3.603448

3.203448

67

5.641025

5.241025

4.841025

4.441025

4.041025

3.641025

3.241025

68

5.677966

5.277966

4.877966

4.477966

4.077966

3.677966

3.277966

69

5.714285

5.314285

4.914285

4.514285

4.114285

3.714285

3.314285

70

5.75

5.35

4.95

4.55

4.15

3.75

3.35

71

5.785123

5.385123

4.985123

4.585123

4.185123

3.785123

3.385123

72

5.819672

5.419672

5.019672

4.619672

4.219672

3.819672

3.419672

73

5.853658

5.453658

5.053658

4.653658

4.253658

3.853658

3.453658

74

5.887096

5.487096

5.087096

4.687096

4.287096

3.887096

3.487096

75

5.92

5.52

5.12

4.72

4.32

3.92

3.52

76

5.952380

5.552380

5.152380

4.752380

4.352380

3.952380

3.552380

77

5.984251

5.584251

5.184251

4.784251

4.384251

3.984251

3.584251

78

6.015625

5.615625

5.215625

4.815625

4.415625

4.015625

3.615625

79

6.046511

5.646511

5.246511

4.846511

4.446511

4.046511

3.646511

80

6.076923

5.676923

5.276923

4.876923

4.476923

4.076923

3.676923

81

6.106870

5.706870

5.306870

4.906870

4.506870

4.106870

3.706870

82

6.136363

5.736363

5.336363

4.936363

4.536363

4.136363

3.736363

83

6.165413

5.765413

5.365413

4.965413

4.565413

4.165413

3.765413

84

6.194029

5.794029

5.394029

4.994029

4.594029

4.194029

3.794029

85

6.222222

5.822222

5.422222

5.022222

4.622222

4.222222

3.822222

86

6.25

5.85

5.45

5.05

4.65

4.25

3.85

87

6.277372

5.877372

5.477372

5.077372

4.677372

4.277372

3.877372

88

6.304347

5.904347

5.504347

5.104347

4.704347

4.304347

3.904347

89

6.330935

5.930935

5.530935

5.130935

4.730935

4.330935

3.930935

90

6.357142

5.957142

5.557142

5.157142

4.757142

4.357142

3.957142

91

6.382978

5.982978

5.582978

5.182978

4.782978

4.382978

3.982978

92

6.408450

6.008450

5.608450

5.208450

4.808450

4.408450

4.008450

93

6.433566

6.033566

5.633566

5.233566

4.833566

4.433566

4.033566

94

6.458333

6.058333

5.658333

5.258333

4.858333

4.458333

4.058333

95

6.482758

6.082758

5.682758

5.282758

4.882758

4.482758

4.082758

96

6.506849

6.106849

5.706849

5.306849

4.906849

4.506849

4.106849

97

6.530612

6.130612

5.730612

5.330612

4.930612

4.530612

4.130612

98

6.554054

6.154054

5.754054

5.354054

4.954054

4.554054

4.154054

99

6.577181

6.177181

5.777181

5.377181

4.977181

4.577181

4.177181

100

6.6

6.2

5.8

5.4

5

4.6

4.2

Level

10

9.6

9.2

8.8

8.4

8

7.6

 

 

 



Counter started 22 September 2004

Email: tgflynn@unsw.edu.au