This is an example showing how to calculate the performance of a locomotive hauling a particular train (or trains). An important part of the process is to choose a suitable motor and gear train. The procedure is in three parts, and reference should be made to the articles that give the background information and explain the methods used. It is recommended that these articles are studied before reading or making use of this procedure.

1. Calculate the tractive effort and locomotive weight,
2. Determine a suitable motor and gear ratio,
3. Predict the performance of the locomotive hauling the required train or trains. Compare results with performance requirements and decide whether the results are satisfactory, or whether some changes should be made.

The method given here can be adapted to other circumstances by changing parameters such as train composition, curve radii, gradients, etc.

Large outdoor system, mainly straight track or large radius curves. The maximum gradient of 1 in 70 occurs on a 2.4m (8ft) radius curve.

To haul passenger trains of up to 12 coaches and freight trains of up to 40 wagons and to be able to start them on the 1 in 70 grade and curve. Desired train speed on level track: passenger 75 mph, freight 45 mph.

The passenger train to accelerate at 3mph/s and the freight train at 2mph/s. (These acceleration rates used in this example are much higher than those of prototype locomotive hauled trains).

Assume an average coach weighs 500g and a wagon 250g (50% of the wagons assumed loaded). At this stage allow 2500 grams locomotive weight (including the tender). This may require correction if it proves insufficient for the starting duty.

Coaches = 12 x 500 = 6000 g = 6.0 kg

Loco = 2500 g = 2.5 kg

Total = 6.0 + 2.5 = 8.5 kg

Wagons = 40 x 250 = 10000 g = 10.0 kg

Loco = 2500 g = 2.5 kg

Total = 10.0 + 2.5 = 12.5kg

Assume rolling stock of average construction with a frictional resistance on level straight track of 20g per kilogram weight. A 2.4m radius curve will increase this by 10%.

The freight train requires a greater tractive effort than the passenger train, and so the adhesion required should be based on that figure. The tractive effort required at the wheeltread to start the freight train is 432g.

Using an average adhesion value of 20% the weight on the driving wheels must be at least

432 x (100/20) = 2160 g = 2.16 kg

The assumed weight of 2.5 kg for the locomotive and tender should be adequate to give the desired starting performance. If the assumed weight was less than the necessary adhesion weight, a higher locomotive weight should be chosen and/or the train size should be reduced, and the calculation repeated.

A motor was selected having a no-load speed of 6000 rpm and a stalled torque of 325 g-cm. At this point there is no guarantee that these will give a satisfactory result, because that can only be checked when the locomotive performance with a train is estimated. If the performance targets are not met, it may be necessary to select a different motor and repeat the calculation from this point onwards.

The mixed traffic locomotive has a driving wheel diameter of 6ft (72 in.) and the desired passenger train speed is 75mph. For a no-load motor speed of 6000 rpm, the optimum gear ratio will be:

(6000 x 0.75 x 72)/(336 x 75) = 12.9 to 1

It is unlikely that the exact gear ratio will be obtainable and therefore the nearest suitable one will be used. In this case, a gear ratio of 12.5:1 was chosen. Based on information given in Gearing, the gear efficiency was assumed to be 30%, which is consistent with a single-start worm and wheel gear of that ratio. A considerably higher efficiency could be obtained by using different gears. A crossed helical gear set in combination with a spur gear set is a likely candidate. If it is desired to use a pre-assembled motor/gearbox, this will influence the choice. Many motor/gearboxes are available with a choice of gear ratios, but manufacturer’s data or data sheets should be examined to ensure that the preferred motor and gearbox are suitable.

From Equation 1 in Locomotive performance requirements the theoretical no-load track speed of the locomotive =

From Equation 2 the stalled tractive effort =

Using these results, the tractive effort can be plotted against speed as shown in Curve A in Figure 1. This is a straight line joining the stalled tractive effort of 580 g at zero speed with the no-load speed of 103 mph.

The tractive effort requirements for this locomotive determined earlier in this example are drawn as horizontal lines in Figure 1.

• To haul a passenger train at 75 mph on level track = 190 g
• To haul a passenger train on 1 in 70 + 2.4m curve = 330 g
• To haul a freight train at 45 mph on level track = 270 g
• To haul a freight train on the grade and curve = 475 g

Figure 1. Typical locomotive performance characteristic.

The starting tractive effort, at 580 g, is clearly adequate to start both trains under all conditions, so that the stall torque of the chosen motor is sufficient for that purpose. The speed of a passenger train on level track is lower than the target value (under 70 mph instead of the target value of 75 mph), although that of the freight train is above target. If this is not acceptable, either the load should be reduced to 9 coaches or the gear ratio lowered to 10 to 1.

The results for the lower gear ratio is shown as curve B in Figure 1. With the lower ratio the target speed for the passenger and freight trains on level track can be achieved, but the speed of the freight train on the grade is very low and in practice the train would stall if the gear efficiency was only slightly lower, the grade slightly higher or the curve radius slightly smaller than assumed. To be practical, the load should be reduced to no more than 30 wagons and then a speed on the grade of about 15 mph is possible.

Another option would be to choose a motor with a higher stall torque and/or a higher no-load speed. These options will depend on what is commercially available (except in the unlikely event that the modeller is able to design and build their own motor), but the different possibilities can be explored in this procedure to find the most satisfactory solution.