Calculation of locomotive performance characteristics

Other articles describe:

• How to calculate the tractive effort which a locomotive has to develop in order to perform a specified duty,
• The various types of motor used for Gauge O locomotives, including the basic theory of their application,
• The selection of suitable gearing to couple them to the driving wheels.

Having determined the gear ratio it is necessary to ascertain whether the locomotive tractive effort will be sufficient for the intended duty. For model purposes it is sufficiently accurate to regard the tractive effort characteristic curve with respect to speed as being a straight line rising from zero at a locomotive speed corresponding to the motor no-load speed to a maximum corresponding to the motor stalled torque. Both the no-load speed and the stalled torque, which are either obtained from the manufacturer’s data sheet or determined by tests, are the values at the maximum motor voltage for the particular application.

The theoretical no-load speed in scale mph is given by:

Equation 1:

where rpm = Motor no-load speed on full voltage

D = Prototype wheel diameter in inches

GR = Gear ratio

(If the wheel diameter is measured in mm, replace 336 in this equation with 8534). The stalled tractive effort in grams is given by:

Equation 2:

where the stalled torque is measured in g-cm, the gear efficiency is in percent and the model wheel diameter is in mm.

In this calculation the friction in the locomotive bearings and motion is not taken into account as it is included in the total tractive resistance of the train (see performance requirement).

A worked example illustrates the use of these equations in the calculation of locomotive performance when hauling a train.

Having determined the characteristic necessary to meet the performance requirements and selected a motor and gear ratio which seem suitable it is necessary to confirm that the motor can carry the load current without overheating.

Current is proportional to tractive effort and, if the stall or intermediate speed values are known, its value at any point on the characteristic can be derived from them. If, however, the no-load current is also known the following formula will give a more accurate result than simple proportioning.

If the current at tractive effort T₁ is I₁ amps and at no-load the current is I₀ amps, then the current I₂ at tractive effort T₂ will be:

Some motor data sheets give the limiting maximum and continuous currents which the motor can withstand and these should not be exceeded. If this information is not available a general guide is that the speed of the heaviest train when on full voltage should not fall below about 60% of the light locomotive speed at the same voltage except when accelerating or climbing short gradients. In order to meet this requirement it may be necessary in some cases to fit a motor which will give the locomotive a higher stalled tractive effort than at first calculated. It is particularly important to check the current capacity of coreless motors as they are easily damaged beyond repair by short-time overloads which other types can withstand without harm.

The final stage in selecting a motor is to check that it will fit into the space available in the locomotive chassis and body. Although accommodating the older types of motor in small locomotives was sometimes a problem, the smaller size of present day motors has largely overcome this. However, if the motor first chosen is found to be too large for the available space it may be necessary to use an alternative requiring some compromise in the performance characteristic.