Before a suitable motor and its associated gearing can be selected, it is necessary to establish the performance required from the locomotive or multiple unit in which it is to be installed. This varies widely and the object of this article is to provide the modeller with information to determine the speed and tractive effort characteristics necessary to provide the desired performance.

It is up to the modeller to set their own performance requirements, but a reasonable rule is that model locomotives should, whenever practicable, be capable of a performance equivalent to that of their prototypes. Some will argue this is more than necessary on small layouts and short trains, but it may be better to install a larger motor in case the opportunity arises to run on a large club layout or test track.

The tractive effort required to haul a train at constant speed must equal its resistance to motion and therefore the first step in determining the performance required from a locomotive is to calculate the resistance to motion of the trains it is desired to haul. This is known as the tractive resistance and made up of:

• The tractive resistance on level straight track
• Additional resistance on curved track
• Additional resistance due to gradients

In addition, a further tractive effort is required to accelerate a train from rest to its steady running speed.

This is the sum of frictional and wind resistance. For full size trains the latter is the major component whereas it is negligible on model ones.

The frictional resistance of different types of rolling stock has been measured, but for most purposes it will be found adequate to assume the following average values:

¹ Some types of current collectors can increase the locomotive frictional resistance. If the current collector exerts a considerable force on the wheel, either the tractive resistance of the loco should be measured or, as an estimate, the numbers given here should be doubled.

² Per driving axle. To get the total weight and resistance for the locomotive, multiply these figures by the number of driving axles.

When rounding a curve the frictional resistance increases due to flange contact and to one wheel having to slip or skid because of the different circumferences of the inner and outer rails of the curve. The coning of the tread compensates to some extent for the latter but there is not the full correction provided by the differential of a road vehicle. The increase in resistance over the value on straight track is a function of the curve radius and is known as the curve resistance.

Measurement of the tractive resistance on curved track gave a nearly constant increase over the value on straight track, soft plastic wheels giving a larger increase than other types due to their higher flange and tread friction. The table and graph show the additional curve resistance as a percentage of that on straight track.

Figure 1. Curve resistance (percentage of resistance on straight track).

This is an additional resistance that depends only on the vehicle weight and the steepness of the grade.

If G is the distance along the slope measured in the same units as the rise (or fall), the gradient can be expressed in two ways, either as 1 in G, or as a percentage obtained by dividing 100 by G, e.g. a gradient of 1 in 50 is 2% and 1 in 100, 1%.

The resistance on a grade of 1 in G is the vehicle weight divided by G. If the gradient is expressed as a percentage the resistance is the vehicle weight multiplied by percent grade divided by 100.

The gradient resistance of a model coach weighing 500g on a gradient of 1 in 50 = 500/50 = 10g.

For the same coach on a 3% gradient, the gradient resistance = 500 x (3/100) = 15g.

In addition to overcoming frictional and grade resistance, the tractive effort must be sufficient to counter the inertia of the train and accelerate it at the desired rate. Model acceleration and braking rates are much higher than those of full size trains but model trains have very small inertia.

For model purposes the acceleration force can be taken as 1.1 grams per kilogram of train weight (including the locomotive) multiplied by the prototype acceleration rate expressed in miles per hour per second. Thus the tractive effort (in grams) to accelerate a twelve coach passenger train weighing 6 kg (12 x 500 grams), hauled by a locomotive weighing 2.5 kg, from standstill to a speed equivalent to 60 mph (1.38 mph actual speed) in 20 seconds is


The tractive resistance of this train is 12 x 10 = 120 g (see Tractive resistance, above), so in this example the acceleration force is approximately 23% of the tractive resistance on level track.

(A full size locomotive hauled train takes much longer to reach 60 mph and most models accelerate more rapidly than the train used for this example).

Because it greatly reduces the danger of motor damage due to overloading it is recommended that any motor used in a locomotive should be able to develop a stalled torque sufficient to slip the driving wheels at standstill. Modern controllers will usually have some form of current limiting that will reduce the danger of burning out a stalled motor, but this remains a good working rule.

The maximum tractive effort which should be developed by a locomotive depends on the factor of adhesion between the driving wheels and the rails. Tests on typical model locomotives have shown the average value to be between 20 and 23%, although, as with their prototypes, much higher values can be attained under ideal conditions or with special design. In other words, the maximum tractive effort which can be exerted at the wheel tread should be assumed to be between 20 and 23% of the weight on the driving wheels, (not the total weight of the locomotive). It is recommended that the lower value be used for performance calculations. This means that the weight of the locomotive should be equal to five times (100/20) of the maximum tractive effort required.

The frictional resistance of the locomotive must be deducted from the calculated total tractive resistance to obtain the tractive effort required at the wheel tread. (Theoretically, only the proportion attributable to the driving axles should be deducted, but in practice it is sufficiently accurate to deduct the total for the locomotive and tender on straight track).

If a tractive effort of 400 grams is required to start a train, the weight on the locomotive driving wheels should be taken as 400 x 5 = 2000 grams or 2kg. (The calculated value should not be greatly exceeded as this would increase the possibility of overloading the motor).

The tractive effort required to start and haul a train is the sum of the tractive resistance, the curve resistance, the gradient resistance and the acceleration force required. Methods to estimate all of these are described in this article above. Using this data, the minimum weight of the locomotive on the driving wheels necessary to avoid stalling the motor without slipping the wheels can be estimated. This is illustrated by means of an example, but the method is applicable to all cases.

The following typical locomotive performance requirements are given as a guide to modellers who do not wish to calculate the requirements for specific applications.

Models of final generation mixed traffic steam locomotives with 1830mm (6ft) driving wheels should develop a stalled tractive effort of not less than 450 grams and a total tractive effort of 180 to 220 grams at a speed equivalent to a prototype 75 mph. Their weight should be about 2.5kg including the tender.

To be fully representative of prototype performance models of the most powerful classes of electric and diesel locomotives should develop 220 to 260 grams total tractive effort at a speed equivalent to a prototype 90 mph with a stalled tractive effort of not less than 600 grams. Very few, if any, model railways will be able to fully utilise the haulage capacity of such a locomotive and consequently many builders of these models motorise only sufficient wheels to meet their performance requirements. This being the case, it is recommended that diesel and electric locomotives should be able to develop at least 100 grams stalled tractive effort per motored axle falling to 50 to 60 grams per axle at 90 mph. The weight on each driven axle should be about 0.75 kg.

The frictional resistance of the locomotive should be deducted from all the above values to obtain the tractive effort at the drawbar on level straight track.

This article was compiled by the Technical Committee for the Gauge O Guild Manual. It was adapted for the GOGWiki by Nick Baines.