### Train Load Estimator

**Aim -** To estimate the maximum load of a train under various operating conditions.

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#### Index

Steam Train Load - Simple - UK Units

Steam Train Load - Simple - US Units

Steam Locomotive Critical Speed

#### Introduction

As described elsewhere, the factors which will affect the load capacity of a can be broadly described by the following aspects:

**Locomotive and Rolling Stock design**- The design of a locomotive will impact the hauling capacity of the locomotive. For example, some design features which will impact the locomotive hauling capacity are, design tractive effort, axle loading (adhesive weight), ability of the locomotive to adjust electronically to slip conditions. Rolling stock design will impact the amount of resistance that the train load offers to the locomotive. For example, long wheel based vehicles will exhibit greater cureve resistance then shorter bogie stock, vehicles with roller bearings will have less resistance then solid bearing vehicles and vehicles with large frontal areas will have increased wind resistance.**Track conditions**- Different track conditions, such as the gradient of any hills, and sharp curves can increase the resistance of the train, and therefore will have an impact upon the load that a train can haul.**Environmental conditions**- The weather will have a large impact upon the adhesion (gripping power) of the locomotive. Dry track provides the best level of adhesion, whereby approx 30% of the adhesive weight force is available. Wet, oily, or icy (snow) track can see a reduction in the adhesion to values of around 10% can be experienced. The use of sand applied to the tracks can increase the level of adhesion between the track and locomotive.

The calculators below calculate the train loads under ideal conditions, i.e. dry tracks. Trains traveling on wet, oily or icy tracks may need to have their loads reduced, or the number of locomotives increased to prevent locomotive slip.

**Multiple locomotives used for haulage** - In case of double - headed locomotives / multi-operation of locomotives, tractive effort gets doubled. Hence, haulage capacity indicated in load calculators can be summated for each of the locomotives attached to the train. Thus for example, two locomotives of the same class attached to the train, will result in the load being doubled. Similarly, for disimilar locomotives, the load that each locomotive can be hauled, can be added together to get the total load.

The methodology and factors used in these calculators are based on "standards" recommended for use by railway staff when calculating train loads. In short, methodology calculates the tractive force of the locomotive, subtracts the locomotive related resistances (air resistance and mechanical resistance), and then calculates the train resistances based upon level track, grade resistance, and curves resistance. This information is then used to calculate the Net Train Force, and provided the __tractive force is greater then the train resistance__ (ie the "Net train force" shown below), then the train should be able to haul the attached load.

This Steam train load calculator uses a freight train as reference, so other styles of train may have minor variations due to different resistance values. The formulas are based upon friction type bearings. The figures produced by these calculators will give a close __approximation__ of the load that a locomotive is capable of hauling.

For a fuller description of the methodology used for the steam train calculators below refer to page 57 of Principals of Locomotive Operation and Train Control by Arthur Julius Wood. If desired, manual calculations can be made using the principals described in the above reference for other types of rolling stock.

**Notes:**

- When entering route and train data use the ruling values for the relevant track section (or route), ie the mmaximum gradient, and the smallest radius curve for the section in question, as this will present the "worst case" effort that the locomotive will need to deal with.

For the steam calculator:

- Max speed should be the speed that the train would be expected to travel up a gradient or around a curve, and not the speed expected to be done on a straight level section of track. Therefore the critical speed of the locomotive should be used as the speed for the purposes of these calculations, as this will be the speed where the maximum power of the locomotive is produced.
- The calculator takes both grade and curve resistance into account, however the ruling curve radius may not occur on the steepest gradient, similarly the steepest gradient may not occur on the tightest curve. To minimse the effect of either of these two values, set either the "Ruling gradient" or "Ruling curve radius" to very large numbers in the UK units, eg 1000000, or set to 0 in US units.

#### Steam Train Load - Simple Expansion - UK Units

Insert the appropriate values in UK units of measure, and hit the calculate button. The calculator will change to a green background if the proposed train load is suitable for the train and route conditions entered. It will turn red if the proposed load is in excess of the locomotives pulling power.

To convert any units of measure, try the conversions tool page

#### Steam Train Load - Simple Expansion - US Units

Insert the appropriate values in US units of measure, and hit the calculate button. The calculator will change to a green background if the proposed train load is suitable for the train and route conditions entered. It will turn red if the proposed load is in excess of the locomotives pulling power.

To convert any units of measure, try the converions tool page

#### Steam Locomotive Critcal Speed

The critical speed of the locomotive is the point at which maximum power is developed by the locomotive. It is dependent upon the speed of the steam cylinder piston, which will vary depending upon whether it is a saturated, superheated or geared locomotive.

For superheated locomotives the maximum power was developed when the steam cylinder piston was operating at 1000 ft/min, for saturated locomotives it was 700 ft/min, for geared locomotives use the known value or 700 ft/min. Thus the critical speed will be determined by the steam cylinder piston speed, cylinder stroke, and the drive wheel diameter, as well as the gearing in the case of a geared locomotive.

To calculate the critical speed of the locomotive, insert the appropriate values and hit the calculate button. The calculated speed value can then be used as the maximum critical speed value in the train load estimators above.

#### Diesel Train Load

Insert the appropriate values in the units of measure indicated, and hit the calculate button. The calculator will change to a green background if the proposed train load is suitable for the train and route conditions entered. It will turn red if the proposed load is in excess of the locomotives pulling power. **Note:** This calculator cannot be used to find the starting tractive effort, i.e. Speed = 0mph. The starting tractive effort is usually quoted in the locomotive specifications, and is equal to the adhesive force. If the available tractive effort is greater then the design starting tractive effort, then the calculator will not show the correct result.

This calculator assumes that the curves have __not__ been grade compensated, and therefore add additional resistance to that already created by the gradient. To estimate the grade compensated load, insert a very high value for curve radius, i.e. 100000m

To convert any units of measure, try the converions tool page